Abstract
This chapter provides an overview of the geometry of metal crystals and surfaces. In crystalline solids, such as metals, atoms are arranged in a regular manner. An ideal single crystal is defined as a body of atoms (ions) stacked to form a 3D net, which is determined by the translation vectors. The 3D lattice is thought to be made up of various sets of parallel planes. Each set of planes has a particular orientation in space. The space position of crystallographic plane is determined by three lattice points not lying on the same straight line. In each crystal lattice, a given lattice point is surrounded by a certain number of neighboring points that are away from it by the same distance. In comparison to fourteen 3D lattices in 3D space, there exist five 2D Bravais lattices— namely, (1) oblique, (2) hexagonal, (3) rectangular (orthorhombic), (4) rectangular centered, and (5) quadratic (regular). These follow from the restrictions imposed by symmetry operations. The lattices are determined by the primitive translation vectors.
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