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The department of theory of nonideal crystals was founded in 1964 under the direction of Doctor of Physics and Mathematics (since 1978 – a corresponding member of Academy of Sciences of Ukrainian SSR) Mikhail A. Krivoglaz, who had been heading the department until his death in 1988. Doctor of Physics and Mathematics, Professor M. A. Ivanov has been heading the department since 1994.

The research activity of the department is mainly connected with development of theory of real crystals (crystals with defects, alloys, amorphous substances, nanosystems, etc.) and theory of research methods of crystal imperfections and is aimed on clarification of physical properties of various imperfect crystals and quasi-crystalline systems widely used in modern physics and technology.

The bases of a large number of the department activity directions were laid by the outstanding theoretical physicist M. A. Krivoglaz. Many outstanding achievements in the field of solid state physics are connected with his name. He carried out many first-class scientific works, predicted a number of new effects, created new scientific directions which had been determining the level of world science for many years and remain relevant till present time. Here, only few of them will be summarized. For details refer a book devoted to life and scientific activity of M. A. Krivoglaz [A].

1. Theory of X-ray and thermal-neutron scattering by real crystals. In this field, M.A. Krivoglaz was, undoubtedly, a universally recognized leader; approaches he proposed are still successfully developed and used by both theorists and experimenters. He developed the method of fluctuation waves allowing to describe a variety of phenomena related to scattering of x-rays by crystals containing defects practically of all types (see monographs [Â-Ñ]). A new approach to systematization of defects in crystals, being presently generally accepted, was offered. Methods of study of short-range order and constants of interatomic interaction in solutions were developed ("Krivoglaz - Clapp - Moss Theory"). The results of these researches became the basis for new powerful methods of studies of crystal lattice defects. A large contribution to theory of x-rays scattering by deformed crystals was made by K.P. Riaboshapka. In particular, he had shown that X-ray methods could be successfully used to study dislocation structure of strongly distorted crystal systems.

2. Numerous studies were conducted in the field of theory of electromagnetic radiation absorption spectra by of impuruty centres. A theory of broadening of such lines was developed. In cooperation with S. Pekar, existence of narrow phononless lines in electronic-vibrational spectra was predicted (an optical analogue of Mössbauer effect).

3. In cooperation with A.A. Smirnov, Ì.À. Krivoglaz developed a theory of order-disorder in crystal alloys (see a monograph [Ä]). They proposed a thermodynamic and statistical theory of ordering and decomposition of alloys, a microscopic theory of diffusion in partially ordered substitutional alloys and interstitial alloys, and many other models.

4. Developing of theory of spectral distributions of elementary excitations in nonideal crystals and their relaxation properties takes a considerable place in M.A. Krivoglaz’s research works. For this purpose, a new method of double-time temperature-dependent Green functions was used. Phonon and magnon damping was found for different values of wave vector and temperature taking into account interaction of the elementary excitations with each other and their scattering by lattice defects. The dynamics of both local and quasi-local vibrations and localized spin excitations appearing in a crystal nearby point defects was thoroughly studied, together with a wide range of phenomena resulting from these excitations . A number of new relaxation mechanisms of localized excitation were proposed, first of all, the modulation mechanism (in cooperation with Ì.À. Ivanov and L.B. Kvashnina), at once experimentally discovered. Ì.À. Krivoglaz and Ì.I.Dykman developed a theory of nonlinear oscillators interacting with the medium. At the present time, this problem is still actively worked out for different applications.

A method of superoperators developed by V.F.Los to describe dynamics of small subsystems interacting with a thermostat and a theory of dynamics and energy spectra of quasi-particles (conduction electrons and phonons) in a deformed lattice containing topological defects (dislocations) studied by I.M.Dubrovskii are also related to the above range of problems.

5. An analysis of electron states in systems with the easily changeable medium parameters (in solutions, magnetic materials etc.) conducted by M.A. Krivoglaz is of fundamental importance for the solid state theory. It was shown a new type of bound states of electrons and fluctuations of medium parameters, so called fluctuons, can arise in such systems. Together with À.I. Karasevskii and B.V. Egorov, M.A. Krivoglaz developed a theory of thermodynamically equilibrium heterogeneous states . For these states, macroscopically heterogeneous distribution of an internal parameter (concentration, phase composition, magnetization, etc.) is stabilized by redistribution of the electron density. Together with D.A.Vul, he showed that long-periodic heterogeneous structures can arise in metals with flat areas of the Fermi surface.

6. In the field of theory of phase transitions, M.A. Krivoglaz developed substantially the Landau theory of critical scattering of radiation nearby phase transition points. He predicted an effect suppression of critical fluctuations in the presence of long-range of dipole forces. M.A.Krivoglaz and V.D.Sadovskii analysed an impact of strong magnetic fields on phase transformations in crystals. They obtained a formula known as “Krivoglaz-Sadovskii formula” in physical metallurgy. I. M. Dubrovskii and M. A. Krivoglaz analysed a character of second-order phase transitions in crystals containing dislocations and large-scale inhomogenuities. They proposed an idea about a phase transition in an infinite cluster of ordered areas. It allowed to explain broadening of second order phase transitions which was observed experimentally.