الملخص
We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3). It is naturally expected that these rank-3 Coxeter-Weyl groups define the point tetrahedral symmetry and the octahedral symmetry of the cubic lattices which have extensive applications in material science. The imaginary quaternionic units are used to represent the root systems of the rank-3 Coxeter-Dynkin diagrams which correspond to the generating vectors of the lattices of interest. The group elements are written explicitly in terms of pairs of quaternions which constitute the binary octahedral group. The constructions of the vertices of the Wigner-Seitz cells have been presented in terms of quaternionic imaginary units. This is a new approach which may link the lattice dynamics with quaternion physics. Orthogonal projections of the lattices onto the Coxeter plane represent the square and honeycomb lattices.
الكلمات المفتاحية
بيانات النشر
- المعرّف الرقمي
- 10.24200/squjs.vol19iss1pp95-104
- المجلة
- مجلة جامعة السلطان قابوس للعلوم, 19(1), 95
- الناشر
- جامعة السلطان قابوس
- وصول مفتوح
- وصول مفتوح ذهبي
- الترخيص
- CC BY 4.0
اقتبس هذه المقالة
APA 7
Koca, N. Ö., Koca, M., & Al-Sawafi, M. (2014). FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions. Sultan Qaboos University Journal for Science, 19(1), 95. https://doi.org/10.24200/squjs.vol19iss1pp95-104
MLA 9
Koca, Nazife Özdeş, et al. "FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions." Sultan Qaboos University Journal for Science, vol. 19, no. 1, 2014, pp. 95. https://doi.org/10.24200/squjs.vol19iss1pp95-104.
شيكاغو (المؤلف–التاريخ)
Koca, Nazife Özdeş, Mehmet Koca, and M.M.S. Al-Sawafi. 2014. "FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions." Sultan Qaboos University Journal for Science 19 (1): 95. https://doi.org/10.24200/squjs.vol19iss1pp95-104.
هارفارد
Koca, N. Ö., Koca, M. and Al-Sawafi, M. (2014) 'FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions', Sultan Qaboos University Journal for Science, 19(1), pp. 95. doi:10.24200/squjs.vol19iss1pp95-104.
فانكوفر
Koca NÖ, Koca M, Al-Sawafi M. FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions. Sultan Qaboos University Journal for Science. 2014;19(1):95. doi:10.24200/squjs.vol19iss1pp95-104
IEEE
N. Ö. Koca, M. Koca, and M. Al-Sawafi, "FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions," Sultan Qaboos University Journal for Science, vol. 19, no. 1, pp. 95, 2014, doi: 10.24200/squjs.vol19iss1pp95-104.