Application of the periodic bond chain method for calculating sapphire crystallographic forms
- PDF / 375,146 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 19 Downloads / 154 Views
TAL GROWTH
Application of the Periodic Bond Chain Method for Calculating Sapphire Crystallographic Forms S. I. Bakholdin and V. N. Maslov Ioffe PhysicalTechnical Institute, Russian Academy of Sciences, ul. Polytekhnicheskaya 26, St. Petersburg, 194021 Russia email: [email protected] Received July 1, 2013
Abstract—The application of the periodic bond chain method for calculating the sequence of the develop ment of corundum single crystal faces is considered. The key role of the faces of pinacoid, high rhombohe dron, and hexagonal prisms is demonstrated. The calculated data are compared with the experimental results on faceting of the lateral surface of cylindrical sapphire single crystals grown by the Stepanov technique and with the faceting data on fluxgrown and natural crystals. DOI: 10.1134/S1063774514040038
INTRODUCTION The fine structure of crystal faces and the crystallo graphic orientation of growth surfaces play an impor tant role in solving the problems of mineral morpho genesis and obtaining crystals and films (not only from melts). In addition, the crystal anisotropy and atomic structure of crystallographic planes with different ori entations should be taken into account when process ing crystals [1]. In recent years, significant progress has been made in the study of real surfaces at the atomic level; however, simple models (wire–ball face structure and reticular density) are used to simulate faceting in practice. The faceting of real corundum crystals was studied in [2–4]. The most detailed analysis of singlecrystal sapphire rods grown by the Stepanov technique were reported in [3], where the ratio of face widths c {0001} : r {10 11} : a {1120} on the lateral surface of cylindrical sapphire crystals was found to be 8 : 4 : 1. Along with the investigations of the faceting of real crystals, there are studies devoted to theoretical faceting. In particu lar, Mackrodt [5] reported the following quantum cal culation data: c {0001} > m {00 10} > R {01 12} > a {1120} > r {10 11}. It can be seen that the theoretical and experimental results are inconsistent. Crystal morphology is known to depend on the growth rates of different faces and the variation in their size with time. In turn, the growth rate of a crystal face is determined by external and internal factors. The internal factors are the crystal structure, the presence and distribution of dislocations, and the existence of twin boundaries. The external factors are temperature; pressure; degree of deviation from equilibrium (super saturation and overcooling); influx of crystallizing particles, determined by their concentration and dif fusion in the noncrystalline phase and the degree of
their intermixing in it; and the presence of foreign materials, including solvents. The most important questions in the study of crys tal faceting are how the external morphology is deter mined by the internal crystal structure and how the external factors affect the internal characteristics of crystal and its morphology. The first question can be answ
Data Loading...
