双边扩散枝晶生长的定量相场模型

Quantitative phase-field model for dendritic growth with two-sided diffusion

本文针对非对称双边扩散条件下的二元合金枝晶生长,建立了一个包含溶质截流项的定量相场模型.本模型耦合了非线性热力学函数并采用化学势相等的界面条件.通过对相场方程进行二阶的薄界面渐进分析,并结合溶质拖拽模型,推导出相场迁移率和溶质截流项.随后将模型简化为二元稀溶液合金等温枝晶生长的相场模型以对其进行理论验证.通过在各种相场界面厚度条件下进行数值模拟,测试了本模型的数值收敛性.用所建立的模型模拟了Fe-0.15mol%C合金的等温枝晶生长,将相场模拟结果和经典Gibbs-Thomson关系,线性可解性理论以及改进的Lipton-Glicksman-Kurz(LGK)解析模型进行比较,取得了良好的符合.模拟结果表明本模型能有效地消除延拓的界面厚度所导致的界面异常效应,具有良好的定量模拟能力.而且,本模型能够定量地描述从单边扩散到对称扩散的各种固相扩散迁移率条件下的枝晶生长.

A quantitative phase-field （PF） model with an anti-trapping current （ATC） is developed to simulate the dendritic growth with two- sided diffusion. The asymptotic analysis is performed at the second-order for the PF equations coupled with nonlinear thermodynamic properties and an ATC term under the equal chemical potential condition. The PF mobility and ATC are derived based on the asymptotic analysis in the thin interface limit, and the solute drag model. Then the model is reduced to the dilute solution limit for dendrite solidification of binary alloys. The test of convergence with respect to the interface width exhibits an excellent convergent behavior of the proposed model. The performance of the model is then validated by comparing PF simulations with the predictions of the Gibbs-Thomson relation, the linearized solvability theory, and the modified-Lipton-Glicksman-Kurz （M-LGK） analytical model, for the isothermal dendritic growth of an Fe-0.15 mol%C alloy. The results demonstrate quantitative capabilities of the model that effectively suppresses the abnormal solute trapping effect when the interface is taken artificially to be wide. It is also found that the present model can quantitatively describe dendrite growth with various solid diffusivities, ranging from the case with one-sided diffusion to the symmetrical model.