Matrix Methods for Teaching Crystallography
Techniques for Understanding Symmetry Operations and Crystal Geometry
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Crystallography, the study of crystal structures and symmetries, is fundamental to materials science, solid-state chemistry, and condensed matter physics. This book presents a comprehensive, matrix-based approach to understanding and calculating the geometric and symmetry properties of crystals, from cubic to triclinic systems.Using metric tensors, vector operations, and matrix representations, readers can compute unit cell volumes, interatomic distances, angles between directions, bonds, and planes, and determine equivalent atomic positions in space groups. Detailed derivations, step-by-step ...
Crystallography, the study of crystal structures and symmetries, is fundamental to materials science, solid-state chemistry, and condensed matter physics. This book presents a comprehensive, matrix-based approach to understanding and calculating the geometric and symmetry properties of crystals, from cubic to triclinic systems.Using metric tensors, vector operations, and matrix representations, readers can compute unit cell volumes, interatomic distances, angles between directions, bonds, and planes, and determine equivalent atomic positions in space groups. Detailed derivations, step-by-step examples, and explicit formulas for all crystal systems make complex calculations accessible and intuitive.Designed for students, educators, and researchers, this text bridges theory and practice, enabling both manual and computational applications, and fostering a deeper understanding of crystal geometry, symmetry, and their influence on material properties.
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