Vacancy Growth of a Faceted Pore in a Crystal via Chernov Mechanism
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ncy Growth of a Faceted Pore in a Crystal via Chernov Mechanism A. V. Redkova,*, S. A. Kukushkina, and A. V. Osipovb a
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199078 Russia b ITMO University, St. Petersburg, 197101 Russia *e-mail: [email protected] Received August 14, 2019; revised August 26, 2019; accepted September 18, 2019
Abstract—The vacancy growth of a faceted pore in a crystal via Chernov mechanism is studied. It is assumed that the growth is due to the diffusion of excess vacancies arising in the bulk of the crystal under the influence of mechanical tensile stress. In the framework of the formalism proposed by Chernov, the distribution of vacancies in the crystal near the step and its rate of advance are found. A connection is established between the normal pore growth rate and the applied mechanical stress. The growth due to the advance of a set of equidistant “void” steps as well as due to advance of the spiral step that arose at the exit point of the screw dislocation are considered. The results can be used to analyze the durability of materials subjected constantly to low tensile stresss. Keywords: pore, growth, vacancy, crystal, fracture, Chernov mechanism DOI: 10.3103/S0025654420010136
1. INTRODUCTION The issues of strength and durability of materials play an important role in modern materials science [1–4]. One of the many known mechanisms of crystal fracture in the high-temperature region is the vacancy mechanism, to which a significant number of works have been devoted [5–9]. In accordance with it, pore growth and coagulation occurs due to the influx of excess vacancies that form in the crystal bulk under the influence of radiation [5], elastic tensile stresses [6–9], or other processes. We note that in most works [5–9], mechanisms of nucleation and growth of mainly spherical pores are considered in detail. They make the assumption that the pore growth is limited either by the diffusion transport of vacancies to the surface of the spherical pore, or by the boundary kinetics of incorporation of vacancies into the pore, the latter being almost always considered linearly dependent on the concentration of vacancies at the surface. However, at low stresses in states close to equilibrium, the pore can become faceted to minimize surface energy [10, 11]. In this case, drawing an analogy of a pore with a faceted “void” crystal [5], one should also expect the appearance of pore growth regimes, when the boundary kinetics depends on the vacancy supersaturation in a more complicated way. For example, in [12], the faceted pore growth by the Burton– Cabrera–Frank (BCF) mechanism, that is, due to the penetration of vacancies from the crystal bulk onto the pore surface, their further diffusion over the surface, and incorporation into the step, was considered. It was shown in the paper that the pore growth rate can depend both linearly and quadratically on the applied elastic stresses. Other growth mechanisms are also possible, which also nonlinearly depend on
