Simulation of surface energies of sapphire crystals

Abstract

A new method for the express analysis of the sapphire lattice, which makes it possible to calculate surface energies of both rational directions and unfaceted surface, has been developed. The results of calcu lations have been compared with the experimental data on faceting the lateral surface of cylindrical sapphire single crystals grown by the Stepanov method.

Facet Appearance on the Lateral Face of Sapphire Single-Crystal Fibers during LHPG Growth

“…In case of an SC fiber, only unilateral faceting on the lateral surface is observed, i.e., the value of surface energy defines the formation probability of this facet. The analysis of the value of surface energy of different crystallographic planes performed according to different theoretical models yields quite different values [33][34][35][36]. At the same time, the experimental results of [16] showed a quite certain sequence of the width of the facets appearing on the lateral surface of a cylindrical crystal grown by the Stepanov method.…”

Material removal rate in polishing anisotropic monocrystalline materials for optoelectronics

“…The removal rate in polishing surfaces of optoelectronic components made of monocrystalline materials greatly depends on the crystallographic orientation of the plane being polished [13,14,21,22]. Looking at hexagonally structured crystals, e.g., sapphire (density ρ = 3.98 g⋅cm -3 , atomization energy = 731 kcal/mol, bond energy E b = 6.3 eV, lattice parameters a = 0.4758 nm, c = 1.2991 nm, c/a = 2.73 [21][22][23]), we can define how clusters (which turn into debris particles when breaking away from the workpiece surface) are made up of individual molecular fragments.…”

“…Looking at hexagonally structured crystals, e.g., sapphire (density ρ = 3.98 g⋅cm -3 , atomization energy = 731 kcal/mol, bond energy E b = 6.3 eV, lattice parameters a = 0.4758 nm, c = 1.2991 nm, c/a = 2.73 [21][22][23]), we can define how clusters (which turn into debris particles when breaking away from the workpiece surface) are made up of individual molecular fragments.…”

“…Put in other words, the debris particle that has formed in pol ishing a crystal features the minimum surface energy σ = (σ 0 and S g are the surface energy and the surface area of the nth face, respectively) [24]. Based on the values of the surface energy for the faces c, a, m, and r of sapphire-σ 0c , σ 0a , σ 0m , and σ 0r [21], we can determine the surface energy of debris particles in pol ishing a given crystal face using the respective formulas: …”

“…The static permittivity ε r and the thermal conductivity coefficient λ r for the sapphire plane r were calcu lated by the formula (α = 57.6° is the angle between the planes r and c [21,23]). The values of the static permittivity of the sapphire planes c, m, a, and r are 11.5, 9.3, 9.3, and 10.5, respectively.…”