Download PDF by D. W. Budworth and G. Arthur (Auth.): An Introduction to Ceramic Science

By D. W. Budworth and G. Arthur (Auth.)

ISBN-10: 0080160964

ISBN-13: 9780080160962

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The great symmetry of the face-centred cubic structure is apparent from the symmetry of the patterns of the interstices. The most helpful way of considering the face-centred cubic structure is, of course, with a unit cell of cubic shape, and Fig. 11 ▲ Tetrahedral interstice B Octahedral interstice FIG. 11. Positions of octahedral and tetrahedral interstices in unit cell of face-centred cubic structure. shows the positions of the various interstices in such a unit cell. The relation of this to the close-packed planes is left as an exercise for the reader.

EQUIVALENT IONS IN THE NaCl STRUCTURE «1 «2 «3 100 110 111 200 210 211 220 221 222 No. of terms 48 48 48 48 48 48 48 48 48 x x x x x x x x x i i i £ 1 i i £ i x x x x x x x x x i = i 1= i = £= 1= i = 1= 1= 6 12 8 6 24 24 12 24 8 Distance Contribution to Madelung constant rVl rV2 rV3 rV4 rV5 rV6 rV8 rV9 rV12 -6/V1 + 12/V2 -8/V3 + 6/V4 -24/V5 + 24/V6 + 12/V8 -24/V9 + 8/V12 39 The Structures of Some Ceramic Crystals slowly (which is the mathematical expression of the fact that the electrostatic force is a comparatively long-range force) and can be summed by straightforward methods only with a very great amount of labour.

Sequence) which is not a close packed arrangement. The corresponding sequences for the face-centred cubic arrangement are as follows: Planes A Tetrahedral interstices First set Second set B A B C A C Octahedral interstices C A B A C B The Bonding of Atoms and the Regular Packing of Spheres 33 So that the tetrahedral interstices are arranged in two interpenetrating face-centred cubic structures {ABC. sequences), and the octahedral interstices form yet another face-centred cubic arrangement. The great symmetry of the face-centred cubic structure is apparent from the symmetry of the patterns of the interstices.

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An Introduction to Ceramic Science by D. W. Budworth and G. Arthur (Auth.)


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