Crystal structures fluorite

Since ceria exhibits a cubic fluorite crystal structure, the noncubic nanostructures, such as NRs, NWs, and nanoplates, are fabricated under experimental conditions that are suitable to break dovm the symmetry. One general way is to exploit an appropriate intermediate, such as Ce(OH)3 or Ce(OH)C03. The rare earth hydroxide crystalline NRs/NWs/ NTs are obtained in basic solutions imder hydrothermal treatment, which is discussed in Section 2.3. If certain oxidant is present in the hydrothermal treatment, the ceria NCs could be obtained in a one pot manner. In this way, rod-like, wire-like, or tube-like nanoceria could be synthesized. If the hydrothermal treatment is carried out under oxygen free... 

Figure 2.3 The cubic fluorite crystal structure of a compound of stoichiometry AX2. The cations (A) occupy alternate cube centers within a simple cubic array of anions (X).

The cubic fluorite crystal structure (space group Fm3 m) can be described as an fee array of cations in which all the tet interstices are filled with anions and the oet sites are empty. Alternatively, as shown in Figure 2.3, the ionic arrangement can be viewed as a simple cubic array of anions with cations occupying alternate cube centers. 

Both NiSi2 and CoSii crystallize in the bulk fluorite crystal structure. The (111) surface of these solids is a stack of Si-Co-Si or Si—Ni—Si trilayers. Consequently, these surfaces are structurally similar to the disulfides and diselenides discussed in sect. 5.3.2. There have been several studies of the (111) surfaces of NiSi2 and CoSi2, although the overall structural trends... 

The only alkali-metal oxide that has been investigated is an early LEED study of fluorite structure NazO lll). The (111) surface of the fluorite crystal structure consists of a stack of Na-O-Na trilayers offering the possibility of two terminations. The Na20(lll) surface is found to terminate at a complete Na-O-Na trilayer. A detailed structural study of surface relaxations was not performed (Andersson et al., 1977)... 

Fluorite crystal structure, which allows accommodation of fission products (see Section 6.5). 

FIGURE 6.7 The fluorite crystal structure. The fluorine ions occupy the eight tetrahedral sites (or the Ca ions occupy half the cube sites with an empty one at the center of the unit cell). 

Besides the co-precipitation method, other common methods for the synthesis of nanomaterials, such as the hydrothermal method, the solvothermal method, the sonochemical method, pyrolysis, the sol-gel process, and the reverse micelles method have also been applied for the synthesis of ceria nanomaterials. The typical shape of as-prepared nanocrystals is always polyhedral because of the fluorite crystal structure of ceria (Fig. 6.1). 

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... 

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-... 

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 fluorite structure is a common one for compounds that have 1 2 stoichiometry. A great many compounds have formulas that have twice as many cations as anions. Examples include compounds such as Li20 and Na2S. These compounds have crystal structures that are like the fluorite structure but with the roles of the cations and anions reversed. This structure is known as the antifluorite structure, in which there are eight cations surrounding each anion and four anions surrounding each cation. The antifluorite structure is the most common one for compounds that have formulas containing twice as many cations as anions. 

Between the two possible defects which may be responsible for hyperstoichiometry (i.e. uranium interstitials or oxygen vacancies) the latter is well evidenced by measurements of lattice parameter and densityand neutron diffraction Oxygen interstitials order in U4O9 to provide a crystal structure which can be derived from the fluorite structure of U02+x-... 

FIGURE 1.39 The crystal structure of fluorite, CaF2. (a) Computer generated unit cell as a ccp array of cations Ca,... 

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