Elastic constants of polycrystalline Al and TiN calculated by an ab initio method within the local-density approximation
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ang Shen Beijing University of Science and Technology, Beijing 100083, China
Jiawen He State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China (Received 30 May 2000; accepted 24 May 2001)
The three single-crystal elastic constants of the cubic materials Al and TiN were calculated by an ab initio method within the local-density approximation of density-functional theory. The values were compared with experiment and averaged by the Kroner method to give polycrystalline results. The results agree well with experiment.
I. INTRODUCTION
Hard coatings are widely employed to improve surface performance. Among different factors, the residual stresses affect the properties of the coating layer significantly, particularly on the aspect of adhesion. The residual stress of the thin film is usually measured by x-ray diffraction (XRD), by which only the lattice strain is obtained, so that the elastic constants are required to calculate the stress value. The elastic constants are key parameters for calculating internal stress by the XRD method. The elastic constants of a thin film may be obtained by different means. If the film is of the same composition as the bulk material, it can be found from a handbook. If no bulk material is available, the elastic constants should be determined by experiment. However, the values from different sources differ greatly, which may result from different techniques of measurement. For example, for the well-known thin-film TiN, the value of Young’s modulus was widely accepted as 640 Gpa1 in Europe but in Japan the value was 250 Gpa.2,3 Usually people pay attention to the internal stress value but not the elastic constant. The same residual stress in the literature may be associated with quite different strains if the elastic constants differ. If the elastic constant of a film has to be measured, there are many factors that could affect the value of the elastic constant such as composition, microstructure, defects, texture, etc. Thus a theoretical calculation is important to calibrate the experimental value, yet very few studies can be found in the literature. In this paper, the elastic constants of pure Al were first calculated to check the procedure, the result was compared with experimental data in the handbook, and then J. Mater. Res., Vol. 16, No. 8, Aug 2001
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the TiN film was selected for calculation. If the result also agrees well with experimental results widely accepted in the literature, we could approach other kinds of thin films. The elastic constants of Al and TiN crystals were calculated by an ab initio method. Because their lattice is cubic, three deformation directions were selected to obtain the different constants c11, c12, and c44. The cohesive energy curves in the three deformation directions were calculated. The results of the second-order partial derivatives at the equilibrium points of the cohesive energy curves lead to the elastic constants of the Al and TiN single crys
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