ヒッツェル，エクハルト   HITZER, Eckhard   ヒッツェル, エクハルト    所属   国際基督教大学教養学部 アーツ・サイエンス学科    職種   上級准教授
言語種別	英語
発行・発表の年月	2010
形態種別	研究論文（国際会議プロシーディングス）
査読	査読あり
標題	Reciprocal space and crystal planes in geometric algebra
執筆形態	単著
掲載誌名	electronic conf. proc. of AGACSE 2010, Amsterdam, The Netherlands, 14-16 June 2010.
掲載区分	国外
著者・共著者	HITZER Eckhard
概要	This contribution discusses the geometry of kD crystal cells given by (k + 1) points in a projective space R^{n+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 R_{n+1} (see [2]) and in the conformal algebra R_{n+1,1}. The crystallographic notions of d-spacing, phase angle (in structure factors), extinction of Bragg re ections, and the interfacial angles of crystal planes are obtained in the same context. [2] H. Grassmann, edited by F. Engel, Die Ausdehnungslehre von 1844 und die Geometrische Analysis, Vol. 1, Part 1, Teubner, Leipzig, 1894.