Generalizing Ellipsoidal Growth

This paper generalizes previous work of Rios and Villa on spherical growth. The generalized equation applies to nucleation of ellipsoids according to an inhomogeneous Poisson point process. Microstructural evolution in three dimensions of nucleation and growth transformations of ellipsoids is simulated using the causal cone method. In the simulation, nuclei are located in space according to an inhomogeneous Poisson point process. The transformed regions grow with prolate and oblate ellipsoidal shapes. The ellipsoids have their corresponding axes parallel. The simulation and the exact analytical solution are in excellent agreement. Microstructures generated by the computer simulation are displayed. From these generated microstructures one can obtain the contiguity. In the contiguity against volume fraction plot, data from the sphere and all ellipsoids fall on the same curve. The contiguity curve for nucleation according to an inhomogeneous Poisson point process falls above the contiguity curve for nucleation according to a homogeneous Poisson point process. This behavior indicates that nucleation according to an inhomogeneous Poisson point process introduced a nucleus clustering effect.本文推广了Rios与Villa此前关于球形生长的研究工作。推广后的方程适用于基于非均匀泊松点过程（inhomogeneous Poisson point process）的椭球形形核过程。本文采用因果锥法（causal cone method）模拟了椭球形形核与生长转变过程的三维微观组织演化。模拟中，晶核按照非均匀泊松点过程分布于空间中。转变区域以长椭球形（prolate）与扁椭球形（oblate）的形态生长，且各椭球的对应轴保持平行。模拟结果与精确解析解吻合度极佳。本文展示了计算机模拟生成的微观组织，并可通过这些组织获取邻接率（contiguity）。在邻接率-体积分数曲线图中，球形颗粒与所有椭球形颗粒的实验数据均落在同一条曲线上。基于非均匀泊松点过程形核的邻接率曲线，位于基于均匀泊松点过程（homogeneous Poisson point process）形核的邻接率曲线之上。该现象表明，基于非均匀泊松点过程的形核方式会产生晶核团聚效应。