Laves phases: a review of their functional and structural applications and an improved fundamental understanding of stability and properties

Abstract

Laves phases with their comparably simple crystal structure are very common intermetallic phases and can be formed from element combinations all over the periodic table resulting in a huge number of known examples. Even though this type of phases is known for almost 100 years, and although a lot of information on stability, structure, and properties has accumulated especially during the last about 20 years, systematic evaluation and rationalization of this information in particular as a function of the involved elements is often lacking. It is one of the two main goals of this review to summarize the knowledge for some selected respective topics with a certain focus on non-stoichiometric, i.e., non-ideal Laves phases. The second, central goal of the review is to give a systematic overview about the role of Laves phases in all kinds of materials for functional and structural applications. There is a surprisingly broad range of successful utilization of Laves phases in functional applications comprising Laves phases as hydrogen storage material (Hydraloy), as magneto-mechanical sensors and actuators (Terfenol), or for wear- and corrosion-resistant coatings in corrosive atmospheres and at high temperatures (Tribaloy), to name but a few. Regarding structural applications, there is a renewed interest in using Laves phases for creep-strengthening of high-temperature steels and new respective alloy design concepts were developed and successfully tested. Apart from steels, Laves phases also occur in various other kinds of structural materials sometimes effectively improving properties, but often also acting in a detrimental way.

Introduction

It was during the 1930s when the German mineralogist and crystallographer Fritz Laves (1906–1978) published his crucial findings about the crystallographic similarity and relationship between various intermetallic compounds of the cubic MgCu₂ and the hexagonal MgZn₂ and MgNi₂ structure types [1, 2]. In 1939, the designation ‘Laves phases’ for this class of AB₂ intermetallic compounds was suggested by Gustav E.R. Schulze [3], whose pioneering work contributed a lot to the fundamental understanding of these intermetallic phases [4, 5].

Since then and continuing until today, there was and is a tremendous interest in these phases for several reasons. Laves phases form a huge class of intermetallic compounds; already in ‘Pearson’s Handbook of Crystallographic Data for Intermetallic Phases’ from 1991 [6] more than 1400 different Laves phases were listed [7], and this number has further increased during the last 30 years. Metal combinations from all over the periodic system can form Laves phases, and especially in multi-component materials, there is a good chance to encounter a Laves phase, the presence of which sometimes is wanted but in many cases also is detrimental. Excellent examples for that may be high-temperature steels and superalloys, where frequently Laves phase precipitates occur which were regarded for a long time as detrimental phases that have to be avoided. However, more recently it was recognized that by a proper control of the precipitation process, Laves phase can well serve as strengthening particles in the matrix. Moreover, based on such findings completely new alloying concepts have been developed for designing improved ferritic as well as austenitic high-temperature steels (as will be described in Sects. 5.2 and 5.3). Furthermore, in the new materials class of so-called high-entropy alloys (HEAs) (which actually are compositionally complex alloys consisting of five or more principal elements), Laves phases were not only identified as the most frequent intermetallic phase in a recent statistical analysis [8], but also various single-phase ‘high-entropy’ Laves phases were found, see, for example, [9] (cf. also Sect. 5.6.5). The use of Laves phases in various functional as well as structural applications is already discussed for a long time. Some Laves phases based on transition metals feature very high melting temperatures and their resulting excellent high-temperature strength encouraged J. D. Livingston to entitle his 1992 review paper “Laves phase superalloys?” [10].

Besides their relevance for structural applications and their utilization in various functional applications, Laves phases are also well-suited candidates to study fundamental properties of intermetallic phases in general. Compared to most other intermetallic compounds, their crystal structure is still simple enough to allow detailed investigations of basic phenomena, while on the other hand, their behavior is already characteristic and representative for intermetallic phases. Therefore, the structure of this review article is as follows: After some introductory remarks about the structure of Laves phases and some peculiarities of this very common structure type (Sect. 2), this review is divided into three main parts:

Section 3 deals with a discussion of some selected topics related to more recent insights into the understanding of the behavior of Laves phases from a more fundamental point of view. This includes discussions about the stability of and site preference in the different polytypes (Sect. 3.1), the occurrence of point defects and their relation to the frequently observed extended homogeneity ranges (Sect. 3.2), and the polytypism of Laves phases with insights on the mechanism and kinetics of transformations between the polytypes (Sect. 3.3). In materials development, theoretical prediction of phase stability, phase equilibria, and kinetics of their formation or transformation plays a central role. A helpful and nowadays routinely used tool is modeling by the CALPHAD approach (see, for example, [11]) the success of which crucially depends on the employed models for the involved phases. The description of Laves phases in CALPHAD modeling is discussed in Sect. 3.4. Section 3.5 treats different structural variants of Laves phase, which, for example, can result from slight distortions either due to changes in electronic structure or due to atomic ordering. Some more complex structural variants are also introduced here. Atomically resolved scanning transmission electron microscopy (STEM) allows interesting insights into the structure and chemistry of planar defects in Laves phases. Such planar defects as well as intergrowth and intergrowth related faulting are the topics of Sect. 3.6. Section 3.7 of this part deals with an improved understanding of the plasticity of Laves phases and with the softening effect of mechanical properties, which was observed in some Laves phases with extended homogeneity ranges as a result of deviations from the stoichiometric composition. While the pronounced brittleness of Laves phases impedes their investigation by classical mechanical testing, more recently introduced micromechanical testing methods have proven to be an efficient tool for getting an improved understanding of the mechanical behavior of Laves phases.

Section 4 of this review summarizes the status of knowledge regarding Laves phases in functional materials. It is especially remarkable that Laves phases not only show many interesting physical properties, but have progressed to the next step forward being in use today in various real functional applications. Topics discussed here comprise the very recent developments related to hydrogen storage in Laves phases (‘Hydraloy’, see Sect. 4.1), the well-established application of Laves phases as wear- and corrosion-resistant materials (‘Tribaloy’, Sect. 4.2), and the utilization of their special magnetic properties, for example as magneto-mechanical sensors and actuators (‘Terfenol’, Sect. 4.3). Many Laves phases also show superconducting behavior (Sect. 4.4), and finally, there are also some more exotic possibilities for functional applications such as for the adjustment of the color of coins via the content of Laves phase (Sect. 4.5).

Section 5 focuses on the role of Laves phases in structural materials. While single-phase or Laves phase-dominated materials appear not to be suited for structural applications due to their pronounced brittleness and, hence, insufficient fracture toughness (Sect. 5.1), it is especially their role in ferritic and austenitic steels, which is of extraordinary importance and is discussed very comprehensively and controversially in the literature (Sects. 5.2 and 5.3). Similarly, Laves phases often occur in Ni- and Co-based superalloys (Sect. 5.4) as well as in other structural materials based on metal M solid solutions (M = Cr, Cu, Mg, Nb, Ti, or Zr; Sect. 5.5) or based on intermetallic phases (mostly aluminides) or HEAs (Sect. 5.6). Adding Laves phase to usually comparably soft metal solid solutions helps to significantly strengthen the material, but simultaneously to this beneficial effect there is an increase in brittleness. Therefore, only a few alloys of this kind have managed the step to real applications even though a huge number of studies were performed to design improved, Laves phase-strengthened structural materials.

Although Laves phases were already frequently reviewed in various textbooks and survey papers including detailed descriptions of their structures and properties (see, for example, [4, 5, 12,13,14,15,16,17,18]), there are still a lot of open questions and discussion about these phases, and a huge amount of new results related to Laves phases was published especially in recent years. The present article tries to focus on some of these more recently discussed aspects and is intended to give an overview especially of the more recent literature.

Some remarks about the Laves phase structures and their particular role and uniqueness among intermetallic phases

The important finding of Fritz Laves was that all phases of the MgCu₂, MgZn₂, and MgNi₂ structure types are homeotect meaning that they are constructed by a common geometrical principle leading to an optimal space filling and maximum coordination number [2, 3, 19,20,21]. They belong to the group of tetrahedrally close-packed (t.c.p.) structures [22,23,24,25], the interstices are exclusively tetrahedral and the coordination polyhedra in these AB₂ phases are Frank–Kasper polyhedra with coordination numbers (CN) of 12 (for the smaller B atoms) and 16 (for the larger A atoms). The highest packing density is achieved for an ideal atomic radius ratio of r_A/r_B = (3/2)^1/2 ≈ 1.225 resulting in a space filling of 71% (for more detailed discussions of such general aspects of the crystal structure, see also the aforementioned textbooks and reviews about Laves phases). The coordination polyhedra of the three Laves phase structure types are shown in Fig. 1, and the crystallographic information is summarized in Table 1.

Figure 1

Coordination polyhedra of the three Laves phases structure types cubic C15, hexagonal C14 and hexagonal C36. Symmetry of the positions as well as type and number of nearest-neighbor atoms are listed in Table 1

Table 1 Crystal structure of Laves phases AB₂ (depending on A and B, the position parameters x and z of the 6h and 4e,f sites can slightly vary around the ideal atom position values of x = 1/6, z_(C14-A1) = 9/16, z_(C36-A1) = 21/32, z_(C36-A2) = 3/32, and z_(C36-B3) = 1/8)

The close relationship between the three structure types becomes most obvious when describing them as layer stacking of alternating A atom and B atom sheets that are packed perpendicular to the [0001] direction in C14 or [111] direction in C15. A stack of four of such layers forms the fundamental unit for all types of Laves phases. This stack consists of one B atom layer ordered in a Kagomé net of regular triangles and hexagons followed by a triple layer A-B-A with triangularly ordered atoms in each layer. As this triple layer can be placed in two ways on top of the single B layer, there are two versions of the four-layered structural unit, which might be called X and X′. Now—similar as in simple, dense-packed fcc and hcp metals—a dense stacking of these units results in the cubic C15 structure for XYZXYZ…, stacking, hexagonal C14 for XY′XY′…, stacking, and hexagonal C36 for XY′X′ZXY′X′Z…, stacking. This idea of describing the crystal structure was already introduced by Laves himself [2] and later on in a more detailed way by Komura [27]. The above three stacking variants C14, C15, and C36 are the most simple and most common ones. More complex, long-periodic stacking sequences are possible but were only very rarely observed in real systems [28, 29]. In ternary systems, fully ordered derivatives of the C14 and C15 Laves phase structures are known to exist. This topic will be discussed in Sect. 3.5.

Among the numerous structure types of intermetallic phases, the Laves phase structures have an exceptional position. Their uniqueness and particular role is demonstrated here by three examples related to (i) the similarity of the atom arrangements to liquids and quasicrystalline phases, (ii) their occurrence as defect clusters in bcc-metals, and (iii) their tendency to form as solid phases in gas mixtures under high pressures, and, related to that, the self-assembly of non-reacting particle mixtures resulting in Laves phase ordering:

• (i) The icosahedral atom arrangements that are characteristic for liquids, metallic glasses, and quasicrystalline phases have similarity to the coordination polyhedra occurring in t.c.p. phases such as the Laves phases (see, for example, [30,31,32]). Therefore, Laves phase structures can be regarded as a bridge between liquids/metallic glass structures and classical close-packed metal structures [33,34,35]. Ghosh et al. [35] studied the glass forming ability of Fe-early transition metal binary and ternary alloys in various systems containing Laves phases. They found that the composition at which the glassy state will be most stable (compared to the solid solution phase) coincides with that of the Laves phase [35]. In an aqueous suspension of spherical polystyrene particles of two diameters (ratio 1.4 to 1.7) with sizes of some hundred nanometers, an amorphous state appeared first after stirring until after a few hours the nucleation of Laves phase ordering was observed [36] (for this aspect of the self-assembly of particles, see also (iii)).

• (ii) Irradiation of bcc-Fe with high-energetic ions or neutrons can result in the formation of nano-sized self-interstitial Fe atom clusters with C15 Laves-type structures as was predicted by density functional theory (DFT) calculations [37,38,39] and molecular dynamics simulations [40, 41]. Such irradiation-induced defect clusters can be highly stable and immobile and exhibit large antiferromagnetic moments [37]. When growing to diameters exceeding 1.5 nm, the C15 clusters start dissolving and dislocation loops become the more stable defect configuration [41]. Experimental evidence for the existence of such kind of Laves phase-ordered clusters, however, still appears to be lacking.

• (iii) A quite exotic type of phase are so-called van der Waals compounds, which are solid compounds obtained from gas mixtures (rare gases or molecular gases as, for example, H₂, N₂, O₂, or CH₄) under high pressures. A very frequently found structure type of such van der Waals compounds are Laves phases. This was experimentally proven, for example, for the rare gas binary systems He-Ne, Ar-Ne, and Ar-Xe, where the only observed room-temperature, high-pressure compounds are hexagonal C14 NeHe₂ (above 12.8 GPa) [42], C14 ArNe₂ (above 4.6 GPa) [43], and cubic C15 XeAr₂ (above 1.1 GPa) [44]. Similarly, high-pressure Laves phases were also found to crystallize in molecular gas systems with A and/or B components being molecules. Examples are C14 Ar(H₂)₂ (> 4.3 GPa) [45], C15 Xe(O₂)₂ (> 3.1 GPa) [46], C15 Xe(N₂)₂ (> 4.9 GPa) [47]. In a 2H₂ + CH₄ gas mixture, the van der Waals compound CH₄(H₂)₂ crystallizes with C14 Laves phase structure at pressures above 5.4 GPa [48]. First principles calculations of the stability of high-pressure phases in the systems He-Ne and Ar-He confirm the existence of the NeHe₂ Laves phase with C14 structure and indicate for very high pressures above 120 GPa a transformation to the cubic C15 structure [49]. For the Ar-He system, the same authors predict the crystallization of a cubic C15 Laves phase, which should transform to an AlB₂-type structure above 13.8 GPa [49].

The frequent observation of the preferred crystallization of Laves-type structures at such high-pressure in interaction-free systems fits well to the results of Monte Carlo simulations on the stability of various dense-packed crystal structures in binary mixtures of large and small hard spheres. By calculating composition versus pressure diagrams, Hynninen et al. [50] could show that for radius ratios r_A/r_B in the range 1.19 to 1.32, Laves phases are the most stable configuration and the only occurring solid compound in the entire composition range. Moreover, when comparing the stability of the three Laves structures C14, C15, and C36, they find that—even though the energy differences are very small—hexagonal C14 should be the most stable variant. Experiments with colloidal suspensions of uncharged hard spheres confirm the preferential formation of C14 Laves phase [51]. Figure 2 shows the calculated phase diagram of binary A + B hard spheres with a radius ratio of r_A/r_B = 1.22 (which is very near to the ideal radius ratio of the Laves phases, see above) [50].

Figure 2

Calculated composition-versus-reduced pressure phase diagram of binary hard-sphere mixtures of large A and small B particles for a r_A/r_B size ratio of 1.22 (x and p are the dimensionless composition x = N_B/(N_A + N_B) and pressure p = Pσ ³/k_BT with P: pressure, σ: diameter of the A spheres). “fcc_A” and “fcc_B” denote the fcc crystals of pure A and pure B spheres, respectively. The light-blue marked regions indicate the pressure-composition range of existence of Laves phase (adapted with permission from [50])

Simulations of crystallization in polydispersive hard-sphere fluids reveal that such mixtures tend to fractionate based on particle size and that in large regions bimodal subpopulations form C14 and C15 Laves phase. While the size ratio—as expected—is a critical parameter for the formation of Laves phase-type ordering, the mixing ratio of small versus large particles interestingly does not play a role and the unused particles remain as coexisting disordered phase [52]. Interestingly, it was also shown by computer simulations that equilibrium Laves phase in binary hard-sphere mixtures of ideal size ratio can contain an extraordinarily high concentration of antisite defects. Stable regions were found where up to 2% of the large-particle lattice sites are occupied by a small particle. Moreover, the calculations indicate that a hard-sphere Laves phase should never be thermodynamically stable at its ideal composition [53].

The effect of the self-assembly of non-reacting particle mixtures with formation of Laves phase ordering was not only predicted by several computational simulations [50, 52, 54,55,56,57,58], but was also observed experimentally in colloidal or copolymeric particle mixtures [51, 59,60,61,62,63,64], in mixtures of DNA-coated colloidal spheres [65] or of monodisperse, hydrophobically coated Au nanoparticles [34], and in aqueous dispersions of soft spherical, oil-swollen micelles [66].

The self-assembly of colloidal C15 Laves phase was also suggested from computer simulations as a route to produce photonic crystals as the tetrahedral sublattice of the small particles can exhibit a bandgap in the visible region [54,55,56,57,58].

Regarding the stability of hard-sphere Laves phases compared to alternative structures, detailed investigations and interesting conclusions were reported by Filion and Dijkstra [67]. For the ideal radius ratio of Laves phases of r_A/r_B = 1.225, there are several other crystal structure types such as α-IrV (orthorhombic, oS8, Cmmm), γ-CuTi (tetragonal, tP4, P4/nmm), AuTe₂ (monoclinic, mS6, C2/m), and Ag₂Se (orthorhombic, oP12, P222) offering a higher packing density than Laves phases. Nevertheless, full free-energy calculations (which were also reported by the same group in Ref. [50]) show that the only stable structures at this size ratio are the Laves phases. Obviously the binary hard-sphere system seems to favor the more symmetric crystal structure over the most dense-packed structure, meaning that optimal space filling alone does not decide about the stable structure type even for hard spheres [67].

These findings on atomic arrangements in non-interacting binary systems also confirm the importance and central role of geometrical factors for the stability of Laves phases.

Fundamental aspects

This section reviews selected topics related to the crystal and defect structure of Laves phases as well as the related thermodynamic and mechanical phenomena. Thus it can be regarded as a kind of continuation of the reviews [16, 17], which are about structure and stability of Laves phases. Here we focus on more recent results in the literature and aspects less emphasized in these two earlier reviews rather than try to cover the entire field of fundamental studies of Laves phases.

Stability and site preference

If a Laves phase AB₂ with a given elemental composition (binary, ternary, multinary) is stated to exist, it is usually implied that this Laves phase is thermodynamically stable under certain conditions or that it can be produced under thermodynamic or kinetic control and retained for observation. Using this type of definition, it has to be kept in mind that formation of a phase is not only influenced by its own thermodynamic stability with respect to the elements, but also by the fact that its formation competes, on a thermodynamic and kinetic level, with formation of other phases of the same or of different composition. So, even if formation of a Laves phase AB₂ from the two elements is thermodynamically favorable, as, maybe, revealed by first-principles calculations, this Laves phase may never be observed if other phases are even more stable and/or form more rapidly. The fact that ‘stability of a phase’ in the described sense cannot be predicted without consideration of alternative states of the system puts limitations on approaches, which try to predict stability of a Laves phase (or of other phases) simply on the basis of its composition. Nevertheless, such approaches (e.g., based on the atomic radius ratio r_A/r_B, see Sect. 2) have some reasonable but limited success for Laves phases, as reviewed in 2004 [16]. A newer approach allows rationalizing existence of Laves phases in comparison to other Frank–Kasper phases using structure maps constructed based on energies from first-principles calculations [68, 69].

Some quite peculiar systems exhibiting Laves phases or Laves-phase-like structure elements such as van der Waals compounds, irradiated metals, polymer particles and pressurized van der Waals compounds were already mentioned in Sect. 2. In a couple of more ‘ordinary’ binary metallic systems, which do not contain Laves phases at ambient pressure, they may form at high pressure as summarized in a review [70]. Notable examples of such Laves phases, which are only stable at elevated pressures, but which can be retained at ambient pressure, are AAl₂ with alkaline earth metals A = Sr or Ba, and AZn₂ with A = Ca or Sr [70,71,72,73]. Except for BaAl₂, a CeCu₂/KHg₂-type phase is formed at ambient pressure as a stable phase instead of the Laves phase. On replacing A by lighter alkaline earth metal elements, the corresponding Laves phases CaAl₂ and MgZn₂ are obtained, both of which are stable at ambient pressure. A low-pressure CeCu₂-type and a high-pressure C14 polymorph also appear to exist for YbAg₂ [74]. Similarly, a pressure-induced CeCu₂ → C15 transition was predicted for YCu₂, but it could not be confirmed experimentally [75]. Pressure also appears to allow or at least ease preparation of a series of C15 and C14 AFe₂ phases with A being rare-earth metal elements [76, 77], in particular for A metals with large atomic radius. Also preparation of CaCo₂ Laves phase was achieved at elevated pressure [78]. Another notable Laves phase requiring high pressure for preparation is C14 KAg₂ [79], whereas KAu₂ is also accessible at ambient pressure [80]. All these examples have in common that the A atom appears to be too large for the Laves phase to form at ambient pressure, i.e., the atomic radius ratio r_A/r_B is very large. This is compensated for by a higher compressibility of the A atoms (as compared to the B atoms) at elevated pressures.

In the case of Laves phases with three or more elements, the question arises how the elements will be distributed on the A and B sites. This question of so-called site preference¹ was discussed, for example, in Refs. [16, 17, 82,83,84,85,86,87]. Upon adding a third element C to a Laves AB₂, i.e., moving into the ternary system A-B-C, C may substitute either A or B to form a solid solution of the general formula (A_1-xC_x)(B_1-yC_y)₂, if we, for a moment neglect the possibility of A and B occupying the opposite sublattices.

In most cases there will be some more or less pronounced site preference, i.e., C will substitute preferentially either A (y = 0) or B (x = 0). The most obvious cases are those, where either a Laves phase CB₂ exists in the B-C system or AC₂ in the A-C system, implying, in most (but not all) cases, complete solid solubility between the two respective Laves phases, see Fig. 3a and b (neglecting possible two-phase regions occurring upon change of the Laves phase polytype; see Sect. 3.3 for this aspect). If the homogeneity range is only of limited extension (e.g., in case of non-existence of CB₂ or AC₂), preferential site occupation can be determined by refining the site occupancies on the basis of Bragg diffraction intensity data or by using the ALCHEMI (Atom Location by Channeling Enhanced Microanalysis) technique [88]. Note that experimental investigations on site preference are complemented more and more frequently by calculations predicting site preference by means of first-principles methods.

Figure 3

Schematic extensions of homogeneity ranges of Laves phases in ternary systems shown in blue (as arrows: length may or may not extend to the respective endmembers), partially following ideas from Ref. [87]. Preferential substitution in a binary Laves phase AB₂ of a A by C and b B by C, especially if corresponding Laves phase CB₂ and AC₂ exist. c Existence of a true ternary Laves phase Nb(Ni_1-yAl_y)₂ in the Al-Nb-Ni system [108, 109]. Case when C can either substitute A or B, as encountered for d the Fe-Mo-Zr systems [111] and for e the Hf-Nb-V system [114, 115]. f Corresponds to the situation in the Al-Ni-Ti system [116] being a variant of (c) where Ti is able to additionally occupy the B sites

NbCr₂ Laves phase is an example for which various experimental methods were applied to reveal site preferences for a considerable series of third elements. The mere shape of the experimentally determined homogeneity range allowed to conclude that Ti substitutes Nb on the A sites (extending to the TiCr₂ Laves phase, see below) [89] and Al [90,91,92,93] and Si [94] substitute Cr on the B sites. In the case of Al, also X-ray diffraction-based site occupancies indicate the same [95]. ALCHEMI, X-ray diffraction and the shape of the homogeneity range also located V on the B sites [96, 97]. Moreover, ALCHEMI revealed preference of Ti for the A sites and V, Mo, W, Ti for the B sites [98]. Phase compositions of Laves phases in further ternary Nb-Cr-C systems indicate that C = Fe [99], Co [100, 101] and Ni [102] substitute Cr on the B sites, where the former two systems also form Laves phases NbC₂. Information about many other elements can be obtained for elements from the shape of the homogeneity ranges. Such studies were complemented by many types of first-principles calculations, referring either strictly to T = 0 K or also to elevated temperatures, and handling a wide series of elements [103,104,105,106,107]. In most instances, the site preferences agree with experimental findings where available. However, V, Mo, W [106] and Mo, W, Pd, Au [107] are predicted to show only moderate site preference, which may depend substantially on factors such as temperature or even on the presence of other elements.

Certain ternary systems containing no Laves phases in the binary subsystems form true ternary Laves phases with homogeneity ranges of different shapes, as also reviewed previously [16]. Figure 3c sketches the homogeneity range as found in the Al-Nb-Ni system [108,109,110] extending along the line NbAl₂-NbNi₂, but lacking Laves phases in the Al-Nb and Nb-Ni binary subsystems. Obviously, Nb occupies the A sites, whereas Ni and Al take over the role of the small atoms in the sense of A(B_1-yC_y)₂.

Composition-dependent site preference can occur for an element C with an intermediate size between A and B so that both CB₂ and AC₂ may exist or are only potentially existing Laves phases. As a result, quite peculiar homogeneity ranges can arise. A ternary system showing three binary Laves phases and extended homogeneity ranges is the Fe-Mo-Zr system [111], with Mo being the atom of intermediate size, which can occupy both A and B sites. Starting from the binary ZrFe₂ Laves phase, quite distinct homogeneity ranges extend toward MoFe₂ and ZrMo₂, which merge around the ZrFe₂ composition, see Fig. 3d. Similar homogeneity ranges appear to exist in the Fe-Nb-Zr system [87, 112, 113] with Nb as the intermediate-size element. The homogeneity range, however, does not reach the composition of a binary ZrNb₂ phase, which appears not to exist. In the Hf-Nb-V system, HfV₂ is the only binary Laves phase with the intermediate-sized element being Nb. Nb is able to substitute both Hf and V [114, 115], leading to a homogeneity range as schematically indicated in Fig. 3e. Composition-dependent site preference leading to a strongly non-linear homogeneity range is also known for the truly ternary C14 Laves phase in the Al-Ni-Ti system. The A sites are exclusively occupied by Ti, but all three elements may occupy the B sites of the Laves phase in the sense of Ti(Ni_1-y-zAl_yTi_z)₂ [116], see Fig. 3f. In this context it may be mentioned that a recent study [117] refuted earlier results, which had implied that C14 Mn(Cu,Si)₂ and C14 Mn(Ni,Si)₂ Laves phase exist at very Mn-rich compositions requiring substantial occupation of the B sublattice by Mn.

Point defects—the binary case

Point defects were already discussed above in terms of site preference in ternary Laves phases. In the present section, typically less abundant point defects in binary Laves phases will be discussed.

The contribution of configurational entropy to the thermodynamics of crystals dictates that in single-element crystals point defects must occur to some extent in equilibrium at T > 0 (thermal point defects). In ordinary metals, these thermal equilibrium point defects are practically only vacancies. In intermetallic compounds with more than one single (crystallographically distinct) sublattice, naturally more different types of (thermal) point defects can exist. At the same time, the third law of thermodynamics predicts complete order at T = 0 K, requiring for binary and multinary intermetallic compounds complete ordering over the sublattices and, hence, fixed composition at 0 K. At T > 0 K, homogeneity ranges have to exist due to generation of configurational entropy by constitutional point defects at T > 0 K.

Comprehensive models for the defect thermodynamics are able to describe the point defect thermodynamics as a function of temperature and composition [118,119,120]. Such thermodynamic models also predict that the highest point defect densities are present at off-stoichiometric compositions in the form of what is called constitutional point defects. The substitution of elements A and B by a third element C in Laves phases in ternary and higher-order systems was already dealt with in Sect. 3.1. The changes in the site occupancies due to constitutional point defects in binary Laves phases are, in most cases, much smaller than the changes, which can occur in ternary and higher-order systems.

The composition dependence of the lattice parameters and of the volume per unit cell as measured by diffraction techniques already may give insights about, e.g., changes in the point defect mechanism. It is usually expected that the average atomic volume of an intermetallic phase increases monotonously with an increasing molar fraction of the larger element, i.e., with x_A in the case of binary AB₂ Laves phases. However, changes in the metallic bonding and magnetism with composition of the Laves phase but also the occurrence of constitutional vacancies may lead to behavior, which is difficult to predict. Hence, a combination of composition-dependent measurements of the mass density and of lattice-parameters is expected to give more reliable insight into the (predominant) type of constitutional point defects. However, mass-density measurements require high-quality alloys, e.g., without porosity, the presence of which would incorrectly suggest the presence of vacancies. Furthermore, the refinement of site occupancies from diffraction-based intensity data already mentioned in Sect. 3.1 can also give valuable information. This, however, requires a critical comparison of the quality of refinement for different types of point defect models. Thereby, it should be kept in mind that, based on the Bragg reflection intensities alone, mutual presence of vacancies on all sublattices cannot be assessed due to complete correlation of the occupancies with the scale factor of the refinement model. The ALCHEMI method is likely not sufficiently sensitive to study the usually low point defect densities in binary Laves phases [88]. Also in the field of predicting the type of constitutional point defects, first-principles calculations play an increasingly important role.

These introductory comments on the different methods to determine point defect characteristics in Laves should be kept in mind when assessing reports in the literature.

Constitutional point defects

The most commonly considered types of constitutional point defects are

• constitutional antisite atoms being the analogues of the ternary substitutional atoms predominating in ternary Laves phases (see Sect. 3.1). These are denoted, for example, as A_B meaning an A atom on a B site, but also

• constitutional vacancies, denoted, for example, as Va_A for vacancies on an A site.

Note, however, that more types of point defects were considered in the past, for example substitution of B₄ tetrahedra by a single A atom [5, 121]. It appears, however, that only antisite atoms and vacancies seem relevant in reality in Laves phases.

In order to appropriately consider the effect of antisite atoms and vacancies on the results of mass density or diffraction measurements one can first consider the general chemical formula

$$ \left( {A_{{1 - y\left( {Va_{A} } \right) - y\left( {B_{A} } \right)}} Va_{{y\left( {Va_{A} } \right)}} B_{{y\left( {B_{A} } \right)}} } \right)\left( {B_{{1 - y\left( {Va_{B} } \right) - y\left( {A_{B} } \right)}} Va_{{y\left( {Va_{B} } \right)}} A_{{y\left( {A_{B} } \right)}} } \right)_{2} $$

(1)

where the different y(X) are (or contribute to) the indices in the chemical formula Eq. (1) and simultaneously correspond to the site fractions of the indicated species X on the A or B sites. The molar fraction x_B of the component B of such a Laves phase is:

$$ x_{B} = \frac{{2 - 2y\left( {Va_{B} } \right) - 2y\left( {A_{B} } \right) + y\left( {B_{A} } \right)}}{{3 - y\left( {Va_{A} } \right) - 2y\left( {Va_{B} } \right)}} $$

(2)

Assuming that only one single type of defect is realized at given side of x_B = 2/3 (x_B < 2/3 or x_B > 2/3), one obtains site fractions of antisite atoms $y\left( {B_{A} } \right)$ and $y\left( {A_{B} } \right)$ as a function of the composition of the Laves phase given in terms of the molar fraction x_B:

$$ {\text{for}}\;x_{B} < 2/3:y\left( {B_{A} } \right) = 0\quad {\text{and}}\quad y\left( {A_{B} } \right) = 1 - \frac{3}{2}x_{B} , $$

(3a)

as well as

$$ {\text{for}}\;x_{B} > 2/3:\;y\left( {A_{B} } \right) = 0\quad {\text{and}}\quad y\left( {B_{A} } \right) = 3x_{B} - 2 $$

(3b)

Similar expressions can be derived for occurrence of only constitutional vacancies.

As detailed in the following, the majority of literature implies predominance of constitutional antisite atoms, A on B sites A_B for a molar fraction x_B < 2/3 as well as antisite B atoms on A sites, B_A for x_B > 2/3. The latter is in contrast to the repeatedly supposed unlikeliness that large A atoms can occupy the sites of the smaller B atoms [122,123,124,125,126]. This in turn leads to the assumption of occurrence of V_B vacancies for x_B > 2/3, which, however, could not be demonstrated to be present. Only in specific cases clear evidence for vacancies V_A exist for x_B < 2/3; see below.

Many Laves phases AB₂ with A being a main-group metal have relatively narrow homogeneity ranges [127]. The ‘classical’ Mg-based Laves phases MgCu₂ [128, 129], MgZn₂ [5] (and citations therein), and MgNi₂ [129], however, were stated to exhibit significant homogeneity ranges. The best experimental evidence appears to exist for MgZn₂ quenched from elevated temperatures. For this Laves phase, antisite atoms exist on both sides of x_B = 2/3 as was shown by combined lattice parameter and mass-density measurements, see Fig. 4a [5].

Figure 4

a Composition dependence of observed mass-density of C14 MgZn₂ (data points) as compared to calculated ones (lines) predicted from experimentally determined lattice parameters and from different models for constitutional point defects (S: substitutional, V: constitutional vacancies, T and DT: substitution models involving substitution of Zn₄ tetrahedra by Mg atoms and vice versa). Adapted with permission from [5]. b Formation enthalpies of C14 MgZn₂ and different supercell structures involving different types of antisite atoms and vacancies, implying preference of antisite atoms on both sides of x_Zn = 1 − x_Mg = 2/3 (adapted with permission from [131])

For MgZn₂ first-principles calculations on different kinds of point defects were reported, considering the energetics of the static structures applying supercell approaches for the defects [130, 131] and also phonon calculations to account for T > 0 K effects. These investigations confirm that generation of antisite atoms is more favorable than generation of constitutional vacancies (see Fig. 4b). Although clear experimental evidence is lacking, first-principles calculations on MgCu₂ also suggest predominance of constitutional antisite atoms as compared to constitutional vacancies [132]. Among Laves phases with A being a main-group metal, comparable computational investigations exist for CaAl₂ [133] and CaMg₂ [134], but again with little experimental evidence.

Convincing experimental evidence for the presence of constitutional vacancies exists for C15 ANi₂ phases with A being rare earth metals Y and La-Lu [135]. Preferentially at low temperatures and ambient pressure, also vacancy-ordered superstructure variants exist for this type of Laves phase [136, 137] (see also Sect. 3.5). Disordering was reported to occur at elevated temperatures and upon applying elevated pressures [138,139,140,141]. The observed maximum fraction of vacancies seems to be largest for La with the largest atomic radius [141], see Fig. 5. In fact, the stoichiometric composition LaNi₂ is not stable at ambient pressure [136], which was also confirmed by first-principles calculations [142,143,144], see Fig. 6.

Figure 5

Maximum content of constitutional A vacancies in C15 ANi₂ Laves phases (formula (A_1-xVa_x)Ni₂) with A = Y, La-Lu, indicating a clear correlation between this content and the atomic radius r_A; redrawn from [141]

Figure 6

Formation energies of various real and hypothetical La-Ni phases (red squares and black points) as obtained by first-principles calculations. The convex hull is shown as red continuous line (the dashed black line is unrelated to the present considerations). Note that the energies of the hypothetical stoichiometric C15/C36/C14 Laves phases are located well above the convex hull (adapted with permission from [143])

Under equilibrium conditions, C15 YAl₂ appears to have a quite narrow homogeneity range. Rapid solidification of Y-Al melts and subsequent diffraction analysis indicated, however, that under such conditions the Laves phase might form over a wide range of composition x_Al = 0.58–0.82 [123]. Based on the x_Al dependence of the cubic lattice parameter, it was concluded that constitutional vacancies Va_Al dominate for x_Al > 2/3 and constitutional antisite atoms Al_Y prevail for x_Al < 2/3. For this, it was assumed that the larger Y atoms are unlikely to occupy the sites of the smaller Al atoms. In contrast to this, first-principles calculations on defect formation in YAl₂ predict preference of constitutional antisite atoms prior to constitutional vacancies on both sides of x_Al = 2/3 [145]. This casts some doubt on the interpretation of the x_Al dependence of the lattice parameters, which was not paired with mass-density measurements (see begin of Sect. 3.2). Likewise, Ir-rich YIr₂ seems to be realized by antisite Ir_Y atoms as deduced from powder-diffraction data evaluated by Rietveld refinement based on critically comparing vacancy and antisite atom models [146].

There are numerous binary Laves phases in systems with A and B being elements from the 3d, 4d and 5d transition metal series with often wide homogeneity ranges. Accordingly, there are many investigations on the kind of point defects, both employing density measurements and comparison with lattice parameter evolutions or diffraction analysis leading to refined occupancies. Table 2 summarizes investigations giving experimental and theoretical evidence, without explicit reference to the Laves phase polytypes considered. The very large majority of the results indicate predominance of antisite atoms on both sides of the stoichiometric composition, while there is apparently no compelling evidence for constitutional vacancies.

Table 2 Overview on publications dealing with the type of constitutional point defects in binary transition metal Laves phases AB₂ with B being an element of the 3d series and A a group-IV/V transition metal

In the Co-Nb system the C14, C15 and C36 polytypes occur with increasing Co content in the sequence C14, C15 and C36, where C14 and C36 are high temperature phases but can be retained by quenching, see Fig. 7 [161]. Two quite general phenomena relevant for off-stoichiometric binary Laves phases were investigated in quite some detail in this system: preferential site occupation and static atomic displacements.

Figure 7

Phase diagram Co-Nb featuring three different Laves phase polytypes C15 (around the ideal composition corresponding to the molar fraction x_Co = 2/3) as well as C14 (Co-poor) and C36 (Co-rich) (adapted with permission from [161])

For the Co-poor C14 polytype (x_Co < 2/3), it was shown [155, 162] based on a single-crystal diffraction-based analysis (assigned crystal composition Nb_1.07Co_1.93) that Nb antisite atoms Nb_Co are located only on the Co^2a sites, while the Co^6h sites are only occupied by Co (compare Fig. 1 and Table 1). At the same time, it was noted that the atomic displacement parameters are larger than those obtained from a similarly performed structure analysis on a stoichiometric C15 NbCo₂ single crystal [155]. These atomic displacement parameters are also found to be larger for a Co-rich C15 NbCo₂ single crystal (Nb_0.88Co_1.12), for which Co antisite Co_Nb atoms are encountered. Such a composition-dependent evolution of refined atomic displacement parameters (pertaining to ambient temperature) implies a static contribution to the atomic displacements due to the point-defect-induced disorder. These static displacements add up to the thermal contributions, which should be the only contribution for the stoichiometric composition.

A C36 polytype develops at x_Co > 2/3 with quite high Co contents [159, 161]. Due to the high content of Co_Nb antisite atoms, a more detailed evaluation of the diffraction data was possible based on a single crystal with assigned composition Nb_0.735Co_1.265 (“NbCo₃”). As in the case of C14 NbCo₂ (Nb_1.07Co_1.93), the antisite atoms are not evenly distributed over the available A sites (now: Nb^4f and Nb^4e, see Fig. 1 and Table 1) [155, 160, 162]. The static atomic displacements caused by the point defects lead to a pronounced non-Gaussian distribution of the electron density (see Fig. 8), which was modeled upon structure refinement in terms of off-center displacements of the Co antisite atoms, which are ‘too small’ for the Nb sites. Detailed reasons for the observed displacements and for the differences in the occupation of the two different Nb sites (supported by first-principles calculations) are discussed in Refs. [155, 160, 162].

Figure 8

Electron density difference maps originating from structure refinements on single-crystal-based X-ray diffraction data of Co-rich C36 NbCo₂ Laves phase. A pronounced, peculiar-shaped electron density difference in the vicinity of the two crystallographically distinct A sites (4e and 4f Wyckoff sites) was obtained after refinement using mixed occupation of these sites by both Nb and Co (with refined anisotropic displacement parameters). This justified a more advanced refinement model involving split positions for the final refinements (adapted with permission from [155])

The preferential occupation of the Co^2a sites in Nb-rich C14 NbCo₂ Laves phase (see Fig. 1 and Table 1) appears to have similarities to the preferred occupation of such sites in Ti-rich C14 TiMn₂ [153]. Nb-rich NbMn₂, however, seems to be a counterexample with the antisite Nb atoms preferentially occupying the 6f sites [155]; see also Sect. 3.3 for the role of similar site preferences in ternary C14 and C36 Laves phases.

Thermal point defects

At T > 0 K, point defects in Laves phases can also be generated at the stoichiometric composition x_B = 2/3. They can, however, only occur in combination to retain composition as resulting from Eqs. (1-2). Table 3 lists the relation between the amounts of defects, if two types of defects balance each other at the stoichiometric composition.

Table 3 Combinations of point defects generated in a stoichiometric Laves phase AB₂ as derived from Eqs. (1 and 2) in the case of only two types of coexisting defects

There are only a few experimental studies determining and quantifying the kind of thermal point defects in Laves phases. For GdPt₂, GdIr₂, GdRh₂, GdAl₂ with typically narrow homogeneity ranges, the occurrence of (non-equilibrium) quadruple defects (i.e., combinations of B_A + 3Va_B; see Table 3) was concluded from an observed ball-milling-induced reduction of the lattice parameters and changes in the magnetic behavior [163,164,165,166]. The same group concluded GdMg₂ to exhibit pairs of antisite atoms (B_A + A_B; see Table 3) [166]. Thereby, it was proposed that the point defects generated upon mechanical activation should be the same as formed thermally.

Comparison of composition-dependent mass-density with lattice parameters of quenched NbCr₂ [151, 152], NbFe₂ and NbCo₂ [151] as well as ZrCo₂ [157] revealed dominance of constitutional antisite atoms in all cases (see Sect. 3.2.1). In the case of NbCr₂, NbCo₂ and ZrCo₂, some measurable contents of thermal vacancies were shown to form, which increase with the equilibration temperature of the respective alloys. Only NbFe₂ did not show any measurable evidence of thermal vacancies [151]. Note however, that these density measurements do not reveal the presence of thermal antisite atoms.

More recently, first-principles calculations on point defects in Laves phases paired with modeling of defect thermodynamics was used to predict thermal defect contents at T > 0 [103, 131,132,133,134, 145, 150, 154]. While in all these calculations the constitutional point defects are found to be antisite atoms (see Sect. 3.2.1), pairs of antisite atoms also constitute the predominant thermal point defects at the stoichiometric composition (see, for example, Fig. 9). An exception is YAl₂ [145]. While the calculations for this Laves phase predict predominance of antisite defects in both Al-poor and Al-rich YAl₂ in line with the other studies, considerable importance of thermal vacancies is predicted at the stoichiometric composition (combination of triple and quadruple defects according to Table 3 [145]). This agrees with findings for the electronically similar rare earth-Al compound GdAl₂ [163]. Nevertheless, all the mentioned first-principles-based calculations indicate the formation of vacancies to a strongly temperature-dependent extent at T > 0, showing no obvious systematics as function of the A and B elements. These amounts of vacancies are, of course, quite relevant for diffusion of the A and B elements in Laves phases [133, 167,168,169,170].

Figure 9

Composition dependence of the site fractions of antisite atoms and vacancies on the Zr and Co sublattices (see Eq. (1)) predicted for ZrCo₂ Laves phase at 1000 K (adapted with permission from [145]). The data indicate dominance of antisite atoms as constitutional vacancies in both Co-poor and Co-rich ZrCo₂ as well as in the form of pairs of antisite atoms at the stoichiometric composition of x_Co = 66.7%. Note the non-linear abscissa. Moreover, the content variables (site fractions) were adapted to comply with the quantities used in the present work

The use of CALPHAD-type thermodynamic descriptions to estimate disordering by formation of antisite atoms at the stoichiometric composition of NbCr₂ is described in Sect. 3.4.

Polytypism

As indicated in Sect. 2, there is an infinite number of Laves phase polytypes differing by their stacking sequences. The simplest polytypes are C15 (MgCu₂ type), C14 (MgZn₂ type) and C36 (MgNi₂ type), but many others were reported in special systems, see, for example, [27, 29, 171]. As indicated in a review on polytypic structures [172], there can be several reasons for occurrence of distinct polytypes:

• (i) There are polytypic phases, which are stable under different thermodynamic conditions (temperature, pressure, composition).

• (ii) Non-equilibrium polytypes may develop during growth from the melt, from the gas phase or from a structurally unrelated solid because growth of the non-equilibrium polytype is more rapid than growth of the equilibrium polytype.

• (iii) Non-equilibrium polytypes may develop from an already existing polytype in the course of a phase transition between two polytypes (polytypic transition). Thereby, a non-equilibrium polytype is formed because it develops more rapidly than the equilibrium polytype.

The possibility to form non-equilibrium polytypes according to (ii) and (iii) should always be taken into account upon interpreting experimental data. Moreover, it should be noted that the observation of some irregular stacking sequence does not automatically mean the discovery of a new polytype as is stated occasionally in the literature. Instead, a given stacking sequence should be repeated several times, although no specific limit exists defining how often some stacking sequence must be repeated to call it a new polytype.

As reviewed [16], Laves and Witte [173] had already pointed out the obviously polytype-influencing role of the valence electron concentration VEC (or, more precisely, the number of valence electrons per atom) in A = Mg-based Laves phases. Similar schemes were reported for transition metal Laves phases [174]. Studies revealing sequences of characteristically changing polytypes are typically performed on alloy series A(B,C)₂ with B, C providing different numbers of valence electrons. Recent investigations of this type, which are often supplemented by electronic structure calculations, deal with x-/VEC-dependent changes of the stacking sequences in Ca(Al_1-xMg_x)₂ [175, 176], Mg(Zn_1-xPd_x)₂ [177], Mg(Ni_1-xGe_x)₂ [178], and Gd(Co_1-xGa_x)₂ [179]. It was, however, emphasized in Ref. [16], that a pure VEC dependence cannot explain all trends in polytype formation, and observations from different systems are contradictory. An early reported additional influencing factor modifying the trends implied by a VEC dependence of the polytype in ternary transition metal Laves phases A(B,C)₂ was proposed to be the difference of the group number of two elements B and C [180].

Much more recently, the following experimentally observed trends on polytype stability in Laves phases with the A atoms being group-IV/V transition metals were rationalized [181]:

• (i) If in a binary system several Laves phase polytypes exist with a composition-dependent polytype stability, the C15 phase is found around the stoichiometric composition given by x_B = 2/3, whereas at B-poor compositions the C14 polytype is encountered and at more B-rich compositions the C36 may be found (not in all cases all three polytypes are encountered). The best investigated system showing this systematic is the Co-Nb system (see Sect. 3.2.1 and, in particular, Fig. 7). As already mentioned, Nb_Co antisite atoms are located very preferably on the Co^2a sites of the C14 Laves phase in the Co-poor regime, and a less pronounced site preference occurs for Co_Nb antisite atoms in the Co-rich C36 Laves phase. Consistent with this, if a binary Laves phase assumes the C14 structure at x_B = 2/3, no polytypism is encountered upon deviating from the stoichiometric composition.

• (ii) Alloying of a binary C15 Laves phase AB₂ by a third element C, which substitutes the B element, frequently leads to a change to a C14 polytype. In several cases, it was demonstrated that also in this situation, a preferred occupation of the 2a site by C occurs at low C contents. This, for example, is known for the extended solid solution series with C = Al, Si [17]. Several of such systems were explored more recently in some detail, as Al-Cr-Nb [93, 95] and Al-Co-Nb [182]. In systems ranging from C15 Laves phase to C15 Laves phase such as NbCr₂-NbCo₂ [155, 183, 184] and ZrV₂-ZrCo₂ [184], C14 Laves phase occurs at intermediate compositions with enrichment of the respective minority element on the 2a site; see Fig. 10.² Energetics of such preferred site occupation was also supplemented by first-principles calculations [183]. In contrast to the effects upon alloying binary C15 Laves phases with a third element, alloying of binary C14 binary Laves phases (e.g., C14 TiFe₂ with Si) does not lead to a change of the polytype.

  Figure 10

  

  Occupancies of the B^2a and B^6h sites by Co in C14 Nb(Cr_1-xCo_x)₂ Laves phase [183, 184] as determined on the basis of single-crystal-based X-ray diffraction data, revealing preferred occupation of the 2a sites by the minority B element being accompanied with an inversion of the occupancies at x ≈ 0.5 (adapted with permission from [184])

Both these observations imply that if a binary C15 Laves phase exists for some stoichiometric binary composition, introduction of substitutional point defects (antisite atoms in the binary system or C atoms on B sites upon making the system ternary) promotes occurrence of hexagonal polytypes. The C36 polytype occurs when different types of species occupy the A sites, i.e., in B-rich binary Laves phases, whereas the C14 polytype occurs when different types of species occupy the B sites (B-poor binary and A(B,C)₂ ternary Laves phases). It was made likely [181] that the larger number of structural degrees of freedom of the hexagonal polytypes and, in particular, the crystallographically independent B (C14, C36) and A (C36) sites (see Fig. 1 and Table 1), which allow for preferential site substitution on the B or on the A sites, stabilize the C14/C36 polytypes with respect to the original C15 polytype. Energies from first-principles calculations confirm this stabilization for C14 with respect to C15 [183, 184]. Assuming that only the simplest polytype is formed, which is necessary to allow for some energetically favorable preferred site occupation, explains why in case of mixed occupation of the B sites the C14 polytype develops whereas for mixed occupation of the A sites the more complicated C36 polytype forms.

Different Laves phase polytypes must essentially be regarded as different phases in the sense of the phase rule, with transitions between different equilibrium polytypes occurring in a first-order fashion. If, as discussed above, polytypes occur in a binary (or ternary) system with varying composition at constant temperature, two-phase regions should be located between these polytypes. These two-phase regions typically appear to be quite narrow in binary and ternary systems. Such two-phase regions C14 + C15 and C15 + C36 are shown in Fig. 7. The widths of such two-phase regions are typically determined from heat-treated, macroscopically homogeneous alloys, where it is, however, difficult to hit the composition of a narrow two-phase field. An alternative method is preparation of diffusion couples, which were used in Ref. [161] leading to composition profiles as shown in Fig. 11 (see also [160]). Whereas the presence of different phases was established by electron backscatter diffraction, expected composition steps indicating the width of the two-phase region are not always visible, see Fig. 11. Other examples for non-detectability of a two-phase region can be found in investigations on the Co-Ta [185] and the Co-Ti systems [186]. As briefly indicated in Ref. [186], the similar crystal structures of the various polytypes likely have quite similar energies but also allow for formation of coherent interfaces upon introducing moderate coherency stresses. As a consequence, the two-phase regions expected due to the continuum thermodynamics of the systems can become narrowed or even absent in diffusion couples due to coherency effects [187,188,189].

Figure 11

Composition profiles measured by electron probe microanalysis on diffusion couples Co-Nb (left) and NbCo₂-Nb (right) after heat treatments at different temperatures [161]. All phases expected from the equilibrium phase diagram (compare Fig. 7) were formed. Whereas a composition step is visible between the regions of the C15 and C14 Laves phase, such a step is not discernible between C36 and C15 (adapted with permission from [161])

There are a couple of binary systems containing Laves phases showing temperature-dependent equilibrium polytypism. It appears that, if several polytypes occur as equilibrium phases, C15 appears to be the lowest-temperature phase and C14 is highest-temperature phase, with possibly intermediate C36 [17]. This temperature-dependent equilibrium polytypism was explored in quite some detail in the Cr-Ti [190,191,192,193,194] and Hf-Cr systems [195,196,197] dealing with transformation kinetics [192, 193, 196] and with the fault structure as a consequence of the transformation [190, 191, 195, 197].

Temperature-dependent equilibrium polytypism with a C14 high-temperature phase had also previously been concluded from various types of experimental evidence for NbCr₂ (see [198, 199] for a review of such evidence): (i) It is possible to obtain C14 NbCr₂ (which can turn out to be actually C36) in as-cast alloys, whereas subsequent annealing produces C15. (ii) Thermal analysis data often show an endothermic thermal signal upon heating just prior to melting, which was attributed to the C15 → C14 transition. A correspondingly exothermic signal is also observed upon cooling. (iii) Extrapolation from the ternary Al-Cr-Nb system to pure NbCr₂ suggests presence of a C14 phase in a small range of temperature.

Quenching experiments on alloys equilibrated in the apparent C14 field were unsuccessful and because C14 was unusually distributed in as-solidified arc-melted ingots [200], doubts arose about the existence of an equilibrium C14 NbCr₂ high-temperature phase. By use of in situ high-temperature neutron diffraction it was shown that C15 NbCr₂ melts without formation of a C14 phase [198]. Moreover, it was shown that the signal in thermal analysis arose due to melting of an η-carbide-type impurity phase NbCrX_z [198, 199]; see also below. Hence, it was concluded that the C14 phase occasionally observed in as-cast alloy is only metastable at all temperatures.

More detailed high-resolution electron microscopy and powder X-ray diffraction investigations of the apparent C14 NbCr₂ phase formed in as-cast alloy indicated that, at least in the investigated specimens, the majority of the hexagonal Laves phase was actually faulted C36 NbCr₂ [191] which is, however, also only metastable at all temperatures. Remnants of true C14 suggested formation of metastable C14 upon solidification, which quite easily transforms to C36. This rapid transformation suggests an important role of (synchro) Shockley partial dislocation dipoles [201]. Such dipoles were indeed observed in C36 NbCr₂ [197], and the irregularities in the stacking sequence of C36 NbCr₂ (and of C36 TiCr₂ having formed from equilibrium C14 TiCr₂) [191] imply that the transformation C14 → C36 is indeed carried out by Shockley partial dislocation dipoles on adjacent lattice planes. This kind of transformation is not possible for the stable C15 phase, which evidently forms much more sluggishly [196].

Beyond the above-mentioned investigations dealing experimentally and theoretically with polytypism, there are further first-principles-based calculations demonstrating the power of these methods to reveal the thermodynamics of polytypism of the Laves phases. For example, the relative stability of polytypes of stoichiometric binary Laves phases at T = 0 K can reliably be predicted for HfV₂ [202], (Ti,Zr,Hf)Cr₂ [150, 203, 204], ZrMn₂ [154, 205], TaV₂ [206], NbCr₂ [202, 207, 208] and TaCr₂ [208]. Dealing with non-stoichiometry, the stability of an intermediate C36 polytype on the CaAl₂-CaMg₂ section [209, 210] was confirmed. Use of the quasiharmonic approach to predict T > 0 thermodynamics of TiCr₂ polytypes [211] gave at least a qualitative agreement with experimental evidence for stability of C15 TiCr₂ at 0 K and increasing stability of C36 and C14 with increasing temperature [194], see also paragraph above. The contribution of magnetic ordering to the binding energy is substantial, so that this contribution can even change the relative stability of polytypes as compared to the nonmagnetic state, as, for example, detailed in Ref. [205] for the case of ZrMn₂.

Two aspects remain to be mentioned in the context of diffraction analysis of Laves phase-containing alloys, which accompany virtually all experimental studies dealing with polytypism. Firstly, care has to be taken upon identifying the polytype present based on diffraction evidence, e.g., powder X-ray diffraction, selected area electron diffraction or by electron backscatter diffraction. As outlined in detail in [195] for the case of diffraction analysis, there are fundamental reflections (or Kikuchi bands), which are common to all Laves phase polytypes, and polytype reflections (or Kikuchi bands), which are specific for the polytype. Hence, it is impossible to assign the type of polytype present simply on the basis of observation of only the (usually strong) fundamental reflections. Moreover, faulting of the stacking sequences can considerably broaden the polytype reflections, possibly hampering polytype identification, whereas the fundamental reflections remain unaffected; see, for example, [191, 195].

Secondly, high-temperature corrosion of Laves phases with A being a group-IV/V transition can lead to the formation of peculiar intermetallic compounds stabilized by small amounts of X = O, N or C. These intermetallic phases can obstruct interpretation of, in particular, powder-diffraction patterns. One example is the η-carbide-type NbCrX_z phase [198, 199] already mentioned above. Such η-carbide type (or Ti₂Ni-type; differing only by the distribution of the metal atoms) phases were also reported in Laves phase-containing alloys in the systems Co-Nb [155], Fe-Nb [155, 212], Mn-Zr [213], Fe-Ta-V [184, 214], and Co-Cr-Nb [183, 184]. In the Fe-Nb system also an M₂₃C₆-type phase was reported [215], whereas impurity-stabilized Th₆Fe₂₃-type phases were observed in Fe-Zr-based alloys [216, 217]. Moreover, a metastable face-centered cubic phase with a lattice parameter of a = 8.17 Å and unknown atomic structure incompatible with the previously mentioned structures was reported in Cr-36 at.% Zr alloy [218], which might also be an impurity phase. Note that this list is definitely incomplete since such impurity phases are often only mentioned in passing. Furthermore, it should be mentioned that due to the low quantity of O/N/C needed to stabilize such phases, uptake of small amounts of such impurities during handling at elevated temperatures can lead to formation of appreciable amounts of the impurity phase.

The frequent occurrence of such phases in turn suggests very low or even negligible solubility of O/N/C in Laves phases, most likely because the tetrahedral interstices are simply too small to accommodate O/N/C. There is, however, some atom-probe field ion microscopy evidence for incorporation of C into (Mo,W)(Fe,Cr)₂ Laves phase in some high-Cr ferritic steels [219, 220]. DFT calculations were performed to estimate the energetics of N and C incorporation into C14 NbFe₂ Laves phase [221]. This study indicates that the dissolution energy of N into the most favorable tetrahedral sites of NbFe₂ is similar to that for N dissolution into α-Fe (showing only low N solubility), whereas C incorporation into NbFe₂ appears to be even less favorable. As discussed in Sect. 4.1, these interstices can, however, well accommodate appreciable amounts of hydrogen.

CALPHAD modeling

Description of the thermodynamics of multicomponent systems using the CALPHAD (CALculation of PHAse Diagrams) method [11, 86] is nowadays routine. This method involves development of a composition-dependent description of the temperature-dependent Gibbs energy for each phase of the system. The simplest way to model the Gibbs energy of Laves phases is in the form of stoichiometric compounds. This was done for Laves phases especially in early publications (but also in later studies, if non-stoichiometry is not an issue) as, for example, in the systems Fe-Ti [222], Cu-Mg [223], and Mg-Zn [224]. Gibbs energies of potentially non-stoichiometric, multicomponent crystalline phases require more complex functional descriptions. In early times, descriptions for non-ideal, simple substitutional solid solutions were employed when describing non-stoichiometric Laves phase in the Co-Cr-Zr system [225], at that time not considering polytypism. As, however, also discussed above, Laves phase polytypes are distinct phases. Hence, they should be (and indeed usually are nowadays) treated as such within the CALPHAD approach.

In current research, modeling of non-stoichiometry is predominantly realized using the compound-energy formalism (CEF) [226, 227] as it allows handling appropriately at least ideal configurational entropy in crystalline phases with several, crystallographically distinct sublattices. Depending on the type of constitutional point defects, which are considered to be responsible for deviations from ideal AB₂ composition, different sublattice models can be used, with or without Redlich–Kister-type description of the excess Gibbs energy. Initially, various types of sublattice models were used for Laves phases, for example in the Cr-Ti [228], Cr-Zr [229], Fe-Ti [125, 230], Mn-Zr [126], and Cr-Ta [231] systems, partially also considering predominance of constitutional vacancies in contrast with later obtained experimental evidence (see Sect. 3.2). The variability of the models arises also from the fact that the C14 and C36 polytypes contain more than two sublattices; see Table 1.

There is a strong desire to develop CALPHAD descriptions of certain systems by using thermodynamic models for phases, which allow the extension into higher-order systems while employing a minimum number of independent parameters. In view of this desire, it was recommended to work, for a given Laves phase polytype, with only one single A and one single B sublattice [7]. Each sublattice can be occupied by both types of atoms, neglecting the possibility of occupation by vacancies.³ In some cases this procedure is exactly followed. Sometimes the crystallographically distinct A and B sublattices (according to Table 1) are considered separately in a formal sense, whereas the relevant parameters are constrained such that the model behaves as a model with only two sublattices.

Within the CEF formalism, consideration of two sublattices for a Laves phase in a binary system implies the assessment of the Gibbs energies of the endmember compounds AB₂ (the stoichiometric, ideally ordered Laves phase), AA₂ and BB₂ (pure A and B in the Laves phase structure), and BA₂ (Laves phase structure with inverse occupation of the sublattice). Note that in all known cases of Laves phases, the AA₂, BB₂ and BA₂ compounds are not accessible experimentally so that corresponding experimental Gibbs energies are not available. The only experimental data available to assess estimated values is the energetics of the Laves phase in the relatively narrow observed homogeneity regions. In view of this, a series of strategies to arrive at thermodynamic descriptions of binary and higher-order systems were employed in the literature [7]. Nowadays, typically direct experimental data are used to assess the Gibbs energy of stoichiometric AB₂, while estimated values for the Gibbs energies are used for AA₂ and BB₂ ensuring that the Laves phase is sufficiently unstable with respect to pure elemental A and B. The Gibbs energy of the BA₂ endmember is typically expressed in terms of the energies of the remaining three endmembers AB₂, AA₂ and BB₂, yielding effectively a Wagner-Schottky model, which should be valid for dilute point defect contents [7, 227]. The available information about the homogeneity range of the actual Laves phase is then typically employed to optimize the Redlich–Kister parameters. Such type of strategy was applied, e.g., for the systems Al-Ca-Mg [232], (Al-)Cu-Mg-Zn [233,234,235], Ca-Mg-Zn [236], Cr-Ti(-Al) [237], Fe-Ti [238], Co-Ti [239], Al-Ni-Ti [240], Fe-Zr [241], Fe-Mo-Zr [111], Mn-Zr [213], Cr-Nb [242], (Al-)Cr-Nb [92], Co-Nb(-Al) [243] and Co-Ta [244].

An increasing number of studies makes use of energy values obtained from first-principles calculations. In particular, formation energy values are calculated for the experimentally not accessible endmembers BA₂, AA₂ and BB₂⁴ of the CEF and the corresponding values are used in the thermodynamic descriptions. Examples for such modeling works are descriptions of the systems Cu-Mg [247], Ca-Mg-Zn [248], Al-Ca-Mg [249,250,251], Cr-Ti [203], Cr-Zr [252], Fe(-Sn)-Zr [253], Cr-Hf [203], Hf-W [254], Cr-Nb [208, 252, 255, 256], Cr-Nb-Fe [257], Cr-Ta [208], Fe-Ta [258], Cr-Ta [259], Co-Ta [260], Ta-V [206], Cr-Nb-Zr [252]. It should be noted that first-principles calculations can yield sublattice-specific Gibbs energies (see, for example, [203, 206]) allowing to arrive at energies of the endmembers of more complex sublattice models for the C14 and C36 polytypes. Recent publications follow the approach of CALPHAD modeling with respect to 0 K [256, 259] (third generation CALPHAD databases).

Thermodynamic descriptions can also be used to predict the difficult-to-measure thermal point defect content, see Sect. 3.2.2. This was done in Fig. 12 for the amount of antisite atoms developing in stoichiometric NbCr₂ (using a thermodynamic description from Ref. [255]).

Figure 12

Fraction of Cr sites occupied by Nb atoms y(Nb_Cr) in stoichiometric C15 NbCr₂ as a function of temperature calculated from a thermodynamic description of the Cr-Nb system [255]: a linear fashion and b in an Arrhenius-type fashion

Going beyond the CEF, recently the cluster expansion approach based on quasi-random structures of Laves phases was used to investigate the thermodynamics in the homogeneity ranges of various C15 Laves phases [261].

Structure variants

Structure variants of the Laves phases are, in the sense of the current section, crystal structures, which result from breaking the space group symmetry of any of the Laves phase polytypes. The cases discussed in the following can be roughly subdivided into (i) simple, largely homogeneous distortions due to changes in the electronic structure, for example by the onset of magnetic ordering or changes in the bonding pattern; see Sect. 3.5.1. Other types of distortions can occur due to (ii) orderly occupation of the A or B sites by different types of species, i.e., different types of atoms or also by vacancies; see Sect. 3.5.2. More complex structures occur by (iii) combination of Laves phase structures with fragments from other crystal structures, typically breaking up the tetrahedral network of the B atoms; see Sect. 3.5.3.

Distortions due to changes in the electronic structure

Ferro-, antiferro-, or ferrimagnetic ordering below some magnetic order–disorder temperature can result in magnetostriction associated with largely homogeneous strain of the crystal structure. In the simplest case, non-symmetry-breaking volume effects are encountered, possibly accompanied by non-symmetry-breaking effects on the axial ratio in the case of hexagonal polytypes. These effects can be pronounced over a narrow temperature range, if first-order magnetic phase transitions can be brought about, for example in the form of a transition from high-moment/high-volume ferromagnetic to low-moment/low-volume antiferromagnetic, which was studied in a series of publications on (Hf,Ta)Fe₂ Laves phases [262,263,264,265].

Generally, in the case of uniaxial (e.g., ferro)magnetic ordering, magnetostriction conforming with the magnetization direction is always expected to break the cubic (nuclear) symmetry of the C15 polytype, and, if the axis of magnetization does not agree with the stacking direction, also the hexagonal symmetry of other polytypes. These effects may be undetectable by conventional diffraction techniques in many systems, but they can become considerable for rare-earth element-based materials, as in (usually C15) Laves phase AB₂ with A a rare-earth element and B typically Mn, Fe or Co. While the magnetic ordering is frequently more complicated (e.g., ferrimagnetic and sometimes antiferromagnetic), the resulting distorted nuclear structures derived from diffraction experiments were described as tetragonal (I4₁/amd, moment direction 〈100〉_C15, NdCo₂ [266, 267], HoCo₂ [268], YMn₂ [269]), rhombohedral ($R\bar{3}m$, moment direction 〈111〉_C15, TbFe₂ [270], SmFe₂ [271]), or orthorhombic (Imma, moment direction 〈110〉_C15, NdCo₂ [267], SmFe₂ [271]) distortion variants, largely resulting from homogeneous strain. Please note however, that in many studies on functional properties, crystal structure is not described explicitly in conventional crystallographic terms (e.g., indicating the space group symmetry) but more in terms of the observed direction of magnetostriction.

In line with considerations on the local symmetry of the rare-earth metal atoms [272], the largest distortions are encountered for the rhombohedral structures with moment direction along 〈111〉_C15. To make the materials magnetically sufficiently soft and in order to make polycrystalline materials suitable for such applications, magnetic anisotropy is reduced by alloying with rare-earth elements favoring the 〈100〉_C15 moment direction. This was also the alloying strategy to arrive at Tb_0.3Dy_0.7Fe₂, Terfenol-D, see Fig. 13 [273] and Sect. 4.3.1.

Figure 13

Pseudobinary phase diagram TbFe₂-DyFe₂ redrawn from [273] with the binary endmembers forming different distortion variants due to magnetostriction of the C15 Laves phase at low temperatures. The varying magnetic anisotropy leads, under the constraint of constant composition, to the morphotropic phase boundary (curved line). Compositions on the rhombohedral side close to this boundary show the best properties for polycrystalline magnetic actuator materials (see also Sect. 4.3.1)

Furthermore, some symmetry-breaking distortive phase transitions, which do not appear to be related to magnetism, are known to occur in some Laves phases either with decreasing temperature or with increasing pressure. Examples are C15 UMn₂ [274, 275], C14 URe₂ [276], C15 ZrV₂ [277, 278], C15 HfV₂ [278,279,280,281,282], C15/C14 CaLi₂ [283] and C15 PbAu₂ [284]. The resulting space groups are the same as for magnetostrictively distorted magnetic Laves phases. Such transitions are often found to be related to special quantum phenomena such as superconductivity, for example in the cases of ZrV₂ and HfV₂; see also Sect. 4.4.

Internal structural distortions are responsible for a cubic-cubic transition in KBi_2-xPb_x (x = 0…0.8), as characterized by experimental and theoretical methods [285]. While KBi₂ and the compounds with up to x = 0.6 have ordinary C15 structure with $Fd\bar{3}m$ symmetry, for higher Pb contents a superstructure with cubic $F\bar{4}3m$ symmetry was found. The symmetry reduction is accomplished by an alternate contraction and expansion of the B atom Bi_4-2xPb_2x tetrahedra, see Fig. 14. For the experimentally unattainable value of x = 1, the small tetrahedra can be imagined to correspond to electron-precise Zintl anions [Bi₂Pb₂]²⁻ [285]. Hence, although atomic substitution occurs, the symmetry reduction is obviously due to changes in the chemical bonding induced by the change in the number of electrons in the system, although occurrence of atomic ordering cannot be excluded to accompany the symmetry reduction as a secondary process.

Figure 14

Intermetallic distances in a pair of tetrahedra within the crystal structure of KBi_2-xPb_x [285] sharing a common corner: (left) at x = 0, with an atomic structure and symmetry of an ordinary C15 KBi₂ Laves phase. The “i” implies a center of inversion. (right) x = 0.8 with the upper tetrahedron expanded and the lower one contracted. Assuming electron transfer from K, the lower, small tetrahedra corresponds to an electron-precise [Bi₂Pb₂]²⁻ Zintl anion for the idealized case of x = 1 (redrawn with slight modifications from [285])

Distortions due to atomic ordering

While in the case of the KBi_2-xPb_x, no obvious occupational ordering occurred on the A or B sites, symmetry-broken Laves phase variants are sometimes formed to accommodate different types of atoms in an ordered fashion on the A or on the B sites. It was noted already in Sect. 3.3 that such a symmetry reduction is necessary if two different atoms have to orderly occupy the B sites in the C15-type structure, whereas this is not the case in the C14 structure, which already contains two different sites B^2a and B^6h (see Table 1). Table 4 lists a couple of cases of ordering-induced symmetry reductions for the C15 and C14 polytypes, including also vacancy ordering in rare-earth nickelides (see also Sect. 3.2.1). Some examples for resulting structures are shown in Fig. 15.

Table 4 Examples for Laves phase variants resulting from ordered occupation of either the A or the B sites by different types of atoms

Figure 15

Example structures showing symmetry reduction by ordering in C15-based Laves phase variants as depicted in (pseudo)cubic unit cells: a Mg₂Ni₃Si in $R\bar{3}m$ symmetry [286] after transformation into a face-centered pseudo-cubic structure, unique axis corresponds to [111] direction of the shown unit cell, b Mg₂Cu₃Si (real composition poorer in Si) in P4₃32 symmetry [293]. a and b show Cu/Ni versus Si ordering on the B sites, respectively. c Y₁₅(Y_0.24Va_0.76)Ni₃₂ with $F\bar{4}3m$ and 2 × 2 × 2 superstructure [317] showing ordering of vacancies (partially occupied by Y) against Y on the A sites

It is striking that all substitutionally ordered cases involving symmetry reduction listed in Table 4 are cases with A = alkali, alkaline earth or rare earth metal. Examples with A = group-IV/V transition metals lack and only occur for the indicated case of the non-symmetry-breaking ordering on the 2a and 6f sites already inequivalent in the C14 structure. This indicates, as already implied by the examples in Sect. 3.3, that the valence electron concentration is a more important polytype-determining criterion in Laves phases with A = alkali metal, alkaline earth than in the case of A = group-IV/V transition metal.

More complex Laves phase variants

Further crystal structures can be considered showing ‘similarity’ with the crystal structures of Laves phases, lacking, however, a one-to-one correspondence of the atomic or vacancy sites with the sites of a particular Laves phase polytype. These structures are as diverse as the diffuse term ‘similar’ may imply. One group of such Laves structure variants results from the fact that the Laves phases belong to the larger group of Frank–Kasper phases, which can be regarded as tetrahedrally close-packed structures of differently sized atoms. Each of these atoms is surrounded by a triangulated polyhedron with the coordination numbers 12, 14, 15 or 16 [22, 23]. All Frank–Kasper phases can be described as layered structures consisting of regular stackings of a particular combination of certain structure fragments (or structural motifs), which can be combined, in principle, in an infinite number of ways [25, 318]. Therefore, Frank–Kasper phases containing fragments of the Laves phase structures might in a sense be regarded as variants of the Laves phases. One example is the μ phase, which contains structure fragments of the Laves phase and the Zr₄Al₃ phase [319], and which exists in many Laves phase-containing binary transition metal systems. The already discussed Co-Nb system is one example containing the Nb₆Co₇ (µ) phase [320]; see Fig. 7. Laves and Zr₄Al₃ fragments also build the crystal structure of the monoclinic Mg₄Zn₇ phase [321, 322]. Combinations of fragments or layers from Laves phase structures with layers containing non-Frank–Kasper structure elements such as the CaCu₅ structure can lead to layered structures of compositions such as A₂B₇ or AB₃ [323, 324]. Other complex types of structures obtained from stackings of Laves phase and non-Frank–Kasper structure fragments occur in a series of Sr-Al and Ba-Al intermetallic phases [176, 325,326,327,328]. Interestingly, Laves phase itself actually is only stable at elevated pressure in both systems (see Sect. 3.1).

Finally, the alkali metal-Au Laves phases, which are known to exist in the systems Au-Na (C15 NaAu₂) [329, 330] and Au-K (C14 KAu₂) [331], appear to be the basis for a wide range of structure variants. To begin with the binary systems, a RbAu₂ Laves does not appear to exist, likely due to the large size of the Rb atoms, whereas a Rb₃Au₇ (RbAu_2.33) phase [332, 333] exists with a structure that can be derived from the Laves phase (see Fig. 16a). This compound contains chains of partially corner-sharing Au₄ tetrahedra as structure motif, within which the large Rb atoms are embedded and in which isolated corners of the Au₄ tetrahedra, which can be regarded as fragments of the B network of a C15 Laves phase, form contacts to another type of Au atoms showing square-planar coordination. Crystal structures with somehow fragmented C15 Laves phase-related networks of partially corner-sharing Au₄ tetrahedra were also reported for a couple of A-Au-B′ compounds with A = K, Rb and B′ = Ga, In, Tl, Ge, Sn, Pb (heavy main-group III and IV metals). All Au atoms of the C15-type tetrahedral network either are common corners of two Au₄ tetrahedra, or they form some apparently directional bond to the additional B′ atoms. Examples are A₄Au₇B′₂ (AAu_1.75B′_0.5) with (A, B′) = (K, Ge) or (K/Rb/Cs, Sn) or (Rb/Cs, Pb) [334,335,336], K₃Au₅B′ (KAu_1.67B′_0.33) with B′ = In, Tl, Pb [337, 338], Rb₂Au₃Tl (RbAu_1.5Tl_0.5) [338], K₄Au₈Ga (KAu₂Ga_0.125) [339], and K₁₂Au₂₁Sn₄ (KAu_1.75Sn_0.33) [340]; see Fig. 16b and c for example. The main-group III and IV metal atoms appear to be tetrahedrally bonded to themselves or to the surrounding Au atoms; see also a recent review on polar gold intermetallic compounds [341].

Figure 16

Crystal structures derived from non-existing C15 RbAu₂ Laves phase still featuring the Au₄ tetrahedra (yellow) partially sharing common additional bonds toward a single Au in the middle of the unit cell depicted in Rb₃Au₇ [332, 333], b toward Tl atoms of an infinite zigzag chain of Tl atoms in Rb₂Au₃Tl [338], and c toward Sn dumbbells in Rb₄Au₇Sn₂ [334]

Planar defects, intergrowth, and intergrowth-related faulting

Peculiar planar defects distinct from faults associated with a variable Laves phase stacking sequence [342] were reported in a series of studies mainly based on observations by transmission electron microscopy (TEM) techniques. The apparently earliest investigation of this type was performed on C14 MgZn₂. By conventional TEM, some features parallel to $\left\{ {10\bar{1}0} \right\}_{{{\text{C}}14}}$ were observed that were interpreted as Mg₂Zn₃ precipitates [343]. A later high-resolution TEM study on the relation of C14 MgZn₂ and Mg₄Zn₇ (which was previously described as Mg₂Zn₃) rationalized such an intergrowth [344, 345].

In an early high-resolution TEM investigation of an Fe-rich, multicomponent (Mo,Ti,W)(Fe,Cr,Ni)₂ C14 Laves phase, which had been extracted from an Fe-based superalloy [319], planar faults were observed on basal ($\left\{ {0001} \right\}_{{{\text{C}}14}}$), prismatic ($\left\{ {10\bar{1}0} \right\}_{{{\text{C}}14}}$), and pyramidal ($\left\{ {10\bar{1}1} \right\}_{{{\text{C}}14}}$) planes [346]. Analysis of the images was based on comparison with an ideal C14 phase and a µ phase (consisting itself of structural motifs of the Laves phase and Zr₄Al₃ stacked along [0001]_C14) using a tiling scheme worked out in Ref. [319] (similar to the scheme used in [344, 345]). It was concluded that all three types of planar defects can be perceived as layers out of the µ phase [346].

More recent atomically resolved scanning TEM (STEM) investigations on single-phase Nb-rich C14 NbFe₂ Laves phase gave direct experimental evidence confirming that the observed planar defects on basal $\left\{ {0001} \right\}_{{{\text{C}}14}}$ (see Fig. 17) and pyramidal $\left\{ {10\bar{1}1} \right\}_{{{\text{C}}14}}$ planes consist of structural motifs from the µ phase [347]. STEM energy dispersive X-ray spectroscopy (EDS) proved these layers to be rich in Nb as expected from the ideal Nb₆Fe₇ composition of the µ phase. Indeed, such kind of planar defects were only observed in Nb-rich NbFe₂ while they were not found in stoichiometric material. Interestingly, none of the observed variants of extended basal planar faults shows a perfect μ phase stacking sequence, even though all of them are composed of the characteristic structural motifs of the µ phase. First-principles calculations showed that such extended defects in off-stoichiometric Laves phase can be thermodynamically more stable than formation of a basal synchroshear-formed stacking fault (see Sect. 3.7) defect structure with a simultaneous accommodation of the excess Nb in correctly stacked, true μ phase precipitates with a constrained basal lattice parameter. Besides the occurrence of antisite atoms, the formation of such kind of coherent planar faults obviously is a way for the accommodation of excess Nb [347].

Figure 17

a High angle annular dark field STEM micrograph of Fe-poor (Nb-rich) C14 NbFe₂ Laves phase with a coherent planar defect consisting of structural motifs from the µ phase (reproduced with permission from [347]). b Atomic structure model in higher magnification (small atoms: Fe, large atoms: Nb) revealing the typical layer arrangements of Nb atoms in the planar defect which is characteristic for the µ phase (note that the thickness of the planar fault in the sketch is reduced compared to the experimental micrograph). For a more detailed description of this kind of defects, see [347]

Whereas the above examples concern B-poor (mainly C14) Laves phase, planar defects in B-rich C15 YIr₂ on $\left\{ {111} \right\}_{{{\text{C}}15}}$ planes appear to be associated with the intergrowth of PuNi₃-type YIr₃ [146]. As already indicated in the previous Sect. 3.5.3, the periodic combination of fragments of different crystal structures can lead to new crystal structure types. The same scheme can, as shown here, also be used to construct lower dimensional features in crystal structures such as planar faults.

Plastic deformation

The deformation mechanism of Laves phases was widely studied beginning in the 1960s and 1970s with detailed investigations on dislocation density and mobility and observation of twinning as the dominating deformation mode, see, for example, [190, 348,349,350]. Most of this early, fundamental work was performed by the group of Paufler and Schulze in Dresden, Germany. A summary of the main results of their partially German-written papers related to mechanical properties of MgZn₂ and other Laves phases is given in two more recent reviews [4, 5]. Today it is generally accepted that plastic deformation in Laves phases occurs via a dislocation-mediated process by (basal) slip or twinning, see, for example, [351,352,353]. The underlying mechanism is the so-called synchroshear process, which is schematically explained in Fig. 18. Synchroshear in Laves phases occurs by the cooperative motion of two coupled Shockley partial dislocations on the adjacent planes of a triple layer of the Laves phase structure [354,355,356,357,358]. Deformation by undulating slip was proposed as an alternative mechanism to synchroshear [359], but from a theoretical comparison of the two alternatives it was concluded later that both models finally describe the same mechanism and only differ in the way of describing the deformation process [358]. Synchroshear as the most likely mechanism for dislocation-mediated plastic deformation in Laves phases had been already suggested by Krämer and Schulze in 1968 from theoretical considerations [360]. Their geometrical analysis of possible slip systems and types of dislocations revealed that this type of synchronous shearing of adjacent planes is the only possibility that results in a stacking fault without lattice expansion. Prismatic and pyramidal slip modes were also identified as energetically possible but their activation was found to be much less favorable [360].

Figure 18

Schematic illustration of the synchroshear mechanism: a Initial arrangement of the big A (orange) and small B (dark blue) atoms in the three-layer stack with the surrounding B single-atom Kagomé layers above and below the three-layer stack indicated by dashed circles. The bottom gray block is considered stationary and the top block responding to a shear stress by moving to the left. b Atomic arrangement after synchroshear. c Illustration of the atomic motions during the synchroshear process. The upper gray block including all the big A atoms in the top layer of the three-layer stack moves in the plane of the paper (y–z plane) to the left by a distance b as shown by the red arrow, while simultaneously the small B atoms move on the vertical plane marked in blue (x–y plane) at 60° to the –y direction as shown by the blue arrow, producing the final configuration shown in (b) (figure and text adapted with permission from [356])

Successful direct observation of synchroshear-induced stacking faults in Laves phases by high-resolution scanning transmission electron microscopy (STEM) was reported for the first time by Chiswick et al. [356]. Since then synchroshear-induced stacking faults in different deformed C14 and C15 Laves phases were observed by various authors [361,362,363,364]. Figure 19 shows a synchro-Shockley dislocation in C14 HfCr₂ Laves phase with the dislocation core in the center of the image as explained in the figure caption [356].

Figure 19

Atomic resolution STEM Z-contrast image of a [$11\bar{2}0$] projection of a synchro-Shockley dislocation bounding a stacking fault in the C14 variant of the HfCr₂ Laves phase. The fault comes in from the right (indicated by the arrows) and terminates at the dislocation core in the center of the image. The Burgers circuit (indicated by the white line) made from Hf atoms failed to close. The schematic below the image, obtained directly from the STEM image, shows a proposed core structure (adapted with permission from [356])

Laves phases (similar to most other intermetallic phases) are brittle at room temperature and exhibit a transition from brittle-to-ductile behavior at high homologous temperatures T/T_m (T_m is the melting temperature) in the range 0.6–0.75 [127, 365,366,367]. Therefore, many transition metal Laves phases remain brittle up to temperatures above 1000 °C. For example, in case of the intensively studied C15 Laves phase NbCr₂, this BDTT (brittle-to-ductile transition temperature) is about 1200 °C and plastic deformation of macroscopic bulk samples is only observable in experiments performed above this temperature [367,368,369]. A chance to study plastic deformation of such brittle phases at room temperature came up with the establishment of micromechanical testing methods in materials science, see, for example, [370]. Micropillar compression tests of single-crystal cubic C15 and hexagonal C14 and C36 Laves phases revealed the occurrence of plastic deformation by basal and, in case of the hexagonal crystals, also non-basal, prismatic and pyramidal slip [364, 371,372,373,374]. An example for a plastically deformed C14 NbCo₂ micropillar is shown in Fig. 20 [373].

Figure 20

SEM image (side view) of a room-temperature-deformed, single-crystal Laves phase (C14 NbCo₂) micropillar showing slip traces. The micropillar was compressed vertically, the arrows indicate the activated slip plane and direction (adapted with permission from [373])

As already discussed in Sect. 3.2 (‘point defects’), many Laves phases exhibit extended homogeneity ranges. Regarding the effect of compositional deviations from the ideal, stoichiometric AB₂ value, the mechanical properties of Laves phases reveal a very interesting behavior. The first detailed investigations on the composition dependence of mechanical properties of C14 MgZn₂ were performed by Paufler et al. during the 1970s [5, 375,376,377,378,379]. Both room-temperature microhardness [375, 376, 378] and yield stress at 350 °C [379] reveal softening at off-stoichiometric compositions (Fig. 21a). Also the stationary creep rate increases with deviating from stoichiometry (Fig. 21b) [378]. This is attributed to a strong increase of the density of mobile dislocations, which overcompensates the simultaneous decrease of dislocation velocity (Fig. 21b) [5, 378].

Figure 21

Composition dependence of mechanical properties of single-phase C14 MgZn₂ Laves phase: a Microhardness H_V (room temperature) [378] and upper yield stress σ_u (at 350 °C) [379] showing macroscopic softening for off-stoichiometric compositions. b Stationary creep rate $\dot{\varepsilon }$ (350 °C, shear stress 10 MPa) [378], dislocation density d [378], and dislocation velocity v (399 °C) [377] also exhibit extrema at the stoichiometric composition (adapted with permission from [5])

Transition metal Laves phases, which are well known for frequently possessing extended homogeneity ranges (cf. Sect. 3.2.1), are perfectly suited to examine if this particular behavior is specific for C14 MgZn₂ or is a more general characteristic of Laves phases. Regarding the effect of deviation from stoichiometry on the hardness, contradicting results were reported in the literature. While hardening by off-stoichiometry was reported in two studies (for C15 ZrCr₂ [380], C15 NbCr₂, C15 NbCo₂, and C14 NbFe₂ [151]), other experimental investigations confirm the aforementioned softening behavior, for example for C15 TiCr₂ [381], C15 ZrCr₂ [382], C15 NbCo₂ [383, 384], C14 NbFe₂ [383, 385], and C15 HfCo₂ [386].

As already discussed in Sect. 3.2, the point defects needed for stabilization of off-stoichiometric compositions in MgZn₂ and in the majority of the transition metal Laves phases are antisite atoms on both sides of the stoichiometric composition. In general, such kind of substitutional defects are expected to result in hardening at low homologous temperatures as is well known for metals (e.g., [387]) and for intermetallics [388,389,390,391]. Solid solution hardening is generally explained as originating from elastic interactions of the solid atom or defect with dislocations. Obviously, the presence of defects in Laves phases instead tends to soften the material in many systems, meaning that the defects can promote the deformation process by facilitating the movement of partial dislocations in the synchroshear process [386]. Another idea discussed by Chen et al. [386] is related to the changes in chemical bonding resulting from wrong site occupations. The strength of Laves phases originates from the strong bonding of dissimilar atoms in the ideal structure. Replacing an A atom by a B atom (or vice versa) will locally increase the number of B-B (or A-A) bonds, i.e., more metallic bonding is created locally, by which deformability might be improved. However, if this argument is correct, the effect should be even more pronounced in B2-type intermetallic compounds, because in this bcc-based AB structure the replacement of, e.g., an A by a B atom changes the number of dissimilar next neighbors from eight to zero. Against this expectation, it was clearly shown that for B2 compounds constitutional defects result in solid solution hardening (e.g., [388, 389]) indicating that this simple chemical bonding model is not suited to explain the observed softening behavior.

In order to study in a systematic way the dependence of mechanical properties of single-crystalline Laves phases on composition, crystal orientation, and crystal structure, Luo et al. [364, 384, 392,393,394] focused on the binary system Co-Nb, in which the Laves phase NbCo₂ exists as stable phase with C36, C15, and C14 structure in adjacent phase fields (from approximately 24.0 to 25.0, 25.0 to 34.3, and 35.5 to 37.0 at.% Nb, respectively). By producing diffusion couples, they obtained several hundred µm thick layers of Laves phase covering the entire homogeneity ranges of the three polytypes. Electron channeling contrast imaging revealed low dislocation densities d of the order of 10⁻¹¹ m⁻² in the C15 composition range around the stoichiometric composition, while d increases by one order of magnitude close to the boundaries to the hexagonal variants C36 (near 25 at.% Nb) and C14 (near 35 at.% Nb) [384]. The occurrence of widely extended stacking faults in these areas close to the transitions C15-C36 and C15-C14 indicates a significant decrease of the stacking fault energy (SFE). Hardness and elastic modulus, which were obtained from nanoindentation experiments along the concentration gradient, show a similar compositional behavior with continuously decreasing values at off-stoichiometric compositions near the boundaries of the homogeneity range. This implies reduction of the Peierls stress [384] as had already been suggested as explanation for the above-described behavior of MgZn₂ [5]. Strength (by micropillar compression tests [364]) and toughness (by microcantilever bending tests [393]) of NbCo₂ were also studied as a function of composition using the same diffusion couples. The critical resolved shear stress behaves very similar to the hardness with highest values in the central region of the C15 homogeneity range and a decrease when approaching the off-stoichiometric boundaries, which is explained by the reduction of the shear modulus and stacking fault energy [364]. The microcantilever bending tests revealed a linear elastic fracture behavior for all compositions. Within the experimental accuracy, the fracture toughness was found to be independent of chemical composition and crystal structure type of the NbCo₂ Laves phase [393].

The crystal orientation of single-crystalline samples was found to have only a negligible effect on strength and hardness in micromechanical testing. Although the pillar orientation can influence the activated slip systems, the energy barriers of dislocation nucleation and motion, which determine the strength of the NbCo₂ micropillars, are independent of orientation [364]. Nanohardness values measured in differently oriented grains of polycrystalline cubic C15 as well as hexagonal C14 and C36 NbCo₂ alloys are shown in Fig. 22. The hardness values of the C15 alloys with 25.6 at.% (b) and 33 at.% Nb (c) as well as those of the C36 alloy (a) are independent of orientation within the given accuracy. For the C14 NbCo₂ Laves phase (d), the hardness measured perpendicular to the basal plane was found to be slightly higher (in the order of 5%) than in the other orientations [384]. A similar, slight anisotropy in the hardness of hexagonal C14 Laves phase with highest values for [0001] orientation was also reported by Paufler [5] for MgZn₂ and CaMg₂ Laves phase.

Figure 22

Inverse pole figures showing nanohardness values of cubic C15 (b, c) and hexagonal C14 (d) and C36 (a) NbCo₂ Laves phase for various crystal orientations (adapted with permission from [384])

The role of the crystal structure type of a Laves phase for the mechanical properties can only be studied in an indirect way, because a change of the stable structure type is always connected with a change in composition (or temperature). Nevertheless, the above-described investigations of cubic C15 and hexagonal C14 and C36 NbCo₂ Laves phase indicate that there is no effect of crystal structure. In all cases, a continuous, smooth change of properties is observed when crossing the boundaries from the C15 to C36 or C15 to C14 homogeneity ranges. This is true for the continuously decreasing values of hardness, elastic modulus [384], and critical resolved shear stress [364] as well as for the composition-independent fracture toughness values [393].

Functional applications

Hydrogen storage materials

Intermetallic phases as effective hydrogen storage materials are discussed since the late 1960s, for example, as fuel tanks in automotive applications [395, 396]. Since then and until today, metal hydrides and their potential application for hydrogen storage are a topic of great interest as described in a wealth of review articles, see, for example, [397,398,399,400] to name but a few. Besides offering a safe and efficient method to store hydrogen, metal hydrides are also materials for the negative electrode of nickel–metal hydride (Ni/MH) batteries. A recent compilation of articles related to the topic ‘Nickel Metal Hydride Batteries’ [401] gives an excellent overview about the status of development of this type of material and also contains a comprehensive review of Laves phase metal hydrides for battery applications [402].

Besides AB₅ compounds and bcc-metal (mostly Ti and Zr)-based alloys, the AB₂ Laves phases are the most important interstitial hydride-forming materials [402, 403]. It was recognized already in very early studies that Laves phases can absorb relatively high amounts of hydrogen (up to 2 wt%) and possess high hydrogenation/dehydrogenation cycle stability [404,405,406]. Compared to the AB₅ compounds, where especially LaNi₅ is widely used in commercial applications as the negative electrode in Ni/MH batteries, most of the Laves phases show faster kinetics, longer life times and have relatively low costs. However, a major problem for application of binary Laves phase alloys is the very high stability of their hydrides at room temperature leading to poor electrochemical properties in alkaline electrolytes. As the hydriding properties of Laves phases very sensitively depend on composition, there were many attempts in the literature to overcome the stability problem and improve their properties by diverse alloying concepts [397,398,399].

As Laves phases belong to the class of tetrahedrally close-packed (t.c.p.) phases, all possible interstitial sites have four nearest neighbors resulting in either A₂B₂, AB₃, or B₄ tetrahedral interstices, see Fig. 23 [407]. The preferential occupation of particular interstitial sites of the C14 and C15 Laves phase lattices by hydrogen atoms and the relative stability of atomic hydrogen at various interstitial sites as defined by the bonding energies is the topic of several investigations, see, for example, [407,408,409,410]. According to some simple criteria formulated by Westlake [411], interstices in stable hydrides must have minimum radii of 40 pm and the hydrogen–hydrogen distances must be a minimum of 210 pm. Shoemaker and Shoemaker [408] performed a detailed theoretical analysis of the Laves phase crystal lattice with respect to the different interstitial sites and found a maximum possible occupancy of about six hydrogen atoms per AB₂ formula unit. Already before, Jacob et al. [412] had studied Zr-based binary Laves phases and developed a phenomenological model based on short-range ordering effects. Their results indicated somewhat lower hydrogen solubilities as was later confirmed by neutron diffraction experiments [413,414,415,416,417] and more recent ab initio total energy calculations [410]. As only particular interstitial sites are occupied, ordering of hydrogen on such sites may occur resulting in crystallographic symmetries of the hydride different from that of the parent Laves phase. An overview of the crystallographic aspects of hydrogen ordering in hydrides of Laves phases is given in a recent review by Kohlmann [407].

Figure 23

The three types of tetrahedral interstices in the crystal structure of a cubic AB₂ Laves phase (C15 type) (A: large, blue spheres; B: small, red spheres) offering possible positions for hydrogen: A₂B₂ (light gray), AB₃ (middle gray), and B₄ (dark gray) tetrahedral interstices. The number of such interstices per unit cell are 96, 32, and 8, respectively. The 8 B₄ tetrahedra are marked with green faces (with the exception of the one that is dark grey). For reasons of clarity, only one interstice of each kind is drawn (reproduced with permission from [407])

Regarding the effect of the type of crystal structure (hexagonal C14 vs. cubic C15) of the Laves phase on the hydrogen storage properties, partially contradicting observations were reported [418,419,420,421,422,423]. The stable structure type cannot be changed without changing chemical composition (or temperature). As it was found that such variations of composition (type and concentration of elements) can have a pronounced effect on the hydrogen storage performance, it is difficult to draw a general conclusion on the effect of crystal structure. Type and number of interstitial sites in cubic and hexagonal Laves phase are identical and it can be assumed that the type of crystal structure does not or only marginally affect the hydrogen storage behavior.

The first detailed investigations on Laves phases as potential hydrogen storage materials date back to the 1970s, when the hydriding properties of ZrFe₂- and ZrCo₂-based cubic C15 Laves phases with small ternary additions of either Al, V, Cr, or Mn were tested [405, 412, 424]. Studies on these Laves phase systems were continued for more than twenty years [425,426,427], but problems with an either too low hydrogen storage capability or a too high stability of the hydrides could not be overcome.

After these first, at least partially promising studies on hydrogen storage properties of this class of compounds, a huge amount of projects started on various other AB₂ Laves phases. Some of these investigations focused on light-weight Laves phases such as (Mg,Ca)Ni₂ [428, 429], CaLi₂ [430], or CaMg₂ [431,432,433], but their hydrogenation properties were found to be insufficient from the viewpoint of applications. Until today clearly the most promising and by far most intensively investigated Laves phases are based on Zr and/or Ti as the large A metal, while the B lattice sites are occupied by one or—in most cases—more of the 3d metals Co, Cr, Fe, Mn, Ni, V. The compositions of both the alloys with mainly Zr on the A sites (e.g., [434,435,436,437,438,439,440,441]) and with mainly Ti on the A sites (e.g., [442,443,444,445,446,447,448,449]) became more and more complex. Many of the currently discussed alloys for applications contain six to nine components, where in some cases small amounts of main group elements such as Al or Sn (e.g., [421, 450, 451]), or lanthanides [452] were added. More recently, also some multi-component, equiatomic or nearly equiatomic alloys (frequently called ‘high-entropy alloys’ (HEAs)) such as CoFeMnTi_xV_yZr_z (0.5 ≤ x ≤ 2.5, 0.4 ≤ y ≤ 3.0, and 0.4 ≤ z ≤ 3.0) [453], CrFeNiTiVZr [454] and CrFeMnNiTiZr [455] were studied with respect to their hydrogen storage properties (cf. Sect. 5.6.5). These alloys consist nearly completely of C14 Laves phase, but do not show any especially remarkable behavior compared to other Zr/Ti-based alloys [453,454,455]. According to Ovshinsky’s concept of compositional disorder [456], the variety of elements in multicomponent alloys can offer a multitude of hydrogen bonding possibilities increasing the hydrogen storage capacity and improving the catalytic activity.

Moreover, it was found that deviations from the stoichiometric composition strongly affect the hydrogen storage properties [439, 457,458,459]. Young et al. [460] studied the effect of vanadium excess in C14 Laves phase alloys for Ni/MH battery applications. Vanadium atoms usually occupy B atom sites in Zr- and Ti-based Laves phase, but due to their relatively large atomic radius, they can partially move from B to A sites in case their number exceeds the available B sites [461]. Such a substitution of vanadium on A sites was reported not only to increase the degree of disorder but also to provide more hydrogen interstitial sites for reversible hydrogen storage [460, 462]. More recently, this strategy of partial substitution on the A site was adopted to C15 Y(Fe,Al)₂ alloys by replacing 10% of Y by Zr, Ti, or V resulting in a remarkable increase of the hydrogen desorption capacity [463].

Besides compositional disorder and off-stoichiometry of a Laves phase, a multiphase microstructure was found to be another important characteristic of Laves phase-based hydrogen storage alloys needed to qualify them for application [456]. The so-called ‘Laves-phase-related bcc solid solution’ concept is an early example for multiphase hydrogen storage alloys [464, 465]. Such alloys are composed of a bcc solid solution based on Ti, V, or Zr coexisting with a Laves phase. The bcc solid solutions can reach high hydrogen storage capabilities, but their activation and the very low plateau pressures are a problem. However, in combination with an easily to activate Laves phase, good hydriding properties can be achieved as was especially demonstrated for bcc-V solid solutions in combination with Laves phase [466,467,468,469,470]. It should be mentioned that in addition to the AB₂ Laves phases also alloys based on the structurally closely related phases A₂B₇ (Ce₂Ni₇ type) and AB₃ (PuNi₃ type), which contain fragments of the Laves phase structure (cf. Sect. 3.5.3), were discussed as electrode materials for batteries, see, for example, [471,472,473].

Regarding industrial applications, a lot of effort was put into the development of alloys for the negative electrode in rechargeable Ni/MH batteries for electrical vehicles. A class of (Ti,Zr)(V,Cr,Mn,Ni)₂ alloys consisting mainly of a C14 and a C15 Laves phase was found to have excellent properties in tests under application conditions [456, 474,475,476,477].

The only commercially available Laves phase-based hydride-forming class of alloys, which is already successfully in application, is so-called Hydralloy [450, 478,479,480,481,482,483]. Hydralloy is always based on a C14 Laves phase containing Ti and Mn in a 1:1.5 ratio as main constituents. Commercially available alloys are Hydralloy C2 (Ti_0.98Zr_0.02Mn_1.46V_0.41Cr_0.05Fe_0.08), C5₁ (Ti_0.95Zr_0.05Mn_1.48V_0.43Fe_0.08Al_0.01) and C5₂ (Ti_0.955Zr_0.045Mn_1.52V_0.43Fe_0.12Al_0.03). As for several battery applications a high-dynamic tank operation is required, storage materials with high heat conductivity are needed. For this reason, pelletized composites of Hydralloy C5 and expanded natural graphite (ENG) were developed, see Fig. 24 [481, 483,484,485].

Figure 24

Hydraloy-ENG pellet consisting of a mixture of Hydraloy C5₂ powder and 5 wt% expanded natural graphite (ENG). A comparison of the as-compacted state to that after 85 hydrogenation cycles reveals that shape and dimensions are kept and that the pellets preserve their mechanical integrity throughout cycling. Graphite is added to ensure high thermal conductivity. The diagram in the middle shows the uptake and release of hydrogen during a typical hydrogenation-dehydrogenation cycle (adapted with permission from [481])

Hydralloy has only a medium gravimetric hydrogen storage capacity (about 1.5 wt% H₂), but a comparably high volumetric hydrogen storage capacity of about 80 g-H₂ l⁻¹. Moreover, it can be easily hydrogenated at moderate hydrogen pressures in the temperature range −20 °C to +100 °C. Therefore, even though it is not well suited, for example, for automotive applications, Hydralloy is in operation in some niche applications, where the high weight of a potential hydrogen tank does not pose a problem [481, 482]. An example for that is the successful use of Hydralloy as hydride tank material for maritime fuel cells in the German Navy submarines of the U212A type (since 2003) and its export version U214 (since 2004) [400, 482]. Another application, where the high weight is even an advantage, are electric forklifts. In this case, heavy counterweights are essential. Series of performance tests with a 3-ton electric forklift were carried out yielding promising results [486,487,488]. Another successful demonstration of the applicability of Hydralloy C5 was its usage as hydrogen tank material on a fuel cell-powered, 4-ton mining locomotive [489]. Hydralloy C5 was also tested as hydrogen tank for fuel cell city cars. Promising intermediate results were reported, but an application is not yet to be expected [490]. More recently, a metal hydride air-conditioning system for fuel cell vehicles consisting of two plate reactors filled with Hydralloy C2 and coupled to a polymer electrolyte membrane fuel cell was developed and suggested as technology to reutilize the compression work in the hydrogen pressure tank [491, 492].

Wear- and corrosion-resistant materials

Tribaloy

The very high hardness of high-melting transition-metal-based Laves phases can be effectively used not only to strengthen high-temperature structural materials, but also for applications requiring a good wear and friction behavior. Tribaloy is the registered trade name (Deloro Stellite Holdings Corporation) for a family of wear-resistant Co- (or Ni-) based Co/Ni-Mo-Cr–Si alloys with very high Mo contents (up to 35 wt%). These alloys were introduced in 1974/5 [493,494,495,496] and today are used extensively especially as coating materials in corrosive environments. Tribaloy alloys contain high volume fractions of up to 65 vol.% C14 Mo(Co,Cr,Si)₂ Laves phase embedded in a softer matrix of Co solid solution or eutectic (which is Co solid solution + Laves phase). A typical microstructure is shown in Fig. 25 (taken from [497]). Due to the high content of hard Laves phase and with Co as main constituent of the material, the Tribaloy alloys show a combination of excellent resistance to high-temperature wear, galling, and corrosion, i.e., the material is especially used for situations where strong wear occurs in combination with high temperatures and corrosive media. The high Mo contents result in good dry-running properties making these alloys especially suitable for use where lubrication is a problem. Maximum application temperatures are in the range 800 to 1000 °C [493,494,495,496, 498,499,500].

Figure 25

Microstructure of T-800 Tribaloy coating after laser deposition on a Ni-based superalloy substrate. The Tribaloy microstructure consists of large, primary Laves phase particles in a matrix of Co solid solution and Co + Laves phase eutectic (reproduced with permission from [497])

At room temperature, the fracture toughness of Tribaloy alloys is low. The matrix of as-cast Tribaloy contains both hcp- and fcc-Co, and this can be strongly varied by the cooling conditions and subsequent heat treatments. It was shown that the faster the cooling rate the greater the volume fraction of primary Laves phase and the larger the proportion of the fcc Co solid solution. With respect to the hardness and fracture behavior, the best combination of room-temperature properties was obtained with the highest volume contents of fcc solid solution, which can also be stabilized by additions of 5–15 wt% Fe [501,502,503].

Until today, only very little work related to further alloy development of this class of wear-resistant alloys was performed. Table 5 shows a complete list of the commercially available Tribaloy alloys. Out of the first-generation Tribaloy alloys (Co-based T-100, T-400, T-800, and the Ni-based counterpart T-700), especially T-400 and T-800 entered into industrial application and were later on starting materials for development of improved alloys. About 30 years after its introduction in the literature, the first-generation Tribaloy T-400 was modified to improve its toughness and corrosion behavior. Tribaloy T-400C contains an increased amount of Cr (14 instead of 8.5 wt%). Immersion corrosion tests in various oxidizing and reducing acids demonstrated an excellent corrosion resistance superior to the T-400 alloy [504, 505]. The newly developed Tribaloy T-401 has a lower Mo and Si content combined with an increased Cr content. Due to the significantly reduced Mo content, the primary phase is no longer the Laves phase but the Co solid solution. This results in a higher ductility but lower hardness and wear resistance compared to T-400 [505, 506]. In tests on the corrosion resistance in molten Zn-Al baths, Tribaloy T-401 performs better than T-400 and T-800 [507]. The increased Cr contents in T-400C and T-401 lead to the formation of Cr-oxide layers, which are not only beneficial for the oxidation behavior, but also for the high-temperature wear resistance [508]. While very thin oxide films on T-400C specimens were found to be removed from the surface during wear exposure, thicker oxide layers resisted this attack and were observed to be squeezed and embedded into the specimen surface, thereby enhancing the hardness and wear resistance of the surface [509].

Table 5 Compositions (in wt%) of alloys from the Tribaloy family (as provided by Deloro Stellite for www.matweb.com)

Tribaloy T-800 has a lower Co content compared to T-400 and, therefore, contains a higher amount of Mo(Co,Cr,Si)₂ Laves phase. This results in a significant hardening and further improvement of the wear behavior in dry conditions as was, for example, demonstrated by hardness measurements and sliding wear tests (ball-on-disk and block-on-ring configurations) of Tribaloy T-800 coatings deposited by laser cladding on a stainless steel (AISI 304) substrate without using lubrication [510]. However, the brittle nature of Laves phases promotes the formation and propagation of cracks in T-800, and this increased cracking susceptibility complicates the development of coatings [511]. Tribaloy T-900 is a modification of the T-800 alloy with a reduced volume fraction of hard Laves phase by replacing some of the Laves phase forming alloying elements (Co, Mo, Si) with Ni. This reduction in Laves phase content results in a higher ductility and fracture toughness and improved crack resistance [511].

Besides mechanical properties, the oxidation behavior of Tribaloy alloys at high temperatures is of central importance for their applicability. A comparison of the oxidation behavior of Tribaloy T-400 and T-800 during long-time tests (up to 1000 h) at 900 °C in synthetic air revealed that T-800 provides a much better oxidation resistance than T-400. Due to the higher Cr content in T-800, dense Cr₂O₃ layers formed after long times, while the scale on T-400 additionally contains the Co-rich spinel Co₂CrO₄ and a much smaller fraction of Cr₂O₃. Moreover, the oxides were observed to protrude deeper into the Laves phase [512]. Short-time (< 60 h) isothermal oxidation tests of T-800 confirmed a good oxidation behavior at 800 °C indicated by a parabolic mass gain with formation of a complex oxide scale. However, a very poor oxidation behavior with a linearly increasing mass gain was observed in similar tests at 1000 °C resulting from the formation of voids and some loose internal oxide SiO₂ at the interface between Cr₂O₃ and the alloy [513]. An application temperature of 1000 °C, therefore, seems to be too high for the T-800 alloy. Cyclic oxidation tests comparing the T-900 and T-401 alloys revealed a much better performance of T-900. This was attributed to the formation of dense continuous Cr₂O₃ layers (with an upper thinner continuous layer of CoCr₂O₄ and NiCr₂O₄ oxides). For the T-401 specimen, severe spallation after 3 cycles (45 h) between room temperature and 1000 °C was observed [514]. Modification of the Tribaloy T-700 [515], T-800 [516], and T-900 [517] alloy compositions by additions of Al (5 wt%) and Y (0.5 wt%) resulted in a significant improvement of the cyclic oxidation resistance due to the formation of protective, compact and continuous external layers of Al₂O₃ at 800 and 1000 °C [515,516,517]. Moreover, the added Y was reported to enhance the adherence of oxide scales during sliding wear [517].

Tribaloy coatings (nearly exclusively T-800, and today often less precisely termed CoMoCrSi coatings) are deposited either by laser cladding techniques [497, 510, 511, 518] or by spraying methods such as the high velocity oxygen fuel (HVOF) thermal spray technique [519,520,521,522,523,524,525,526] or atmospheric plasma spraying (APS) [527]. Tobar et al. [511] report that, when compared to the spraying methods, laser cladding gives coatings of higher quality on steel substrates as it produces dense and pore-free layers with finer microstructure and better adherence with the substrate. HVOF-sprayed layers of T-800 alloy were found to be mostly amorphous in the as-deposited state resulting especially in a worsened wear behavior. However, after short-time heat treatment for 1 h at 600 °C, the Laves phase and Co solid solution crystallized again and the coating showed the expected beneficial protecting properties [523, 524].

Besides pure Tribaloy coatings, also composite coatings consisting of a tin-bronze matrix reinforced by T-401 alloy particles were successfully deposited by HVOF spraying [528, 529]. Bushings of a journal bearing coated with the composite were found to exhibit superior tribological properties to the leaded tin/bronze bushings [528]. Likewise, polytetrafluoroethylene (PTFE)-based composite coatings containing T-401 Tribaloy particles were developed for sliding bearing applications [530].

In general, Laves phase-dominated Tribaloy coatings have proven to be suitable for applications in various industrial fields such as aerospace, turbine, oil, pump, energy, and mining industry [525]. They are candidates for hard-facings of valve spindles and seat rings in natural gas engines [531, 532], they were successfully tested for the repair of gas turbine shafts [519] and low Cr-Mo steel components used in steam circuits in thermal power stations [518], and they are currently in use for the protection of fuel nozzles against fretting wear in high-temperature gas turbine engines [521].

Other Laves phase-based materials

Besides Tribaloy, also other Laves phase-based materials were suggested as wear- or corrosion-resistant coatings. Very similar to the Tribaloy composite concept of combining a very hard, high-melting Si-stabilized C14 Laves phase with a more ductile metal or intermetallic phase, a class of wear-resistant ternary alloys was developed which are composed of an A₂B₃Si-type (i.e., A(B_0.75Si_0.25)₂) C14 Laves phase with A = Ti, Mo or W and B = Co or Ni in combination with varying second phases for toughening. This group of alloys comprises Ti(Ni_0.75Si_0.25)₂ Laves phase composites with cubic B2 NiTi [533,534,535,536,537] or hexagonal Ni₃Ti [538], Mo(Ni_0.75Si_0.25)₂ Laves phase with bcc Mo solid solution [539] or with orthorhombic NiSi [540,541,542], W(Ni_0.75Si_0.25)₂ Laves phase with bcc W solid solution [543, 544] or tetragonal W₅Si₃ [535, 545], and Mo(Co_0.75Si_0.25)₂ Laves phase with fcc Co solid solution [546,547,548,549]. The combinations of hard but brittle Laves phase with a toughening second phase such as the metal solid solutions allow the adjustment of properties via variation of the phase contents. Laser-clad coatings were produced on various substrates and wear and corrosion tests revealed very good properties. However, to the best of the authors’ knowledge these alloys did not enter into industrial applications.

To protect oxidation and corrosion-sensitive Ti- and TiAl-alloys, it was suggested to coat them with Ti(Cr,Al)₂ Laves phase which is known to form a dense alumina scale on the surface, see Sect. 5.6.3.

High-entropy alloys consisting of a tough disordered solid solution and a hard Laves phase (see Sect. 5.6.5) were tested as coatings on steels [550,551,552,553,554,555,556] and pure Ti [557]. Because of the high Laves phase contents, the coatings were reported in all cases to show excellent wear and oxidation behavior.

Magnetic materials

Magnetostrictive applications

Laves phase rare earth–iron compounds AFe₂ (A = rare earth metal) have attracted a lot of attention due to their extraordinary magnetic properties. The large anisotropic 4f charge density of the rare earth A³⁺ ions and the strong Fe-Fe and A-Fe exchange interactions result in large magnetic anisotropy and magnetostriction up to room temperature [558,559,560], see also Sect. 3.5.1. The field dependence of the magnetostriction for the AFe₂ compounds (A = Sm, Tb, Dy, Er, Tm) is shown in Fig. 26. The C15 Laves phases TbFe₂ and SmFe₂ reach giant room-temperature magnetostriction coefficients exceeding those of traditional magnetostrictive materials by one order of magnitude [271, 561,562,563].

Figure 26

Room temperature magnetostriction of rare earth-Fe₂ Laves phase polycrystals (redrawn from [558]). λ_||–λ_⊥ denotes the fractional change in length as an applied field is rotated from perpendicular to parallel to the measurement direction

A maximum magnetostriction/anisotropy ratio, λ/K₁, was found for the pseudobinary compound Tb_xDy_l-xFe₂ with x = 0.3 [558, 559, 561]. This Laves phase compound with an exact composition Tb_0.3Dy_0.7Fe_1.93 was developed by the Naval Ordnance Laboratory (NOL) and registered under the trade name Terfenol-D. It offers the highest strain of any magnetostrictive material, which makes it an excellent choice for applications in magnetomechanical sensors and actuators, for example, as acoustic and ultrasonic transducers [558, 559, 564,565,566,567,568,569,570,571,572,573,574]. In a more recent study, further improvements of its magnetostrictive properties by partial substitution of Dy by Nd were reported [575]. In order to reduce the brittleness of the material, low-melting Dy-Cu alloy was added to cover the grain boundary with a ductile (Dy,Tb)Cu phase. While the magnetostriction remained at a high value, the bending strength was found to be significantly improved [576]. An overview of the manifold applications of Terfenol-D is given by Olabi and Grunwald [565], for reviews on the magnetostrictive properties, see [577,578,579]. The spectrum of applications ranges from magnetostrictive underwater sound transducers in naval sonar systems [564] to more recent developments of magnetostrictive–piezoelectric composites of Terfenol-D and PZT (Pb(Zr,Ti)O₃) for energy harvesting to supply low-power electronics [573, 574].

The giant magnetostrictive effects in TbFe₂ leads to a distortion of the cubic C15 structure resulting in a symmetry reduction to rhombohedral $R\bar{3}m$ (hR18) symmetry [270]. The same is true for other strongly magnetostrictive C15 rare earth Laves phases AFe₂ (A = Sm, Tb, Dy, Ho, Er, Tm) [580]. This kind of symmetry reduction in C15 Laves phases is also discussed above in Sect. 3.5.1. In case of SmFe₂, spin reorientation and a change of the direction of easy magnetization from [111]_cubic to [110]_cubic leads to a transformation from the rhombohedral $R\bar{3}m$ room-temperature structure to an orthorhombic Imma low-temperature structure at 200 K [271].

Magnetocaloric applications

Rare-earth-containing Laves phases AB₂ (with A = rare earth metal, B = Al, Co and Ni) belong to the magnetic materials which exhibit a large or unusual magnetocaloric effect (MCE) [581]. With respect to applications, there is a lot of discussion about utilizing materials with a large MCE for magnetic refrigerators that could replace conventional refrigerators which are based on vapor–gas cycles [582, 583]. ACo₂ and AAl₂ (A = Er, Ho, Dy) Laves phase compounds show MCEs at very low transition temperatures and were suggested as magnetocaloric materials for hydrogen liquefaction [584,585,586,587]. Magnetization and heat capacity measurements of the C15 Laves phase TbMn_1.6Fe_0.4 indicate that this phase could be a promising candidate for magnetic refrigeration in the temperature range 70 to 162 K [588]. Studies on the MCE and magnetostrictive behavior of a series of single-phase Laves phase alloys Tb_0.2Dy_0.8-xGd_xCo_2-yAl_y (x = 0.3, 0.4, and 0.5; y = 0 and 0.1) did not indicate an improvement of properties by the compositional variations [589]. Magnetocaloric Laves phases with transitions near room temperature that could be suitable for application as magnetic refrigerators were not reported.

Hard magnetic applications

Pure Laves phases are unsuitable as permanent magnets, because they tend to have low magnetization, low Curie temperature, and in the cubic structure low anisotropy [590]. Among the few Laves phases that might be an exception to this rule, C14 FeBe₂ was identified as an interesting candidate. Powders of this ferromagnetic phase were investigated revealing a comparably high Curie temperature (823 K) and magnetic moment (1.95 μ_B/Fe), but—most likely because of the toxicity of Be—no further investigations were reported [591, 592]. More recently, hard magnetic properties of off-stoichiometric Zr₂₇Fe_73-xSi_x (0 ≤ x ≤ 15) and Zr_33−yFe_52+ySi₁₅ (0 ≤ y ≤ 11) C14 Laves phases [593], nanocrystalline C14 Ti_0.75Zr_0.25Fe_2+x (x = 0–0.4) and Ti_0.75−yB_yZr_0.25Fe_2.4 (y = 0–0.35) [594], and melt-spun nanocomposites based on Fe-enriched out-of-equilibrium C14 NbFe_2+x and TaFe_2+x Laves phases [595] were studied. However, in all cases these materials were found not to be suitable for application as permanent magnets.

Laves phases are not only unsuitable as permanent magnets, but their presence in magnets may even be detrimental. An example is the role of C15 Laves phase CeFe₂ in Ce-based hard magnetic materials. As an alternative to the well-established but expensive, rare-earth-based (Nd,Dy)-Fe-B permanent magnets, the hard magnetic phase CeFe₁₁Ti is currently under discussion. The main challenge for production of this new type of hard magnetic material indeed is the formation of the more stable C15 CeFe₂ Laves phase, which tends to dominate the microstructure and retards the crystallization of the desired hard magnetic phase. In experimental investigations, the CeFe₁₁Ti phase was only observed at high temperatures above 1000 K. Below this temperature, only the phases C15 CeFe₂ and Ce₂Fe₁₇ were detected. This is confirmed by ab initio free-energy calculations, which reveal that the presence of the CeFe₂ Laves phase suppresses the formation of CeFe₁₁Ti up to 700 K [596, 597]. In Ce-based Ce-Fe-B alloys containing hard-magnetic Ce₂Fe₁₄B, partial substitution of Ce by La was found to suppress the Laves phase CeFe₂ and to promote the formation of (Ce,La)₂Fe₁₄B with increased saturation magnetization and Curie temperature [598].

Superconducting materials

Together with the A15 (Cr₃Si-type) and B1 (NaCl-type) crystal structures, the C15 and C14 Laves phases form the group of the most favorable compound structures for the occurrence of superconductivity [599, 600]. The observation of superconductivity in some Laves phases ARu₂ (A = Sc, Y, La, Ce) was already described as early as in 1958 [601]. Since then, a very large number of other superconducting Laves phases were detected. However, the superconducting transition temperatures T_c in most cases are below 5 K and critical fields H_c are low, which means that these compounds are not suited for applications. The by far highest transition temperatures among the Laves phases were found for the C15 compounds ZrV₂ (8.8 K [600]) and HfV₂ (9.6 K [602]). Interestingly, both of them show a structural transition below about 120 K [277, 279, 603], where the C15 lattice is distorted in a way that it becomes orthorhombic in case of HfV₂ [279] and rhombohedral in case of ZrV₂ [277], see also Sect. 3.5.1. Such structural instabilities are known to occur especially in high-T_c superconducting phases, but the reason for this relation is not well understood [603, 604]. Experimental results for the pseudobinary system Hf_xZr_1−xV₂, indicate an inverse relation between superconducting transition temperature T_c and the structural transformation temperature T_s, see Fig. 27 [604]. Mixing Hf and Zr on the A lattice site results in an increase of T_c and the record holder is Hf_0.5Zr_0.5V₂ with a T_c of 10.1 K [605].

Figure 27

Superconducting transition temperature T_c and structural transformation temperature T_s as a function of Zr/Hf ratio in the C15 (Hf,Zr)V₂ Laves phase (adapted with permission from [604])

Because of its very good superconducting properties (high T_c, upper critical fields of µ₀H_c2 = 21 T and critical current densities of about J_c = 1 × 10⁵ A/cm² at 13 T and 4.2 K) and as it is less brittle than the high-T_c A15 compounds (e.g., Nb₃Al) and shows high tolerance to neutron irradiation, (Hf,Zr)V₂ Laves phase attracted a lot of interest for applications as high-field superconductor in fusion reactors [606,607,608,609]. To further improve the superconducting properties and especially the workability, replacement of Zr by Nb and addition of Ti were also tested [610, 611]. Various fabrication methods for the production of (Hf,Zr)V₂ tapes and wires were applied, all of them are multi-step composite processes starting, for example, from Hf-Zr binary alloy rods and V-based tubes or from elemental Hf, Zr, and V metal powders. Figure 28 shows an example of material in an intermediate production step. The final steps were either cold-drawing to wires or cold-rolling to tapes always followed by high-temperature heat treatments in the range of 1000 °C to transform the phase mixtures to single-phase Laves phase material [606, 612,613,614]. To avoid the high-temperature annealing step, which often resulted in an only incomplete transformation leaving over unwanted phases, an alternative method was developed applying a rapidly heating/quenching process [607,608,609].

Figure 28

Intermediate step in the production of superconducting (Hf,Zr)V₂ wires showing a cross section of a 1 mm thick, 1425-core Hf-Zr-V wire with V-1at.%Hf alloy matrix and Zr-45at.%Hf cores. To obtain this structure, Hf-Zr rods had been inserted into drilled holes in a V-1at.%Hf alloy matrix, followed by cold-drawing into wires, cutting into short pieces and packing into a V-1at.%Hf alloy tube (reproduced with permission from [606])

Colored materials

Intermetallic phases often have characteristic colors that cannot be produced by pure metals or alloys, which is why they are frequently used in jewelry. Recently the Laves phase MgCu₂ was tested as an addition to Cu to adjust the color of coins. By changing the Mg content of the alloys, the ratio of Cu-to-MgCu₂ phase was systematically changed resulting in color variations from the reddish orange of Cu to the pale yellow color of MgCu₂, see Fig. 29 [615].

Figure 29

Compositional tuning of the color of Cu-Mg coins containing 0, 10, 13, and 15 at.% Mg corresponding to increasing amounts of C15 MgCu₂ Laves phase from 0 to about 40 vol.%. While the reflectivity of Cu shows a drastic increase to values above 90% in the orange and red region of the wavelengths of visible light (explaining its reddish orange color), MgCu₂ instead shows a more continuous increase resulting in its less red and more brownish yellow color (reproduced with permission from [615])

Structural applications

Laves phase-based alloys

Single-phase: Laves phases, especially those based on transition metals, often have very high melting temperatures and can keep high strength up to temperature ranges even higher than that of superalloys. Figure 30 shows high-temperature proof stresses of some ternary C14 Laves phases in comparison to the oxide dispersion strengthened (ODS) Ni-base superalloy MA6000 [616]. However, even though this seems to make Laves phases natural candidates for high-temperature structural applications, single-phase Laves phase alloys are not suited as structural materials, especially due to their usually extreme brittleness at ambient temperatures, see, for example, [10, 15, 367, 617,618,619].

Figure 30

Temperature dependence of 0.2% yield stress obtained from compression tests (strain rate 10⁻⁴ s⁻¹) of various single-phase C14 Laves phase alloys in comparison to the ODS superalloy MA 6000 (adapted with permission from [616]). Data for MA 6000 are from [620] as cited in [616]

A multitude of studies were undertaken to find if and how the mechanical behavior of single-phase Laves phases, especially the room-temperature fracture toughness, changes by compositional deviations from the ideal AB₂ stoichiometry (see, for example, [151, 364, 368, 380,381,382, 384, 386, 393, 394, 621]) or by substitutional replacement of the A or B metal by alloying additions (see, for example, [89, 102, 148, 361, 621,622,623,624,625]). There was also a theoretical attempt to predict which element addition should be most effective in enhancing the fracture toughness. Taking NbCr₂ as an example and assuming that the elements which can increase the atomic free volume are likely to improve the fracture toughness, rhenium was predicted to be the best choice to improve the fracture toughness of NbCr₂ [626]. However, even though partially very strong compositional effects on the high-temperature strength were reported [621], the room-temperature fracture toughness of single-phase Laves phase alloys always stays on a very low level and in many cases no visible effect on the fracture toughness was observed. Therefore, it must be concluded that—as already stated in Liu et al.’s review article [15]—unfortunately the room-temperature fracture toughness of single-phase Laves phase cannot be effectively improved by the introduction of defects such as antisite atoms or solid solution of alloying additions. Likewise, the introduction of thermal vacancies does not affect the fracture toughness at room temperature as was found for stoichiometric ZrCo₂ containing a thermal vacancy concentration of 1% [157]. For a discussion about off-stoichiometry of Laves phases and about its role on mechanical properties from a more fundamental point of view, see Sects. 3.2 and 3.7, respectively.

Addition of a second phase: Besides the above-described attempts to improve the room-temperature fracture toughness of single-phase Laves phase materials, dual-phase alloys consisting of a Laves phase toughened by the addition of ductile precipitates such as soft metals is another concept. For example, toughening of C15 NbCr₂ Laves phase by introducing fine and uniformly distributed, ductile bcc-Nb or bcc-Cr particles was already suggested in 1990/1991 by Anton and Shah [627] and Takeyama and Liu [628], respectively, and this concept was pursued for the same system for a long time, see, for example, [629,630,631,632,633]. In NbCr₂ Laves phase fabricated by spark plasma sintering (SPS), trace amounts of Nb and Cr solid solutions are observed to distribute among the grain boundaries. This kind of dual-phase toughening also resulted in an increase of fracture toughness, which, however, is still far from being sufficient for applications [634,635,636]. After a 500 h heat treatment at 1000 °C, a (Ti,Mo)Fe₂-based Laves phase alloy, which was slightly poor in Fe (nominal composition Fe-10Mo-30Ti in at.%), contained a volume fraction of about 12% of fine, ~ 250 nm sized, bcc-(Mo,Ti) precipitates. The fracture toughness was found to be increased from 1.1 to 2.2 MPa m^1/2, which still corresponds to an extreme brittleness [637].

Also toughening of Laves phase alloys by addition of larger amounts of a ductile metal phase was tried out in many studies (see also Sects. 5.2.5 and 5.5), but such efforts likewise were not sufficient to qualify the material for real structural applications.

It must be concluded that Laves phase-based alloys, neither in a single-phase state toughened by off-stoichiometry or alloying additions nor as dual-phase materials containing soft second-phase precipitates, are suited as structural materials, which mainly is because of their insufficient room-temperature fracture toughness.

Nevertheless, Laves phases can find application in structural materials when introduced as minor phase added to strengthen ductile metallic matrices as is discussed in the following sections.

Ferritic(-martensitic) steels and alloys

Introduction

Laves phases play an important role in ferritic steels for high-temperature structural applications. Especially the need to increase the effectiveness of fossil fuel-fired power plants by increasing the working temperature has led to intensive research for the development of improved, high-temperature creep- and corrosion-resistant ferritic steels for boiler, pipework and steam turbine parts.

To qualify ferritic steels for high-temperature application, usually various metallic and non-metallic elements are added to the α-Fe (bcc) matrix. While the corrosion resistance is especially improved by Cr additions of at least ~ 9 wt% (leading to the formation of protecting Cr-oxide scales), the creep resistance is enhanced by solid-solution- and/or precipitation-strengthening of the material. Besides several types of carbides (and, less frequently, carbonitrides or borides), these strengthening particles can also be intermetallic phases such as a Laves phase, see, for example, [638,639,640].

It is not possible to draw a general conclusion stating that Laves phase particles have either a beneficial or a detrimental effect on the mechanical high-temperature behavior of ferritic steels. As will become obvious in this section below, the effect of Laves phase particles strongly depends on factors such as the composition of the steel, the mechanical load, and the temperature and time of its application. Already in 1956, Gemmill et al. [641] wrote in a study on the effect of Ti additions to a creep-resistant ferritic 8Cr-3Mo steel (numbers are wt%) that it would be desirable to avoid the precipitation of TiFe₂ Laves phase because the Ti consumed in the Laves phase is no longer available as solid solution strengthener for the ferritic matrix. On the other hand, improving the strength of iron by Laves phase particles instead of carbides is also a rather old idea [642,643,644,645,646]. Bhandarkar et al. [645, 646] reported that a dispersion of spherical TaFe₂ Laves phase particles within the grains of a ferritic Fe-Cr alloy produced good high-temperature strength up to 600 °C without low-temperature embrittlement. Nevertheless, Laves phases still have a reputation as an embrittling phase in steels and other structural alloys. Even though in various studies it was shown that finely dispersed Laves phase precipitates can strongly improve the creep behavior, the effect of Laves phase particles on the high-temperature mechanical properties of ferritic(-martensitic) steels is a topic of controversial discussions until today.

In the following subsections, the vast (and, therefore, only selectively cited) amount of literature dealing with Laves phases in ferritic steels and alloys is roughly divided into four groups which are (i) the so-called ‘9-12Cr’ (9 to 12 wt% Cr) ferritic-martensitic steels, (ii) stainless steels with about 15 to 22 wt% Cr and C contents below ~ 0.1 wt%, (iii) superferritic steels with more than ~ 25 wt% Cr and very low C contents (below ~ 0.02 wt%, often termed ‘ultra-low C steels’), and (iv) C-free ferritic α-Fe alloys containing some Laves phase. As in the entire literature about steels, it is customary to express compositions in wt%, we will follow this convention here.

The ‘9-12Cr’ steels

Ferritic-martensitic steels containing 9 to 12 wt% Cr and 0.1 wt% C are currently applied materials for the hot parts of fossil fuel power plants, where steam temperatures are exceeding 600 °C. Due to the urgent need to reduce the enormous emission of harmful greenhouse gases, the energy efficiency of power plants must be increased, which is most effectively done by further increasing the steam temperature. Therefore, for many years an impressive amount of work is going on world-wide aiming at the development of modified 9-12Cr ferritic(-martensitic) steels with improved temperature capability. The most critical property is the long-term creep resistance at application temperature, which could be improved by controlled, fine dispersion of long-term stable strengthening particles. This is where Laves phases can play an important role.

Critical point and reason why there are so many studies about this kind of high-temperature materials is the fact that these steels are not in an equilibrium state during application. Prior to being built into the power plant, the cast material experiences some heat treatments for normalizing/austenitization and subsequent formation of a martensitic matrix with or without certain precipitates resulting in a metastable material. During application at high temperature, this metastable state moves in the direction of thermodynamic equilibrium with a composition-, temperature-, and also mechanical-load-dependent kinetics resulting in a very complex interplay of growing or dissolving particles, formation of new phases, shifting of the matrix composition, and changes of the microstructure in general. As in parallel with the microstructure also the mechanical properties such as the creep resistance will change, it is an important goal to slow down the kinetics (especially that of particle coarsening) as far as possible. Investigations of long-time aged steels and modeling of phase evolution in such steels show that even after more than 10 years, equilibrium may not yet be achieved, and new phases such as Laves phases or so-called Z phase (a complex (Cr,Fe)(Nb,V)N nitride [647,648,649]) may nucleate and grow only after long times (see, for example, [639, 650,651,652]). Because such aging times of 10 or more years of course by far exceed available times in experimental studies, the kinetics of phase precipitation and coarsening was often investigated by theoretical simulations [650, 651, 653,654,655,656,657,658,659,660]. An example of a simulation of the time-dependent change of phase fractions in two different steels is shown in Fig. 31 [651], details are discussed later in this section.

Figure 31

Time dependence of phase fractions of precipitates in P91 (a) and P92 (b) steels at 600 °C as obtained by numerical simulations (adapted with permission from [651])

The two most important alloying additions to increase high-temperature strength are Mo and W, and both form C14 Laves phases with Fe. Mo-containing ferritic steels are already in use since the 1950s [641, 661, 662] and Mo contents usually are in the range 0.5 to 2 wt%. Most prominent representative of this group of ferritic-martensitic steels is so-called P91 steel (9Cr-1Mo + various minor additions), see, for example, [639, 652, 656, 663,664,665,666,667,668]. While in 9Cr-2Mo steels, a significant loss of toughness after only 1000 h at 600 °C was observed that was attributed to precipitation of MoFe₂ Laves phase [669,670,671], P91 (1 wt% Mo) steels were successfully creep-tested for more than 100000 h at 550 °C [672, 673] and 600 °C [652] without fracturing but finally also showing creep damage that at least partially was attributed to strongly coarsened MoFe₂ Laves phase precipitates.

With respect to strengthening, W is an even more effective alloying addition than Mo. W diffuses more slowly than Mo and WFe₂ Laves phase precipitates coarsen less rapidly than MoFe₂ particles (see, for example, [674, 675]) and are also stable to higher temperatures compared to MoFe₂. While the Mo-modified 9Cr steel P91 was introduced as steam pipe steel in fossil fuel power plants in the late 1980s, the improved W-modified steels P92 (9Cr-2W-0.5Mo + minor additions) and E911 (9Cr-1Mo-1W + minor additions) came into application in 2001 and 2002, respectively [639]. The Laves phase-containing P92 steel until today is a kind of benchmark for high-temperature steels and its properties and behavior especially with respect to the Laves phase were discussed in many publications, see, for example, [639, 660, 676,677,678,679,680,681,682,683].

Figure 31 shows a comparison of the variation of phase fractions of the diverse precipitates in P91 (left) and P92 (right) steel at 600 °C as a function of time as obtained from numerical simulations [651]. In both steels, Laves phase only starts to precipitate after 100–1000 h from the Mo/W supersaturated matrix and it needs in the range of 10000 h until the complete amount of Laves phase has precipitated. In the following time, where the material is still far from equilibrium, the precipitates will start to coarsen, and finally after times in the range of 100000 h (i.e., more than 10 years) Z phase will start to form in parallel to dissolution of V nitride.

There is general agreement in the literature that the precipitation of fine (Mo,W)Fe₂ Laves phase particles increases the strength of the steels as long as the coarsening process has not yet started. Simultaneously with the formation of Laves phase, the effect of solid solution strengthening decreases as Mo and W are consumed from the supersaturated matrix. However, from a rough estimation of the solid solution strengthening effect by Mo and W and comparing it with the precipitation hardening effect of the Laves phase, Hald [639] concluded that solid solution strengthening from Mo and W actually has no significant effect on the long-term microstructure stability of 9-12Cr steels and that Laves phase precipitation is much more effective for strengthening. As, for example, shown by Abe [674, 675], precipitation of Laves phases leads to a decrease of the creep rate, but with the onset of rapid coarsening the creep rate reaches a minimum value and starts to strongly increase again. The nucleation of Laves phase precipitates was found to start at grain boundaries near M₂₃C₆ carbides (see Fig. 32) [684,685,686], followed by incoherent (and, therefore, comparatively rapid) growth into the matrix. This can result in void formation and de-cohesion effects initiating crack formation, which finally may lead to the failure of the steel. An especially critical situation regarding unwanted precipitation and coarsening of Laves phase particles exists in weld joints (for example in similar welds of P92 [687] or dissimilar welds of 9Cr steel with austenitic steels [688,689,690,691,692]), where microstructural changes during melting and subsequent cooling are difficult to control.

Figure 32

STEM images of a Laves phase precipitate connecting two M₂₃C₆ particles on a grain boundary of the matrix of a 12Cr-1Mo steel after 2400 h creep at 550 °C and 120 MPa: a HAADF image, b bright field image, and c corresponding EDX map (reproduced with permission from [685])

Therefore, a central goal of developing optimized ferritic-martensitic high-temperature steels is to minimize the coarsening rate of Laves phase precipitates, which as fine particles are very beneficial to increase the creep resistance. The risk of void formation at the interface between a Laves phase particle and the matrix does not only depend on the particle size, but also on the level of strain energy at the interface, which in turn will depend on the composition of matrix and particles. By systematically studying the role of the amount and ratio of Mo/W additions and of the Cr content, it was shown that compositional changes of the Laves phase particles may strongly vary their embrittling effect independent of their size [693]. Regarding changes of the Cr content, various types of (10-)12Cr-xW steels were developed including the P122 (12Cr-2W) steels [220, 694,695,696,697] and a group of steels containing higher amount of W (3–5%) and further alloying additions [650, 657, 698,699,700,701,702]. With respect to the Mo and W contents, various modifications of the 9Cr steels P91 and P92 were studied such as the 1Mo-1W steels with 9% Cr (designated as E911 steels [639, 662, 667, 678]) or 10% Cr [703,704,705,706], or model steels with varying Mo/W ratios [658, 671, 674, 675, 707].

Moreover, quite a lot of studies dealing with the effect of further alloying additions to 9-12Cr steels were performed always including effects on Laves phase precipitation. For example, alloying 3(−5) % Co to 9-12Cr steels (e.g., [708,709,710,711,712,713,714,715,716,717,718,719]) was found to promote the precipitation of Laves phase (due to the fact that Co reduces the solubility of Mo/W in the Fe matrix). In addition, Co was predicted (by a computational design approach coupling thermodynamic and kinetic data involving a genetic algorithm optimization routine) to drastically reduce the coarsening rate of Laves and M₂₃C₆ particles, thereby yielding a much improved long-time creep resistance compared to the Co-free counterpart steel [659]. Cu is another frequent alloying addition aiming at positively affecting the precipitation processes [657, 699,700,701]. Cu should be beneficial for the creep resistance as it affects a finer distribution of the precipitates [640]. In order to study the precipitation of (Mo,W)Fe₂ Laves phase particles and the impact on creep behavior as a separate effect (i.e., unaffected by carbides), a series of C- and N-free (< 50 ppm) Fe-9Cr-X alloys with varying amounts of X = W, Mo, Co and further typical steel additions were creep-tested at 650 °C [720]. For up to about 3% W + Mo, Laves phase was found to precipitate only on grain boundaries and, hence, contributed little to precipitation strengthening. For 4.5% W + Mo, Laves phase precipitates were observed both at the grain boundary and homogeneously within the grains with a precipitation-free zone on both sides of the grain boundaries. The creep rupture time was mainly influenced by the size of Laves phase particles precipitated at grain boundaries [720]. However, it has to be kept in mind that the precipitation process in real steels is different due to the simultaneous presence of carbide/carbonitride particles.

Finally, it should be mentioned that creep-resistant ferritic-martensitic 9-12Cr high-temperature steels are not only applied in fossil fuel power plants, but they are also candidates for application in nuclear power plants both for fission as well as fusion reactors [640, 721,722,723,724,725,726]. High-energy neutron irradiation leads to significant changes in the microstructure and the formation of Laves phase precipitation can be completely suppressed by irradiation [640]. In case Laves phase is already present in a steel, larger particles can become completely amorphous by ion irradiation and smaller Laves phase particles may completely disintegrate, while instead some new, non-equilibrium phases may nucleate and grow [722, 726]. These partially complex processes are not yet well understood.

Ferritic 15–22% Cr steels

Ferritic steels with increased Cr contents in the range 15 to 22 wt% were developed as oxidation-resistant structural materials for the temperature range of about 600 to 900 °C. Intended fields of application are a) improved high-temperature power plant steels for temperatures above 620 °C, b) automotive parts for the hot regions of the engines such as exhaust manifolds, which see temperatures of up to 900 °C or even higher, and c) interconnects for solid oxide fuel cells (SOFCs), where temperatures in the same range of about 650 to 900 °C can be reached. In all cases, Laves phases play an important role as is briefly discussed in the following.

A reason for the limitation of the 9-12Cr steels to maximum temperatures of 600–620 °C is the insufficient steam oxidation resistance at higher temperatures. This could be significantly improved by higher Cr contents. However, at the same time higher Cr contents lead to strongly increased formation of large Z-phase particles replacing fine, strengthening MX (M = Nb,V and X = C,N) carbonitrides, which causes a breakdown of creep strength [647, 727]. Starting from typical 9-12Cr steel compositions, WFe₂ Laves phase containing 15Cr steels with fully ferritic matrix were developed by a Japanese group and continuously improved over the last twenty years for application at 650 °C [728,729,730,731,732,733,734,735,736,737,738,739]. The loss in creep strength due to the increased Cr content is compensated by increased W contents up to 6 wt% and the addition of 3 wt% Co [728, 729] leading to precipitation of not only WFe₂ Laves phase but also of intermetallic µ (Fe₇W₆)- and χ (Fe₃₆Cr₁₂W₁₀)-phase particles as well as M₂₃C₆ carbides [730]. As a decrease in long-term creep strength was attributed to the large amount of coarse carbide particles, the C content was reduced from the initial amount of 0.1 wt% to 0.05 wt% and even C-free alloys were tested [733]. Addition of Ni up to 2 wt% led to formation of a two-phase matrix consisting of ferrite and some martensite both containing Laves phase precipitates [732, 736,737,738]. Testing the creep properties of these 15Cr steels at temperatures of 650 to 750 °C gave partially promising results, but also indicated that further optimization is needed before they can be applied in power plants [735, 737,738,739].

NbFe₂-containing ferritic stainless steels with Cr contents in the range 15 to 19 wt% and low C contents of 0.01 wt% or less were developed for application in automotive exhaust systems, which currently are working at temperatures in the range of up to 900 °C [740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756]. Typical Nb additions are in the range 0.4 to 0.8 wt% and lead to significant solid solution strengthening of the ferrite matrix with precipitation of NbFe₂ Laves phase and small amounts of Nb(C,N) and Fe₃Nb₃C during aging. Owing to the low C and high Cr contents, the Laves phase can—compared to 9–12Cr steels—exist as stable phase up to much higher temperatures (> 1000 °C depending on composition [750, 754]). While the incongruently growing Laves phase was reported to be detrimental for the long-term strength at 700 °C [742], its formation along grain boundaries was found to effectively prevent grain growth at higher temperatures, thus preserving the high-temperature strength over a long time period [750, 755]. To reduce emissions of conventional car engines, higher discharge temperatures are needed and the operating temperatures of exhaust manifolds will approach 1000 °C or more [747, 752]. A very critical issue at such high temperatures is the corrosion resistance of the material. Therefore, the oxidation behavior of a 19Cr-0.5Nb ferritic stainless steel containing additions Mo, W, and Ce was studied at 950 to 1100 °C. It was found that the Laves phase precipitates can effectively hinder the inward growth of the oxide film. However, with a W content increased to 1 wt%, a reduction of the adhesion of the oxide film was observed [752]. Effective retardation of oxidation by Laves phase precipitates was also reported for a Nb-containing 20Cr steel tested at 800 and 900 °C [757].

Interconnects for SOFC stacks are another application of high-Cr stainless ferritic steels containing Laves phase [758,759,760,761,762,763,764,765,766,767,768,769,770,771]. Alloying elements and concentrations are similar to those in steels for automotive exhaust systems, C contents are < 0.01 wt% and Cr contents are in the range 18 to 22 wt% to ensure formation of protecting chromia scales. Interconnect materials must not only have good high-temperature mechanical properties, but also a low electrical resistivity, high thermal conductivity, and very good corrosion resistance and chemical stability in both anode and cathode gases, i.e., in reducing and oxidizing atmosphere [762]. The role of Laves phase is mainly to provide good mechanical properties [759, 763, 764], but there is also a complex interplay between Laves phase precipitation and the formation of different types of surface oxides [771].

One of the alloys originally developed for the application in SOFCs is so-called Crofer 22 H, which is a commercially available 22Cr ferritic steel containing some (Nb,W)(Fe,Cr)₂ Laves phase, see, for example, [759, 762, 763, 772, 773]. Due to its promising high-temperature mechanical properties, the idea came up to modify and optimize this Laves phase forming, fully ferritic steel for structural applications at 600 to 650 °C in power plants [774,775,776,777]. Very good properties were obtained for a series of modifications with 17 wt% Cr and varying amounts of Nb and W, which were patented as HiperFer (High Performance Ferritic) steels [778,779,780,781,782]. The Cr content was reduced from 22 to 17 wt% in order to minimize FeCr (σ) phase formation at temperatures of 600 to 650 °C [774]. Detailed tests of the high-temperature creep performance and cyclic fatigue behavior indicated that this kind of high-strength, Laves phase-forming, fully ferritic steels has a potential to replace currently applied martensitic 9–12 Cr steels in power plants enabling working temperatures > 620 °C [778,779,780,781]. Promising results were also obtained in first tests performed at the linear plasma generator PSI-2 at Forschungszentrum Jülich to study possible applications of HiperFer as a reduced activation ferritic steel for nuclear fusion applications [783].

Superferritic steels (≥ 25% Cr)

Following a definition given by Azevedo and Padilha [784], superferritic steels are stainless ferritic alloys containing less than 0.02 wt% C, more than 25 wt% Cr, between 2 and 4 wt% Mo as well as Ni, and sometimes additions of Nb or Ti. They are especially suited as structural materials for applications in harsh, corrosive environments at ambient temperatures up to a maximum of about 300 °C. At higher temperatures, detrimental embrittling intermetallic phases such as σ (FeCr), χ (Fe₃₆Cr₁₂M₁₀), and Laves phase (Mo,Nb,Ti)Fe₂ can precipitate. Due to the high Cr contents, the Cr-rich σ phase is the most frequently observed precipitating phase, while the occurrence of Laves phase has only rarely been described [784,785,786,787,788,789,790,791,792,793]. In a typical superferritic alloy of composition 25Cr-(2-3)Mo-4Ni containing 0.3 wt% Nb, Laves phase was found to nucleate as first intermetallic phase during aging at 850 °C. It precipitates as fine particles along the ferrite grain boundaries and does not significantly grow due to the start of precipitation of σ phase and the exhaustion of the available Nb [785, 787]. Similar observations were made in 27Cr-4Mo-2Ni superferritic steel after hot rolling, solution treatment at 1050 °C and/or aging between 600 and 800 °C [789,790,791,792]. Increased Cr contents were found to promote the precipitation of σ and Laves phase and to widen the precipitation temperature region of the Laves phase, but annealing at temperatures above 1000 °C can result in complete dissolution of the detrimental phases [788]. A review about the role of the deleterious effect of σ, χ, and Laves phases on the processing and service life of superferritic steel components is given by Azevedo and Padilha [784].

Other ferritic C-free alloys

Precipitation of AFe₂ Laves phase from α-Fe solid solution is known for many systems (e.g., A = Hf, Mo, Nb, Ta, Ti, W, Zr) and was already studied long time ago as a measure to improve the strength of iron (see, e.g., the aforementioned (Sect. 5.2.1) early studies on Fe-Nb [642, 643], Fe–Ta [644,645,646], and Fe-Ti [643] α-Fe + AFe₂ alloys). Due to the poor oxidation behavior of Fe, usually Cr (as in the above discussed steels) and/or Al are added to produce protective chromia or alumina scales on the alloy surfaces. Some examples for Laves phase containing α-Fe alloys suggested for high-temperature applications are described in the following. It should be noted that particular care must be taken when comparing alloy compositions in different publications in this research field as both ‘wt%’ as well as ‘at.%’ are frequently used. To allow comparison with the above discussed ferritic steels, we stick to the wt%-description in this section. In cases where original compositions were given in at.%, we also include this information here.

(i) A = Nb, Mo, W: NbFe₂-strengthened Fe-7.6Al-8.7Nb alloys (Fe-15Al-5Nb in at.%) with or without some minor additions of Zr and B were hot-forged at 1150 °C resulting in a uniform dispersion of coarse Laves particles arranged along the triple junctions of a fine-grained α-Fe matrix. The forged alloy showed a good creep resistance at 700 °C [794, 795]. Heat-resisting Fe-Cr-Nb(-Ni) alloys with about 9–14 wt% Cr, 1–8 wt% Nb, and 0–5 wt% Ni (Fe-(10–15)Cr-(0.5–5)Nb-(0–5)Ni in at.%) with varying amounts of NbFe₂ Laves phase adjusted by the Nb content were tensile-tested at 600 and 700 °C as well as at room temperature. A good balance between room-temperature ductility and high-temperature strength was obtained for about 1.5–2.5 wt% Nb (1–1.5 at.%) [796, 797]. Replacing Nb by 4.5 wt% W (1.4 at.%) and adding further elements such as Co and Si resulted in more complex precipitation processes as besides Laves phase, a rhombohedral R phase and a quasicrystalline phase I also appear [32, 798].

Nb- and/or Mo-containing Fe-Cr-Al alloys with small additions of Y (Fe-13Cr-(4.5–6)Al-0.15Y-(0-2)Mo-(0-2)Nb) consisting of a ferritic matrix + fine (Mo,Nb)Fe₂ precipitates were developed as promising accident-tolerant fuel cladding for light water reactors [799, 800]. By applying a thermomechanical treatment, a fine dispersion of Laves phase particles especially along grain/subgrain boundaries in the α-Fe matrix was obtained, which effectively stabilized the recovered and recrystallized microstructures [800].

High-Cr (30Cr-3Al) ferritic Fe-Cr-Al alloys with strengthening Nb- or W-based Laves phase (1 or 2 wt% Nb and 0 or 6 wt% W + minor amounts of Zr, Mn, and Si) were developed aiming at application in future fossil fuel power plants operating at 700 °C. The very high Cr content was chosen to improve the ash-corrosion resistance in fire-side corrosive environments encountered in fossil fuel-fired power plants. A good combination of corrosion resistance and creep strength was achieved comparable or superior to commercially available austenitic high-temperature stainless steels [801,802,803].

By addition of 3 wt% Ni and 3 wt% W (+ 1 wt% Zr) to Fe-12Cr-3Al, dual precipitation of coherent B2 NiAl and incoherent (W,Zr)Fe₂ Laves phase was achieved. Creep properties at 650 °C were tested for this alloy, which is intended for application in nuclear power plants. Creep fracture was primarily ductile, but strongly coarsened Laves particles locally led to partially brittle fracture [726, 804].

(ii) A = Ti: Ti is another transition metal leading to the formation of strongly hardening Laves phase when added to α-Fe, see, for example, [643, 805]. Investigations of the temperature dependence of mechanical properties of Fe-based two-phase ferrite + Ti(Fe,Si)₂ alloys in the ternary system Fe-Si-Ti were performed by hardness, compression and bending tests. Si tends to dissolve in the Laves phase, and increasing Ti as well as Si content lead to significant strengthening and loss of ductility by Laves phase particles precipitated inside the ferrite grains and on the grain boundaries. Alloys with additions of about 5 at.% Si and 4 at.% Ti were suggested for further alloy development [806].

(iii) A = Zr: Yield strength and flexural fracture strain of two-phase α-Fe + ZrFe₂ Laves phase alloys were studied as a function of temperature up to 1200 °C for Fe-based Al-Fe-Zr with 0 or 5 wt% Al (10 at.%) and varying Zr contents increasing from 0 to 43 wt% Zr (0 to 30 at.%, corresponding to phase fractions of the Laves from 0 to 100%). Figure 33 shows the strong increase of the yield strength with increasing content of Laves phase, which however goes in parallel to an increase of brittleness. The brittle-to-ductile transition temperatures (BDTT) obtained from the temperature dependence of the measured flexural fracture strains strongly increases from below room temperature for the Laves phase-free material to, e.g., about 600 °C for alloys with 1:1 volume content of α-Fe and Laves phase. With respect to the oxidation behavior, Zr additions were found to have a very negative effect resulting in strongly increasing oxidation rates [807].

Figure 33

0.2% yield stress as function of temperature for different amounts of Zr(Fe,Al)₂ Laves phase in Fe-based two-phase α-Fe + Laves phase Al-Fe-Zr alloys with a fixed Al content of about 5 wt% (10 at.%) (adapted with permission from [807])

A new class of ZrFe₂-strengthened Fe-(9-12)Cr-(3-10)Zr-based alloys (with some quaternary additions of Ni or W) was reported to be promising for applications as cladding materials in nuclear reactors because of the enhanced high-temperature strength and resistance to creep and radiation hardening compared to traditional P91 ferritic-martensitic steels [808,809,810].

(iv) A = Hf: An alternative way to produce homogeneously distributed, fine Laves phase particles for strengthening of a ferritic matrix was recently introduced by Kobayashi et al. [811,812,813,814]. In Fe-Cr-Hf alloys with about 9 wt% Cr and low Hf contents ≤ 0.5 wt% (0.15 at.%), regularly arranged rows of fine HfFe₂ particles with sizes of about 20 nm were produced through so-called interphase precipitation (see [815, 816]) along the reaction path δ-ferrite → γ-austenite + HfFe₂ with a subsequent phase transformation of the γ phase into the α-ferrite phase [811,812,813,814], see Fig. 34.

Figure 34

BSE (back-scattered electron) SEM image of regularly precipitated, nanometer-sized HfFe₂ Laves phase particles in a ferritic Fe-9Cr matrix obtained by interphase precipitation (reproduced with permission from [811])

Austenitic steels and alloys

Heat-resistant austenitic steels contain high amounts of Cr (for oxidation resistance, usually in the range 15 to 25 wt%) and Ni (as austenite stabilizer, strongly varying between about 8 and 30 wt%). Compared to the ferritic 9–12Cr steels, they can be applied at higher temperatures up to 675 °C, but due to the high Cr + Ni contents they are much costlier. Very similar to their ferritic counterparts, both solid solution strengthening and precipitation strengthening by alloying additions contribute to their high-temperature strength and creep resistance. Most used alloying metals for this purpose, which can also lead to precipitation of Laves phases, are Mo, Nb, and, to a much lesser extent, Ti and W.

Similar as in the case of ferritic steels, for a long time the occurrence of precipitation of Laves phases in the austenitic matrix was regarded as a deleterious effect leading to embrittlement and creep fracture, see, for example, [817,818,819,820,821,822,823,824]. The common opinion was that in development of new austenitic steels it is most important to suppress the formation of Laves phase [820], even though in a review about precipitation in creep-resistant austenitic stainless steels, it had been stated that “Whether or not Laves phase has a detrimental effect on creep properties is still discussed” [825].

A concept to benefit from controlled precipitation of finely dispersed Laves phase particles in the austenite (γ-Fe) grains and on the grain boundaries was introduced by Takeyama et al. [826]. Based on their earlier phase diagram studies [827, 828], a C-free alloy with a composition of Fe-20Cr-30Ni-2Nb (at.%, corresponding to Fe-18.4Cr-33.1Ni-3.3Nb in wt%) was designed [826]. While at 1200 °C the alloy is single-phase fcc-Fe, it is two-phase with Nb(Fe,Cr,Ni)₂ Laves phase precipitates at 800 °C, and becomes three-phase by additional precipitation of γ” (Ni₃Nb) in the fcc-matrix during cooling to 700 °C [829, 830]. In a series of investigations, the properties of this alloy were later on further improved by modifications of composition and heat treatments [829,830,831,832,833,834,835,836,837,838]. These studies showed that strengthening in this alloy is especially determined by the grain boundary precipitation of Laves phase and that the coverage of the grain boundaries by precipitates and their morphology can be controlled by small additions of B. The authors showed that the creep strength directly depends on the grain boundary fraction ρ covered by Laves phase precipitates [829, 830]. Figure 35 shows a comparison of microstructure and creep behavior of the alloy without and with B-doping (0.03 at.%). A higher coverage ρ of the grain boundaries results in an increased creep life and reduced creep rate, which was found to decrease linearly with ρ [829]. A more detailed study regarding the effect of B-doping in this alloy showed that B segregates to the grain boundaries and promotes the precipitation of Laves phase effecting not only a higher number but also a refinement of the Laves phase precipitates [834]. From room temperature tensile and Charpy impact tests, it was concluded that the Laves phase on the grain boundaries has no negative effect on the room temperature ductility. There was no indication of crack propagation within the Laves phase precipitates or along the interface between γ-Fe matrix and Laves phase, and fracture was found to be always transgranular [836].

Figure 35

Microstructures of Fe-20Cr-30Ni-2Nb (at.%) without (a) and with 0.03 at.% B doping (b) after aging for 1200 h at 800 °C, and (c) creep-rates at 700 °C as a function of time of the two aged alloys revealing a strong improvement in creep life by increasing the grain boundary coverage with Laves phase from 52 to 89% (adapted with permission from [829])

Thermokinetic calculations combined with experimental observations on the precipitation process of the NbFe₂ Laves phase and the γ” (Ni₃Nb) phase in Fe-20Cr-30Ni-2Nb (at.%) revealed that above 700 °C, the Laves phase first nucleates on grain boundaries and precipitation within the grain interior starts later. The nose of the time–temperature-transformation curve for the Laves phase is located at about 1000 °C [837]. The effect of partial or complete replacement of Nb by Ta on the alloy microstructure and kinetics of the precipitation processes of the Laves and γ” phases was found to be complex. For Ta/(Nb + Ta) ratios above 0.6, Ta was found to stabilize the Laves phase against γ” [838].

On the basis of the Fe-20Cr-30Ni-2Nb (at.%) alloy composition suggested by Takeyama [826, 827], a series of Laves phase strengthened austenitic alloys was designed and tested at Oak Ridge National Laboratory [802, 831, 839,840,841,842,843,844,845,846,847,848]. The most important difference is the addition of 2.5 to 4 wt% Al (about 5 to 8 at.%) to the base composition resulting in the formation of a dense, protective alumina scale on the alloy surface. Such beneficial, external alumina scales exhibit one to two orders of magnitude slower oxide growth kinetics compared to chromia scales, and are far more stable in water vapor containing environments at elevated temperatures [849, 850]. This is why they were introduced as a new class of stainless steels termed alumina-forming austenitic steels or ‘AFA steels’ [842, 843]. Overviews of the development of this type of austenitic steels, which besides Laves phase also contain Al-stabilized B2-NiAl and, depending on composition, γ′(L1₂) Ni₃Al precipitates, are given by Yamamoto et al. [802, 847].

The growth of Laves phase and B2 precipitates at 800 °C in the ‘base’ alloy Fe-20Cr-30Ni-2Nb-5Al (at.%) was studied with samples heat-treated up to 1325 h. Within the austenitic matrix, Laves phase was found to grow only very slowly compared to B2 precipitates. However, the growth of both phases was much faster on the grain boundaries, and the coverage of the grain boundaries by precipitates increased from an initial value of 56% to 93% after 1325 h. This also resulted in an increased yield strength, while interestingly the elongation at room temperature still reached a high value of 19% [851]. As the authors tentatively assigned the surprisingly high room-temperature ductility to the low-misfits of the precipitates with the austenite matrix, they additionally analyzed the orientation relationships of both phases with the matrix in another study [852]. For the interfaces between Laves phase (Lp) and matrix (γ), they confirmed an orientation relationship (111)_γ//(0001)_Lp, [$\bar{1}10$]_γ//[$10\bar{1}0$]_Lp, which had already been reported before by Denham and Silcock [853] for hexagonal C14 NbFe₂ Laves phase in an fcc austenitic matrix. For the B2 precipitates, they found a Kurdjumov–Sachs orientation relationship (111)_γ//(011)_B2, [$\bar{1}01$]_γ//[$\overline{11} 1$]_B2 [852].

Trotter and Baker also studied the effect of severe plastic deformation on the microstructure and precipitation process of this alloy [854]. By cold working of the solution-treated (1250 °C) alloy, the thickness was reduced by 90% resulting in a high density of dislocations that served as nucleation sites for precipitation during subsequent aging at 700 and 800 °C. The introduced defects not only caused an accelerated precipitation in the matrix but also an increase in the total volume fraction of precipitates as compared to material that had been aged at the same temperatures without prior cold working [854]. The same observations were also made for a cold-worked AFA steel of wt%-composition Fe-14Cr-32Ni-3Nb-3Al-2Ti-0.1C (corresponding in at.% to Fe-15Cr-30Ni-2Nb-6Al-2Ti-0.45C) [855]. By introducing 2 wt% W in a Laves phase-containing 14Cr-20Ni-3Mo-2.5Al-2Mn-1Nb-0.1C (wt%) AFA steel (and reducing Mo to 1.5%), a significantly increased creep lifetime was obtained in tests at 700 °C. This improved behavior was traced back to an increased fraction and reduced size of Laves phase precipitates due to an increased content of W in the Laves phase [856]. The same positive effect of W addition was reported for an AFA stainless steel Fe-15Cr-25Ni-3Al-NbWCu (wt%) [857].

The Laves phase ZrFe₂ plays an especially important role in nuclear waste management, where austenitic stainless steels alloyed with 15 wt% Zr alloys were developed as nuclear waste form materials [858,859,860,861,862,863]. Neutron diffraction results showed that the addition of U does not result in the formation of discrete U-rich phases. The lattice parameters of the ZrFe₂ Laves phase are larger in U-containing 15Zr stainless steel alloys and are consistent with the substitution of U at Zr sites of the ZrFe₂ lattice indicating that U (and also other actinides) dissolves in the Laves phase [863].

Superalloys

Ni- and Co-based superalloys are developed for structural applications at very high temperatures as, for example, in the hot parts of gas turbines, where steels can no longer be used. High-temperature strengthening of the fcc Ni- or Co-matrix (‘γ phase’) is usually achieved by coherent intermetallic precipitates (such as fcc-ordered γ′ or bct-ordered γ″ phases) and by solid solution hardening. This is why superalloys are usually highly alloyed materials. An often observed, unwanted effect of these alloying additions is the precipitation of incoherent intermetallic phases, which can negatively affect the mechanical behavior [864]. Very frequently these unwanted intermetallic phases are Laves phases, which were found in both Ni-based and Co-based superalloys, see, for example, [865, 866].

Laves phases in superalloys are considered as very detrimental for the mechanical behavior. The best investigated example is the Ni-based superalloy Inconel 718 (IN718, typical composition in wt% Ni-19Cr-18Fe-5Nb-3Mo-1Ti and minor other additions). IN718 is by far the most important superalloy for applications, and it is used in gas turbine components since the early 1960s and until today [867]. Laves phase forms due to the high Nb content and can impair the mechanical properties of IN718 through several mechanisms, which were summarized in an overview by Schirra et al. [868]. According to these authors, the most dominant mechanism probably is brittle fracture of the Laves phase. In addition, similar to steels, the formation of Laves phase consumes large amounts of Nb depleting the matrix of the principal hardening element. Finally, during welding processes the Laves phase may melt, and cooling of the partially melted material can lead to the initiation and propagation of microcracks in the re-solidified material [868]. Especially in superalloy welds [869,870,871,872,873,874,875] and dissimilar welds of superalloys with steels [876,877,878,879,880,881], Laves phases were consistently considered as highly detrimental to the mechanical properties. The effect of liquation cracking also plays an important role in the production of superalloys by additive manufacturing (AM) methods (e.g., [882, 883]). Parts as well as coatings made of Ni-based superalloys (mostly IN718) are often produced by electron beam melting or laser AM, and a large number of investigations were performed to understand and control the formation and distribution of Laves phase during the AM process, see, for example, [884,885,886,887,888,889,890,891] to name but a few.

Amount, size and morphology of Laves phase precipitates sensitively depend on the cooling process. Therefore, several detailed studies (see, for example, [892,893,894,895,896,897,898]) were performed to precisely understand the solidification process of superalloys. The most common method to reduce the amount of Laves phase precipitates is their decomposition at high temperatures by heat treatments above the eutectic temperature, see, for example, [897, 899,900,901]. However, while it is possible to dissolve most of the interdendritic Laves phase in IN718 superalloy, at the same time needle-shaped δ phase precipitates and the matrix grains may coarsen substantially [899]. Minor alloying additions may also play an important role for stabilizing the Laves phase. Doping with elements such as P and B was reported to promote the formation of Laves phase, i.e., both should be avoided [902,903,904]. From DFT-based ab initio calculations on the effect of different solute elements on the interface energies between Laves phases and matrix grains, it was concluded that Ru additions should notably increase the interfacial energy and, thereby, increase the difficulty of nucleation of Laves phase [905]. Another interesting approach to reduce the amount of Laves phase was presented by Chen et al., who were able to significantly suppress the formation of Laves phase by introducing carbon nanotubes in a laser melting process of IN718 [906].

It should be noted that the occurrence of Laves phases in superalloys is not always regarded as detrimental. Sui et al. [888] studied differently heat-treated IN718 samples with varying sizes and morphologies of Laves phase precipitates. They conclude that the size and the morphology are the key factors in determining whether Laves phase precipitates are good for the mechanical properties of IN718 superalloy or not. A certain amount of small and granular Laves phase is found to be beneficial for the room temperature tensile properties [888].

There is also a class of superalloys neither containing γ′ nor γ″ phase, but being purely strengthened by Laves phase. Superalloys such as the W-rich Ni-based alloys HR6W (Ni-23Cr-25Fe-7W-Ti-Nb) and HR35 (Ni-30Cr-15Fe-6W-Ti) (which is additionally strengthened by α-Cr) were developed for boiler tubes and pipes in advanced ultra-supercritical (USC) power plants with 700 °C steam temperature. Even after long-term aging of WFe₂-strengthened HR6W superalloy for 3000 h at 750 °C, the microstructure exclusively contained fine Laves phase precipitates and M₂₃C₆ carbides, and no σ phase precipitation was observed [907]. Creep tests conducted at 800 °C (with 70 MPa load) and 700 °C (100 MPa load) revealed that the amount and size of Laves phase precipitates remained constant over time [908].

Cr-, Cu-, Mg-, Nb-, Ti-, or Zr-based alloys

Strengthening of soft metal solid solutions by strong Laves phase particles is an old concept for designing new structural materials, which is not only applied to Fe-, Co-, and Ni-based alloys (such as the above discussed steels and superalloys), but was also considered and tested for several other metals. Here, some examples of Laves phase-forming alloy systems are briefly summarized.

Cr-based alloys

Alloys based on Cr are of longstanding interest as high-temperature structural materials especially due to their good high-temperature oxidation and corrosion resistance in combination with a high melting point and moderate density. Laves phase in equilibrium with bcc-Cr solid solution exists in the Cr-X systems with X = Ti, Zr, Nb, Hf, or Ta (and interestingly in all these binary systems, Laves phase is the only intermetallic phase). The microstructures and mechanical behavior of two-phase alloys from all these five systems have been intensively explored, see, for example, [381, 909, 910] for Cr + TiCr₂ alloys, [911, 912] for Cr + ZrCr₂, [15, 628, 630, 631, 911,912,913,914,915,916,917,918] for Cr + NbCr₂, [15, 919,920,921] for Cr + HfCr₂, and [15, 922,923,924,925,926] for Cr + TaCr₂ alloys. Increased high-temperature strength in parallel to decreased room-temperature fracture toughness are the two opposing effects resulting from addition of Laves phase to the bcc solid solution. Various attempts were made to get improved property combinations, for example, by producing directionally solidified eutectic material [913, 914] or by various alloying additions such as Ni, Co, Fe, Al and Re at levels up to 16 at.% to Cr + NbCr₂ alloys [927], Si [926, 928,929,930,931], Al, Mo [929], Fe [932], or Ru [933] to Cr + TaCr₂ alloys. For a fully eutectic quinary Cr-12Nb-5Ti-5Mo-5Si alloy consisting of Cr solid solution and about 55 vol.% NbCr₂-based Laves phase, a room-temperature yield strength of nearly 2000 MPa and a fracture toughness in the range of 14.0–14.8 MPa m^1/2 was reported [633]. To increase the strength of the ductile bcc-matrix, a three-phase Cr-Mo-Nb ternary alloy with 30 at.% Mo and 20 at.% Nb was designed containing two bcc solid solution phases, one rich in Cr and the other rich in Mo, in combination with strengthening NbCr₂ Laves phase. During aging at 1200 °C, the alternating bcc-Cr/bcc-Mo morphology remained stable, but the growing Laves phase on the grain boundary consumed more and more of the Cr-rich bcc phase [934].

Cu-based alloys

Because of their excellent electrical and thermal conductivity properties, Cu-based alloys are extensively applied especially in electronic materials. As the low mechanical strength of Cu often is an issue in applications of such materials, strengthening by alloying is an important topic. A very good combination of high strength and good conductivity was achieved by alloying Cu with Be. However, the problem in production and handling of such alloys is the enormous toxicity of Be. Two-phase Cu + MgCu₂ alloys were suggested as an alternative reaching nearly the same strength and conductivity values as Cu-Be alloys, see Fig. 36 [935]. Early well documented investigations of mechanical properties of Cu-based alloys strengthened by Laves phase had already been reported in a study on directionally solidified Cu + MgCu₂ alloyed with up to 4 at.% Ni [936].

Figure 36

Yield strength versus electrical conductivity for different Cu-based alloys (logarithmic plot) revealing a very good property combination for Cu + MgCu₂ Laves phase alloys (adapted with permission from [935])

At the NASA Lewis Research Center (renamed to Glenn Research Center in 1999), Cu alloys strengthened by NbCr₂ Laves phase were developed in the early 1990s as liners in rocket engine main combustion chambers [937,938,939,940,941,942,943,944]. Best properties were obtained for a Cu alloy containing 8 at.% Cr and 4 at.% Nb, which consists of a Cu matrix with about 14 vol.% of NbCr₂ Laves phase. This alloy received the brand name GRCop-84 (for Glenn Research Center Copper-8Cr-4Nb) [944]. A comparison of mechanical properties between GRCop-84 and various other Cu-based alloys with high thermal conductivity proved it to be superior to the other alloys due to its high strength and creep resistance at temperatures above 500 °C and very good ductility at room temperature [945]. Parts of this material are usually processed by consolidation of powders followed by warm-rolling or extrusion (see, for example, [946, 947]), more recently material of this alloy was also produced by additive manufacturing techniques such as selective laser melting (SLM) [948, 949]. Figure 37a shows a micrograph of GRCop-84 powder particles revealing fine NbCr₂ Laves precipitated in the pure copper matrix, and the right-hand photograph presents some parts obtained by vacuum plasma spraying of such powder [944].

Figure 37

a GRCop-84 powder obtained by gas atomization consisting of NbCr₂ Laves phase particles embedded in a pure copper matrix. NbCr₂ immediately precipitates from the molten metal when the melt temperature starts to drop. The volume fraction of NbCr₂ particles is about 14%. b In addition to extrusion and HIPing, GRCop-84 can be vacuum plasma sprayed (VPS) into complex shapes. The photograph shows a full-scale space shuttle main engine (SSME) main combustion chamber (MCC) liner and some other parts as produced by NASA Marshall Space Flight Center (pictures reproduced from [944])

A Cu-Cr-Nb alloy containing about 0.6 at.% Cr and 0.1 at.% Nb (actual composition given in wt% in the reference: Cu-0.47Cr-0.16Nb) was cold rolled to 80% reduction after homogenization at 950 °C, and aged at 450 °C for 30 min. Besides NbCr₂ Laves phase precipitates, the authors observed the formation and growth of Cr-rich precipitates during aging, resulting in a good strength of the alloy at the elevated temperature [950].

Cu-based Cu-Cr-Nb alloys containing Laves phase were also suggested as components in fusion reactors. As besides high-temperature strength and creep resistance combined with good thermal and electrical conductivity, also a suitable neutron irradiation resistance at 300–450 °C is needed, the effect of small additions of Zr (0.1 at.%) and variation of the Cr/Nb ratio was systematically investigated [951, 952].

Mg-based alloys

As a consequence of their excellent strength to weight ratio, Mg-based alloys are used in various ambient-temperature structural applications such as automotive, railway and aerospace; see, e.g., the review of Nie [953]. Thermodynamically stable binary Laves phases containing Mg are the AMg₂ phases with A = Ca, Sr, Y, Ba and the MgB₂ phases with B = Co, Ni, Cu, Zn [954]. For Mg-based materials, the ones of highest relevance are the hexagonal C14 Laves phases CaMg₂ and MgZn₂ as well as the cubic C15 Laves phase CaAl₂ [953]. The system studied in most detail is Mg-Al-Ca. Besides the two Laves phases C14 CaMg₂ and C15 CaAl₂, as-cast and high-temperature heat-treated alloys of this system also contain ternary C36 Laves phase (approximate composition Ca(Al_0.67Mg_0.33)₂), which decomposes into C14 + C15 Laves phase at lower temperatures [175, 176, 209, 955,956,957].

Three-phase Mg-Al-Ca alloys with a Mg matrix and a strengthening combination of C14 CaMg₂ and C15 CaAl₂ Laves phases were intensively discussed and characterized in detail as mechanical properties can be adjusted by the Ca/Al ratio, which controls the ratio and amount of the two Laves phase components; see, for example, [958,959,960,961,962] and references therein. According to Khorasani et al. [960, 961], CaAl₂ Laves phase is harder than CaMg₂ Laves, which explains the observation of decreasing tensile strength with increasing Ca/Al ratio in extruded material. A more complex behavior was reported by Zhang et al. [959], who performed room-temperature tensile tests and found decreasing ultimate tensile strength, elongation, and strain hardening rate with increasing Ca/Al ratio, while the yield strength showed an inverse tendency. Finally, Zubair et al. [962] reported that a higher Ca/Al ratio improves the yield strength and creep resistance, which mainly was explained by an increased volume fraction of Laves phase.

MgZn₂-containing alloys were studied to a lesser extent. This is because Mg-based alloys with Zn can contain the Laves phase only in a metastable state since the Mg-richer phase MgZn should be in equilibrium with Mg. Examples for studies on the mechanical properties of such alloys are investigations on the deformation behavior of Mg_95.9Zn_3.5Gd_0.6 and Mg_94.4Zn_3.5Gd_0.6Cu_1.5 alloys reinforced with MgZn₂ Laves phase and the icosahedral quasicrystalline I phase [963, 964]. Quaternary Mg-Al-Zn-Ca alloys with 2 wt% Ca and 8 wt% Al + Zn contained a C15- and a C36-type Laves phase. Increasing the Al content increased the amount of C36 Laves phase, and the alloy containing the majority of networked C36 phase was found to show optimal mechanical properties at both room and elevated temperature [965].

A Mg-base alloy strengthened by Laves phase was also tested for application as biodegradable medical implants. Applying the metal injection molding (MIM) technique, orthopedic implants for biomedical applications were produced from pure Mg containing 0.9% Ca, which exhibited a Mg matrix with small C14 CaMg₂ Laves phase precipitates [966].

Nb-based alloys

Because of the very high melting temperature of Nb of more than 2400 °C, Nb-based alloys are of interest for the development of materials for very high temperatures, not only to replace the currently applied Ni-based superalloys but also to go beyond. Nb forms a high-melting eutectic with the C15 Laves phase NbCr₂ (1681 °C [967]) and microstructure and mechanical properties of respective Nb + NbCr₂ alloys were studied by several authors [618, 627, 629, 913, 914, 968, 969]. To improve the fracture behavior, ternary additions such as Ti and Hf were shown to be beneficial [89, 623, 970,971,972,973].

Three-phase alloys consisting of Nb solid solution, NbCr₂ Laves phase and Nb₉(Si,Cr)₅ silicide form a ternary eutectic and respective alloys were found to have a very high creep resistance [974]. High-temperature mechanical properties of Nb-silicide containing in situ composites consisting of (Nb), Nb₅Si₃, and NbCr₂ Laves phase were reviewed by Bewlay et al. [975] and various further alloying additions such as Ti, Hf, Ge [976] or Ti, Hf, Mo, and Al [84, 977] were tested. However, fracture toughness remained as a very critical issue for these types of alloy impeding their application as structural materials.

Ti-based alloys

Laves phase containing, Ti-based alloys are especially of interest for hydrogen storage applications, see Sect. 4.1. Much less work was done regarding structural applications. Microstructure and mechanical properties of binary β-Ti (bcc) + C15-TiCr₂ alloys with high volume fractions of Laves phase were studied by Chen et al. [381, 909, 910], but this concept was not further explored later on.

A very important Ti-based alloy being in use for various structural and biomedical applications is so-called Ti64 (Ti-6Al-4 V in wt%), which does not contain Laves phase. However, in an attempt to further improve the properties, an alloy of composition Ti-6.0Al-4.5Cr-1.5Mn (wt%) consisting of α-Ti (hcp) solid solution and TiCr₂ Laves phase was developed and tested, but was found to show poor plasticity compared to other Ti-base alloys [978].

The mechanical properties of β-Ti-based Ti-Zr-Fe-X alloys (33–35 wt% Zr, 3–7 wt% Fe) with either C15 Laves phase (X = 2–4 wt%Cr [979,980,981]) or C14 Laves phase (X = 0–8 wt% Mn [981, 982] or 1–2 wt% Sn [983]) were investigated at room temperature by compression and Vickers hardness tests. From comparing the results, the authors conclude that addition of the C14 Laves phase increases the strength of the β-Ti-based alloys while the C15 Laves phase improves plastic deformability [981].

As a potential material for graded medical implants in spinal fixation surgeries, a Ti-xCr (9 ≤ x ≤ 28 at.%) graded alloy containing TiCr₂ Laves phase was additively manufactured via laser-engineered net shaping. The as-deposited alloy consisted of α-Ti and Laves phase particles in a metastable β-Ti matrix with volume fractions changing along the concentration gradient. Heat treatments of the metastable material were applied to initiate partial transformation of the β-Ti matrix allowing to adjust the Young’s modulus [984].

Zr-based alloys

Zr is widely used in the nuclear industry because of its excellent corrosion resistance, low thermal neutron cross section, and good heat resistance. Since the construction of the first nuclear reactors, Zr-based alloys are applied as cladding material for uranium fuel rods and for other nuclear applications. Well-established alloys are Zircaloy-2 (approximate composition Zr-1.5Sn-0.2Fe-0.1Cr-0.05Ni, in wt%), Zircaloy-4 (same composition but no Ni and reduced Fe content to reduce hydrogen up-take) [985], and ZIRLO™ (Zr-1Nb-1Sn-0.1Fe) [986]. Owing to the alloyed Fe, Cr and Nb, these Zr alloys contain ZrFe₂, Zr(Fe,Cr)₂ or Zr(Fe,Nb)₂ Laves phase precipitates, the presence and behavior of which strongly affect the materials properties. Therefore, detailed studies have been performed on structure and precipitation of the Laves phases [987,988,989,990,991,992,993] and on the irradiation behavior [994,995,996,997,998,999,1000,1001,1002]. It has long been known that irradiation by neutrons and bombardment by protons or various types of ions can result in amorphization of the Laves phase particles as was summarized in a review by Yan et al. [1002] (see Fig. 38). The authors assume that the irradiation initially produces single defects in the Laves phase structure and their accumulation finally results in amorphization. According to investigations by Shishov et al. [990, 999], neutron irradiation results in a transfer of Fe atoms from the Laves phase precipitates to the matrix leading to transformation and dissolution of Laves phase particles, while they did not observe any amorphization.

Figure 38

Irradiation dose to amorphization under ion irradiation as a function of irradiation temperature for Zr(Fe,Cr)₂ Laves phase precipitates (adapted with permission from the review [1002], data points were collected from various studies cited in [1002])

Zr-based, Laves phase containing alloys were also studied with respect to their behavior in nuclear waste management. Zr alloyed with 8 wt% stainless steel (Zr-8SS) was developed as a baseline waste form for Zr-based and Zircaloy-clad spent nuclear fuels [858, 861, 862, 1003]. The ZrFe₂ Laves phase was found to incorporate and immobilize highly radioactive and long-lived constituents that are present in the waste forms [858].

Intermetallic-phase-based and HEA-based materials

Fe₃Al-/FeAl-based alloys

Fe-Al alloys based on the aluminides Fe₃Al and FeAl (which are the D0₃-ordered and B2-ordered variants of the disordered bcc-Fe(Al) solid solution) have long been considered as excellent candidates to replace heat-resistant steels or possibly even superalloys in high-temperature applications up to 800 °C especially because of their excellent oxidation- and corrosion resistance even in aggressive environments [1004,1005,1006,1007]. Compared to steels and superalloys they have a lower density and are a relatively cheap material, while they suffer from their poor high-temperature strength. Strengthening by intermetallic phases such as Laves phases is one of the concepts tested to improve the properties of iron aluminide-based alloys [1005, 1007,1008,1009]. Systems in which an iron aluminide matrix can exist in thermodynamic equilibrium with a Laves phase and which have been tested with respect to the mechanical properties are those with addition of one of the metals A = Nb [1010,1011,1012,1013,1014,1015,1016], Ta [1017,1018,1019,1020], Ti [805, 1021], or Zr [807, 1013, 1022,1023,1024,1025]. The resulting C14 A(Fe,Al)₂ Laves phases either form as fine particles through precipitation from the supersaturated aluminide matrix, or—depending on the alloying amount—exist in a eutectic mixture with iron aluminide. A major problem for high temperature application of such alloys is the strong coarsening tendency of the incoherently growing Laves phase particles. In attempts to better control the precipitation and growth of Laves phase particles, small amounts of non-metallic elements such as B and C have been added resulting in formation of borides [1024, 1026] or carbides [1027,1028,1029]. In Fe-Al-Nb-B alloys containing 26–33 at.% Al, 1–2 at.% Nb, and 0.07 at.% B, the B-doping was found to lead to preferential precipitation of the Laves phase along grain boundaries and—with higher supersaturation of Nb in the Fe-Al matrix—to an even distribution of additional precipitates within the grains. However, no improvement of the high-temperature creep properties was reported [1026].

NiAl-based alloys

The cubic B2-ordered intermetallic phase NiAl was considered for gas turbine applications to replace Ni-base superalloy owing to its very high melting temperature, very good oxidation resistance, comparably low density, and a good thermal conductivity [1030, 1031]. To improve its insufficient high-temperature creep resistance, various alloying additions were tested for strengthening. This especially included the C14 Laves phase forming metals Nb [616, 1032,1033,1034] and Ta [616, 1034,1035,1036,1037,1038,1039]. The solubility of Ta in NiAl is very low and additions up to 3 at.% Ta result in Ta(Ni,Al)₂ Laves phase precipitates primarily on the grain boundaries of the B2 NiAl grains. At higher Ta contents, the Laves phase can cover the grain boundaries completely to form a continuous skeleton [1036]. Nb and Ta can completely replace each other. In a systematic study, the role of the Nb/Ta ratio as well as the additional effect of other alloying additions such as Cr, Fe, or Si were investigated [1036, 1037, 1040]. Optimum properties for application at high temperatures above 1000 °C were achieved for an alloy with a composition NiAl-2.5Ta-7.5Cr (in at.%). This alloy, which was termed IP75 and later on also patented [1041], was found to show a good combination of high-temperature strength and creep resistance, tolerable brittleness at room temperature and excellent corrosion and thermo-shock resistance at temperatures up to 1350 °C [1034, 1038, 1039, 1042]. Prototype pins for application in diesel-engine pre-chambers were produced by powder injection molding, and cast IP 75 plates were brazed to a commercial brake disk for cars, which was tested successfully under service conditions [1039]. In addition, panels were produced by investment casting and by hot isostatic pressing [1043,1044,1045,1046], and tested as liners for the combustion chamber of stationary gas turbines [1044].

Properties and further possible applications of IP75 were discussed in several more recent investigations [1047,1048,1049,1050,1051,1052]. NiAl-Ta-Cr IP75 coatings were produced by thermal spraying applying the HVOF (high-velocity oxygen fuel) technique [1047], and fiber composites consisting of single-crystal α-Al₂O₃ fibers that were PVD-coated with IP75 and hot-pressed in vacuum were tested with respect to their mechanical properties [1048, 1049]. However, a thick amorphous layer formed at the interfaces where debonding occurred making this kind of composite material unsuitable for high-temperature applications [1048]. A Cr-free variant containing additions of Nb and consisting of NiAl grains with (Nb,Ta)(Ni,Al)₂ Laves phase covering the grain boundaries was patented in 2015 for gas turbine applications [1053], but no further results about the materials’ properties were published.

TiAl-based alloys

γ-TiAl-based alloys are one of the most successful intermetallics-based structural materials, they found industrial application, e.g., as energy-saving turbine blades in the low-pressure section of jet engines. However, in contrast to FeAl and NiAl, they have a poor high-temperature oxidation resistance. Their Al content is too low to allow the formation of dense, oxidation- and corrosion-resistant Al₂O₃ surface layers, and instead fast growing TiO₂ is formed. Interestingly, the substitution of 8 or more at.% Cr for Ti in Ti-Al was found to reduce the level of Al needed for protective Al₂O₃ scale formation [1054, 1055]. This so-called “Cr effect” results from formation of Ti(Cr,Al)₂ Laves phase, which has a low oxygen permeability and is capable of alumina scale formation despite its relatively low Al content of 37–42 at.% Al [1054]. The beneficial effect of the formation of continuous Laves phase layers was later on confirmed in several studies, see, for example, [1056,1057,1058,1059]. Oxidation tests at 800 and 900 °C in air were performed on Ti-48Al-2Ag (at.%) alloys with Cr additions varying from 0 to 7 at.%. The best oxidation resistance was observed for the highest Cr content, as in this alloy a continuous Ti(Cr,Al)₂ Laves phase layer existed beneath the external Al₂O₃ scale [1056]. Smaller amounts of Cr are not sufficient to result in continuous layers, but nevertheless Ti(Cr,Al)₂ Laves phase forms as an equilibrium phase. This was shown for Ti-46.5Al-4(Cr,Nb,Ta,B)-0.22O (at.%), so-called γ-MET alloy, by thermodynamic calculations and TEM investigations revealing the formation of C14 Ti(Cr,Al)₂ precipitates on α₂/γ interfaces [1060, 1061]. Some efforts were also put into the application of Laves phase containing Ti-Al-Cr alloys as coatings for Ti-Al alloys [1058, 1059, 1062, 1063]. However, strong interdiffusion between substrate and coating at high temperatures can lead to depletion of that phase and results in poor oxidation resistance for long-term use [1059, 1063].

FeTi-based alloys

The observation of deformation-induced precipitation of C14 Laves phase in the B2 FeTi phase of a sintered Co-Fe-Ti alloy was reported in Ref. [1064]. An alloy with composition Ti-26.5Fe-10Co (at.%) was produced by spark plasma sintering and subsequently deformed under compression to a total strain of 5%. The sintered material consisted of B2 FeTi, bcc β-Ti, and cubic C15 TiCo₂ Laves phase. After deformation to 5%, additional C14 TiFe₂ Laves phase precipitates were found inside the B2 FeTi grains. TEM analysis revealed that these 30–100 nm sized Laves phase particles have coherently precipitated in dislocation walls within the deformed FeTi parent phase. Subsequent compression tests show a markedly increased strength and ductility compared to the sintered material. The authors conclude that the fine-scaled, deformation-induced Laves phase particles significantly contribute to this improved mechanical behavior [1064].

HEA-based alloys

The designation ‘high-entropy alloys’ (HEAs) was originally introduced for a group of multicomponent, equiatomic alloys forming single-phase bcc or fcc solid solutions [1065, 1066]. It was later on shown that high configurational entropy is not the critical factor for the formation of a single-phase multicomponent alloy [1067] and it actually would be better to use a more general term such as ‘multi-principal element alloys’ [1068]. Nevertheless, the notation HEA is kept until today and used for all kind of multicomponent, near-equiatomic alloys, which in many cases also contain secondary phases besides the bcc or fcc solid solution. Interestingly, it was found that these secondary phases very often are close-packed Frank–Kasper phases such as σ, µ, or Laves phases (see, for example, [1069]), and a more recent statistical analysis even proved Laves phases to be the most frequent intermetallic phase in HEAs [8]. As discussed in Ref. [181] (cf. also Sect. 3.3), the hexagonal C14 Laves phase crystal structure possesses a higher flexibility to accommodate atoms of different sizes when compared to the cubic C15 version. This might explain why the structure type of Laves phases in HEAs nearly always is of the C14 type. An exception to this rule (and the only one known to the present authors) are CrNbTiZr and CrNbTiVZr, which are reported to consist of bcc solid solution and C15 Laves phase [1070, 1071].

Discussions about criteria for the formation of Laves phases in HEAs revealed that atomic size difference, valence electron concentration, and enthalpy of mixing are the main factors defining their occurrence [9, 1072, 1073]. Gorban’ et al. [9] studied a large number of equiatomic HEAs regarding especially the role of the number of valence electrons for the occurrence of phases. Results for some HEAs with very high content of C14 Laves phase are listed in Table 6 (including some additional data from the literature), and Fig. 39 shows plots of Laves phase content as well as alloy hardness and modulus of elasticity as a function of the average valence electron concentration (VEC). The left diagram indicates a clear dependence of Laves phase content on the VEC. In a certain range between about 6 and 7 electrons/atom, single-phase C14 HEAs (sort of ‘high-entropy Laves phases’) can exist as was also confirmed in other studies [453, 1074, 1075]. Another interesting observation is that also the type of the disordered cubic solid solution coexisting with the C14 Laves phase depends on the VEC, i.e., for VECs below about 6 this is always bcc, while for VEC > 7 it is fcc. This behavior qualitatively agrees with a rule formulated by Guo et al. [1076] for single-phase, cubic solid solution HEAs saying that for VEC < 6.87 bcc is the stable structure while single-phase fcc solid solutions exist for VEC > 8.

Table 6 Composition of equiatomic HEAs with more than 50 vol.% Laves phase, average valence electron concentration VEC, hardness H, reduced modulus of elasticity E, and phase contents (data taken from [9], with additional data from [453, 455, 1074, 1075])

Figure 39

Effect of valence electron concentration of HEAs on a content of Laves phase, and b microhardness (triangles) and modulus of elasticity (squares). Diagrams adapted with permission from Gorban et al. [9] with additional data (open circles) from [453, 455, 1074, 1075]

Numerous examples for bcc + Laves phase (see, for example, [554, 557, 1071, 1077,1078,1079,1080]) as well as fcc + Laves phase (see, for example, [553, 1081,1082,1083,1084,1085,1086,1087,1088,1089,1090]) two-phase HEAs were reported in the literature. Sometimes ordering of the solid solution phase is observed as, for example, B2-ordering of the bcc solid solution in B2 + C14 Al-Cr-Nb-Ti-V-Zr [1091] or L1₂-ordering in the superalloy-type three-phase fcc + L1₂ + C14 HEA Al-Co-Cr-Fe-Nb-Ni [1092]. There are also several reports about three-phase HEAs consisting of C14 Laves phase and two different solid solutions such as bcc + fcc + C14 [1093, 1094], bcc + hcp + C14 [1095], and bcc₁ + bcc₂ + C14 [1078, 1096,1097,1098], some authors also added carbon for further strengthening by carbides [555, 556, 1099].

Regarding high-temperature structural applications, one focus is on two-phase fcc + C14 HEAs based on CoCrFeNi with additions of Nb [553, 1081,1082,1083,1084,1085, 1087, 1089, 1100], Hf [1090], Ta [1088, 1089], Mn + Nb [551, 1086], or Cu + Nb [550, 1101]. All of these alloys contain a fine eutectic mixture of a tough disordered fcc solid solution and a hard Laves phase the amount of which can be controlled by the added elements. Similar as for steels and other applied alloys, the occurrence of hard and brittle Laves phase precipitates was regarded as detrimental for a long time, see, for example, [1078]. However, today HEAs are intensively discussed as wear- and oxidation-resistant coatings for structural materials [1102], and the high hardness and excellent wear resistance of Laves phase have been recognized as very beneficial to improve the properties of such coatings [550,551,552,553,554,555,556,557].

Finally, it should be mentioned that HEAs are also under investigation as hydrogen storage material. As already discussed in Sect. 4.1, multi-element Laves phases—especially those based on Ti and/or Zr—can provide very good properties for hydrogen storage. Therefore, HEAs based on Laves phases might be natural candidates, and, e.g., a CrFeMnNiTiZr HEA containing 95 wt% C14 Laves phase can absorb and desorb 1.7 wt% of hydrogen at room temperature with a fast kinetics and without activation treatment [455]. However, in general HEAs were found to offer no especially remarkable hydrogen storage behavior compared to other Zr/Ti-based Laves phase alloys.

Conclusions and outlook

With the present review, we have tried to contribute to a better understanding of Laves phases in general and their potential for applications. Out of the huge number of possible crystal structures that can be formed from two or more metallic elements, the comparably simple and very frequently found Laves phase structures appear to play a very special role. The large number of representatives, their polytypism and their frequently extended homogeneity ranges along with their not too complicated crystal structure make Laves phases ideal candidates to study fundamentals of intermetallic phases.

Their structure, stability, and properties in case of deviation from the ideal composition were discussed here in some detail. Defects, which in most cases could be proven to be antisite atoms, may stabilize Laves phases to strongly off-stoichiometric compositions resulting in wide homogeneity ranges. The different number of available sublattices (i.e., of crystallographically different symmetry sites) of the three Laves phase structures C15 (1 A and 1 B site), C14 (1 A and 2 B sites), and C36 (2 A and 3 B sites) and the occurrence of site preference, i.e., preferred occupation of specific sublattices, result in an unequal stability of the three structure types in case of off-stoichiometry. This kind of higher structural flexibility of the hexagonal structure types can, at least qualitatively, explain the observation that A(B,C)₂ Laves phases in ternary systems in most cases have the C14 structure and those of the (A,B)C₂ type tend to adopt the C36 structure. For the same reason, Laves phases stabilized at off-stoichiometric compositions in binary systems as a second (or third) stable polytype are always C14-type Laves phases on the A-rich side, and C36 Laves phase on the B-rich side, while the cubic C15 variant is only stable at and around the stoichiometric composition.

Besides point defects, excess atoms resulting from off-stoichiometry can also be accommodated by planar defects. High-resolution TEM investigations of different kind allowed detailed investigations of structure and composition of such kind of faults revealing that they contain structural fragments of the neighboring intermetallic phases.

Another possible effect resulting from defects is related to atomic ordering or changes in the electronic structure. In such cases slight, regular distortions can result which lead to various new structure variants of the original Laves phase structure.

A very interesting and for some time controversially discussed point is the effect of off-stoichiometry on the mechanical behavior. It is now clearly proven that deviations from the ideal composition can result in softening in Laves phases. In case of the classical solid solution hardening, defects serve as obstacles for the movement of dislocations, while in Laves phases the presence of defects obviously assists the more complex plastic deformation process. Detailed investigations on plastic behavior and its composition dependence were reported in the literature, but still the reasons for the softening behavior are not completely clear.

The second focus of the review was on the role of Laves phases in functional and structural materials for real applications. The main goal was to provide a systematic overview for both classes of materials. On the one hand, this gives an idea about the manifold of possible applications, and on the other hand, it was also intended to show ‘the dark side of Laves phases’ as especially in many metal- or intermetallic phase-based structural materials, the presence of Laves phases can have a detrimental effect on the materials’ properties.

In summary, it can be stated that the fundamentals of Laves phases regarding their stability, structure and properties are still far from being completely understood, even though during recent years important new findings were reported, which led to a significant increase in knowledge about this kind of intermetallic phase. In particular, it was attempted to review and systematize this knowledge in view of the constituting elements by comparison of the data and observations for a multitude of Laves phases. Following the literature about applications of Laves phases, one finds a very diverse situation. In some cases, Laves phase materials are well established in application, as, for example, Tribaloy for wear- and corrosion-resistant coatings or Terfenol in magnetomechanical sensors and actuators. Then there is a second group of examples, in which the first step to applications has been done and material was successfully tested or is in use in some niche applications. Some examples for this group are Hydraloy and other Laves phase compounds for hydrogen storage, grain boundary precipitation-strengthened austenitic or HiperFer ferritic high-temperature steels, or IP75 as a liner for gas turbine combustion chambers. Finally, in many cases the potential of a Laves phase for a certain application has been well recognized, but the first steps into application are still missing. Due to the strong current and future need of improved or completely new materials, for example, for saving energy or reduction of greenhouse gases, one might expect and hope that the interesting, often still unexplored properties of Laves phases can help in future materials development for respective applications.