Separation Factors and Peclet Numbers in Evaporation Refining of Elemental Substances near Their Melting Point

On Application of Burton-Prim-Slichter Equation in Calculations of Evaporation Refining

“…Distillation and sublimation are among the main methods for obtaining high-purity substances, and therefore there is interest in their theory [1][2][3][4][5][6][7][8][9][10][11]. In the general case, these processes are described by a system of equations with two parameters: with the equilibrium separation factor β 0 and with the Peclet number Pe = vX/D, where v is the linear velocity of the evaporation surface, D is the impurity diffusion coefficient, X is the dimensional factor of the evaporated material (for example, the initial thickness of the liquid layer in the crucible).…”

“…In the general case, these processes are described by a system of equations with two parameters: with the equilibrium separation factor β 0 and with the Peclet number Pe = vX/D, where v is the linear velocity of the evaporation surface, D is the impurity diffusion coefficient, X is the dimensional factor of the evaporated material (for example, the initial thickness of the liquid layer in the crucible). Due to the complexity of the equations, their solutions cannot be obtained in an analytical form, but can be found by numerical methods [8][9][10][11]. At the same time, to describe distillation and sublimation, a simple equation is applicable with an effective separation factor β depending on the degree of distillation g [10,11]:…”

“…Due to the complexity of the equations, their solutions cannot be obtained in an analytical form, but can be found by numerical methods [8][9][10][11]. At the same time, to describe distillation and sublimation, a simple equation is applicable with an effective separation factor β depending on the degree of distillation g [10,11]:…”

“…where δ is the thickness of the near-surface layer with varying impurity concentration in the evaporated material. The similarity of the equations describing various mass transfer processes, including both crystallization and distillation, was noted [3,8,10]. However, there is a difficulty in using equation (1) in calculations of evaporation processes with an arbitrary temperature T. The difficulty is due to the fact that the values of δ and D are unknown at temperature T. Meanwhile, from the study of crystallization, it is known that at the melting point T m of a substance δ/D ~ 10 2 -10 3 s/cm [10,11].…”

“…The Burton-Prim-Slichter equation was used in calculations of evaporative refining at temperatures T = T m ±200 K under the assumption of constant δ in the specified temperature range [10]. However, it was later found that this assumption is incorrect [14] in connection with which it is necessary to rethink the results of the work [10].…”