Curved surfaces upon dissolution as a manifestation of physicochemical properties of crystal structure
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ICAL PROPERTIES OF CRYSTALS
Curved Surfaces upon Dissolution As a Manifestation of Physicochemical Properties of Crystal Structure V. I. Rakin Institute of Geology, Komi Science Center, Ural Branch, Russian Academy of Sciences, Pervomaiskaya ul. 54, Syktyvkar, 167982 Russia email: [email protected] Received March 22, 2010
Abstract—The curved surfaces of natural diamond are described by central secondorder surfaces: a pair of planes, an elliptical cylinder, and a triaxial ellipsoid. The curved form of the elementary surface area of dia mond maps the characteristic surface of the secondrank tensor, which describes the stability of the chemical bonds of atoms on an arbitrary crystal surface during normal dissolution. Diagrams of diamond forms are pro posed for the descriptive presentation of the crystal form. DOI: 10.1134/S1063774511020155
INTRODUCTION The first quantitative description of the forms of rounded crystals of placer diamonds of the Ural–Bra zilian type was made by Fersman with the aid of goni ometry [1]. This description was based on the classical crystallographic concepts of polyhedra. The funda mental works by Shafranovskii [2] and Kukharenko [3] in the framework of this concept made a large con tribution to the study of rounded diamonds. They investigated and detailed the crystallographic charac teristics of polyhedra and compiled numerous tables of indices of flat nets that can be used to approximate the rounded diamond forms. The characteristic crystallo graphic directions in which faces become curved were revealed, and the relationship between the diamond symmetry and the form of reflection from the surface in the crystallographic projection is established. Shafranovskii approved the method of complicating simple forms to describe extended light reflections from the surface of a rounded diamond and selected 14 conditional cones with axes coinciding with the four and threefold axes of the diamond. These cones limit the reflections from the rounded faces of the diamond dodecahedra. Kukharenko established statistical regu larities in the frequencies of occurrence of particular flat nets on curved diamond surfaces. Nevertheless, the final result—a quantitative description of the roundeddiamond form—was not achieved. The method of complicating flat forms to approximate the curved surface of a Uraltype diamond crystal, which was proposed by Shafranovskii [2, 4], is difficult to implement in practice, because it is based on the cal culation of many interrelated parameters: Miller indi ces and central distances for each subface. Highparameter experiments prove that natural diamonds of the Ural–Brazilian type have a form that
corresponds to the conditions of true diamond disso lution at high pressures and temperatures in the pres ence of water [5, 6]. Note that there is an important difference between the true dissolution of crystal under thermodynamic conditions, at which the crystal can reach equilibrium with the crystallization medium, and etching a crystal with a nonequilibrium (m
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