Transitions between equilibrium and nonequilibrium phenomena in the description of crystal growth

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Abstract

The close intertwining of equilibrium and nonequilibrium thermodynamic representations and transitions between the two limiting principles of thermodynamics: the second beginning and the principle of least coercion (minimum entropy production in the stationary regime) constitute the main content of phenomenological theories of crystal growth. The difference of basic postulates of two sections of thermodynamics forces to discuss problems of reversibility and irreversibility of time, scales of observed phenomena and rules of conjugation of thermodynamic forces and flows in theories of crystal growth. A variant of the solution of some conjugation problems is shown on the example of the fluctuation model of dislocation crystal growth, which is based on the stationary isothermal process of thermodynamic free energy fluctuations. In the case of the limiting mode of adsorption of impurities on the crystal face according to the Langmuir model, the free energy fluctuations possessing the absence of the memory effect allow us to identify three chemical potentials of building particles that determine the corresponding values of solution supersaturations realized at different scale levels at the growing crystal face containing a helical dislocation. The supersaturations control quasi-equilibrium and nonequilibrium thermodynamic processes that constitute a single dislocation mechanism of crystal growth.

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About the authors

V. I. Rakin

Institute of Geology FRC Komi SC UB RAS

Author for correspondence.
Email: rakin@geo.komisc.ru
Russian Federation, Syktyvkar

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Supplementary files

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2. Fig. 1. Arrangement of surface atoms around a screw dislocation on a face with tetragonal symmetry. The first layer of the nearest 16 atoms is shown. The atoms in direct contact with the dislocation are highlighted in dark color here and in Table 1.

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3. Fig. 2. Interferogram of polygonal growth pyramids of two screw dislocations on the surface of the (111) face of alum. The spatial frequency of the interference fringes is proportional to the frequency of the elementary steps. The lower dislocation (black arrow) has a Burgers vector twice as large, and its growth pyramid actively absorbs the upper pyramid (white arrow). The angle between the base surface of the face of the octahedron of alum and the inclined flat face of the growing pyramid, which is a simple crystallographic form of tetragontrioctahedron, usually varies in the range from 10 to 20 angular minutes [14].

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4. Fig. 3. AFM image of a potassium biphthalate face obtained in [3]. The dots mark the exits of four dislocations with a unit Burgers vector. Crystallographic directions are highlighted in accordance with the symmetry of the face described in [24].

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5. Fig. 4. Kinetics of crystal facet growth of aluminum-potassium alum in an aqueous solution with active stirring, obtained using a Michelson interferometer [23]. T = 20°C. Facets of simple shapes: 1 – {111}, 2 – {100}, 3 – {110}.

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