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By Riseborough P.S.

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As atoms are not hard spheres, there is no reason for this value to be found in naturally occurring crystals, and deviations from the ideal value are found most frequently. Only He has the ideal c to a ratio. The most frequently occurring structures are the close packed structures. 68, respectively. Both simple and transition metals frequently form in the hexagonal close packed structure, or other close packed structures. c. p. at 23 K via a Martensitic transition. 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 volume of the primitive unit cell is found to be 14 a3 . The angles between the primitive lattice vectors are π3 . The Wigner-Seitz cell for the face centered cubic lattice is best seen by translating the conventional unit cell by a2 along one axis. After the translation has been performed, the unit cell has the appearance of being a cube which has lattice sites at the body center and at the mid-points of the twelve edges of the cube. The Wigner-Seitz cell can then be constructed by finding the twelve planes bisecting the lines from the body center to the mid-points of the edges.

Neri, Acta. Crystallogr. Sec. A 40, 580 (1984)). To illustrate this, consider a square two-dimensional lattice, with lattice constant a. On any unit cell, construct two parallel lines with slope tan θ passing through opposite corners. The equations of the lower line is given by y = x tan θ (73) and the upper line is determined by y = a + ( x + a ) tan θ (74) For rational values of the slope, tan θ = pq , the lattice points cross the line periodically, with repeat distance q a along the x direction and have periodicity p a along the y direction.

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