Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel - V.A. Tatarenko; O.V. Oliinyk (Журнал нано- та електронної фізики)
The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n)  0 and Bvv(n)  0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n)  0 and Bvv(n)  0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n)  0 and Bvv(n)  0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted.