Calculation of sublimation with allowance for impurity diffusion

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

“…It is noteworthy that in some cases β/β 0 strongly depends on the choice of the value of δ/D (100 or 1000 s/cm). Table 1, constructed using a simple equation (1), -without the use of complex calculations within the framework of the theory with β 0 and the Peclet number [9], -gives an idea of the possible values of β/β 0 for the particular case T = T m (when the temperatures of technological refining processes differ of these substances from T m by about 100-200 K). The deviation of T from T m is reflected in the value of β/β 0 due to the temperature dependences v(T), δ(T), and D(T) for the considered substance but accounting for these dependencies is not an easy task.…”

“…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]:…”

Effective and Ideal Separation Factors at Sublimation Refining of Sm, Eu, Tm, Yb

“…Sublimation is one of the main methods for obtaining high-purity substances (as well as distillation and crystallization), in connection with which interest is shown in the theory of sublimation refining [1,2]. It was shown that high-temperature sublimation (at a temperature near the melting point) is described by the same simple equations as distillation.…”

“…One of the questions of the theory of distillation and sublimation is the question of the applicability of the ideal separation coefficient β i in the calculations of these processes. The interest in using β i in the calculations of distillation and sublimation refining of simple substances is related to the fact that β i values are known for most binary systems in a wide temperature range -since vapor pressures of almost all chemical elements are known [1], while values of the effective separation coefficient β for real distillation or sublimation processes depend on many factors and cannot be calculated before the experiment (β i =p i /p, where p and p i are the vapor pressure of the base and the impurity, respectively).…”