Calcium fluoride fluorite structure

Pure stoichiometric CeOj has the calcium fluoride (fluorite) type of structure with space group / m3m. It has been also well known as a Non-stoichiometri compound and there are variety of studies concerning about the defect and redox chemistry [17-19]. Among them, Stefano has already reported the electron localization in pure and defective ceria by a unified LDA+U approach as shown in Figure 4-9 [20]. Here we can see the decrease of band gap of both cerium sub oxide... 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

Anion Interstitials The other mechanism by which a cation of higher charge may substitute for one of lower charge creates interstitial anions. This mechanism appears to be favored by the fluorite structure in certain cases. For example, calcium fluoride can dissolve small amounts of yttrium fluoride. The total number of cations remains constant with Ca +, ions disordered over the calcium sites. To retain electroneutrality, fluoride interstitials are created to give the solid solution formula... 

FIGURE 7.5 The calcium fluoride structure (also known as the fluorite structure). 

The fluorite structure is named after the mineral form of calcium fluoride, CaF2, which is found in the U.K. in the famous Derbyshire Blue John mines. The structure is illustrated in Figure 1.39. It can be described as related to a ccp array of calcium ions with fluorides occupying all of the tetrahedral holes. There is a problem with this as a description because calcium ions are rather smaller than fluoride ions, and so, physically, fluoride ions would not be able to fit into the tetrahedral holes of a calcium ion array. Nevertheless, it gives an exact description of the relative positions of the ions. The diagram in Figure 1.39(a) depicts the fourfold tetrahedral coordination... 

Crystals with the Rutile and the.Fluorite Structures Interionic Distances for Substances of Unsymmetrical Valence Type.—In a crystal of a substance of unsymmetrical valence type, such as fluorite, CaFs (Fig. 13-10), the equilibrium cation-anion interionic distance cannot be expected necessarily to be given by the sum of the crystal radii of the bivalent calcium ion and the univalent fluoride ion. The sum of the univalent radii of calcium and fluoride, 2.54 A, would give the equilibrium interionic distance in a hypothetical crystal with attractive and repulsive forces corresponding to the sodium chloride arrangement. 

Many ionic compounds of AX2 stoichiometry possess the CaF2 (fluorite), or Na20 (antifluorite) structures shown in Figure 3.15. Fluorite is similar to CsCl, but with every other eight coordinate cation removed. Each fluoride anion is tetrahedrally coordinated by calcium ions. This structure is adopted by several fluorides and oxides. In the antifluorite structure, the coordination numbers are the inverse. Most oxides and other chalcogenides of the alkali metals (e.g. Na2Se, K2Se) possess the antifluorite structure, but so do some more covalent compounds, such as the silicides of Mg, Ge, Sn, and Pb. 

The fiaorite structure Calcium fluoride crystallizes in the fluorite structure cubic F/n3m (Fig. 43). The coordination numbers are 8 for the cation (right fluoride ions form a cube about each calcium ion) and 4 for the anion (four Ca- ions tetrahedrally arranged about each F ion). 

The fluorite structure. Figure 7-9, can be described as having the calcium ions in a cubic close-packed lattice, with eight fluoride ions surrounding each one and occupying all of the tetrahedral holes. An alternative description of the same structure, shown in... 

In this paper we are considering the metastable states of some of the chemical compounds with formula RX2 which crystallize in a lattice similar to that of calcium fluoride (Cap2) known as fluorite Hayes). In such structure crystallizes pure stoichiometric UO2 as well as its non-stoichiometric coimterparts known as hyperstoichiometric UO2+X and h q)ostoichiometric... 

The general formula of crystals with the fluorite structure is MAS. The mineral fluorite, calcium fluoride, CaF2, which names the group, is sometimes also called fluorspar. 

Of substances MX.j, silicon dioxide (radius ratio 0.29) forms crystals with tetrahedral coordination of four oxygen ions about each silicon ion, magnesium fluoride (radius ratio 0.48) and stannic oxide (radius ratio 0.51) form crystals with octahedral coordination of six anions around each cation (the rutile structure, Figure 18-2), and calcium fluoride (radius ratio 0.73) forms crystals with cubic coordination of eight anions around each cation (the fluorite structure. Figure 18-3). The ligancy (coordination number) increases with increase in the radius ratio, as indicated in Figure 18-1. 

Calcium fluoride, Cap2, occurs in the mineral fluorite. The purple color is caused by defects in the crystal structure. 

Fluorite, CaF2, shows a radius ratio of 0.96, which predicts that the calcium ions will occupy cubic holes formed by the fiuoride anions. Note in Figure 7.22a that the calcium ions do indeed occupy such sites. However, as required by stoichiometry (see Problem 7.39), half of the cubic holes must be unoccupied. (Note that the center of the unit cell is an unoccupied cubic hole formed by the fluoride ions.) The unit cell of the lattice therefore cannot be the simple cubic of fluorides with one calcium in the body. Rather, a larger unit cell of fee calcium ions with fluorides filling the tetrahedral holes is the more appropriate description. Note that the coordination number of the fluorides is 4, which is consistent with Equation (7.6). Table 7.11 indicates that there is a 90% correlation between the known crystal structure and the calculated radius ratio for compounds that assume the fluorite structure. 

Cerium dioxide CeOg has a fluorite-type structure (space group Frr m), which is named after the mineral form of calcium fluoride. Figures 1.2(a)-(c) show the crystal structure of cerium dioxide CeOs. The cerium and oxygen atoms are located at the 4a 0,0,0 and 8c 1/4,1/4,1/4 sites, respectively. 

Fluorite is a mineral composed of calcium fluoride, CaF2- This mineral gives its name to the fluorite structural type. Its structure (Figure 14.11a) has cubic symmetry, the space group is Fm-3m (a = 5.471 A [31]). The structure can be described as a face-centred cubic (fee) array of cations in which all the fourfold coordinated interstices are filled with anions and the sixfold coordinated ones are empty (Figure 14.11a). The coordination number of cations is eight (cube) and that of anions is four (tetrahedron). 

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... 

The crystal structure of fluorite is characterized by a cubic close-packed structure of calcium ions with fluoride ions in all tetrahedral holes. Other compounds with this structure include the fluorides of Ba, Pb(II) and Hg (II) and the oxides of Ce(IV) and Zr(IV). 

Figure 51 The structure of fluorite visualized as cubic packing of fluoride ions. The calcium ions are located at the centers of cubes, staggered in both the vertical and horizontal directions.

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