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Symmetry in Crystals

Wai-Kee Li, Gong-Du Zhou, and Thomas Chung Wai Mak

in Advanced Structural Inorganic Chemistry

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199216949
eISBN:
9780191711992
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216949.003.0009
Subject:
Physics, Crystallography: Physics

The symmetry properties of molecules were discussed in Chapter 6, and the corresponding properties of crystals are presented here. In contrast to discrete molecules, crystals have a lattice structure ... More


Basics of crystallography, part 3

Ulrich Müller

in Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199669950
eISBN:
9780191775086
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199669950.003.0006
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

The molecular symmetry is called the point group of the molecule. A point group can be represented by a set of matrices W. The point group of a crystal is the symmetry group of the bundle of normals ... More


Crystal symmetry: point groups, space groups, symmetry-related properties and quasiperiodic crystals

Christopher Hammond

in The Basics of Crystallography and Diffraction

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198738671
eISBN:
9780191801938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198738671.003.0004
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

Chapter 4 is about symmetry and crystal habit. It looks at thirty-two crystal classes; centres and inversion axes of symmetry; crystal symmetry and properties; translational symmetry elements; space ... More


Symmetry

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0005
Subject:
Earth Sciences and Geography, Geochemistry

All single crystals possess translational symmetry, and most possess other symmetry elements as well. In this chapter we describe the 32 crystallographic point groups used for single crystals. The ... More


Ferroic crystals

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0018
Subject:
Earth Sciences and Geography, Geochemistry

Twinned crystals are normally classified according to twin-laws and morphology, or according to their mode of origin, or according to a structural basis, but there is another classification that ... More


Transformation operators for symmetry elements

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0006
Subject:
Earth Sciences and Geography, Geochemistry

Since the physical property tensors depend on symmetry, mathematical methods for determining the influence of symmetry are needed. More specifically, transformation matrices are required for the ... More


Piezoelectricity

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0014
Subject:
Earth Sciences and Geography, Geochemistry

The prefix “piezo” (pronounced pie-ease-o) comes from the Greek word for pressure or mechanical force. Piezoelectricity refers to the linear coupling between mechanical stress and electric ... More


Dielectric constant

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0011
Subject:
Earth Sciences and Geography, Geochemistry

The dielectric constant K is a measure of a material’s ability to store electric charge. In scalar form the defining relations are as follows: . . . D = εE, . . . where D is the electric ... More


Nonlinear optics

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0031
Subject:
Earth Sciences and Geography, Geochemistry

In most dielectrics, the linear relation between electric polarization and applied electric field is accurately obeyed even for fairly large fields of 107 V/m. The reason is that the atomic ... More


Magneto-optics

Robert E. Newnham

in Properties of Materials: Anisotropy, Symmetry, Structure

Published in print:
2004
Published Online:
November 2020
ISBN:
9780198520757
eISBN:
9780191916601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198520757.003.0033
Subject:
Earth Sciences and Geography, Geochemistry

The magneto-optic properties of interest are the Faraday Effect, Kerr Rotation, and the Cotton–Mouton Effect. In 1846, Michael Faraday discovered that when linearly polarized light passes through ... More


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