}, post: function (sUrl, sArgs, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { //alert(errmsg); } } }; xhr2.open('POST', encodeURI(sUrl), bAsync); xhr2.setRequestHeader('Content-Length', sArgs.length); xhr2.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded'); xhr2.send(sArgs); }, get: function (sUrl, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { alert(errmsg); } } }; xhr2.open('GET', encodeURI(sUrl), bAsync); xhr2.send('Null'); } } function SetSearchLink(item) { var url = "../journal/recordsearchinformation.aspx"; var skid = $(":hidden[id$=HiddenField_SKID]").val(); var args = "skid=" + skid; url = url + "?" + args + "&urllink=" + item; window.setTimeout("showSearchUrl('" + url + "')", 300); } function showSearchUrl(url) { var callback2 = function (xhr2) { } ajax2.get(url, true, callback2, "try"); }
JMP> Vol.6 No.5, April 2015
Share This Article:
Cite This Paper >>

Lattice Stability and Reflection Symmetry

Abstract Full-Text HTML XML Download Download as PDF (Size:726KB) PP. 691-697
DOI: 10.4236/jmp.2015.65074    3,012 Downloads   3,486 Views  
Author(s)    Leave a comment
Shigeji Fujita1, James R. McNabb III1, Hung-Cheuk Ho2, Akira Suzuki3*


1Department of Physics, University at Buffalo, SUNY, Buffalo, USA.
2Sincere Learning Centre, Kowloon, Hong Kong, China.
3Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan.


Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional; no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.


k-Vectors, Conduction Electron, Reflection Symmetry, Crystal Structure, Lattice Stability

Cite this paper

Fujita, S. , McNabb III, J. , Ho, H. and Suzuki, A. (2015) Lattice Stability and Reflection Symmetry. Journal of Modern Physics, 6, 691-697. doi: 10.4236/jmp.2015.65074.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Lee, T.D. and Yang, C.N. (1956) Physical Review, 104, 254.
[2] Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics. Saunders, Philadelphia, 216-217, 228-229, 6-7.
[3] Fujita, S., Takato, Y. and Suzuki, A. (2011) Modern Physics Letters B, 25, 223.
[4] Fujita, S. and Suzuki, A. (2010) Journal of Applied Physics, 107, Article ID: 013711.
[5] Zhang, Y., Tan, Y.W., Stormer, H.L. and Kim, P. (2005) Nature, 438, 201.
[6] Kang, N., Lu, L., Kong, W.J., Hu, J.S., Yi, W., Wang, Y.P., Zhang, D.L., Pan, Z.W. and Xie, S.S. (2003) Physical Review B, 67, Article ID: 033404.
[7] Debye, P. (1912) Annalen der Physik, 39, 789.

comments powered by Disqus
JMP Subscription
E-Mail Alert
JMP Most popular papers
Publication Ethics & OA Statement
JMP News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.