Crystal fluorite

Instead of using a reactor or other source of radiation, natural ionizing radiation can excite electrons in the crystal. Fluorite can be red, green, or purple due to natural irradiation. The same irradiation can cause topaz to be brown (see below). 

Analytical Methods. Fluorite is readily identified by its crystal shape, usually simple cubes or interpenetrating twins, by its prominent octahedral cleavage, its relative softness, and the production of hydrogen fluoride when treated with sulfuric acid, evidenced by etching of glass. The presence of fluorite in ore specimens, or when associated with other fluorine-containing minerals, may be deterrnined by x-ray diffraction. 

A small but artistically interesting use of fluorspar is ia the productioa of vases, cups, and other ornamental objects popularly known as Blue John, after the Blue John Mine, Derbyshire, U.K. Optical quaUty fluorite, sometimes from natural crystals, but more often artificially grown, is important ia use as iafrared transmission wiadows and leases (70) and optical components of high energy laser systems (see Infrared and RAMAN spectroscopy Lasers) (71). 

The fluorite stmcture, which has a large crystal lattice energy, is adopted by Ce02 preferentially stahi1i2ing this oxide of the tetravalent cation rather than Ce202. Compounds of cerium(IV) other than the oxide, ceric fluoride [10060-10-3] CeF, and related materials, although less stable can be prepared. For example ceric sulfate [13590-82-4] Ce(S0 2> certain double salts are known. 

Solids tend to crystallize in definite geometric forms that often can be seen by the naked eye. In ordinary table salt, cubic crystals of NaCl are clearly visible. Large, beautifully formed crystals of such minerals as fluorite, CaF2, are found in nature. It is possible to observe distinct crystal forms of many metals under a microscope. 

The compounds of the MMe205F type, where Me = Nb or Ta M = Rb, Cs, Tl, crystallize in cubic symmetry and correspond to a pyrochlore-type structure [235-237]. This structure can be obtained from a fluorite structure by replacing half of the calcium-containing cubic polyhedrons with oxyfluoride octahedrons. 

Due to the intermediate coupling the sign of the crystal field matrix element 6 is reversed compared to the pure Russell-Saunders state. Thus for 8-fold cubic coordination a F7 ground state was found. From EPR measurements on Pu3"1" diluted in fluorite host lattices, a magnetic moment at T=0 K can be calculated, ranging from li ff = 1.333 (in Ce02) to y ff = 0.942 (in SrCl2) (24,... 

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... 

Huggins, who has particularly emphasized the fact that different atomic radii are required for different crystals, has recently [Phys. Rev., 28, 1086 (1926)] suggested a set of atomic radii based upon his ideas of the location of electrons in crystals. These radii are essentially for use with crystals in which the atoms are bonded by the sharing of electron pairs, such as diamond, sphalerite, etc. but he also attempts to include the undoubtedly ionic fluorite and cesium chloride structures in this category. 

The Fluorite Structure.—In Table XI are given the observed interatomic distances in crystals with the fluorite structure. There is good... 

Inter-Atomic Distances in Fluorite Type Crystals... 

We have accordingly shown that for values of the ratio of the crystal radius of the cation to that of the anion greater than 0.65 the fluorite structure is stable for values less than 0.65 the rutile structure is stable. 

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-... 

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,... 

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. 

Many complex ions, such as NH4+, N(CH3)4+, PtCle", Cr(H20)3+++, etc., are roughly spherical in shape, so that they may be treated as a first approximation as spherical. Crystal radii can then be derived for them from measured inter-atomic distances although, in general, on account of the lack of complete spherical symmetry radii obtained for a given ion from crystals with different structures may show some variation. Moreover, our treatment of the relative stabilities of different structures may also be applied to complex ion crystals thus the compounds K2SnCle, Ni(NH3)3Cl2 and [N(CH3)4]2PtCl3, for example, have the fluorite structure, with the monatomic ions replaced by complex ions and, as shown in Table XVII, their radius ratios fulfil the fluorite requirement. Doubtless in many cases, however, the crystal structure is determined by the shapes of the complex ions. 

The theoretical result is derived that ionic compounds MXS will crystallize with the fluorite structure if the radius ratio Rm/Rx is greater than 0.65, and with the rutile (or anatase) structure if it is less. This result is experimentally substantiated. 

Crystal stmcture monoclinic or cubic (fluorite) when stabilized... 

Powder XR diffraction spectra confirm that all materials are single phase solid solutions with a cubic fluorite structure. Even when 10 mol% of the cations is substituted with dopant the original structure is retained. We used Kim s formula (28) and the corresponding ion radii (29) to estimate the concentration of dopant in the cerium oxide lattice. The calculated lattice parameters show that less dopant is present in the bulk than expected. As no other phases are present in the spectrum, we expect dopant-enriched crystal surfaces, and possibly some interstitial dopant cations. However, this kind of surface enrichment cannot be determined by XR diffraction owing to the lower ordering at the surface. 

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