1 Introduction

Conventional hard coatings like TiN and CrN are extensively employed to augment the performance of cutting tools [1, 2]. However, their efficiency is hindered by limited oxidation resistance or strength. To counteract these deficiencies, the addition of Al to TiN and CrN has emerged as a pivotal strategy, giving rise to the formidable (Ti,Al)N and (Cr,Al)N coatings [3,4,5,6]. These innovations exhibit a remarkable enhancement in oxidation resistance and performance for various industrial applications.

For example, high-speed, dry cutting applications demand coatings with low friction, high-temperature oxidation resistance, and excellent mechanical properties. (Cr,Al)N coatings surpass (Ti,Al)N due to their superior tribological properties [7], especially in Al-rich compositions, enhancing stability at high temperatures. Despite slightly lower hardness than (Ti,Al)N, (Cr,Al)N coatings endure higher temperatures, forming protective oxides. However, they face limitations due to Cr‑N bond dissociation starting around 900 °C.

Alloying transition metals to CrN-based coatings, such as Cr1-xAlxN or Cr1-yTMyN (transition metal, TM = Ti, Ta, Zr, Mo, W, V), enhances structural and mechanical properties [4, 7,8,9,10,11,12,13,14,15,16,17]. For instance, a Mo or W addition improves the tribological properties and toughness by forming Magnéli-phase oxides acting as solid lubricants [9, 10, 16]. Yet, debates persist on their crystallographic structures. Alloying elements like Y, Ti, Zr, V, Ta, Mo, and W to (Cr,Al)N coatings show varied effects on properties such as oxidation resistance, friction, and hardness [18,19,20,21,22,23,24,25,26,27,28]. Yttrium enhances the thermal stability and oxidation resistance, but an excessive incorporation can be detrimental [21]. Similarly, V addition leads to lubricious effects [29,30,31], while Zr alloying affects the oxidation progression [32]. These alloying strategies present avenues for enhancing the performance of (Cr,Al)N coatings. Further research is needed for a comprehensive understanding of their effects.

In the quest of ongoing research, the efficiency of alloying elements continues to be scrutinized, yielding nuanced insights into their impact on the performance landscape of (Cr,Al)N coatings. This relentless pursuit of excellence underscores a collective commitment to innovation and progress in the realm of advanced materials science.

Here, we further extend the calculational alloy design by studying alloying effects of IIIB, IVB, and VB transition metal elements (TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) on Cr1-xAlxN materials. The impact of such a fourth element on the phase stability as well as structural and mechanical properties of (Cr,Al)N is systematically discussed using ab initio calculations. In this contribution, we deliberately avoid group VIB alloying elements, which form substoichimetric nitrides and thereby make the ab initio evaluation significantly more extensive. Examples of such treatments for Mo-Cr-Al‑N can be found in Ref. [33].

2 Calculational Methods

The chemical disorder between Cr, Al, and TM atoms on the metal sublattice of the face centered cubic (fcc) B1 structure (NaCl prototype, space group Fm\(\overline{3}\)m), and also the paramagnetic state induced by Cr atoms are obtained by the special quasi-random structures (SQS) approach [34, 35] as implemented in our previous studies [36, 37]. Mixing of Cr↑, Cr↓, Al, and TM atoms takes place on the metal-sublattice while the nitrogen-sublattice is fully occupied with N atoms. 4 × 3 × 2 (48 atoms) and 3 × 2 × 2 (48 atoms) supercells are used for the cubic B1 and hexagonal close packed (hcp) wurtzite B4 Cr1-x-yAlxTMyN structures, respectively. The short-range order parameters (SROs) are optimized at least up to the fifth coordination shell.

The Density Functional Theory-based calculations are performed using the Vienna Ab initio Simulation Package (VASP) [38, 39]. The ion-electron interactions are described by the projector augmented wave method (PAW) [40] with an energy cutoff of 500 eV, and the generalized gradient approximation (GGA) for the exchange-correction effects as parameterized by Perdew-Burke-Ernzerhof (PBE) [41]. The k-point meshes are 5 × 6 × 7 and 5 × 8 × 4 for the cubic B1 and the wurtzite B4 structures, respectively. The energy convergence criterion for the electronic self-consistency was set to ~0.1 meV/atom. The structural models were fully optimized with respect to cell shape, cell volume and atomic positions.

3 Results and Discussions

3.1 Impact of TM Additions on Maximum Al Solubility in the Cubic Phase

The stability of the quaternary systems is determined from their energy of formation, Ef, calculated as:

$$E_{f}=E_{{Cr_{1-x-y}}{Al_{x}}{TM_{y}}N}-0.5\left[\left(1-x-y\right)E_{{Cr^{\mathrm{bcc}}}}+xE_{{Al^{\mathrm{fcc}}}}+yE_{{TM^{\xi }}}+0.5E_{{N_{2}}}\right]$$
(1)

where \(E_{{Cr_{1-x-y}}{Al_{x}}{TM_{y}}N}\) is the total energy per atom of Cr1-x-yAlxTMyN, \(E_{{Cr^{\mathrm{bcc}}}}\), \(E_{{Al^{\mathrm{fcc}}}}\), and \(E_{{TM^{\xi }}}\) are the total energies of the respective elements in their stable configurations. \(E_{{N_{2}}}\) denotes the total energy of a nitrogen molecule. Figure 1 presents the maximum AlN content x in the fcc-Cr1-x-yAlxTMyN phase as a function of the TM content y based on the energy of formation differences between B1 and B4 structures, evaluated according to Eq 1. Clearly, all elements cause a decrease of the maximum Al solubility in the fcc-Cr1-x-yAlxTMyN phase. We ascribe this to larger lattice distortions resulting from the typically larger atomic radius of the IIIB, IVB, and VB TMs than that of Cr and Al.

Fig. 1
figure 1

The maximum AlN content (AlNmax, xmax) in the fcc-Cr1-x-yAlxTMyN phases as a function of their TM metal-fraction, y. The horizontal dotted lines denote the maximum AlN content in the fcc-Cr1-xAlxN phase. The figure is divided into (a), (b), and (c) panels, according to the TM groups, IIIB, IVB, and VB, respectively

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For our studies, the alloying effect of TM elements on the fcc-Cr1-xAlxN phase, the presentation of the quaternary Cr1-x-yAlxTMyN phases within a pseudo-binary system of Cr1-xAlxN and TMN is more illustrative. The influence of Ti and V on the maximum solubility of Al is significantly smaller than that of the other elements. Our results suggest that the lattice parameters exhibit a major role in promoting either the B1 or B4 structure (the B4 structure, wurtzite-type, has a significantly larger specific volume), although the binding characteristics are important as well.

The nitrides VN and TiN exhibit the smallest lattice parameters among the alloying TMN’s studied here, with a = 4.128 and 4.252 Å, respectively. These are very similar to that of Cr1-xAlxN with a between ~4.11 and 4.16 Å for Al-contents x between 0.7 and 0.0, respectively.

The TMN’s of IIIB (ScN), IVB (ZrN, HfN), and VB (TaN, NbN) have very comparable effects on the phase stability ranges, due to their very similar lattice parameters of 4.423–4.618 Å, Table 1. The addition of YN to Cr1-xAlxN causes a pronounced reduction of the maximum Al solubility, because YN exhibits also the largest lattice parameter of 4.920 Å.

TABLE 1 The lattice parameters a of the fcc-TMNs and the bowing parameters b to calculate with Eq 2 the lattice parameters ay of fcc-(Cr0.5Al0.5)1-yTMyN (with TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta). \(a_{{Cr_{0.5}}{Al_{0.5}}N}\) = 4.1155 Å
Full size table

3.2 Structural Properties

As mentioned in the section above, the quaternary Cr1-x-yAlxTMyN alloys can be treated as pseudo-binary systems between Cr1-xAlxN and TMN, which provides a straightforward approach to quantify the alloying effect of TMs on the structural and mechanical properties of Cr1-xAlxN. The following calculations were performed for the (Cr0.5Al0.5)1-yTMyN systems with a compositional step of ∆y = 1/6. The calculated values were fitted with a quadratic polynomial after:

$$a_{y}=y\cdot a_{TMN}+\left(1-y\right)\cdot a_{{Cr_{0.5}}{Al_{0.5}}N}+b\cdot y\cdot \left(1-y\right)$$
(2)

where b is a bowing parameter describing the deviation from the linear Vegard’s-like behaviour, aTMN and \(a_{{Cr_{0.5}}{Al_{0.5}}N}\) are the lattice constants of TMN and Cr0.5Al0.5N, respectively, and ay is the lattice constant of (Cr0.5Al0.5)1-yTMyN.

Figure 2 presents the lattice parameters of (Cr0.5Al0.5)1-yTMyN (TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) phase as a function of TMN content, and the corresponding bowing parameters are listed in Table 1. The bowing parameters of (Cr0.5Al0.5)1-yTMyN with TM = Sc, Ti, and V, are significantly smaller than those for the other systems. Consequently, these systems provide the most linear behaviour out of these systems, in agreement with the results obtained for Sc, Ti, and V alloyed Cr‑N reported in Ref. [42]. We speculate that this is related to the fact that the covalent sp3d2 hybridization is formed from the same d orbitals supplied by 3d group TM elements.

Fig. 2
figure 2

Calculated equilibrium lattice parameters a for fcc-(Cr0.5Al0.5)1-yTMyN (TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) solid solutions as a function of their TM metal-fraction, y. The horizontal dotted lines denote a of fcc-Cr1-xAlxN. The figure is divided into (a), (b), and (c) panels, according to the TM groups, IIIB, IVB, and VB, respectively

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VN has almost the same lattice constant as Cr0.5Al0.5N and hence there is only a minimum variation of the lattice constant of (Cr0.5Al0.5)1-yVyN with VN mole fraction, y. Cubic lattice parameters of (Cr0.5Al0.5)1-yTMyN (with TM = Y, Zr, Hf, Nb, and Ta) systems exhibit a distinct bowing towards larger values, hence, a distinct positive deviation from the Vegard’s estimations. This behaviour suggests that compressing larger compounds is energetically more expensive than expanding smaller ones, which is in agreement with the slightly asymmetric bonding energy potential curve.

The lattice parameters, as given in Fig. 2 and Table 1 by the bowing parameter b for Eq 2, provide useful information for designing coatings, and especially for the interpretation of experimental observations.

For example, the nearly constant behaviour of the lattice constant of (Cr0.5Al0.5)1-yVyN with VN mole fraction could be potentially interesting for epitaxial, coherency stress-free multilayers of (Cr0.5Al0.5)1-yVyN and VN.

3.3 Ductility Criteria

The alloying effect of TMNs on the mechanical properties is discussed in terms of impact on ductility or brittleness. The single-crystal elastic constants, Cij, were calculated employing the stress-strain method as described in Refs. [36, 43]. Subsequently, the isotropic equivalents of polycrystalline properties are computed via the self-consistent Hershey approach from single-crystal elastic constants [44].

According to the criteria proposed by Pettifor [45] and Pugh [46], positive Cauchy pressure (CP = C12–C44 > 0) values, and bulk-to-shear moduli ratios (B/G) above 1.75 indicate a ductile behaviour of materials, respectively. Consequently, our results suggest that alloying IVB and VB group elements (Ti, Zr, Hf, V, Nb, and Ta) significantly increases the B/G ratio and the Cauchy pressure of Cr0.5Al0.5N, see Fig. 3a and b, respectively.

Fig. 3
figure 3

The bulk-to-shear moduli ratio B/G (a) and the Cauchy pressure CP = C12–C44 (b) of fcc-(Cr0.5Al0.5)1-yTMyN (with TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) solid solutions as a function of their TM metal-fraction, y. The horizontal dotted lines mark the ductility criteria B/G > 1.75 and CP > 0 GPa

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But only for the addition of VB nitrides, VN, NbN, and TaN, B/G ratios above 1.75 and positive Cauchy pressures (C12–C44 > 0) are obtained. Especially TaN exhibits an extremely positive effect on the ductility of Cr0.5Al0.5N, as already for additions of y ~ 0.2, the Pettifor and Pugh criteria are obtained. This can be attributed to the changes of the bonding characteristic: IVB elements decrease the directional character slightly while VB elements even revert the dominant character to metallic bonding. Alloying Cr1-xAlxN with group IIIB elements (Sc and Y) causes no improvement in ductility, as the B/G ratio as well as the Cauchy pressure is almost unchanged over the whole composition range.

The alloying impact on the brittle/ductile trends of our Cr1-xAlxN is closely related with their changes in the electronic structure. Sangiovanni et al. pointed out that there is a relationship between the Cauchy pressure and the valence electron concentration (VEC), suggesting that improved ductility can benefit from higher VEC [47,48,49]. However, it is not always the case that higher VEC shows higher ductility. Cubic (Cr0.5Al0.5)1-yTMyN with TMs from the same group have all the same VEC, while their ductile behaviour differs. The most prominent example is (Cr0.5Al0.5)1-yTayN with significantly higher B/G and Cauchy pressures (hence, higher suggested inherent ductility) than (Cr0.5Al0.5)1-yVyN, although both elements belong to VB. The positive effect of Ta on fracture toughness has been experimentally discussed in Ref. [24]. This is because the essence of inherent ductility is related with the bonding character rather than with VEC. Consequently, the key point for ductility is to analyze the bonding character, as conducted here for (Cr0.5Al0.5)1-yTMyN.

Figure 4 presents the total density of states (DOS) of fcc-Cr0.42Al0.42TM0.16N (with TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) along with the comparison to the fcc-Cr0.5Al0.5N reference material. Alloying Sc and Y to fcc-Cr0.5Al0.5N has a much smaller effect on their electronic structure than alloying other TMs. By the addition of Sc and Y, the band gap is almost unchanged and open. This may be understood by the fact that both nitrides, ScN and YN, are semiconductors on their own. Furthermore, also the directional bonding character of Cr0.5Al0.5N is unchanged, and hence there is no improvement of the ductile behaviour.

Fig. 4
figure 4

The total density of states (DOS) of fcc-Cr0.42Al0.42TM0.16N (with TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) phase (solid lines). The red dash dotted lines denote the total DOS for fcc-Cr0.5Al0.5N as a reference

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The addition of IVB elements increases the metallic behaviour by occupying some conduction band states. Thereby, metal-metal d-d bonding is enhanced and the ductility of fcc-Cr0.5Al0.5N increases. However, there is a large pseudo-gap very close to the Fermi level (EF) for Ti, Zr, and Hf alloyed fcc-Cr0.42Al0.42TM0.16N (TM = Ti, Zr, and Hf), which represents the semiconducting character and limits the improvement of the ductility.

However, alloying fcc-Cr0.5Al0.5N with group VB elements even closes this pseudo-gap. Hence, a fully metallic behaviour is obtained leading to the enhanced ductility. Furthermore, the addition of Nb and Ta induces a peak splitting at the Fermi level together with a development of a second peak just above the Fermi level, which stems mainly from their TM d-states. This is similar to the behaviour reported for the Ti1-x-yAlxTMyN (TM = Nb and Ta) quaternary system [50,51,52]. The peak splitting indicates a significant enhancement in metal-metal d-d bonding. Therefore, the alloying of Cr0.5Al0.5N with Nb and Ta is superior with respect to ductility improvement than the alloying with the same VB group element V.

4 Conclusions

The alloying effect of transition metal elements from the groups IIIB, IVB, and VB on the phase stability, structural, and mechanical properties of fcc-Cr1-xAlxN is investigated in detail by ab initio calculations. Our results clearly show that the maximum solubility of Al within fcc structured Cr1-x-yAlxTMyN (with TM = Sc, Y, Ti, Zr, Hf, V, Nb, and Ta) mainly depends on the lattice parameter of the corresponding fcc-structured TMN. The addition of Y significantly decreases the maximum solubility of Al within fcc structured Cr1-xAlxN, while the addition of V and Ti has the smallest effect among the TMs studied. The lattice parameters of quaternary fcc-Cr1-x-yAlxTMyN increase both from 3 to 5d as well as from IIIB to VB. This behaviour suggests a combined effect of valence electrons and atom size on the lattice parameters of fcc-Cr1-x-yAlxTMyN. More pronounced is the obtained effect on the ductility, which significantly increases by the addition of Ta or Nb, as thereby the bonding character of fcc-Cr1-xAlxN massively changes towards metallic. Based on our results we can conclude that even for the same valence electron concentrations a different ductile behaviour is obtained, as the individual elements have a different effect on the binding characteristics, which determine ductility.