二维准晶的声子及其熔化性质

本文研究具有五次对称性的二维Penrose准晶的声子及其熔化性质,我们找到了一个相似变换矩阵,利用它成功地对动力学矩阵进行约化。这约化一方面大大地减少了计算量,另一方面通过它可解析地得出振动模中有2/3是双重简并的,而余下的1/3是非简并的结论。利用原子均方位移判据,我们研究了二维Penrose准晶格的熔化性质,得出边界较内部先熔化,原子间相互作用大的系统不易熔化等合理结论。

PHONON AND MELTING PROPERTY OF THE TWO-DIMENSIONAL PENROSE QUASICRYSTALS

This paper is devoted to the study of phonon and melting property of two-demensional Per.rose latrice with five-fold rotational symmetric axis. We intrtoduce a similarity transformation which transforms the dynamical matrix into a block-diagonal matrix, which helps to determine analytically the degeneracies of the modes of the phonon spectra and reduce the numerical calculation. It is found that two thirds of the modes are doubly degenerate and the remains are nondegenerate. By using the atomic mean-square displacement criterion, we study the melting property of the two-demensional Penrose lattice. We find that boundary atoms. alawys have lower melting temperature thanthat of bulk, and when the interaction among atoms is larger, the system will have a higher melting temperature.