Mechanical properties of engineering alloys are strongly correlated to their microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka type is one of the principal mechanisms through which the scale of the microstructural features are determined during solidification. In contrast to binary systems, in multicomponent alloys with arbitrary interdiffusivities, the growth rate as well as the maximally growing wavelengths characterizing these instabilities depend on the the dynamically selected equilibrium tie-lines and the steady state growth velocity. In this study, we derive analytical expressions to characterize the dispersion behavior in isothermally solidified multicomponent (quaternary) alloys for different choices of the inter-diffusivity matrices and confirm our calculations using phase-field simulations. Thereafter, we perform controlled studies to capture and isolate the dependence of instability length scales on solute diffusivities and steady state planar front velocities, which leads to an understanding of the process of length scale selection during the onset of instability for any alloy composition with arbitrary diffusivities, comprising of both independent and coupled diffusion of solutes.
Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability
在包晶合金定向凝固过程中，两个稳定的固相（母相和包晶相）竞争生长成亚稳液相，其杂质含量大于任何一个固相。当母相或两个固相在形态上不稳定时，即，对于小的温度梯度/生长速率比（$G/v_p$），一个固相通常生长出并覆盖另一个相，导致与在稀二元合金的单相凝固过程中形成的胞状-枝晶阵列结构非常类似的胞状-枝晶阵列结构。相反，当$G/v_p$大到足以使两相形态稳定时，微结构的形成受到两个固相的成核和生长之间的微妙相互作用的控制。在这种情况下观察到的结构（在对流效应被抑制的小样品中）包括垂直于生长方向的母相和周相的交替层（带），其通过一个相交替成核和横向扩散到另一个相上而形成，如最近的模型[R. Trivedi，Metall. Mater. A 26，1（1995）]，以及部分填充的带（岛），其中周晶相不完全覆盖连续生长的母相。我们开发了一个相场模型，结合成核过程，以探索这些结构的形成的周向凝固。该模型的模拟揭示了从岛屿到乐队的形态过渡，在母相上的成核后，这原来是由一个显着的恒定的加速度，和生长形态的类型，人们可能会期望在纯扩散生长条件下观察到的大样品的周边相的传播的动态。
A level-set formulation to simulate diffusive solid/solid phase transformation in polycrystalline metallic materials -- Application to austenite decomposition in steels
