Third-order elastic constants of ZnO and size effect in ZnO nanowires

Higher order elastic constants are very useful in understanding the anharmonicity of ZnO due to finite strain. The third-order elastic constants of zinc oxid (ZnO) and the size effect of the strain dependent Young's moduli of ZnO nanowires have been studied by first-principles calculations and molecular mechanics methods. The whole set of the third-order elastic constants were obtained for the first time for ZnO with homogeneous deformation method. The Young's modulus along the [0001] direction is evaluated to be Y=142.4−173.4ξ (GPa). Strain dependent Young's moduli were obtained for [0001] oriented ZnO nanowires with diameter ranged from 1.8 nm to 6.0 nm. The constant term of Young's moduli of ZnO NWs is smaller than those of the bulk, and it decreases from 121.5 to 96.7 GPa as the diameter decreases. The linear term increases rapidly as the diameter decreases and changed from negative to positive when the diameter is 3.6 nm. The linear term was −124.4 GPa when diameter is 6.0 nm, and it reached 248.8 GP...