透過相場晶體模型模擬，我們發現在受橫向應變的雙晶體系統中晶界會產生形態不穩定性。我們發現晶界結構轉變和位錯發射。定量上，我們研究擾動的增長率並確定了臨界應變量。另外，我們發現幅度依賴的增長率和在位錯發射之前形成的特定三角形輪廓，這些觀察結果通過重合點網格方法的分析，並可被搓板位勢模型預測。同時，我們構建了不穩定行為的相圖。為了理解潛在的機制，我們提出軟邊界模型並理論上分析此模型。此最簡理論定量地預測擾動的增長率和相圖中相界。它還表明此不穩定性應該是由彈性能量梯度驅動而此梯度是由不均勻的應變分佈所引起。最後，此理論預測的應變分佈與模擬觀察結果非常吻合。

Morphological instability of grain boundary is observed in bicrystal systems subject to lateral applied strains by using the simulation of phase field crystal model. The grain boundary structural transformation is discovered and the dislocation emission is observed. Quantitatively, we study the growth rate of perturbation and identify the critical applied strain. Furthermore, we discover the amplitude-dependent growth rate and the formation of the specific triangular profile right before dislocation emission. These observations are analyzed through coincidence site lattice approach and predicted by the washboard potential model. Plus, we construct the phase diagram of the instability behavior. To understand the underlying mechanism, we propose a soft boundary model and theoretically analyze it. The minimal theory quantitatively predicts the growth rate of perturbation and the boundaries in the phase diagram. It also shows that the instability should be primarily driven by the elastic energy gradient generated by the inhomogeneous strain distribution. And it turns out that the predicted strain distribution is in good agreement with the simulation observation.

Contents ii
List of Tables iii
List of Figures vii
1. Introduction 1
2. Phase Field Crystal Model 3
3. Simulation Result 8
4. Theoretical Calculation 25
5. Conclusion and Future Work 36
Appendix 38
Reference 41

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