Jarratt, John David (1978) Geometric properties of crystal lattices in spaces of arbitrary dimension. PhD thesis, University of Warwick.

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Abstract

The main theme of this thesis (excepting Chapter 5) is to investigate properties of crystal lattices which are of particular significance in higher dimensions i.e. > 3, but which barely show up in low dimensions. We study lattices T and pairs (H,T), where H is a finite subgroup of the orthogonal group acting on T.

In Chapter 1 we present some basic properties of lattices which are used throughout. In Chapter 2 we discuss crystal families and prove that the Face Theorem of [12] can be extended to these.

In Chapter 3 we investigate the decomposability properties of the RH-module V and the QH-module QT and the relationship between them. We introduce the ideas of typically orthogonal decompositions and inclined point groups. We prove some general criteria for determining these.

In Chapter 4 we extend the decomposability study to families and show how our work can be used to describe some higher dimensional families which we consider to be of particular significance. Specific results are given.

In particular, we reduce the problem of describing the descendants of one, two and three dimensional families to a problem involving only the partition function.

In Chapter 5 we formulate and study an approach to the problem of the stability of symmetry in lattice hyperplanes. The full solution corresponding to this formulation is given in 3 dimensions. We venture to hope that this solution might be of some interest to practising crystallographers, possibly in the study of twinned crystals with rational twinning planes.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QD Chemistry
Library of Congress Subject Headings (LCSH):	Crystal lattices, Geometric analysis, Geometry, Dimension theory (Algebra)
Official Date:	July 1978
Dates:	Date Event July 1978 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Schwarzenberger, R. L. E.
Sponsors:	Commonwealth Scholarship Commission in the United Kingdom ; British Council
Extent:	xi, 103 leaves
Language:	eng

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