Ab-initio calculation of elastic constants of TiN

Elastic constants are important for internal stress measurement, yet the value for thin films is difficult to test by mechanical methods. In this paper the elastic constants of TiN crystal were calculated ab initio. The cohesion energy curves in three deformation directions were calculated. The results of the second-order partial differential at the equilibrium point of the cohesion energy curve lead to the elastic constants of the single crystal. The effect of Poisson's ratio or the deformation of the lattice must be taken into consideration otherwise large errors are involved. The theoretical elastic model of the polycrystalline, Kroner model, was employed to obtain the elastic constant of the polycrystalline aggregate. This study shows that the calculated elastic constants are in good agreement with the experimental data. For the X-ray diffraction method the residual stress is calculated from strain data measured and the elastic constant of a designated (hkl) plane must be known. Four-point bending was used to measure the X-ray elastic constants of (422) and (331) planes of TiN film. The calculated values were in good agreement with the experimental results. For the measurement of the elastic constants of thin films, texture and columnar grain size of the deposited film may result in a large scatter of the X-ray diffraction results. (C) 2001 Elsevier Science B.V. All rights reserved.