研究目的
To study the grain boundary migration and preferential grain growth in beta-tin (β-Sn) under electric current stressing using a phase field model incorporating the electrostatic free energy and the grain orientation effect.
研究成果
The phase field model developed in this study successfully simulates the grain boundary migration and preferential grain growth in β-Sn under electric current stressing. The results highlight the competition between grain boundary energy and electrostatic free energy, showing that high-density electric current can induce grain morphology instability. The study provides valuable insights into the microstructure evolution under electric current stressing, with implications for reliability analysis and design of materials.
研究不足
The study is limited by the assumptions made in the phase field model, such as the smooth variation of order parameters across grain boundaries and the constant grain boundary width. The model also assumes specific values for parameters like the grain boundary mobility pre-exponential factor, which may not be accurately known.
1：Experimental Design and Method Selection:
A phase field model incorporating the electrostatic free energy and the grain orientation effect was developed to simulate grain boundary migration and preferential grain growth in β-Sn under electric current stressing.
2：Sample Selection and Data Sources:
The study focused on β-Sn due to its anisotropic electrical conductivity properties. Simulation parameters were set based on known material properties and previous studies.
3：List of Experimental Equipment and Materials:
The study utilized computational modeling, with parameters such as grain boundary energy, activation energy, and electrical conductivity tensor derived from literature.
4：Experimental Procedures and Operational Workflow:
The partial differential equations governing grain morphology evolution and electric potential distribution were solved using the finite element method, with the backward difference formula used for time derivatives.
5：Data Analysis Methods:
The evolution of grain boundaries and the variation of voltage across the system were analyzed to understand the competition between grain boundary energy and electrostatic free energy.
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