Elastic constants of Al and TiN calculated by ab initio method

The elastic constants of Al single crystal were calculated by ab initio method for calibration. Three deformation directions were selected in order to obtain the different constants of c11, c12 and c44. The cohesion energy cures of the three deformation directions were calculated. The results of the second order partial differential at the equilibrium point of the cohesion energy curve provide the elastic constants of the Al single crystal. The changes of crystal symmetry and lattice can lead to the deviations of the calculated cohesion energy curves and the accurate elastic constants can not be obtained. But when the correction is taken into calculation, the calculated results are very close to the literature data. It is very difficult to obtain the elastic constants of thin films by experiment and the data from the handbook are scattered in a large scale. However, the elastic constants calculated by this method can be served as a standard. Though the errors of TiN elastic constants calculated by this method are a little higher than that for Al, the results are acceptable.