马氏体相变微观模拟中的表面能
Surface Energies Arising in Microscopic Modeling of Martensitic Transformations
摘要：
在本文中，我们构造和分析了一个二维原子晶格上的两阱哈密顿量。哈密顿量的两个阱分别由两个一秩相连的马氏体孪晶所描述。通过将形变组态约束到特殊的一维原子链上，并在垂直方向上具有与位置相关的伸长矢量，我们发现在适当的边界条件下，基态的结构接近于宏观预期的孪晶组态，在孪晶界面附近有额外的边界层。此外，我们进行到一个连续极限，显示渐近分段刚性的最小化序列和严格推导出相应的极限形式的表面能。
英文摘要：
In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic lattice. The two wells of the Hamiltonian are prescribed by two rank-one connected martensitic twins, respectively. By constraining the deformed configurations to special 1D atomic chains with position-dependent elongation vectors for the vertical direction, we show that the structure of ground states under appropriate boundary conditions is close to the macroscopically expected twinned configurations with additional boundary layers localized near the twinning interfaces. In addition, we proceed to a continuum limit, show asymptotic piecewise rigidity of minimizing sequences and rigorously derive the corresponding limiting form of the surface energy.
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