Further Studies on the Solution Anisotropy and the Shape of Solution Bodies in Tetragonal, Hexagonal, and Rhombohedral Crystals

Abstract

It is shown that the anisotropy of the solution rate along any direction, υ, and that of the radius vestor along the same direction, γ, from the origin to the circumference of a solution body produced from an originally sphere crystal, are generally expressed by υγ=υ_cγ_c•cos⁴θ+(υ_aγ_a•cos²2φ+υ_bγ_b•sin²2φ)sin⁴θ+(4•υ_dγ_d-υ_cγ_c-υ_aγ_a)cos²θsin²θ for tetragonal crystals, by υγ=υ_cγ_c•cos⁶θ+(υ_aγ_a•cos²3φ+υ_bγ_b•sin²3φ)sin⁶θ+1/3(24•υ_dγ_d-8•υ_eγ_e-10•υ_cγ_c+3•υ_aγ_a)cos⁴θsin²θ+1/3(-8•υ_dγ_d+24•υ_eγ_e+3•υ_cγ_c-10•υ_aγ_a)cos²θsin⁴θ for hexagonal crystals, and by υγ=υ_cγ_c•cos⁶θ+(υ_aγ_a•cos²3φ+υ_bγ_b•sin²3φ)×sin⁶θ+1/3{12(υ_dγ_d+υ_gγ_g)-4(υ_eγ_e+υ_fγ_f)-10•υ_cγ_c+3•υ_aγ_a}cos⁴θsin²θ+1/3{-4(υ_dγ_d+υ_gγ_g)+12(υ_eγ_e+υ_fγ_f)+3υ_cγ_c-10υ_aγ_a}cos²θsin⁴θ+(4/√3){-(υ_dγ_d-υ_gγ_g)+(υ_eγ_e-υ_fγ_f)}cosθsin³θcos3φ+(16/3√3){3(υ_dγ_d-υ_gγ_g)-(υ_eγ_e-υ_fγ_f)}cos³θsin³θcos3φ for rhombohedral crystals, where θ and φ are, respectively, the polar and azimuthal angles of the direction referred to a polar coordinate system of which the polar axis and zero line for φ are, respectively, the [001]and [100]axes for tetragonal crystals, the [0001]and [1010]axes for hexagonal crystals, and the [111]and [211]axes for rhombohedral crystals.