Point and space groups and elastic behaviours of one-dimensional quasicrystals
Point and space groups and elastic behaviours of one-dimensional quasicrystals
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DOI：
10.1088/0953-8984/9/11/009
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发表时间：
1997-03
期刊：
影响因子：
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通讯作者：
Renhui Wang;Wenge Yang;Cheng-zheng Hu;D. Ding
中科院分区：
文献类型：
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作者：
Renhui Wang;Wenge Yang;Cheng-zheng Hu;D. Ding
一维准晶是指在x-y平面内具有周期性，在第三维空间内具有准周期性的三维晶体。已知1D QC的可能对称操作为1、2、3、4、6、m、（反转）、（水平二重旋转）和（水平镜面反射），已推导出1D QC的31个可能的点群。这31个点群分为10个劳厄类和6个系统。考虑螺旋（仅）和滑移（仅a，B和）操作，也得到了80个可能的一维量子点空间群。根据我们的广义弹性理论，讨论了每一类一维量子点的弹性行为，包括独立的弹性常数和不变量。
A one-dimensional (1D) quasicrystal (QC) is defined as a three-dimensional body which is periodic in the x - y plane and quasiperiodic in the third dimension. Knowing that the possible symmetry operations for a 1D QC are 1, 2, 3, 4, 6, m, (inversion), (horizontal twofold rotation) and (horizontal mirror reflection), 31 possible point groups of 1D QCs have been deduced. These 31 point groups are divided into ten Laue classes and six systems. Considering screw (only ) and glide (only a, b and ) operations, 80 possible space groups of 1D QCs have also been obtained. According to our generalized elasticity theory of QCs, the elastic behaviours, including independent elastic constants and invariants, for each Laue class of 1D QCs have been discussed.