Cubic close-packed lattice interstitial holes

Many ionic compounds are considered to pack in such as way that the anions form a close-packed lattice in which the metal cations fill holes or interstitial sites left between the anions. These lattices, however, may not necessarily he as tightly packed as the label close-packed implies. The radius of an F ion is approximately 133 pm. The edge distances of the cubic unit cells of LiF, NaF, KF, RbF, and CsF, all of which... 

When the radius ratio is less than 0.59 the alloy is normal and the mclal—interstitial atom arrangement is face-centred cubic, close-packed hexagonal or body-centred cubic. The complex interstitial alloys have a radius ratio greater than 0.59 and are less stable. Carbon and nitrogen always occupy octahedral holes in interstitial alloys hydrogen always occupies the smaller tetrahedral interstices. In face-centred cubic and close-packed hexagonal lattices there are as many octahedral holes as metal atoms and twice as many tetrahedral holes. 

Although it is more stable than Ti3N4, strong heating converts it to ZrN. The interstitial nitrides, like the carbides TiC and ZrC, have the NaCl structure alternatively they may be regarded as cubic close-packed arrangements of Ti atoms with nitrogens in the octahedral holes. As the metals have h.c.p. lattices, these have not been simply expanded to admit the N atoms. 

Wustite is a nonstoichiometric microheterogeneous solid. Its idealized structure is rather similar to the magnetite structure. Both lattices are built from a cubic, close packed, oxygen lattice with the iron ions located only in octahedral voids for wustite, and in both octahedral and tetrahedral voids for magnetite. Wustite is thermodynamically metastable below 833 K but can be easily supercooled to room temperature. The composition of the material is variable and always deficient in iron Fei j,0 with x varying from 4.5% to 11%. Electroneutrality is preserved by the presence of Fe ions. These ions and the holes in the iron sublattice are not statistically distributed throughout the material but form a variety of clusters centered around the ferric ions placed in tetrahedral interstitial sites. ... 

Tetrahedral and octahedral interstitial holes are formed by the spaces left when anions pack in a cubic dose-packed array, (a) Which hole can accommodate the larger ions (b) What is the size ratio of the largest metal cation that can occupy an octahedral hole to the largest that can occupy the tetrahedral hole while maintaining the close-packed nature of the anion lattice (c) If half the tetrahedral holes are occupied, what will the chemical formula of the compound M. Ay be, where M represents the cations and A the anions ... 

Even in the close packed structures, a considerable part of the total volume remains unfilled, since between the spheres there are holes of considerable volume. This volume is greater in the body centred cubic structure and in the diamond lattice. The relative volumes occupied by the spheres and by the interstitial space are given in Table CXXXVII. 

The bcc structures of iron, molybdenum, and tungsten are not close-packed as are those of fee and hep, and more interstitial sites are available for the free valence electrons. In the bcc lattice the octahedral holes are in the middle of the faces and in the center of the edges of the unit cell. Four tetrahedral sites form a circle in the eight faces of the unit cell. A second group of four tetrahedral sites forms a circle around all twelve edges of a cubic bcc unit cell. A maximum of two free electrons per face and per edge can be accommodated in the octahedral sites and two electrons... 

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