in the step of 0.03 are applied in the first and second strain modes, and δ from -0.04 to 0.04 in the step 0.01 are adopted in the third strain mode. Once the independent elastic constants for single crystal properties are obtained through the above procedure, the elastic moduli (e.g., the shear modulus and the bulk modulus) of polycrystalline aggregates can be estimated according to the Voigt-Reuss-Hill approximation $^{33–35}$. In the Voigt average$^{33}$, the shear modulus and the bulk modulus of cubic lattice are given by G$_{V}$ = 1 5 [( c$_{11}$ − c$_{12}$ ) + 3 c$_{44}$ ] (1) B$_{V}$ = 1 3 ( c$_{11}$ + 2 c$_{12}$ ) , (2) and while in the Reuss average 34 they are given by and with the relations c$_{44}$ = s $_{−}$1 44 , c$_{11}$ − c$_{12}$ = ( s$_{11}$ − s$_{12}$ ) $^{$_{−}$1}$, and c$_{11}$ + 2 c$_{12}$ = ( s$_{11}$ + 2 s$_{12}$ ) $_{−}$1 in the cubic lattice, where s$_{ij}$ are the elastic compliance constants. Therefore, G$_{R}$ and B$_{R}$ in the cubic lattice can be rewritten as G$_{R}$ = 5 4( s$_{11}$ − s$_{12}$ ) + 3 s$_{44}$ (3) B$_{R}$ = 1 3 s$_{11}$ + 6 s$_{12}$ (4) G$_{R}$ = [ 4 5 ( c$_{11}$ − c$_{12}$ ) $_{−}$1 + 3 5 c $_{−}$1 44 ] $_{−}$1 , (5) B$_{R}$ = 1 3 [( c$_{11}$ + 2 c$_{12}$ )] = B$_{V}$ . (6) and In the Hill empirical average $^{35}$, the shear modulus and the bulk modulus are taken as G = 1 $_{2}$( G$_{V}$ + G$_{R}$ ) and B = 1 $_{2}$( B$_{V}$ + B$_{R}$ ), respectively. Knowing G and B , the Young’s modulus E and Poisson’s ratio ν , which are frequently measured for polycrystalline materials when investigating their hardness, can be calculated from the isotropic relations: and E = 9 BG 3 B + G (7) ν = 3 B − 2 G 2(3 B + G ) . (8) 4