Determination of Entropy and Debye Temperature of the Phases of Al-Cu-Co and Al-Ni-Co Decagonal Quasicrystals at the Normal and High Temperatures

This paper deals with determination of the entropy of quasicrystalline phases of Al-Cu-Co and Al-Ni-Co alloys by the information-and-statistical method at the temperature of 300 К. Scanned digital images of quasicrystals were processed with the use of this method. Statistical data of the multicomponent structure were divided into separate components of the normal distribution of parameters corresponding to certain phases. We calculated the Gaussian parameters on the basis that dependence of the logarithmic representation of the normal distribution function took the form of a quadratic function. It allowed us to find the mean-square deviation and to calculate the entropy of quasicrystalline phases at 300 К. The resulting values were further used to calculate the Debye temperature of the phases. Decagonal quasicrystals have anisotropic structure. It is assumed that anisotropy manifests itself in the difference of the dispersion laws in the xy plane and in the direction of the z axis, which is described by the model of anisotropic crystals. Using this model, we have found an expression describing the dependence of the entropy on the temperature and Debye temperature of the phases. From here, we calculated the Debye temperature of the phases. Next, using the Debye temperature values, we calculated the entropy of phases at higher temperatures. Therefore, with the use of the presented calculation methods, it is possible to determine the Debye temperature and the entropy of quasicrystalline phases that was done in our study for Al–Cu–Co and Al–Ni–Co quasicrystals. Key words: quasicrystals, entropy, Debye temperature, dispersive law, anisotropy, probability density distribution.