Please wait a minute...
Chinese Physics, 2006, Vol. 15(9): 2065-2079    DOI: 10.1088/1009-1963/15/9/029
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Group-theoretical method for physical property tensors of quasicrystals

Gong Ping(龚平), Hu Cheng-Zheng(胡承正), Zhou Xiang(周详), Wang Ai-Jun(王爱军), and Miao Ling(缪灵)
Department of Physics, Wuhan University, Wuhan 430072, China
Abstract  In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.
Keywords:  quasicrystals      elastic constants      basis functions  
Received:  24 February 2006      Revised:  13 April 2006      Accepted manuscript online: 
PACS:  52.55.Fa (Tokamaks, spherical tokamaks)  
  52.25.Vy (Impurities in plasmas)  
  52.38.Mf (Laser ablation)  

Cite this article: 

Gong Ping(龚平), Hu Cheng-Zheng(胡承正), Zhou Xiang(周详), Wang Ai-Jun(王爱军), and Miao Ling(缪灵) Group-theoretical method for physical property tensors of quasicrystals 2006 Chinese Physics 15 2065

[1] Substitutions of vertex configuration of Ammann-Beenker tiling in framework of Ammann lines
Jia-Rong Ye(叶家容), Wei-Shen Huang(黄伟深), and Xiu-Jun Fu(傅秀军). Chin. Phys. B, 2022, 31(8): 086101.
[2] Bose-Einstein condensates in an eightfold symmetric optical lattice
Zhen-Xia Niu(牛真霞), Yong-Hang Tai(邰永航), Jun-Sheng Shi(石俊生), Wei Zhang(张威). Chin. Phys. B, 2020, 29(5): 056103.
[3] First-principles investigation on ideal strength of B2 NiAl and NiTi alloys
Chun-Yao Zhang(张春尧), Fu-Yang Tian(田付阳), Xiao-Dong Ni(倪晓东). Chin. Phys. B, 2020, 29(3): 036201.
[4] Composition effect on elastic properties of model NiCo-based superalloys
Weijie Li(李伟节), Chongyu Wang(王崇愚). Chin. Phys. B, 2020, 29(2): 026102.
[5] Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals
Dongsheng Yang(杨东升) and Guanting Liu(刘官厅)†. Chin. Phys. B, 2020, 29(10): 104601.
[6] Structural, electronic, elastic, and thermal properties of CaNiH3 perovskite obtained from first-principles calculations
S Benlamari, H Bendjeddou, R Boulechfar, S Amara Korba, H Meradji, R Ahmed, S Ghemid, R Khenata, S Bin Omran. Chin. Phys. B, 2018, 27(3): 037104.
[7] First-principles calculations on elastic, magnetoelastic, and phonon properties of Ni2FeGa magnetic shape memory alloys
Wangqiang He(贺王强), Houbing Huang(黄厚兵), Zhuhong Liu(柳祝红), Xingqiao Ma(马星桥). Chin. Phys. B, 2018, 27(1): 016201.
[8] Electronic and mechanical properties of half-metallic half-Heusler compounds CoCrZ (Z=S, Se, and Te)
Hai-Ming Huang(黄海铭), Chuan-Kun Zhang(张传坤), Ze-Dong He(贺泽东), Jun Zhang(张俊), Jun-Tao Yang(杨俊涛), Shi-Jun Luo(罗时军). Chin. Phys. B, 2018, 27(1): 017103.
[9] Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal
Guan-Ting Liu(刘官厅), Li-Ying Yang(杨丽英). Chin. Phys. B, 2017, 26(9): 094601.
[10] First-principles study of the new potential photovoltaic absorber: Cu2MgSnS4 compound
Belmorsli Bekki, Kadda Amara, Mohammed El Keurti. Chin. Phys. B, 2017, 26(7): 076201.
[11] First-principles investigation of the effects of strain on elastic, thermal, and optical properties of CuGaTe2
Li Xue(薛丽), Yi-Ming Ren(任一鸣), Jun-Rong He(何俊荣), Si-Liu Xu(徐四六). Chin. Phys. B, 2017, 26(6): 067103.
[12] Effects of pressure on structural, electronic, and mechanical properties of α, β, and γ uranium
Hui-Jie Zhang(张慧杰), Shi-Na Li(李世娜), Jing-Jing Zheng(郑晶晶), Wei-Dong Li(李卫东), Bao-Tian Wang(王保田). Chin. Phys. B, 2017, 26(6): 066104.
[13] The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals
Li-Juan Jiang(姜丽娟), Guan-Ting Liu(刘官厅). Chin. Phys. B, 2017, 26(4): 044601.
[14] Mechanical properties of GaxIn1-xAsyP1-y/GaAs systemat different temperatures and pressures
A. R. Degheidy, E. B. Elkenany. Chin. Phys. B, 2015, 24(9): 094302.
[15] Accurate calculations of the high-pressure elastic constants based on the first-principles
Wang Chen-Ju (王臣菊), Gu Jian-Bing (顾建兵), Kuang Xiao-Yu (邝小渝), Yang Xiang-Dong (杨向东). Chin. Phys. B, 2015, 24(8): 086201.
No Suggested Reading articles found!