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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 rA/rB = (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
figure1

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:

  1. (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)).

  2. (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.

  3. (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 rA/rB 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 rA/rB = 1.22 (which is very near to the ideal radius ratio of the Laves phases, see above) [50].

Figure 2
figure2

Calculated composition-versus-reduced pressure phase diagram of binary hard-sphere mixtures of large A and small B particles for a rA/rB size ratio of 1.22 (x and p are the dimensionless composition x = NB/(NA + NB) and pressure p =  3/kBT with P: pressure, σ: diameter of the A spheres). “fccA” and “fccB” 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 rA/rB = 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 rA/rB, 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 rA/rB 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 preferenceFootnote 1 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 (A1-xCx)(B1-yCy)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
figure3

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(Ni1-yAly)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(B1-yCy)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(Ni1-y-zAlyTiz)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 xA 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 AB meaning an A atom on a B site, but also

  • constitutional vacancies, denoted, for example, as VaA 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 xB 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 xB = 2/3 (xB < 2/3 or xB > 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 xB:

$$ {\text{for}}\;x_{B} < 2/3:y\left( {B_{A} } \right) = 0\quad {\text{and}}\quad y\left( {A_{B} } \right) = 1 - \frac{3}{2}x_{B} , $$
(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 AB for a molar fraction xB < 2/3 as well as antisite B atoms on A sites, BA for xB > 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 VB vacancies for xB > 2/3, which, however, could not be demonstrated to be present. Only in specific cases clear evidence for vacancies VA exist for xB < 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 xB = 2/3 as was shown by combined lattice parameter and mass-density measurements, see Fig. 4a [5].

Figure 4
figure4

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 xZn = 1 − xMg = 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
figure5

Maximum content of constitutional A vacancies in C15 ANi2 Laves phases (formula (A1-xVax)Ni2) with A = Y, La-Lu, indicating a clear correlation between this content and the atomic radius rA; redrawn from [141]

Figure 6
figure6

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 xAl = 0.58–0.82 [123]. Based on the xAl dependence of the cubic lattice parameter, it was concluded that constitutional vacancies VaAl dominate for xAl > 2/3 and constitutional antisite atoms AlY prevail for xAl < 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 xAl = 2/3 [145]. This casts some doubt on the interpretation of the xAl 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 IrY 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
figure7

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

For the Co-poor C14 polytype (xCo < 2/3), it was shown [155, 162] based on a single-crystal diffraction-based analysis (assigned crystal composition Nb1.07Co1.93) that Nb antisite atoms NbCo are located only on the Co2a sites, while the Co6h 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 (Nb0.88Co1.12), for which Co antisite CoNb 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 xCo > 2/3 with quite high Co contents [159, 161]. Due to the high content of CoNb antisite atoms, a more detailed evaluation of the diffraction data was possible based on a single crystal with assigned composition Nb0.735Co1.265 (“NbCo3”). As in the case of C14 NbCo2 (Nb1.07Co1.93), the antisite atoms are not evenly distributed over the available A sites (now: Nb4f and Nb4e, 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
figure8

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 Co2a 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 xB = 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 BA + 3VaB; 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 (BA + AB; 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
figure9

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 xCo = 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:

  1. (i)

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

  2. (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.

  3. (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(Al1-xMgx)2 [175, 176], Mg(Zn1-xPdx)2 [177], Mg(Ni1-xGex)2 [178], and Gd(Co1-xGax)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]:

  1. (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 xB = 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, NbCo antisite atoms are located very preferably on the Co2a sites of the C14 Laves phase in the Co-poor regime, and a less pronounced site preference occurs for CoNb antisite atoms in the Co-rich C36 Laves phase. Consistent with this, if a binary Laves phase assumes the C14 structure at xB = 2/3, no polytypism is encountered upon deviating from the stoichiometric composition.

  2. (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.Footnote 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
    figure10

    Occupancies of the B2a and B6h sites by Co in C14 Nb(Cr1-xCox)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
figure11

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 NbCrXz [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 NbCrXz 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.Footnote 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 BB2Footnote 4 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
figure12

Fraction of Cr sites occupied by Nb atoms y(NbCr) 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 Tb0.3Dy0.7Fe2, Terfenol-D, see Fig. 13 [273] and Sect. 4.3.1.

Figure 13
figure13

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 KBi2-xPbx (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 Bi4-2xPb2x 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
figure14

Intermetallic distances in a pair of tetrahedra within the crystal structure of KBi2-xPbx [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 KBi2-xPbx, 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 B2a and B6h (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
figure15

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(Y0.24Va0.76)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 (RbAu2.33) 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 A4Au7B2 (AAu1.75B0.5) with (A, B′) = (K, Ge) or (K/Rb/Cs, Sn) or (Rb/Cs, Pb) [334,335,336], K3Au5B′ (KAu1.67B0.33) with B′ = In, Tl, Pb [337, 338], Rb2Au3Tl (RbAu1.5Tl0.5) [338], K4Au8Ga (KAu2Ga0.125) [339], and K12Au21Sn4 (KAu1.75Sn0.33) [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
figure16

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
figure17

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
figure18

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 (yz 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 (xy 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
figure19

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/Tm (Tm 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
figure20

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
figure21

Composition dependence of mechanical properties of single-phase C14 MgZn2 Laves phase: a Microhardness HV (room temperature) [378] and upper yield stress σu (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
figure22

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
figure23

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 CoFeMnTixVyZrz (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 (Ti0.98Zr0.02Mn1.46V0.41Cr0.05Fe0.08), C51 (Ti0.95Zr0.05Mn1.48V0.43Fe0.08Al0.01) and C52 (Ti0.955Zr0.045Mn1.52V0.43Fe0.12Al0.03). 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
figure24

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
figure25

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 [