HITZER, Eckhard
Senior Associate Professor Division of Arts and Sciences, College of Liberal Arts, International Christian University |
|
Language | English |
Publication Date | 2011 |
Type | Research Paper (Scientific Journal) |
Title | Crystal planes and reciprocal space in Clifford geometric algebra |
Contribution Type | Single Work |
Journal | Math. Methods in the Applied Sciences |
Journal Type | Another Country |
Publisher | Wiley |
Volume, Issue, Pages | 34(12),pp.1421-1429 |
Responsible for | Everything |
Author and coauthor | HITZER Eckhard |
Details | This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ℝn+ 1. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(ℝn+ 1) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(ℝn+ 1, 1). The crystallographic notions of d-spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. |
DOI | 10.1002/mma.1442 |