形態不勻向性是固液介面上的一個重要特性並且能夠決定固化過程中的樹突結
構。我們使用兩模相場晶格模型和以其推導而來的振幅方程式來研究二維四方
晶格的表面能不勻向性。我們發現此不勻向性主要是來自於密度波的振幅在固
液介面上的不同變化造成的，同時第二模式的強度能夠大幅度的影響表面不勻
向性，甚至造成大小順序的反轉。在本文中，我們成功的利用自由能的對稱性
來解釋這種順序反轉。

Morphological anisotropy, which can dictate the dendrite growth in solidification, is an essential property for the solid-liquid interface. We use the two-mode phase-field crystal model and the amplitude equation derived from it to study the anisotropy of interface energy in the two-dimensional square lattice. We find that the anisotropy of interface energy is determined by how amplitudes of the density wave change through the interface. Moreover, the strength of the second mode has a strong influence on the interface energy, even reversing the ordering of its anisotropy. In this thesis, we successfully use the symmetry property of the free energy to explain this ordering reversal.

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