Trends in the elastic response of binary early transition metal nitrides

Motivated by an increasing demand for coherent data that can be used for selecting materials with properties tailored for specific application requirements, we studied elastic response of nine binary early transition metal nitrides (ScN, TiN, VN, YN, ZrN, NbN, LaN, HfN, and TaN) and AlN. In particular, single-crystal elastic constants, Young's modulus in different crystallographic directions, polycrystalline values of shear and Young's moduli, and the elastic anisotropy factor were calculated. Additionally, we provide estimates of the third order elastic constants for the ten binary nitrides.

Figure 1

Dependence of the ZrN elastic constants on the range $-{\delta }_{\max }\le \delta \le {\delta }_{\max }$ of deformation taken into account, and the order of the fitting polynomial. The upper and lower rows correspond to $C_{11}$ and $C_{44}$, respectively, as obtained from various approaches described in Sec. 2a.

Figure 2

Single-crystal elastic constants $C_{11}$, $C_{12}$, and $C_{44}$ and resulting Cauchy pressure, $C_{12}-C_{44}$, of the compounds investigated here.

Figure 3

Young's modulus in the $\langle 100\rangle$, $\langle 110\rangle$, and $\langle 111\rangle$ directions.

Figure 4

Zener's anisotropy ratio $E_{\langle 111\rangle }/E_{\langle 100\rangle }$ and $B/G$ values for the ten nitrides studied here.

Figure 5

3D representation of the directional dependence of Young's modulus for (a) AlN, (b) YN, and (c) TiN.

Figure 6

Calculated bulk modulus $B$, polycrystalline Young's $E$, and shear $G$ moduli. The shaded area corresponds to the Reuss's and Voigt's limit cases. The full symbols denote experimental values from literature. (${}^{\mathrm{a}}$Reference 61, ${}^{\mathrm{b}}$Reference 62, ${}^{\mathrm{c}}$Reference 63, ${}^{\mathrm{d}}$Reference 64.)

Figure 7

The polycrystalline third-order elastic constants. The shaded area corresponds, for each compound, to the spread between Voigt- and Reuss-type approach, while the solid line with data points represents Hill's average [see Eq. (24)].