Condensed matter physics I by Riseborough P.S.

By Riseborough P.S.

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C. positions and the Li cations form a simple cubic array. 12 The Copper Three Gold Structure The Cu3 Au structure is cubic, and has the space group P m3m. The Bravais lattice corresponds to a primitive cubic structure. There are 3 Cu atoms and one Au per unit cell. All the atoms are located on the sites of a face centered cubic 47 unit cell. The Au atom can be envisaged as being positioned on the corners of the cube, whereas the 3 Cu atoms sit on the centers of the faces of the cube, forming octahedra.

How many atoms are in the primitive unit cells of graphite? 5 Hexagonal Close-Packed Structure The hexagonal close packed structure has hexagonal symmetry, the space group is P 63 /mmc. It is composed of the hexagonal Bravais lattice, and has a basis composed of two atoms. The two identical atoms are positioned at [0, 0, 0] which is at the vertex of the primitive lattice cell, and has the other atom located at [ 13 , 13 , 12 ] as expressed in terms of the primitive lattice vectors. ) The primitive lattice vectors are a1 = a2 = a3 = a eˆx √ a eˆx + 3 eˆy 2 c eˆz (36) Thus, the hexagonal close packed structure has a basis of two atoms one at r1 = (0, 0, 0) and the other at 1 a 2 3 a c a √ eˆy + = eˆx + eˆz 2 2 2 3 r2 = 1 3 a1 + a2 + (37) Since a1 and a2 are inclined at an angle π3 , the structure can be considered to be formed by two interpenetrating simple hexagonal Bravais lattices.

P. p. c. value a . 8 Other Close Packed Structures One can form other close packed structures by altering the sequence of stacking of the close packed layers. The hexagonal close packed can be characterized by the repeated stacking sequence A - B - A - B etc. That is, the atoms in the planes above and below the triangular lattice have centers directly over the dimples and each other, thereby creating a two layer unit cell. Another stacking sequence is given by A - B - C in which the unit cell consists of three layers.

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