Temperature Dependences of the Peclet Number in Sublimation Processes of Simple Substances

Abstract

The results of calculating the Peclet number Ре = wr/(ρD) (where D is the diffusion coefficient; w is the evaporation rate of the substance; ρ is the density of the substance; r is the size factor) in sublimation processes of simple substances with high values of vapor pressure (≈ 1 mm Hg and above at the melting temperature): As, Gd, Tm, Lu, Cr, Yb, Sm, Mg, Ra, Ca, Sr, Ni, Co, Eu, Mn, Ba. It is shown that the nature of the temperature dependence Pe(T) is determined by the properties of the components of the sublimated system “base–impurity” (including the diffusion activation energy Q of impurity). For each substance for given Q and r, the dependence Pe(T) is monotonic. A decrease in the process temperature can improve the purification of a substance from one of several impurities, accompanied by deterioration in the purification from another impurity.

On Parameters of Evaporation Refining

“…The previously presented in a number of articles [7][8][9][10][11][12] theory of evaporation refining which takes into account the difference in the vapor pressure of the components and the diffusion of impurities (but not other possible factors, for example, such as the capture of impurities by the vapor of the main component) is analyzed. It is noted that to calculate the efficiency of refining depending on the yield at a given temperature, taking into account the diffusion of impurities, a large number (nine, not counting η) of parameters of the substance and material are required: molar mass M, density ρ, melting point T m , equilibrium separation factor β 0 , vapor pressure of the main component p, the activation energy of impurity diffusion in the refined substance Q, the diffusion coefficient D m of the impurity at temperature T m and the size factor of the material X, -while the theory, which takes into account only the difference in the vapor pressure of the components, uses only one parameter close to β 0 (equation ( 5)).…”

“…Distillation and sublimation are the main methods for obtaining high-purity substances (as well as directional crystallization) for applications in electronics, and therefore there is an interest in the theory and practice of evaporation refining [1][2][3][4][5][6][7][8][9][10][11].…”

“…According to current concepts [7][8][9][10][11], the dependence of the efficiency of refining the "baseimpurity" substance on the degree of distillation at a given temperature T of the process in the general case, taking into account the diffusion of impurities in the evaporated material (but without taking into account other possible factors, for example, such as the capture impurities by the vapor of the main component or the chemical interaction of the components of the substance with the formation of volatile or non-volatile compounds) -is determined by two parameters: the equilibrium separation factor β 0 (which is considered constant) and the Peclet diffusion number Pe = wX / ρD, (1) where w is the rate of evaporation of the substance from a unit surface, D is the diffusion coefficient of the impurity, ρ is the density of the substance, X is the size factor of the evaporated material (for example, the initial thickness of the material layer in the crucible and the radius of the evaporated ball) [7][8][9][10]. The evaporation process is described by a system of equations, the solution of which can be found by numerical methods.…”

“…(3) where T m is the melting point of the substance, D m is the impurity diffusion coefficient at temperature T m , Q is the activation energy of impurity diffusion in the substance under consideration, and R is the universal gas constant [9,10]. It is generally accepted that D m ~ 10 −5 cm 2 /s during distillation and ~ 10 −6 cm 2 /s during sublimation.…”