Physics of the Solid State, 2022, Vol. 64, No. 13 08,11 Calculation of the dynamics of the amorphous phase-crystal interface during solid-phase explosive crystallization © A.A. Chevrychkina, N.M. Bessonov, A.L. Korzhenevskiy Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia E-mail: alekorzh@mail.ru Received July 5, 2021 Revised July 10, 2021 Accepted July 10, 2021 The nonlinear differential equation described a dynamics of solid-phase explosive crystallization front in a much larger parameters domain in comparison with the theoretical results available in literature was obtained. The features of the self-oscillating mode transition of the front motion to the mode of its self-propagation with a constant velocity was numerically studied in detail. Ketwords: Explosive crystallization, self-oscillations of the interface glass-crystal, self-propagating front. DOI: 10.21883/PSS.2022.13.52323.162 1. Introduction The dynamics of explosive crystallization (EC) occu- pies a special place in the kinetics of various fronts of physical or chemical nature, such as crystal growth faces, interphase boundaries during phase transitions, magnetic or ferroelectric domain walls, etc. The study of EC in amorphous phase crystallization is important, because the underlying positive feedback between the latent heat release and the front velocity plays a key role and in many other phenomena, that are more difficult to describe quantitatively, for example, in autocatalytic exothermic chemical reactions or the interaction of competing phase transitions in self- propagating high-speed synthesis [1–3]. At the same time, despite the qualitative similarity with some other diffusion- controlled processes, for example, with rapid directional solidification of liquid alloys, a more detailed analysis of EC also indicates the differences in their mathematical description. In early theoretical studies, the EC analysis was carried out under the assumption of a constant front velocity [4–6], see also review [7]. It was shown that for self-propagating EC fronts, their velocity is determined by the heat balance condition, which at certain parameters values allows for a non-unique solution [5–7]. The discovery of this circum- stance made it possible to predict the possibility of thermal hysteresis not only in the constant front velocity approxima- tion, but also in more general cases, however, fundamentally limited by the requirement of quasi-stationarity of mode, see, for example [8]. Experimentally EC was observed in films of a number of pure elements and chemical compounds belonging to materials of various classes. At the same time the typical features of the phenomenon observed on sufficiently large spatial scales and times were identified: the threshold character of the occurrence and suppression of EC, its dependence on the substrate temperature, amorphous film thickness, the method of its preparation, thermal properties of the substrate material, etc. It was found that, depending on the experimental conditions, EC can take place both in the hardness-retaining material and with the formation of an intermediate liquid phase. In addition, the process kinetics can be accompanied by the nucleation of many crystallites in an amorphous matrix or be realized by the spread of a single glass-crystal front, see, for example, [9–15]. Special attention was drawn to the experiments, in which post mortem periodic changes in amorphous films thickness and specific grain sizes in polycrystalline products EC [16] were observed. To explain these effects, an assumption was made, that they are a consequence of periodic oscillations of the front velocity [6]. The possibility of the occurrence of such oscillations was demonstrated within the framework of the analysis of linear stability of the uniform motion of plane fronts [6,17–19]. In subsequent theoretical studies, their nonlinear mode of motion was also studied for both self-propagating EC fronts and under the conditions of weak support of their motion by a mobile heat source (usually a scanning laser beam [17,20,21]). It should be noted, however, that the methods used to derive formulas are rather complicated, the formulas obtained themselves are very cumbersome and, moreover, are applicable only in very narrow ranges of parameter values, that complicates and greatly restricts their practical application. In its turn, numerical calculations performed within the framework of widely used phase field method, see, for example, [22–24] or by molecular dynamics method [25–27], are effective only for describing EC features in models of specific glasses, but do not allow generalizing predictions. In recent years significant progress has been made in the experimental possibilities of observing in situ the processes accompanying EC. It is primarily associated with the development of a new procedure (dynamic transmission 10 * 2179