Wahab M. Mirror Symmetry. The Mother of all Crystal Symmetries 2024

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Wahab M. Mirror Symmetry. The Mother of all Crystal Symmetries 2024

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Textbook in PDF format This graduate-level textbook deals with different aspects of plane mirrors and mirror-related symmetries. It provides us with some new ways of understanding symmetries in crystals and the mirror combination schemes. The inclusion of topics such as the Wigner–Seitz unit cell, reciprocal lattice, Brillouin zones, diffraction of crystals, etc., based on the mirror combination scheme, are extremely helpful in understanding many other concepts in crystallography. A mirror is the only fundamental symmetry in crystals, and all other permissible symmetries in crystalline solids can be derived from suitable combinations of mirrors, called derived symmetries. A rudimentary knowledge of symmetry in crystallography is essential to students, researchers, and professionals in many subjects in science and technology: physics, chemistry, mathematics, molecular biology, geology, metallurgy, and particularly materials science and mineralogy. Preface About the Author Fundamental Concepts Related to a Plane Mirror Mirror: The Only Fundamental Symmetry in Crystals Mirror Combination Scheme in Direct Lattice Mirror Combination Scheme in Reciprocal Lattice Importance of d-Spacing in Diffraction of Crystals Study of Diffraction Results of Some Cubic Crystals Possibility of Translational Symmetry (if Any) in Crystals Resolution of Existing Discrepancies, Ambiguities and Confusions Fundamental Crystallography