Pyrochlore

From WolfWikis

Pyrochlore Structure

The A₂B₂O₆O' pyrochlore structure is complex (figure 1), but can be viewed as an ordered oxygen-vacancy fluorite. In figure 2, the [001] cross section of A and B cations at a=0 and anion and anion vacancies at a= ~0.125 is shown, where the cations alternate in the direction of any crystallographic axis. The vacancy destroys fluorite symmetry, and removes the vacancy's corresponding O' from the symmetry of the remaining six O.

Figure 1: The A₂B₂O₆O' pyrochlore structure. Blue BO₆ octahedra and maroon O'A₄ tetrahedra are shown. The crystal structure [1] of Tl₂Mn₂O₇ (A=Tl, B=Mn) is used as a representative structure.

Figure 2: A [001] projection of O, O', and vacancies packing on top of a ccp (A=Tl, B=Mn) layer, portraying the pyrochlore structure as an oxygen deficient fluorite (A₂,B₂)(vac,O₆,O'). The viewing direction is perfectly aligned along the [001] axis so that displacement of O away from a high symmetry position can be seen.

The A site cation, typically a trivalent rare earth [2], is coordinated by six O and two O' neighbors. Symmetry dictates that the AO₆O'₂ units are rhombohedra, which are compressed (α=β=γ>90) in the model crystal used in figures 1-4. The B site cation, typically a tetravalent transition metal, is coordinated by six O and has two neighboring O vacancies. By symmetry, the BO₆ octahedra are distorted, although in some cases, such as Tl₂Mn₂O₇, this distortion is minimal. The pyrochlore structure is prone to disorder due to exchange of O' and vacancy sites, as well as the solid solutions which exist in many materials given O' excess (leading to a fluorite) or deficiency.

As can be seen in figure 3, a [| Kagome lattice] is present in the BO₆ sublattice. The B site-B site connectivity can be viewed as cornersharing tetrahedra. Figure 4 displays the metal-metal connectivity, as well as the ordering of vacancies and O' in the pyrochlore structure.

Figure 3: A cross section of the unit cell, normal to the body diagonal of the pyrochlore Tl₂Mn₂O₇ (A=Tl, B=Mn).

Figure 4: The lattice of yellow vac(BO₆)₄ and maroon O'A₄.

Substitutional Effects

A₂Mn₂O₇ (A=Tl,Y,In,Lu)

A₂Mn₂O₇ is a very interesting pyrochlore series (figures 1-4), in that the A=Tl member displays giant magnetoresistance above its magnetic transition temperature [7]. Specific heat and magnetization measurements indicate the presence of a long range ordered ferromagnetic state [8]. Although ferromagnetic, rather than antiferromagnetic, interactions may not be expected a priori, the ferromagnetic state of this system is simple as Mn⁴⁺ has quenched angular momentum.

Unlike the other members of the series, the electronic structure of the A=Tl pyrochlore has a d band (mixed with Tl s and O p orbitals) in the minority spin which crosses the fermi level [8]. Although there exists a gap within the bandstructure of each spin, the material is not an insulator. At the fermi surface, there exist small numbers of holes in the majority spin, and corresponding electrons in the minority [8]. The bands that cross the fermi level in the minority spin have a large curvature, while the bands in the majority spin that cross the fermi level do not. The 86% decrease in resistivity at a field of 7 tesla [7] is believed to be caused by this unusual electronic structure behavior. This is of interest due to the small number of carriers naturally in the system -- other giant magnetoresistant manganites (typically perovskites) necessitate doping to introduce significant number of carriers.

Bi₂Ru₂O₇

Figure 5: Crystal structure of Bi₂Ru₂O₇ shown without and with polyhedra. Red atoms are Bi, gray atoms are Ru and Blue atoms are O.

Bi₂Ru₂O₇ forms an A₂B₂O₆O' pyrochlore structure as described in the pyrochlore structure introduction. The coordination environment around each Oxygen is a distorted tetrahedra composed of two Bi atoms and two Ru atoms. The size of the A cation, Bi, dictates the geometry of B site connectivity, i.e. the Ru-O-Ru bond angel and the Ru-O bond distance.

Bi₂Ru₂O₇ exhibits metallic behavior while pyrochlores such as Y₂Ru₂O₇, Nd₂Ru₂O₇and Yb₂Ru₂O₇exhibit semiconducting behavior[10]. The reason for the difference in metallic behavior between the above structures is related to the size of the A cation, and the degree of distortions caused by the A cation in the structure. In the case of Bi₂Ru₂O₇, the RuO₆ octahedra are compressed along the three fold axis of the crystal structure[19]. Larger A cations such as Bi induce larger Ru-O-Ru bond angles and thus a greater degree of compression of the RuO₆ octahedra. This compression lowers the coordination symmetry around the Ruthenium from Oh to D3d[19]. The lowered symmetry of the ruthenium causes the t2g band to split into a filled eg band and an empty a1g band[20]. The eg band lies at the top of the Fermi energy and the a1g band lies just above the Fermi energy[20]. In Bi2Ru2O7, these bands overlap. The splitting encountered in BiRu2O7 also occurs in Yb₂Ru₂O₇, Y₂Ru₂O₇ and Nd₂Ru₂O₇, however the width of the t2g bands is not large enough to overlap because a critical bond angle needed to produce wide enough t2g bands for overlap is not reached[10,20].

The structural distortions of the RuO6 corner sharing octahedra induced by cation substitution is a characteristic of the Ru⁴⁺ pyrochlores discussed above as well as the Ru⁴⁺ perovskite SrRuO₃ found in the Perovskite section.

Bi₂MTaO₇ (M= Y, rare earth)

In recent years the urge to find alternative energy sources has prompted more extensive research into the study of direct water splitting through photocatalysis. Metal oxide semiconductors tend to be a main focus because of their low costs, ease of production, and stability with respect to decomposition in water. To be an effective photocatalyst, compounds must be good charge carriers, not decompose or be consumed in a reaction, and their band gaps must be greater than the minimum 1.23eV required to break water into H₂ and O₂. These traits have opened new methods of research in finding not only new compounds that are capable of splitting water, but changing existing compounds through doping, ion substitution, etc., to make better photocatalysts. Research of modifying structures to tailor electronic properties is band engineering. Using a pyrochlore compound as a photocatalyst is a good approach toward effective water splitting. The A and B sites can be exchanged with different atoms to change the level of the bands and increase or decrease the bandgap size. An example of the size effect versus the bandgap is investigated in the B-site substituted Bi₂MTaO₇ pyrochlore.

Figure 6: Bi₂YTaO₇ unit cell with space group Fd-3m. MO₆ octahedra are shown in green. The red atoms correspond to oxygen atoms, and the yellow spheres correspond to bismuth atoms

Figure 7: Extended structure view of Bi₂YTaO₇ pyrochlore

Bi₂MTaO₇ is a pyrochlore (A₂B₂O₇) type crystal belonging to the cubic crystal system with space group Fd-3m (See Figures 6 and 7). M³⁺ and M⁵⁺ were doped into the (B⁴⁺)₂ site to improve charge carrier concentration [11,12]. The crystal structure is composed of MO₆ octahedra, where M is either a Ta or a substituted metal. The Bi atoms are located in the A³⁺ site. The metal site in the octahedra are disordered and show some as being Ta and others occupied by the doped metal cation. The metals were doped with Yttrium and the rare earth lanthanide series. The f-shell strongly influences chemical and physical properties of the lanthanide elements as you move across the row [12].

Zou found through investigation of the photoactivity that the band gap and activity of the sample was linearly dependant on the size of the doped ion in the B₂ site (See Figure 8). The one exception found was Cerium. Ce tends to readily exchange between Ce³⁺ and Ce⁴⁺ through oxidation (see CeO₂ in the fluorite section), but the reported band gap of the mixed valence ion fit the trend quite well [11]. The most active photocatalyst of the series was the Y³⁺ doped catalyst, while the least active was the La³⁺ doped catalyst.

Figure 8: The band gap increases as you increase ionic radius* and the activity increases with decreasing ionic radius. *Ce³⁺ and Ce⁴⁺ are exceptions. Image used from Zou, et. al., reference [11].

Ho₂Ti₂O₇, spin ice

Figure 9: Tetrahedron drawn to indicate one possible arrangement of spins "in" and spins "out".

Ho₂Ti₂O₇ can be considered similar to the Tl₂Mn₂O₇ shown in Figure 1, with holmium cations at the A sites and titanium cations at the B sites. Ho₂Ti₂O₇ is considered a spin ice [13].

Frustration is the state when a system cannot minimize all pairwise interactions simultaneous (see FeSbO₄ on the Rutile page). The first crystalline system studied with degenerate lowest energy arrangements was cubic ice, where each oxygen atom is coordinate to 4 protons. Two of these protons are closer to the oxygen atom and are bound covalently, while two are farther away and interact via hydrogen bonding. An analog of this system, with spins instead of protons, and spin directions instead of bond distances is known as a "spin ice" system [13]. The pyrochlore structure with magnetic ions may, but will not necessarily, result in macroscopically degenerate ground states which are described by the "spin ice" model. Ho₂Ti₂O₇ (HTO) is one such structure. When one tetrahedron of the structure is considered, the spins can be characterized as two spins "in" and two spins "out". See Figure 9. When the unit cell network of tetrahedra is considered, no spin configuration is possible that satisfies (minimizes) all of the pairwise interactions, and degenerate arrangements of these tetrahedra are an analog to cubic ice. Furthermore, studies of HTO show no long range spin ordering. [14,16]

A good introduction to spin ice behavior, and its relevance to lone pair ordering in pyrochlores, is given in [6]. Other spin ice systems include Dy₂Ti₂O₇, Y₂Ti₂O₇, Dy₂Sn₂O₇, and Ho₂Sn₂O₇ [16,17].

References

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[3] Lee, S. et al, Nature 2002, 418, 856-858.

[4] Hizi, U.; Henley, C. Phys. Rev. B 2006, 73, 054403.

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[6] Seshadri, R. Solid State Sci. 8 (2006) 259-266.

[7] Shimakawa, Y.; Kubo, Y.; Manako, T. Nature 1996, 379, 53-55.

[8] Shimakawa, Y.; Kubo, Y. et al Phys Rev B 1999 59, 2, 1249-1254.

[9] Yasukawaa, M., Kuniyoshia, S., Konob, T. Solid State Communications 2003, 126, 213–216.

[10] Lee, K. S.; Seo, D. K.; Whangbo, M. H. J. Solid State Chemistry 1994, 131, 405-408.

[11] Zou, Z.; Arakawa, H. Journal of Photochemistry and Photobiology A 2003, 158, 145.

[12] Luan, J. et. al. J. Mater. Sci 2006, 41, 8001.

[13] Bramwell, S. T. et al. Science 2001, 294, 1495.

[14] Harris, M.J. et al. Phys. Rev. Letters 1997, 79, 2554.

[15] Bramwell, S.; Harris, M. Phys. Rev. Letters 2001 87, 4, 047205.

[16] Hayward, M. A. Chem.Mater. 2005, 17, 670.

[17] Shastry, B. S. LT23 Proceedings preprint 3 April 2007.

[18] Pauling, L. "The Nature of the Chemical Bond" (1945) 301

[19] Cava, R. J. Dalton Trans., 2004, 2979-2987.

[20] Avdeev, M., et. al. J. Solid State Chem.,2002, 169, 24-34.