The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture by constructing a renormalized Hamiltonian. The relative volumes occupied by each of the coexisting structures define the corresponding geometric probabilities. In the case of a frozen heterophase system these probabilities should be given a priori. And in the case of a thermal heterophase mixture the structural probabilities are to be defined self-consistently by minimizing a thermodynamical potential. This permits to find the temperature behavior of the probabilities which is especially important near the points of structural phase transitions. The presense of these structural fluctuations yields a softening of a crystal and a decrease of the effective Debye temperature. These effects can be directly seen by nuclear gamma resonance since the occurrence of structural fluctuations is accompanied by a noticeable sagging of the Mössbauer factor at the point of structural phase transition. The structural fluctuations also lead to the attenuation of sound and increase of isothermic compressibility.
I. INTRODUCTIONThere are many examples of matter consisting of regions, chaotically distributed in space, with different structural properties. For instance, such are some polymorphic materials. Another example is a crystal subject to strong mechanical stress after which the cracks and branches of dislocation are formed in it. These defects have a tendency to group inside compact regions. The latter, from the point of view of statistical physics, can be treated as nuclei of the amorphised phase inside a crystalline matrix [1]. A similar picture develops in crystals under the action of irradiation by fast neutrons when the pores and regions of disorder arise. Under strong irradiation cracks also appear. These defects form groups and clusters randomly distributed in space, e.g. as is shown in Figs. 1 and 2. For a statistical description of an irradiated crystal the defected regions can be treated as embryos of disordered, usually rarefied, phase inside an ordered, more dense, crystalline structure [2,3]. The relative volume occupied by the disordered phase can be measured, with a good accuracy, by investigating the nuclear gamma resonance spectra and the behavior of the Mössbauer factor [4,5].In the considered examples the germs of a disordered structure are randomly distributed in space inside an ordered structure. This is why these germs can be called the spatial structural fluctuations. With respect to time, they are frozen, which means that their average lifetime, τ f , is much longer than the characteristic time of an experiment, or the observation time, τ obs , that is: τ f ≫ τ obs . In the opposite case, when τ f ≪ τ obs , we have thermal structural fluctuations. The example of the latter are even more numerous than those of the frozen structural fluctuations.Water, the most widespr...