M.Dvinyaninov, V.N.Romanenko

Solidification features of high purity substances used as temperature reference points have bean considered using analytical and numerical methods. The cases of planar and cylindrical solidification are studied. A series of peculiarities is first revealed being of a certain practical interest. Calculated results are compared with available experimental data of other authors.

Аналитически и численно изучаются особенности кристаллизации особо чистых веществ, применяемых для создания реперов температурной шкалы. Изучены два случая — плоской и цилиндрической кристаллизации. При этом впервые обнаружен ряд особенностей, представляющих определенный практический интерес. Результаты расчетов сравнены с имеющимися экспериментами других авторов.

Directional solidification (DS) is widely used in many scientific and technological fields, such as crystal growth, purification, temperature reference points etc. In many cases, it is necessary to know the impurity redistribution at DS in various conditions (phase transition rate, physical properties of materials, layers width, sample geometry etc).

A number of studies have been published on this subject [1 -13]. A solution for quasi-equilibrium solidification conditions was presented by Pfann [1]. Quasi-equilibrium conditions suppose that: (a)there are no concentration gradients in the liquid phase, (b) diffusion in the solid state is negligible and (c) there are equilibrium impurity concentrations on the interphase boundary, corre -sponding to the equilibrium distribution co -efficient. The impurity redistribution for semi-infinite sample solidification at constant rate under above assumptions (b) and (c) and under account for diffusion mass transfer in the liquid phase was studied in several articles. (See, for example, Smith et

al. [2], Memelink [3], Landau [4] and Alek-sandrov et al. [5]). The most complete of them is [2]. The impurity distribution de -scribed in [2] can be used for high-speed planar solidification, when the influence of the second wall is negligible.

A number of attempts were made to obtain distribution during solidification on an infinite plate at constant speed. Analytical attempts were made by Lyubov [6], Lyubov and Timken [7], Kartashov and Lyubov [8], Kulik and Zil’berman [9]. Numerical attempts were made by Goryainov [10] and Martinson [11]. Goryainov [10] has found the solution in the form of an ordinary dif -ferential equation. Martinson [11] has solved numerically the Fick problem with a moving boundary. In our opinion, he used wrong boundary conditions. Schmidt [12] has made an attempt to use Pfann [1] and Smith [2] solution for solidification of a cylindrical sample.