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In a crystal with a face-centered cubic structure, the basic cell can be taken as a cube of edge a with its center at the origin of coordinates and its edges parallel to the Cartesian coordinate axes; atoms are sited at the eight corners and at the center of each face. However, other basic cells are possible. One is the rhomboid shown in the figure below, which has three vectors b, c and d as edges. (b) Show that the corresponding angles between pairs of edges of the rhomboid defined by the reciprocal vectors to 5, č and d'are each 109.5°. (This rhomboid can be used as the basic cell of a body-centered cubic structure, more easily visualized as a cube with an atom at each corner and one in the center.)

In a crystal with a face-centered cubic structure, the basic cell can be taken as a cube of edge a with its center at the origin of coordinates and its edges parallel to the Cartesian coordinate axes; atoms are sited at the eight corners and at the center of each face. However, other basic cells are possible. One is the rhomboid shown in the figure below, which has three vectors b, c and d as edges. (b) Show that the corresponding angles between pairs of edges of the rhomboid defined by the reciprocal vectors to 5, č and d'are each 109.5°. (This rhomboid can be used as the basic cell of a body-centered cubic structure, more easily visualized as a cube with an atom at each corner and one in the center.)

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In a crystal with a face-centered cubic structure, the basic cell can be taken as a cube of edge a with its center at the origin of coordinates and its edges parallel to the Cartesian coordinate axes; atoms are sited at the eight corners and at the center of each face. However, other basic cells are possible. One is the rhomboid shown in the figure below, which has three vectors b, č and d as edges. (b) Show that the corresponding angles between pairs of edges of the rhomboid defined by the reciprocal vectors to 5, č and d are each 109.5°. (This rhomboid can be used as the basic cell of a body-centered cubic structure, more easily visualized as a cube with an atom at each corner and one in the center.)
Transcribed Image Text:In a crystal with a face-centered cubic structure, the basic cell can be taken as a cube of edge a with its center at the origin of coordinates and its edges parallel to the Cartesian coordinate axes; atoms are sited at the eight corners and at the center of each face. However, other basic cells are possible. One is the rhomboid shown in the figure below, which has three vectors b, č and d as edges. (b) Show that the corresponding angles between pairs of edges of the rhomboid defined by the reciprocal vectors to 5, č and d are each 109.5°. (This rhomboid can be used as the basic cell of a body-centered cubic structure, more easily visualized as a cube with an atom at each corner and one in the center.)
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