Fluorite-Type and Related Structure Systems
4.2. FLUORITE STRUCTURE WITH ANION DEFICIENCY
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cations are a little larger than oxygen anions which are represented by two types of shaded patterns for distinguishing their layers. When viewed along (112), the structure clearly exhibits tripoles, 02-(type l)-M4+ _02- (type 2), and the surface has no residual charge; thus, the tripoles parallel array is a stable configuration (Fig. 4.2b).
structure is probably the basis of fast oxygen diffusion in fluorite-related compounds with modulated structure. The anion-deficient model in Fig. 4.3b is known as the coordinated defect model (Martin, 1974; Hoskins and Martin, 1976, 1995), and is very useful for understanding the structure and properties of fluorite-related structures.
4.2.1. OXYGEN MIGRATION IN FLUORITE STRUCTURE
Any oxygen anion vacancy will cause the corrugation of two adjacent cation c1ose- packing layers due to local distortions of the cations for extra-positive charges. The extra- positive charges should attract the negatively charged oxygen anions, resulting in migration of the oxygen anions. The migration may compensate the local extra-positive charge near the vacancy site, but leaves some unbalanced charges at the other site. The continuous jump of the anions is the oxygen diffusion process. Anion diffusion in the fluorite structure does not require significant change in the cation sublattice but only needs the cation sub lattice to be modulated, resulting in the formation of distortion waves. If the cations can vary their valent states, oxygen migration could be promoted by the valence variation (or electron hopping). This may be the reason that the oxygen diffusion is so fast and easy in Ce, Pr, Tb high oxides. If we use the temperature at which the diffusion constant is measured divided by the melting point (Matzke, 1975) as the normalized temperature, the diffusion constants of anion sublattices in various fluorite compounds, as a function of the normalized temperature, are rather scattered, similar to the liquid-like behavior even at low temperature (Oishi et al., 1981).
Figure 4.4 demonstrates the oxygen diffusion process in a fluorite structure with an oxygen vacancy. Figure 4.4a exhibits a fluorite structure in which one oxygen anion is missing and the positions of the cations in the tetrahedron containing the vacancy are distorted. The distortions of the cations would increase the distances between them,
(a)
Figure 4.4. Schematics showing the oxygen diffusion process in a fluorite structure with an oxygen vacancy.
(a) Fluorite unit cell with an oxygen vacancy, (b) the cation charge variation and the possible displacement directions of the cations and the neighbor anions, (c) the migration of an oxygen atoms, and (d) the displacements of the cations as a result of oxygen diffusion.
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forming a pathway for the migration of oxygen atoms. At the same time the neighboring oxygen anions, the B anion for example, are attracted by the excess local positive charges to move closer to the vacancy site. These two factors are shown in Fig. 4.4b-d, resulting in anion migration from the left side toward the right side. If the distortions form a waving structure across the specimen, the propagation of the distortion wave will promote oxygen anion diffusion. However, the distortions are locally small, (0.03 nm for oxygens and 0.02 nm for cations (Kang and Eyring, 1997a,b» and can be minimized by forming a distorted standing wave, resulting in the ordering of oxygen vacancies.
4.2.2. MODULES OF FLUORITE STRUCTURE WITH OXYGEN DEFICIENCY
Oxygen anion deficiency is a key characteristic of fluorite and related structures. The cation tetrahedra have caught the attention of many chemists (Martin, 1974; Ray and Cox, 1975; Ray et al., 1975; Hoskins and Martin, 1976). Using the nondeficient and deficient coordinated tetrahedra, a variety of structures can be built and the results agree very well with the data provided by x-ray and neutral diffraction (Martin, 1974; Hoskins and Martin, 1976, 1995). Although the idea of using coordinated defects in constructing the unit cells of many important materials was initiated more than two decades ago, it is only recently that a new approach has been proposed for understanding the structure of the entire family of fluorite-related compounds (Kang and Eyring, 1995, 1997a,b; Kang et al., 1996). Moreover, the new theory predicts the structures of compounds with known unit cell parameters but not atom positions. The key difference between the new approach and the coordination defect model is that the structure is divided into deficient fluorite units (called modules) rather than the local coordinated defects assumed in traditional theory. The basis of this approach is that the fluorite-related structures always exhibit superstructures and substructures closely related to fluorite. In this section, a variety of possibilities for introducing oxygen anion deficiency into the fluorite structure are described.
Figure 4.5 gives the possible fluorite modules with oxygen anion deficiency. There are only three possible configurations for creating oxygen vacancies: (1) no oxygen vacancy (denoted F); (2) one oxygen vacancy per unit cell for two cases: the vacancy is located in the top layer ofthe tetrahedra (denoted Ui , with i = 1, 2, 3,4, where i indicates the positions of the four tetrahedra), or the vacancy belongs to tine tetrahedra at the bottom half of the unit cell (denoted Di ); and (3) two oxygen vacancies (denoted
W;,
where (i,j) = (1,3), (2,4), (3, 1), or (4, 2), respectively, representing the upper and lower halves of the fluorite unit cell). The numbers I, 2, 3, 4 indicate the order of the tetrahedra in a fluorite module. The modules viewed along [112] are also displayed in Fig. 4.5, where the triangle represents a tetrahedron with anion vacancy and U4 , DI , and (Ul , D3)
(or
WD
indicate the positions of the anion-deficient tetrahedra in the fluorite unit cell. If a unit cell loses more than two anions, the structure will transform into different crystal systems rather than the fluorite-related structure. Thus, this situation is unlikely to occur if the structure is still fluorite related.As we discussed, the arrays can exist due to the balance between the repulsive and attractive Coulomb forces among the cations and anions. These four types of fluorite modules should have different dipole moments due to the missing oxygen anions and the newly balanced configuration. From the energy point of view they have metastable state, but they can assemble to form a stable state for a new fluorite-related structure.
From the point of view of atom distortions, Fig. 4.6 shows the possible configurations of lattice distortion due to the creation of anion vacancies corresponding to the U, D, and W types of modules, where the unit cell is projected along [112]. In the U and D types of anion-deficient modules (Fig. 4.6), cation distortion is indicated by a curve and it is possible to find a way to assemble these unit cells linearly along a direction to compensate the distortions. The curvature of the distortion of a module also implies the electric dipole orientation. When they are assembled to form a sinusoidal-like distortion wave, the macroscopic average of the dipoles or displacements of cations and anions is zero. Thus, the entire structure is stable.
This analysis simply indicates that the four fluorite modules could be the building blocks for constructing the entire fluorite-related phases. This is the case for homologous phases of rare earth higher oxides and some fluorite-related structures, as will be shown.
4.2.3. PYROCHLORES AND C-TYPE RARE EARTH SESQUIOXIDE STRUCTURES
Ideal pyrochlore structure is a body-centered cubic with space group Fd3m and composition formula A2M20 7, or M40 7 type (Fig. 4.7). Gd2(Ti1_ xSnx)z07 is an example.
The pyrochlore structure can be described from the fluorite structure (Aleshin and Roy, 1962; Longo et al., 1966) or viewed as an oxygen octahedra of M cations, with comer- sharing to form a 3-D network with cubic symmetry, interpenetrated with Cu20-like
F = fluorite unit cell without vacancy
Dj ( i
=
I, 2, 3,4) Fluorite module with one oxygen vacancy at bottom partUi ( i= 1. 2, 3, 4. ) Fluorite module with one oxygen vacaney at top part
wJ(i,j = 1 and 3, 2 and 4, 3 and 1,4 and 2) Fluorite module with two oxygen vacancie at top and bottom parts
Figure 4.5. Four types of fluorite modules for constructing the unit cell. (a) Fluorite without oxygen vacancy, designated F, (b) fluorite with one oxygen vacancy in the top tetrahedron layer, designated Ui , (c) fluorite with one oxygen vacancy in the bottom tetrahedron layer, designated Di , and (d) fluorite with two oxygen vacancies along a body diagonal direction, designated as WJ.
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network (i.e., A20) (Sleight, 1968). In our approach the pyrochlore structure can be assembled by four U and four D fluorite modules. The composition of U and D modules is M407 . If M has two kinds of cations (A and M), the structure is A2M207 • As discussed U and D have four orientational variants, so a compound with composition Rg014 can be modeled using only eight possible fluorite modules with only one vacancy in each.
However, if we disallow six of the possibilities and utilize the remaining U and D fluorite modules we can build a slab with a different arrangement of the U and D modules. The
Figure 4.6. The fluorite modules viewing along the [112] direction of the fluorite unit cell, where the local distortion waves are indicated.
resulting structure is pyrochlore. Figure 4.7 gives the structure and model of pyrochlore derived from the U3 and Dl fluorite modules. The arrangement of the two types of fluorite modules builds the ideal pyrochlore structure, where the oxygen vacancies in these drawing are denoted with open circles labeled V. Modules U3 and Dj , form a pair of body-diagonal vacancies. This situation occurs also in all phases of the rare earth homologous series. The pyrochlore structure should have four orientational variants because only two modules are chosen from the possible eight modules. Pyrochlore microdomains have been observed in samples quenched from a single phase. Doping is a way to limit the number of modules. Adding tetravalent cations could fix oxygen in the adjacent anion sites. The smaller size of cations with tetravalence and a little larger size rare earth cations can be ordered so that the closest packing layers of cations are separated into two types: trivalence and larger rare earth cation layers, and smaller tetravalence cation layers. These two types of closest-packing layers stack alternately with two oxygen close-packing layers inserted to form the pyrochlore structure.
Obviously the oxygen layers located close to the trivalence cation layer prefer to have oxygen vacancies to match the charge balance and the dimensional requirements. The oxygen layers located close to the tetravalence cations have to be modified to satisfy the demands of tetravalent cation. For ionic cation it is the size matching and charge
U ( here i U3) type module D ( here i Dl> type module
,,1.
- - - -
-
Dl- -
Dl...-
...- --
--
U3- -
U3,...- ....- --
-- -
~.-
Pyrochlore structure is a 3-D sembling of U3 and Dl modules
Ideal pyrochJore tructure model built b d on the U3 and Dl modele
Figure 4.7. Ideal pyrochlore structure built by fluorite modules U (for example U3) and D (for example Dj ),
where V denotes vacancy sites formed by sharing the common face of the two fluorite modules.
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balancing, but for transition metal it is not only the size factor and charge balance but also the ligand field effects that are important for determining the structure. If the difference between the tetravalent and trivalent cations is very small, as binary rare earth high oxides, the phase with pyrochlore structure is unlikely to exist. It is true that no binary rare earth pyrochlores have been found. But numerous pyrochlores containing rare earth ions are known, such as Pr2Ru207. The A and M cation ordering is expected, and A2M206 or A4M4012 is possible because of the modules changing to M406 with double vacancies in a module.
The structure of pyrochlore really is transitional between fluorite (M40S) and AB03
(M406) perovskite. It is very common since the vast majority of the elements in the periodic table can form this structure. Based on different elements it is either like fluorite (an oxygen position is larger in x axis, for example 0.375) or similar to perovskite (an oxygen position is smaller in x axis, for example 0.3125). Compounds with the pyrochlore structure have widely diverse properties. Some are insulators, while others are low-activation-energy semiconductors. In rare cases A2 HM2 4+07 pyrochlores may have metallic properties. Ferroelectricity is observed for pyrochlore compounds except for R2HM24+07 (R
=
rare earth elements). Diamagnetism, paramagnetism, and ferromag- netism also have been observed (Subramanian et ai., 1983; Subramanian and Sleight, 1993). The M cations usually are transition metals that usually have perovskite structure (for example, Ti, Mn, Mo, Sn, V, Fe, Zr, Nb, Cr, Pt, Ru, etc.). The A cations usually are rare earth elements having fluorite-related structure. But the A cations also can be trivalent transition metal elements such as Bi, TI, and In, and double-valent cations, such as Mn2+ and Ca2+, or single-valent cations such as Na+.From a functional materials point of view compounds with pyrochlore structure and metallic conductivity are very interesting: Nd2Ir20 7 (Prt
=
28 X 10-2 0 cm, where rt stands for room temperature), Sm2Ir207 (Prt=
3.5 X 10-2 0 cm), EU2Ir207 (Prt=
7.0 X 10-2 0 cm), DY2Ir207 (Prt=
2.0 X 10-1 0 cm), Gd2Pt20 7 (Prt=
7 X 10-2o
cm), EU2M0207 (Prt=
5 X 10-2 0 cm), etc., and metallic Ir02 and Ru02 (Subramanian and Sleight, 1993). Electric conductivity is due to the mixture of the narrow d bands with the broad posttransition metal 6s or 6p bands, broadening the t2g band to allow metallic conduction. Nd2M020 7, Sm2Mo207' and Gd2M020 7 have ferromagnetism and highest electric conductivity as metals (Greedan, 1991). Oxygen ion conductivity has been found in Gd2Zr207 (Van Dijk et ai., 1983). The structure of this compound at high temperature is disordered fluorite structure with ionic conductivity is 68 (0 cm)-l at 727°C (Van Dijk et ai., 1983). These properties also indicate that the pyrochlore structure is an intermediate structure between perovskite and fluorite structures.The C-type rare earth sesquioxide structure is fluorite related. In the C-type sesquioxide, which is a body-centered cubic, every cation has two vacant nearest- neighbor anions. A W module, which has two vacant oxygen sites, has four orientational variants providing every anion site an equal opportunity to be vacant. These modules yield the correct composition, but, they alone cannot be packed together to give the C- type structure. But if only three types of W's are required to construct the unit cell of the C-type sesquioxide it will do it. Figure 4.8c (Galasso, 1970) gives the structure of the C- type sesquioxide. Three types of units are found in which the origin of the fluorite unit cell is shifted down to [0,0,4]. Then each cube has only six oxygens, leaving two oxygen vacancies
(wi>.
The oxygen cube in this unit has a missing body-diagonal oxygen and three units have missing oxygens along three different body-diagonal directions (Fig.4.8b). Stacking these three units by sharing faces (Fig. 4.8c), gives the C-type sesquioxide
structure. The oxygens missing in the C-type rare earth sesquioxide equally belong to the two sublattices (Fig. 4.8). This reveals an important rule: in the fluorite structure there are eight oxygens, which equally belong to the two sublattices; i.e., each sublattice has four oxygens which form tetrahedron arrays that are oriented against each other, and they interpenetrate to build the oxygen cube in the fluorite structure. These two oxygen sublattices in fluorite structure should be treated equally in any case. In other words, if one oxygen sublattice has a vacancy, the other one must also have one. In our oxygen- anion-deficient modules, four U must be equivalent to four D. This equal choice can be tailored by doping cations with different valences.
Oxygens construct a close-packing layer in the rutile structure, while oxygens and the A cations create a close-packing layer in the perovskite structure. These layers are the fundamental elements to be stacked with the cation layers which only occupy half of the
(a)
Fluorite unit cell
Gal 0' fluorite unit cell as the origin bifted to [00 112)
Type 3 Galas 0' fluorite unit cell with body diagonal oxygen mi ing
Module W?
Type I Gal 0' fluorite unit cell with body diagonal oxygens mi ing
o g
Cation atomOxygen anion in the flf t oxygen ublattice Oxygen anion in the
econd oxygen ublattice Oxygen vacancy in the first oxygen sublanice Oxygen vacancy in the
econd oxygen ublattice
Type 2 Galas 0' fluorite unit cell with body diagonal oxygen mi sing
C-type rare earth se quioxide structure
Figure 4.8. The C-type rare earth sesquioxide structure, (a) Kang and Eyring's fluorite modules, (b) Galasso's fluorite units, and (c) the arrangement of these units in the C-type rare earth sesquioxide structure.
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. available sites of the oxygen close-packing layers for rutile and perovskite structures. The cations in rutile and perovskite structures always have the ability to move from one suitable site to another, causing the octahedra to vary the connection from corner sharing to edge sharing or face sharing. In the fluorite structure, however, the cations and the anions both form close-packing layers, but only two oxygen sublattice can create equal numbers of vacancies which make oxygen migration easy without tailoring the cation sublattice. In the C-type rare earth sesquioxide structure the cation frame remains the same as in fluorite, but only two oxygen sublattices have been tailored to form vacancies.
This feature is a key point for understanding the structural characteristics of fluorite- related compounds.