From WolfWikis

Fluorite/Antifluorite

Figure 1: An ideal cubic fluorite CaF₂ with Pm-3m symmetry. Pink atoms are F^1- anions and turquoise atoms are Ca²⁺ cations.

Figure 2: Fluorite structure showing anion centered tetrahedra with cation corners and edge sharing.

CaF₂ has the basic crystal structure knowns as fluorite, which is shown in Figure 1. It is one of the most common crystalline solid types found in nature. The basic structure for a fluorite can be described as face centered cubic packing of cations, with anions in all of the tetrahedral holes. It can also be described as simple cubic packing of anions with cations in the cubic (8-coordinate) holes. The unit cell can also be described as composed of 8 tetrahedra, each with cations at the corners and an anion in the center. These tetrahedra form a three-dimensional edge-sharing network. See Figure 2. To maintain the ideal fluorite structure with cation-anion contact and closest packed cations, the cation to anion radius ratio must be 4.38. A smaller cation to anion radius ratio would push the cations apart such that they would not be closest packed, as observed in all known compounds. A larger ratio would mean that the anions could not be in contact with all 4 coordinating cations at once and thus is not possible. Fluorite tends to have mainly ionic cation-anion bonds. Although an ideal fluorite/antifluorite structure has a very high atom density, cation to anion radius ratios tend to be much closer to one, forcing the closest packed atoms apart and dramatically decreasing the density. [1]

Figure 3: An ideal cubic antifluorite with Pm-3m symmetry. Pink atoms are cations and turquoise atoms are anions.

The antifluorite structure has exchanged positions of the cations and anions. The anions adopt a face centered cubic arrangement with cations in the tetrahedral intersticies. A basic antifluorite structure is shown in Figure 3. The ideal antifluorite would have a cation to anion radius ratio of 0.228. As discussed for the fluorite, the ideal ratio is not observed - for the antifluorite structure observed cation to anion ratios are higher than the ideal. Antifluorite structures tend to occur for more covalent materials because of the imcreased covalency required by 4 coordination. By contrast the 8-coordination of the fluorite cation site is well suited for ionic charge cancelation.

Fluorescence is named after the archetypal structure, CaF₂ and is a property often found in fluorite minerals due yttrium and other impurities.

Ag₂Te

Figure 4: Crystal structure of α-Ag₂Te with Fm3m symmetry. The green atoms represent the Te anions and the pink atoms represent the Ag cations.

The crystal structure of one of the polymorphs of Ag₂Te is considered an anti-fluorite structure with Te atoms occupying the face centered lattice positions and Ag atoms occupying the tetrahedral interstitial sites in the face centered lattice[2]. Three structural modifications of Ag₂Te exist at different temperature phases, but only one structure phase, α-Ag₂Te, adopts an antifluorite structure. The α-Ag₂Te occurs at temperatures between 418 K and 1075 K and has a face centered cubic anti-fluorite structure as shown in Figure 4[3]. In the α-Ag₂Te anti-fluorite structure, each of the Ag atoms is tetrahedraly coordinated to four Te atoms and each Te atom is coordinated to eight Ag atoms.

Figure 5: Crystal structure of α-Ag₂Te.

The anti-fluorite α-Ag₂Te structure displays ionic conductivity properties. Ionic conductivity involves the movement of current via transport ions. In the case of solid ionic conductors, current flows by diffusion of ions within the lattice. Crystalline solids with ionic conductivity must have interstitial vacancies that provide spaces for ions to move to. If vacant sites are available, ions can travel through the crystal lattice by hopping from an occupied site to a vacant site[4]. In the case of α-Ag₂Te, Ag ions in the lattice move between tetrahedral sites through empty octahedral intersticies[5].

To illustrate the importance of structural relations to ionic conductivity, the other two Ag₂Te structures are briefly discussed. The other two structures of Ag₂Te are β-Ag₂Te and γ-Ag₂Te. The first phase β-Ag₂Te, which occurs at temperatures below 400K, has a monoclinic type structure and displays no ionic conductivity properties. Only at temperatures above 400K, is ionic conductivity properties are observed, coincident with the phase change from the monoclinic structure of β-Ag₂Te to the anti-fluorite structure of α-Ag₂Te. The ionic conductivity of Ag₂Te increase even more at temperatures above the second phase change at 1075K when the body centered cubic structure of γ-Ag₂Te is thermodynamically favored[3]. The increase in ionic conductivity is due to the increased availability of vacant sites through which the Ag ions can move.

CeO₂

Figure 6: CeO₂ Fluorite Structure with space group Fm-3m. Red atoms are Cerium and Blue atoms are Oxygen.

Cerium(IV) Oxide adopts a classic cubic fluorite structure with space group Fm-3m (see Figure 1). The unit cell, conisting of cerium atoms arranged face-centered with the oxygen atoms, are located within the cell in the tetrahedral intersticies. (Figure 6). SEM images of CeO₂ nanoparticles prepared by hydrothermal synthesis show fastest crystal growth occured in the 100 direction, resulting in octahedral shaped crystals with faces along the 111 [6]. Crystalline CeO₂ is known to exhibit minor defects in which the Ce atoms are reduced from a 4+ state to a 3+ in an oxygen deficient environment. This behavoir can be extrapolated as high surface area ceria nanoparticles grown in open air increase the ability of Ce to change oxidation states. Ce³⁺'s high affinity for oxygen absorption allow for O₂ uptake [7]. Prepared CeO_2-x nanotubes exhibit higher oxygen absorption than the nanoparticles because of their larger surface area (both inner and outer surface of the tubes) [8]. Increased surface area allows greater reactive boundaries for oxygen uptake and release (equation 1). This compound is useful in catalytic converters as oxygen storage material to reduce CO and NO emissions in automobiles.

                     Eq. 1    CeO2 <--> CeO2-x + X/2 O2

K₂PtCl₆

Figure 7: One unit cell and neighboring chlorines of the K₂PtCl₆ structure.

The archetypal K₂PtCl₆ structure [9] can be seen in figure 7 as a molecular/complex antifluorite. One can refer back to figure 3 for the antifluorite structure. A face centered cubic arrangement of PtCl₆^2- octahedra occupy anion sites in the antifluorite structure. Potassium cations occupy tetrahedral interstices, surrounded by four PtCl₆^2- octahedra. Each potassium cation has twelve Cl^- nearest neighbors. Cubic symmetry is maintained (Fm3m) in this structure, but many molecular (anti)fluorites exhibit lower symmetry.

Interesting properties are displayed by members of this family. For example, Mg₂FeH₆ has, according to a 2004 review [10], the highest volumetric hydrogen density of any known hydride. Not only is this of obvious technical merit, but is also chemically interesting because of the high stability of a early transition metal ternary hydride. V through Cu binary hydrides are either poor (in the sense of amount of hydrogen) or non-existent [10], yet it is these types of light materials which would be desirable for hydrogen storage and transportation.

Full-potential DFT suggests that the high stability of Mg₂FeH₆ is due to the relatively large ionic character of the K₂PtCl₆ type structure, compared to other early transition metal hydrides [11]. Unfortunately, this high stability means that it is very difficult to extract hydrogen, but it has been suggested that this stability may in turn allow adjustments which make extraction easier.

LiCaN

Figure 8: Crystal structure of LiCaN.(N-pink, Ca-blue, Li-red)

The LiCaN structure is a derivative of the antifluorite structure.

The calcium atoms occupy half the tetrahedral holes whereas the lithium atoms are displaced from the tetrahedral center positions of the approximately cubic close packed nitrogen matrix, being only 0.135Å from a tetrahedral face.

LiCaN can be prepared from the elements using a mixture of lithium and calcium. LiCaN is obtained as orange colored single crystals with a plate-like habit. This synthesis method also has minor product, Li₃N, with another crystal structure. [12]

PtN₂

It is known that the most popular structure for transition metal nitrides is the rock-salt (NaCl) structure, in which N atoms occupy all the octahedral sites of the FCC metal lattice, as shown in Figure 10. However, platinum nitride was found to be stable with the fluorite structure, in which N atoms occupy all the tetrahedral holes of the FCC Pt lattice, as shown in Figure 11.[13]

Density function calculations show that compared with late transition metal nitrides, less charge is transferred from metal atoms to N atoms in platinum nitride.[14] Therefore the radius of N atoms in platinum nitride are shorter than those in late transition metal nitrides. And the size of the N atoms is small. So platinum nitride should be more stable for the N atoms to occupy small tetrahedral holes and crystallize in fluorite structure.

Calculated total density of states (DOS) shown in Fig.12 of PtN₂ suggests that the stability of fluorite PtN₂ structure can be attributed to the pseudogap effect. [13]The decrease of total DOS at the Fermi level is accompanied by shifting the occupied bonding states to lower energies and the unoccupied antibonding states to higher energies, which makes the fluorite PtN₂ structure stable.

Figure 10: Unit cell schematics of [NaCl] structured PtN. The large and small spheres denote Pt and N atoms, respectively.

Figure 11: Unit cell schematics of the fluorite-structured PtN₂. The large and small spheres denote Pt and N atoms, respectively.

Figure 12: Calculated total density of states (DOS) of PtN₂. The Fermi level is at 0.[13]

Fluorite/Antifluorite Derivative Structures

The Fluorite/antifluorite structure type also can provide the framework from which to understand a series of structures that result from fractional occupancy of the tetrahedral sites.

Figure 13:Drawing of the zinc blende (ZnS) structure type. Zinc atoms are drawn in blue, sulfur in yellow.

The Zinc blende (ZnS) structure type, shown in Figure 13, represents an anti-fluorite derivative in which half of the tetrahedral sites (those on opposing corners of a simple cube of tetrahedral sites) are vacant. This structural packing motif results in an equivalent packing geometry for both anions and cations, each with a tetrahedral coordination by the opposite type of ion, but packed in a face centered cubic (fcc) arrangement.

Removing anions from half the tetrahedral sites on opposing edges of the cube of tetrahedral sites of the antifluorite-type unit cell gives the platinum sulfide (PtS) structure type shown in Figure 14. While the sulfur anions retain their tetrahedral coordination geometry, this anion occupation results in square planar coordination geometry about the platinum centers. From the expanded view of the PtS lattice on the right hand side of Figure 14, it is apparent that this structure type consists of orthogonal chains of edge-sharing PtS4 square planes.

Figure 14. Drawing of the platinum sulfide (PtS) structure type. (Left) Drawing of a cube extracted from the PtS structure to emphasize the relationship to the antifluorite structure. (Center) expanded lattice view looking down the tetragonal c axis. (Right) View looking down the tetragonal a or b axes showing the chains of edge sharing square planes. Platinum atoms are drawn grey and sulfur atoms yellow.

The lead oxide (PbO) structure type also described as a defect version of the halite structure-type can be viewed as a derivative of the fluorite structure type in which half of the tetrahedral oxygen sites are removed from between every other layer of lead atoms, as shown in Figure 15. This is a result of the lone pair on lead (II) which occupies space in the “van der Walls” layer between lead oxide sheets.

Figure 15. Drawing of the structure of lead oxide (left) emphasizing the relation to the fluorite structure type, and (right) showing an extended lattice view emphasizing the layered nature of this structure-type. Lead atoms are drawn blue and oxygen atoms red.

The mercuric iodide (HgI₂) structure type can be described as an antifluorite with 3/4 of the tetrahedral sites removed as shown in Figure 16. Like PbO above, no Hg cations are found in the tetrahedral sites of one face (layer) of the simple cube of tetrahedral sites, and only half of the tetrahedral sites on opposing corners are occupied in the other face (layer). The unit cell of HgI2 is twice the size of this simple box since the Hg cations occupy alternating pairs of the opposing corners in the layers above and below as shown in the drawing on the right in Figure 16.

Figure 16. Drawings of the mercuric iodide structure type (HgI2) emphasizing (left) the derivation from the antifluorite structure, (center) the extended lattice looking down the tetragonal c axis, and (right) the extended lattice emphasizing the layered nature of the structure. Mercury atoms are drawn blue and iodine orange.

In cuprous oxide (Cu₂O) again 3/4 of the tetrahedral sites from the antifluorite structure are vacant. Only those on opposing corners of the cube of tetrahedral sites are occupied as shown in Figure 17. This pattern of filling the tetrahedral sites results in an expanded diamond-type lattice as shown on the right of Figure 17. Here the copper site is only two coordinate whereas the oxygen site is four coordinate.

Figure 17. Drawings of the cuprous oxide (Cu₂O) structure type emphasizing (left) the relation to antifluorite structure type and (right) the extended lattice demonstrating the diamond-like lattice connectivity. Copper atoms are drawn in blue and oxygen atoms in red.

References

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[6] Wang, Z.; Feng, X. J. Phys. Chem. B 2003, 107, 13563-13566.

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[12] Cordier, G.; Gudat, A.; Kniep, R.; Rabenau, A. Angewandte Chemie 1989, 101(12), 1689-95.

[13] Yu, R.; Zhang, X.F. Applied Physics Letters 2005, 86, 121913.

[14] Yu, R.; Zhang, X.F. Physical Review B 2005, 72, 054103.

[15] Patil, S. K. R. et al. Physical Review B 2006, 73, 104118