Condensed matter physics I by Riseborough P.S.

By Riseborough P.S.

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The centers of the mid-plane equilateral triangles are located directly over the (central) lattice sites of the base. There are two possible orientations for these triangles. On choosing any one orientation, the set of lattice sites on this mid-plane are located such that they lie directly over the centers of every other equilateral triangle in the base. These mid-plane lattice sites are designated as the B sites. Consider a line, parallel to the c axis. The line is equidistant between two neighboring B lattice sites and is equidistant to the two A lattice sites that form 37 the section of the perimeter of the basal hexagon which is parallel to the line connecting the above two B lattice sites.

Glide planes are denoted by a, b, c (according to whether the translation is along the a, b and c axis), or n and d (the diagonal or diamond glide which are special cases involving translations along more than one axis). The hexagonal close packed lattice structure has both of these types of nonsymmorphic symmetry operations. The hexagonal close packed structure can be described by a three-dimensional unit cell which contains a centered hexagonal base, and which has an identical centered hexagonal top located at vertical distance c directly above the base.

Thus, the CsCl structure resembles a body centered 45 cubic structure in which one type of atom is at the simple cubic sites and the other type of atom is at the body center. Each ion is surrounded by eight atoms √ 3 of opposite charge located at a distance 2 a away, which corresponds to half the length of the body diagonal of the cube. Each atom has six neighbors of similar charge located a distance a away. 42, ionic compounds prefer the N aCl structure. Examples of compounds that form the CsCl structure are the Cs halides, T l halides, CuZn (beta brass), CuP d, AgM g and LiHg.

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