Electronic structure and mechanical properties of ternary ZrTaN alloys studied by ab initio calculations and thin-film growth experiments

The structure, phase stability, and mechanical properties of ternary alloys of the Zr-Ta-N system are investigated by combining thin-film growth and ab initio calculations. ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ films with $0\le x\le 1$ were deposited by reactive magnetron cosputtering in $\mathrm{Ar}+{\mathrm{N}}_2$ plasma discharge and their structural properties characterized by x-ray diffraction. We considered both ordered and disordered alloys, using supercells and special quasirandom structure approaches, to account for different possible metal atom distributions on the cation sublattice. Density functional theory within the generalized gradient approximation was employed to calculate the electronic structure as well as predict the evolution of the lattice parameter and key mechanical properties, including single-crystal elastic constants and polycrystalline elastic moduli, of ternary ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ compounds with cubic rocksalt structure. These calculated values are compared with experimental data from thin-film measurements using Brillouin light scattering and nanoindentation tests. We also study the validity of Vegard's empirical rule and the effect of growth-dependent stresses on the lattice parameter. The thermal stability of these ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ films is also studied, based on their structural and mechanical response upon vacuum annealing at 850 °C for 3 h. Our findings demonstrate that ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ alloys with Ta fraction $0.51⩽x⩽0.78$ exhibit enhanced toughness, while retaining high hardness ∼30 GPa, as a result of increased valence electron concentration and phase stability tuning. Calculations performed for disordered or ordered structures both lead to the same conclusion regarding the mechanical behavior of these nitride alloys, in agreement with recent literature findings [H. Kindlund, D. G. Sangiovanni, L. Martinez-de-Olcoz, J. Lu, J. Jensen, J. Birch, I. Petrov, J. E. Greene, V. Chirita, and L. Hultman, APL Materials 1, 042104 (2013)].

Figure 1

Formation energy $\left(E_f\right)$ of cubic ordered, SQS disordered, and hexagonal structures of ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ alloys.

Figure 2

Evolution of the lattice parameter of ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ alloys as a function of Ta fraction $x$. Open symbols refer to calculated values $(a$_calc), while filled symbols denote experimental values $\left(a_0\right)$. For binary nitride thin films, experimental data taken from the literature are also reported for comparison. (^aRef. [57], ^bRef. [28], and ^cRef. [29]).

Figure 3

Total and partial DOS of cubic ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ alloys with $x$ = 0, 0.25, 0.5, 0.75, and 1. The vertical dashed line denotes the Fermi level.

Figure 4

(a) Charge density distribution and (b) Charge density difference maps in the (100) plane of cubic ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ alloys.

Figure 5

A representative XRR scan of a ∼50-nm-thick magnetron sputtered ${\mathrm{Zr}}_{0.49}{\mathrm{Ta}}_{0.51}\mathrm{N}$ film (open blue symbols) together with best-fit scan (red line) obtained using Parratt's formalism. The inset shows the three-layer model used for the calculations.

Figure 6

(a) Evolution of XRD patterns of ∼300-nm-thick magnetron sputtered ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ films with Ta fraction $x$. The corresponding angular positions for binary cubic ZrN and δ-TaN compounds are indicated by vertical dashed lines, together with those for hexagonal ε-TaN and γ-${\mathrm{Ta}}_2\mathrm{N}$ phases. (b) Cross-sectional SEM micrographs of ZrN (left) and TaN (right) films. (c) Evolution of XRD patterns of magnetron sputtered ${\mathrm{Zr}}_{0.49}{\mathrm{Ta}}_{0.51}\mathrm{N}$ films as a function of film thickness $h_f$. The inset shows the evolution of the (200) texture coefficient, $T_{200}\hspace{0.17em}=\hspace{0.17em}{I}_{200}/(I_{200}$ + $I_{111})$, where $I_{200}$ and $I_{111}$ are the integrated intensities of 111 and 200 cubic lines, as well as the volume fraction of hexagonal phases $f$_hex with increasing film thickness.

Figure 7

Comparison of XRD patterns of ∼300-nm-thick magnetron sputtered ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ films before (open symbols) and after thermal annealing at 850 °C for 3 h under vacuum (filled symbols).

Figure 8

MOSS data during sputter deposition of ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ films with different Ta contents (a) evolution of the stress × thickness product and (b) evolution of the average stress σ_avg.

Figure 9

${\sin }^2$ψ plots of ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ films before (filled symbols) and after vacuum annealing at 850 °C for 3 h (open symbols) for $x$ = 0.24, 0.51, and 0.78. The bulk lattice parameter of ZrN and TaN reference powders is also reported. The vertical dashed line shows the intersection point (${\sin }^2$ψ₀ ∼ 0.8; $a_0$) of the ${\sin }^2$ψ lines for a given alloy composition.

Figure 10

(a) Calculated bulk modulus $B_H$ (circles), shear modulus $G_H$ (diamonds), and Young's modulus $E$ (filled squares) of ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ alloys as a function of Ta fraction $x$. The measured elastic modulus $E_m$ from nanoindentation is also reported (open squares). (b) Brittleness vs ductility map of the ${\mathrm{Zr}}_{1-x}{\mathrm{Ta}}_x\mathrm{N}$ compounds as estimated in this work (filled circles), and compared to other binary or ternary TMN from the literature (open symbols) [11, 12, 64]. Numbers in parentheses indicate the number of VEC.

Figure 11

Rayleigh surface wave velocity $V_R$ (triangles) and transverse velocity $V_T$ (circles) measured from BLS experiments as a function of Ta fraction $x$. Filled symbols refer to Ar working pressure of 0.3 Pa (this paper) whereas open symbols correspond to the values for a single-phase, cubic δ-TaN film deposited at 1.0 Pa [64].

Figure 12

Shear elastic constant $C_{44}$ measured from BLS experiments (filled symbols) as a function of Ta fraction $x$. Crosses correspond to calculated effective $\langle C_{44}\rangle$ values assuming a (111) or (200) texture. Filled symbols refer to Ar working pressure of 0.3 Pa (this paper), whereas the open circle refers to a δ-TaN film deposited at 1.0 Pa [64].