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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. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/24924

In comparison with classical Lifshitz—Slyozov—Wagner’s theory and, where it is possible, with available experimental data, the physical kinetics of evolution of a microstructure of f.c.c.-Nі—Fe alloys is simulated by means of the Onsager-type equations of microdiffusion and with the account of the effects caused by magnetic interatomic interactions and elastic interactions of inclusions of phases. Magnetism proper in f.c.c.-Nі—Fe alloys essentially influences a tendency to atomic ordering and development of their microstructure; magnetic interactions promote stabilisation of a precipitated phase and dilate an interval of two-phase coexistence. In Elinvar alloys, elastic interactions essentially change morphology of an intermixture of formed phases of the superstructural L10 and L12 types (or of structural A1 type), giving the anisotropic character to the shape of inclusions of phases as well as to their relative spatial arrangement. Meanwhile, for an intermixture of phases of structural A1 type and superstructural L12 type in Permalloys, the anisotropic effects of such interactions are inappreciable. У порівнянні з класичною теорією Ліфшиця—Сльозова—Ваґнера і, де можливо, з наявними експериментальними даними змодельовано фізичнукінетику еволюції мікроструктури стопів ГЦК-Ni—Fe за допомогою рівнань мікродифузії Онсаґерового типу та з урахуванням ефектів, спричинених магнетними міжатомовими взаємодіями та пружніми взаємодіями вкраплень фаз. Властивий стопам ГЦК-Ni—Fe магнетизм істотно впливає на тенденцію до атомового впорядкування та розвиток їхньої мікроструктури: магнетні взаємодії сприяють стабілізації фази, що виділяється, та розширюють інтервал співіснування фаз парами. Пружні ж взаємодії істотно змінюють морфологію суміші утворених фаз надструктурного типу L10 і L12 (або структурного типу A1) в елінварних стопах, надаючи анізотропного характеру як формі вкраплень фаз, так і їхньому взаємному розташуванню; але для суміші фаз структурного типу A1 та надструктурного типу L12 в пермалоях анізотропні ефекти таких взаємодій є незначними. В сравнении с классической теорией Лифшица—Слёзова—Вагнера и, где возможно, с имеющимися экспериментальными данными смоделирована физическая кинетика эволюции микроструктуры сплавов ГЦК-Ni—Fe с помощью уравнений микродиффузии онсагеровского типа и с учётом эффектов, вызванных магнитными межатомными взаимодействиями и упругими взаимодействиями включений фаз. Присущий сплавам ГЦК- Ni—Fe магнетизм существенным образом влияет на тенденцию к атомному упорядочению и развитие их микроструктуры: магнитные взаимодействия способствуют стабилизации фазы, которая выделяется, и расширяют интервал попарного сосуществования фаз. Упругие же взаимодействия существенным образом изменяют морфологию смеси образованных фаз сверхструктурного типа L10 и L12 (или структурного типа A1) в элинварных сплавах, придавая анизотропный характер, как форме включений фаз, так и их взаимному расположению, но для смеси фаз структурного типа A1 и сверхструктурного типа L12 в пермаллоях анизотропные эффекты таких взаимодействий являются незначительными.

A kinetic model for the influence of external noise, such as fluctuations of the point-defects’ production rate and inhomogeneity of irradiated f.c.c. crystal, on the formation of modulated defect-distribution structure is considered. Defect-production rate and density of sinks for point defects are simulated as independent uniform and stationary stochastic fields with certain parameters. The interaction between vacancies is taken into account. Such stochastic fields can induce a spatial point-defects’ distribution, which is a stationary uniform stochastic field. Its mean value and correlation functions are estimated, and restricting conditions are determined when this stochastic field becomes unstable because of interaction between defect- density fluctuations and a stochastic field with a spatially-periodic mean value is formed. A formula for evaluating its spatial period is analysed. This geometrical parameter of such a dissipative structure is determined also by kinetic characteristics. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35438

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. The behaviour of k-dependent Fourier components of the strain-induced vacancy–vacancy interaction energies near the Brillouin zone centre, A(n)+B(n)k2, is analysed. As shown, A(n) < 0 and B(n) > 0 along all the high-symmetry [100], [110], [111], [½10] 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 modulatedstructure period on temperature is plotted. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/20841

The short-range atomic order for a single crystal of f.c.c.—Ni-9 at.% Al solid solution quenched from 1073 K, as well as the short-range order transformations initial stages during isothermal annealing at 373 K have been investigated using the diffuse X-ray scattering method. Specific features of the thermal two-phonon diffuse scattering have been analyzed. It is shown that in quenched state, the short-range order corresponds to the presence of concentration waves in the alloy with ordering vectors kₛ = X(001) and kₛ = (000.2). The initial ordering kinetics stages are accompanied by a considerable increasing of the short-range order diffuse intensities for vectors close to the structural one. The time dependence of the Warren-Cowley short-range order parameters, as well as local atomic configurations simulation results (using the Monte-Carlo technique), have shown that such transformations correspond to the nucleation and growth of the two short-range ordered regions: clustered (decomposing) and L1₂-type weakly ordered (Ni₃AI) ones.