Fluorite-type crystals

Inter-Atomic Distances in Fluorite Type Crystals... 

This theoretical result is completely substantiated by experiment. Goldschmidt,31 from a study of crystal structure data, observed that the radius ratio is large for fluorite type crystals, and small for those of the rutile type, and concluded as an empirical rule that this ratio is the determining factor in the choice between these structures. Using Wasastjerna s radii he decided on 0.67 as the transition ratio. He also stated that this can be explained as due to anion contact for a radius ratio smaller than about 0.74. With our radii we are able to show an even more satisfactory verification of the theoretical limit. In Table XVII are given values of the radius ratio for a large number of compounds. It is seen that the max-... 

In this discussion, two mutually canceling simplifications have been made. For the transition value of the radius ratio the phenomenon of double repulsion causes the inter-atomic distances in fluorite type crystals to be increased somewhat, so that R is equal to /3Rx-5, where i has a value of about 1.05 (found experimentally in strontium chloride). Double repulsion is not operative in rutile type crystals, for which R = i M + Rx- From these equations the transition ratio is found to be (4.80/5.04)- /3i — 1 = 0.73, for t = 1.05 that is, it is increased 12%. But Ru and Rx in these equations are not the crystal radii, which we have used above, but are the univalent crystal radii multiplied by the constant of Equation 13 with z placed equal to /2, for M++X2. Hence the univalent crystal radius ratio should be used instead of the crystal radius ratio, which is about 17% smaller (for strontium chloride). Because of its simpler nature the treatment in the text has been presented it is to be emphasized that the complete agreement with the theoretical transition ratio found in Table XVII is possibly to some extent accidental, for perturbing influences might cause the transition to occur for values a few per cent, higher or lower. 

Big off-centre motions 1 A) have been reported from EPR measurements performed on IT (Ni+, Cu + or Ag +) [47, 65-67,120,121] and (Cr +j [212-214] impurities in some fluorite type crystals (Table 2). Experimental results collected in Table 2 again indicated that off-centre instabilities are not due to size effects. In fact, Ni moves off-centre in the three Cap2, Srp2 and SrCl2 lattices [68, 120,121], while the smaller isoelectronic Cu ion remains on-centre in Cap2, the fluorine ligands suffering an orthorhombic T2g t2g + eg) IT distortion [47,48,68]. 

Off-Centre Impurities in Fluorite-Type Crystals Microscopic Origin... 

In ionic crystals, reconstruction effects can also be involved in the stabilization of polar surfaces (Tasker s type 3). For instance, the (100) surface of the fluorite-type crystal of Li20 becomes stable if half of the Li atoms are moved from the bottom face of the slab to the top face above the oxygen atoms to produce a zero-dipole structure (Figure 39). In fact, this kind of surface has been observed experimentally. ... 

In deriving theoretical values for inter-ionic distances in ionic crystals the sum of the univalent crystal radii for the two ions should be taken, and corrected by means of Equation 13, with z given a value dependent on the ratio of the Coulomb energy of the crystal to that of a univalent sodium chloride type crystal. Thus, for fluorite the sum of the univalent crystal radii of calcium ion and fluoride ion would be used, corrected by Equation 13 with z placed equal to y/2, for the Coulomb energy of the fluorite crystal (per ion) is just twice that of the univalent sodium chloride structure. This procedure leads to the result 1.34 A. (the experimental distance is 1.36 A.). However, usually it is permissible to use the sodium chloride crystal radius for each ion, that is, to put z = 2 for the calcium... 

TI2O3 has a cubic crystal structure, K7h, la 3, and a = 10.5344 A. It is a fluorite-type structure with vacancies in oxygen layers (Figure 6.19). 

Praseodymium dioxide crystallizes in the fluorite-type structure (space group Fm3m) with four praseodymium atoms and eight oxygen atoms per unit cell. This structure may be visualized easily as an infinite array of coordination cubes (each consisting of a Pr atom at the center with eight O atoms at the corners) stacked so that all cube edges are shared. 

Yttrium oxyfluoride and several similar compounds have the fluorite type of structure with the oxygen and the fluorine distributed among the anion positions. Both Templeton (118) and Hoppe (51) have considered the Madelung constants of the crystals. There are three forms, tetragonal, rhombohedral, and cubic. Their Madelung constants are given in Table VII. 

There are two main types of ionic oxides which are empirically formulated MOg. Where the metal ion is large (Th, 0.95 A Ce +, 0.92 A U, 0.89 A) the crystals are built up of fluorite-type unit cells with 8 4 co-ordination. But where the metal ion is smaller (Sn, 0.71 A Ti, 0.68 A) the structure is based on the rutile lattice with 6 3 co-ordination. Other examples of this structure are VOg, RuOg, PbOg and TeOg. The rutile lattice is slightly deformed in MoOg and WOg. 

A simple possibility for a complex halide is that it adopts a structure of a halide (or oxide) A, X with A and B replacing, either statistically or regularly, the positions occupied by atoms of one kind in the binary halide (oxide) these form our class (a) in Table 10.1. Known examples are all fluorides, that is, they are ionic crystals, and the basic requirement is that the ions A and B are of similar size and carry charges appropriate to the structure, as in Na Y F4 or KaU Fg with structures of the fluorite type. Other complex halides are conveniently classified according to the type of grouping of the B and X atoms in the crystal. These atoms may form a finite group, in the simplest case a mononuclear group BX , or the B... 

The dioxides of Ce, Zr, Th, and U all crystallize with structures of the fluorite type, and it is interesting to note that three of the complexes we have described... 

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