Abstract Analytical solution of the segregation problem is found for the arbitrary crystal growth law using the quasi-steady-state approximation. The segregation in this case is caused by the displacement of dissolved gas by moving plane crystallization front. The effect of solidification shrinkage on the crystallization process was taken into account. The comparison made between obtained solution and existing exact solutions shows good agreement. It is shown that in the case of “equilibrium crystallization” (when the growth rate is inversely proportional to time) the solution of the problem becomes self-similar. In this case gas concentration at the crystallization front instantly increases to a certain value and than stays the same during the whole process. At the same time the diffusion layer thickness increases proportionally to time. The conditions for the inevitability of gaseous release leading to the formation of pores in solidified material is formulated for the general case.

中文翻译：

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平面结晶前沿解析熔体中溶解气体偏析问题

摘要 利用准稳态近似，找到了任意晶体生长规律的偏析问题的解析解。在这种情况下的偏析是由移动平面结晶前沿移动溶解气体引起的。考虑了凝固收缩对结晶过程的影响。获得的解与现有精确解之间的比较显示出良好的一致性。结果表明，在“平衡结晶”的情况下（当生长速度与时间成反比时），问题的解决方案变得自相似。在这种情况下，结晶前沿的气体浓度会立即增加到某个值，然后在整个过程中保持不变。同时，扩散层厚度与时间成比例地增加。