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Numerical Problems in Crystallography

  • 2021
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About this book

This book aims at enhancing the understanding of topics in crystallography through solving numerical problems. Designed into nine chapters on major topics in crystallography, the book deals with more than 600 carefully selected solved examples, problems, and multiple-choice questions. Unit cell composition, construction and calculations, Miller indices, structure factor calculations, and X-ray diffraction methods are some of the many useful topics discussed in this book. Each chapter begins with a brief theoretical explanation of the topic followed by solved numerical examples for further clarity on the subject.

The topic “crystallography” is interdisciplinary in nature. Its rudimentary knowledge, therefore, is essential to the beginners in physics, chemistry, mathematics, molecular biology, geology, metallurgy, and particularly materials science and mineralogy. This book also is of immense value to senior undergraduate and graduate students of physics, chemistry, and other basic sciences.

Table of Contents

Frontmatter
Chapter 1. Unit Cell Composition
Abstract
When an object (say the number 7) is repeatedly translated through an interval ‘a’, we obtain a one dimensional array of the number 7, as shown in Fig. 1.1a. When each object in the array is replaced with a point, a collection of points is obtained as shown in Fig. 1.1b. This is known as a linear lattice. Since, a geometrical point has no (or zero) dimension, therefore the lattice point is an imaginary concept but the array of the number ‘7’ is real.
M. A. Wahab
Chapter 2. Unit Cell Construction
Abstract
A Wigner–Seitz unit cell is an alternative way of selecting a primitive unit cell of area \((\vec{a} \times \vec{b} = ab\;\sin\upgamma)\)
M. A. Wahab
Chapter 3. Unit Cell Calculations
Abstract
The location of any point within a unit cell (oblique or orthogonal).
M. A. Wahab
Chapter 4. Unit Cell Representations of Miller Indices
Abstract
In order to locate the atomic sites (positions) in cubic or orthogonal unit cells, rectangular axes are used
M. A. Wahab
Chapter 5. Unit Cell Transformations
Abstract
In order to know the exact relationships (in terms of planes, directions, unit cell volumes, etc. both in direct and reciprocal lattices) between the two sets of unit cells such as one primitive to another, primitive to non-primitive or vice-versa, the transformation of one set of indices to another is carried out simply by the use of vector algebra. It is customary to take one unit cell as the first unit cell (corresponding to the first set of axes) and the other unit cell as the second unit cell (corresponding to the second set of axes).
M. A. Wahab
Chapter 6. Unit Cell Symmetries and Their Representations
Abstract
It represents a combined operation of rotation followed by a reflection (mirror plane perpendicular to the axis of rotation). The two operations are taking place consecutively. There exists a rotoreflection axis corresponding to each proper rotation axis.
M. A. Wahab
Chapter 7. Diffraction of Waves and Particles by Crystal
Abstract
X-rays are produced when a beam of highly accelerated charged particles such as electrons is allowed to strike a metal target.
M. A. Wahab
Chapter 8. Structure Factor Calculations
Abstract
We know that the intensity of the diffracted beams depends on atomic scattering factor and the position of each atom in the unit cell.
M. A. Wahab
Chapter 9. Determination of Crystal Structure Parameters
Abstract
Crystal structure determinations in general are not easy and straightforward.
M. A. Wahab
Backmatter
Title
Numerical Problems in Crystallography
Author
Prof. M. A. Wahab
Copyright Year
2021
Publisher
Springer Singapore
Electronic ISBN
978-981-15-9754-1
Print ISBN
978-981-15-9753-4
DOI
https://doi.org/10.1007/978-981-15-9754-1

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