Читать книгу Engineering Physics of High-Temperature Materials - Nirmal K. Sinha - Страница 45

The three‐dimensional structure or arrangement of atoms is called the crystal structure of the solid. The unit cells are the repeating structures in the crystal, and the smallest repeating unit is called the primitive unit cell. The Bravais lattice concept is generally used to define the structure. There are 14 Bravais lattices that define arrangements that can fill three‐dimensional space. Lattice constants refer to the physical dimensions of the unit cells and are generally denoted by a, b, and c.

To describe crystallography, points, direction, and planes are given indices that are used in conjunction with the lattice constants. Points are given labels, like points in a Cartesian coordinate system so that the point represented by coordinate ua, vb, and wc is u, v, and w units along the corresponding lattice direction. A direction is denoted with square brackets such that [uvw] represents a direction parallel to the direction of the origin with the point at coordinates ua, vb, and wc. A family of directions represents all directions in the lattice that are similar by symmetry and are denoted as <uvw>. In crystallography, planes are defined by their Miller indices. Miller indices rely on the reciprocal lattice vectors rather than the direct Bravais lattice. For simplicity, a plane with Miller index (hkl) represents the plane that passes through the points (a/h, 0, 0), (0, b/k, 0), and (0, 0, c/l). A family of planes represents all planes in the lattice that are similar by symmetry and are denoted as {hkl}. For more information on crystallography, there are several resources available, such as Vainshtein et al. (1982) and Mak and Gong‐Du (1992).