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Principles of Materials Characterization and Metrology$
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Kannan M. Krishnan

Print publication date: 2021

Print ISBN-13: 9780198830252

Published to Oxford Scholarship Online: July 2021

DOI: 10.1093/oso/9780198830252.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 06 December 2021

Crystallography and Diffraction

Crystallography and Diffraction

(p.220) 4 Crystallography and Diffraction
Principles of Materials Characterization and Metrology

Kannan M. Krishnan

Oxford University Press

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

Keywords:   Crystallography, Diffraction, Bravais lattice, Point and space groups, Reciprocal lattice, Zonal equation, Bragg law, Ewald Sphere, Laue criterion, Quasicrystals

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