Visnyk of the Lviv University. Series Physics 60 (2023) ñ. 3-17
DOI: https://doi.org/10.30970/vph.60.2023.3

Study of elastic and acoustic characteristics of AgAlTe2 crystal

Ì. Rudysh

(íå ìåíøå 1800 çíàê³â) The work is devoted to the theoretical study of the elastic and acoustic properties of the AgAlTe2 crystal from the first principles. The studies were carried out using the CASTEP program, which is based on density functional theory (DFT). Within the framework of the chosen approach, using the BFGS method, the optimization of the crystal structure was carried out using the local density approximation (LDA) and the generalized gradient approximation (GGA) to describe the exchange-correlation interaction of electrons. During the optimization, both the parameters of the crystal lattice and the coordinates of the atoms were changed. The optimized crystal structure turned out to be close to the experimental one presented in the literature. It was found that the optimized parameters of the crystal lattice differ slightly from the experimental ones. Using the GGA functional leads to an overestimation of 1.9\% and 3.9\% for parameters a and c, respectively. For the LDA functional the lattice parameter a is underestimated by 1.3\%, while the value of parameter c is 1.5\% higher than the experimental one. Using the standard method, the elements of the matrix of elastic constants, Young's modulus E, bulk modulus B, shear modulus G, and Poisson's ratio v were calculated and analyzed for the investigated crystal in tetragonal symmetry. It is shown that the Pugh’s ratio for the studied material is BH/GH > 1.75, from which it follows that this material has inherent plasticity. Using the universal anisotropy index AU, the degree of anisotropy of elastic properties is shown. It was found that for both used methods the universal anisotropy index is different from zero, which indicates the anisotropy of the elastic properties of the AgAlTe2 crystal. A detailed analysis of anisotropy is carried out using the construction of 3D surfaces and their planar projections for various parameters. Spatial distributions of Young's modulus E, bulk modulus B, and shear modulus G are plotted. B is shown to be nearly isotropic, while E and G exhibit significant anisotropy of the opposite character. Using the calculated matrix of elastic constants Cij and solving the Green-Christoffel equation, the speed of acoustic plane waves propagation in the crystal was calculated. Planar projections of the velocity V in the (100) and (001) planes were constructed and their anisotropy was discussed.

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