From WolfWikis

Perovskite

The highly versatile ABX₃ perovskite crystal structure is formed by the B cations filling 25% of the octahedral holes in the cubic close-packed AX₃ array[1]. In the ideal cubic structure, each A cation is coordinated to twelve X anions and each B cation is coordinated to six X anions. An example of the ideal cubic structure is shown in Figure 1. The substitution of different atoms into the A and B positions is possible if they are of similar size to A and B respectively, and total equivalent oxidation state[2].

Figure 1: An ideal cubic perovskite SrTiO3 with Pm-3m symmetry

Figure 2: A distroted perovskite SmNiO3 with orthorhombic symmetry.

Most perovskite structures are distorted and do not have cubic symmetry. Common distortions such as cation displacements within the octahedra and tilting of the octahedra are related to the properties of the A and B substituted atoms. Factors that contribute to distortion in the structure include radius size effects and the Jahn-teller effect[1]. The SmNiO3 structure shown in Figure 2 is a distorted perovskite with orthorhombic symmetry.

Octahedral tilting distortions present in many perovskites was first examined by Goldschmidt in 1926[2]. According to Golschmidt, the degree of distortion in ABO3 perovskites can be determined using the following equation

where R_A is the ionic radius of A, R_B is the ionic radius of B, and R_O is the ionic radius of oxygen. If the value of t is close to 1, the structure is expected to adopt the ideal cubic symmetry. When the value of t is 0.81 or less and the value of the A site ion is smaller than ideal, and the BO6 octahedra will tilt in order to fill space. Stable perovskite structures have values approximately 0.78 < t< 1.05. The tolerance factor however, is based on the ionic radius and should only be used as an estimate because perovskites are not exclusively ionic.

Perovkites containing cations such as Cu²⁺ and Mn³⁺ in their octahedral cation site tend to exhibit distortions caused by the Jahn-Teller effect. The Jahn-Teller distortion theorem states that a nonlinear molecule cannot be stable in a degenerate electronic state and must undergo distortion in order to break down the degeneracy and become stable[3]. Distortion caused by the Jahn-Teller effect in perovskites usually involves four of the octahedral bonds contracting and two of the octahedral bond legthening which gives an elongated octahedral shape.

The distortions exhibited by perovskites as a consequence of cation substitution can be used to fine tune and adjust properties of interest. A few of the physical properties of interest in various perovskite systems include conductivity, dielectrics, and colossal magnetoresistance. The following subsections contain examples of perovskite type structures and explanations of their properties and relations to the ideal perovskite structure.

BaTiO₃

The ferroelectricity of BaTiO₃ makes it an interesting example of a perovskite structure.

In BaTiO₃, the displacement of Ti causes a distorted (non-cubic) perovskite structure. BaTiO₃ has a structure similar to that of SrTiO₃. In BaTiO₃, Ti occupies the B positions, while oxygen atoms occupy the corners of the octahedra. However, this structure is only stable above 120 °C for BaTiO₃. Below 120 °C, the Ti atoms (shown in yellow in Figure 3) are slightly displaced from their original position toward the one oxygen, as shown in Figure 3. This distortion creates a net polarization if all Ti atoms are displaced off the centre about 0.1Å in the same direction, which is confirmed by X-ray crystallography.

The dipole resulting from this distortion results in the ferroelectricity of BaTiO₃. If an electric field is applied to BaTiO₃, the individual dipoles, resulting from distorted TiO₆ octahedra, will align with the field, and reach the saturation polarization when all dipoles are aligned. Ferroelectric materials such as BaTiO₃ can have many domains, which each have a variable orientation of their respective dipoles. The net polarization of a ferroelectric material is the vectore resultant of the polarizations of different oriented domains. Together, these domains and the net polarization cause the high dielectric constant of BaTiO₃

Ferroelectric oxides,e.g. BaTiO₃ do have limitations. They are used in capacitors due to their high dielectric constants, but cannot be used for high temperature applications because their unique distortion structure will break down. The increased thermal energy at high temperatures results in enough vibration of atoms that it is difficult to form a net dipole moment. It may happen only the a permanent dipole forms after vibration when the field is shut off.

Figure 3 Ti moving up a little bit causes a net dipole moment

Figure 4 Distorted TiO₆ in the middle of the unit cell

In summary, a little displacement of Ti causes the extreme large dielectric constant of BaTiO₃ (έ=10³ to 10⁴) as well as the mismatch of positive charge center and negative charge center.

SrRuO₃

SrRuO₃ freezes out of a cubic symmetry into a tetragonal symmetry at 945 K, and below 825 K, SrRuO₃ is an orthorhombic (Pnma #62) distorted perovskite with Ru-O-Ru angles of 162 degrees [4]. This distortion is difficult to rationalize, as the Shannon's radius for ruthenium is very close to that found for titanium in the above undistorted SrTiO₃. However, the average Ru-O bond distance seen in the compound is 1.986 Å, slightly different from the sum of covalent radii for Ru⁺⁴(CN=6) and O^-2(CN=6), 2.02 Å. Using the dimensionless Goldschmidt tolerance factor (at the top of page), and the radius found for Sr²⁺(CN=12), it is clear that SrRuO₃ would not be expected to be distorted with a tolerance factor of 0.994, very close to ideal.

SrRuO₃ is of interest due to its relative similarities to the parent perovskites (La,Ca)MnO₃ of the collosal magnetoresistance manganites, which display properties of interest in the field of spintronics. SrRuO3₃ is also a member of the Ruddlesden-Popper Series Sr_n+1Ru_nO_3n+1, of which n=infinity (the title compound, a perovskite), n=1, and n=2 are shown in figures 5 - 7, respectively. These systems can best be thought of as composites of the halite and perovskite structure, consisting of n layers of SrRuO₃ for every layer of SrO.

Although SrRuO₃ displays interesting ferromagnetic properties, the literature shows disagreements between different researchers on the nature of the ferromagnetism, the spin state of ruthenium, and the presence of significant (>0.01 Å) Jahn-Teller distortion, in SrRuO₃. Of additional interest, SrRuO₃ displays the Invar effect (below ~100 K for a and b axes, ~60 K for c axis), or near-zero thermal expansion, arising from frozen octahedral tilting angles (and bond-lengths), which in turn is believed by some to be coupled to the FM transition at T_c=160-165 K.

Figure 5: The structure (Pnma) of metallic ferromagnet SrRuO₃ as determined by neutron diffraction at 1.5 K [4]

Figure 6: The structure (I4/mmm) of superconducting (T_c = 1.15 K) Sr₂RuO₄ from 0.1 K neutron diffraction [5]. Unlike the molecular layered perovskite shown below, the octahedra in adjacent layers are displaced from each other such that axial oxygens of different layers do not line up.

Figure 7: The structure (Bbcb) of Sr₃Ru₂O₇ from R.T. electron and neutron diffraction [6]

NaTaO₃

Recently, perovskite compounds have been 'rediscovered' for their unusual photocatalytic properties. The ABO₃ formula is ideal for this behavoir. A valence band consisting of O 2p orbitals is formed below the fermi level, while the conduction band is formed from the B site (usually an early transition metal d⁰ ion) above the fermi level. NaTaO₃ has gained increasing attention during recent years for its high photocatalytic rate. The structure of sodium tantalate is deviated from the ideal cubic perovskite structure. The unit cell is orthorhombic with space group Pcmn. A single tantalum atom is located in the center of the unit cell (B position) bonded in an octahedral coordination to 6 oxygen atoms located on the faces. Sodium atoms occupy the cavities (A position). A distortion of the cell is visualized by a shear of a (100) face and a perpendicular contraction of the derived cubic cell [7]. X-Ray diffraction data shows the tilting of the octahedra indicate a displacement of sodium atoms in the cell, as shown in figures 8 and 9 [8]. NaTaO₃ shows interesting optical properties as well. In 2000 Domen reported highly efficient water splitting of Lanthanum-Doped Sodium Tantalate, prepared by conventional solid state methods. A reported band gap of 4.0eV clearly overcomes the minimum 1.23eV required to split water into hydrogen and oxygen. The valence band, localized on the oxygen 2p orbitals, is located below the oxidation potential of water, while the conduction band, localized on the Ta 5d orbitals, is located above the reduction potential of hydrogen [9]. Water decomposition is therefore allowed when an electron is promoted to the conduction band by absorption of a photon of proper wavelength. In 2006 Porob reported an increase in photocatalytic activity of NaTaO₃ when prepared by molten salt, or flux method, compared to the conventional solid state method. Smaller crystal size and particle morphology is attributed as the cause of the increase in activity [10].

Figure 8: NaTaO₃ shown here with space group Pcmn

Figure 9: NaTaO₃. The 'shear' of the sodium atoms are more clearly visible from this view.

Figure 10: Band Potential of NaTaO₃. The valence band is formed from Oxygen 2p orbitals. The conduction band is formed from Ta 5d orbitals.

Halide Perovskite Sheets

Although most perovskite structures involve oxides, many halide perovskite structures are also known. One subtype of these structures is an inorganic-organic hybrid structure composed of [MX₆]^4- octahedra separated by organic (A type) cations similar to the layer separation in the previously discribed Ruddleson Popper phases. This results in 2D "perovskite sheets", layers of corner sharing octahedra separated by organic cations. Cations may be alkyl substituted ammonuim ions, with carbon chain lengths ranging from one to sixteen or more carbons in the alkyl chain, or more bulky groups like the 2-substituted phenethylammonium shown in Figures 11 and 12. [11] The separation between prevoskite layers means that adjacent layers no longer share an axial ligand and A type cation, this addition of AX results in a formula unit of A₂BX₄.

Changes in the unit cell and properties of these inorganic-organic hybrids occur due to distortions from the ideal 2-D perovskite structure that would exhibit a square net of corner sharing octahedra. These distortions primarily appear as changes to the M-X-M bond angle and the equatorial M-X bond distances due to the sterics and position of the A type organic cations. Further study of the specific perovskite sheet structure shown below (Figures 11 and 12) reveals a displacement of the ammonium head of the A type organic cation due to hydrogen bonding. While most metal halides and perovskites are insulating, perovskite sheets can be semiconducting, depending on the B type cation. The bands are determined by the B type cation (and its relative oxidation state) and can then be tuned by variations in the A type organic cation. Organic cation effects can adjust the band up to 2 eV in magnitude. [12] A thin-film transistor has been made using (C₆H₅C₂H₄NH₃)₂SnI₄ perovskite [13]. Communication between the metals through the halide bonds creates a relatively high carrier mobility with Hall mobilities of 50cm²/V*s). [13] These mobilities are comparable to amorphous silicon. Perovskite sheets show potential for cheaper and more easily processed semiconductors.

Figure 11: (2-BrPEA)₂SnI₄ viewed from the "side".

Figure 12: (2-BrPEA)₂SnI₄ viewed from the "top"

Oxygen-Deficient Perovskite

REBaM₂O₅ is a type of oxygen-deficient perovskite, where RE is rare earth, M is Mn, Fe or Co. These oxides form alternating stacks of rare earth and barium layers along the c axis. A layered arrangement has been formed due to the presence of oxygen vacancies in the rare earth plane, reducing the rare earth coordination number to 8, while barium occupies a typical 12-coordinate perovskite site. The manganese-oxygen network consists of double layers of MnO₅ square pyramids linked through all their apices. Oxygen-deficient perovskites have many interesting properties. Take YBaMn₂O₅ as an example:

YBaMn₂O₅ crystallizes in space group P4/mmm in high temperature, with a unit cell in which the basal and apical Mn-O distance are almost equal, as shown in Figure 13.[14] At lower temperatures, it has the space group P4/nmm with two kinds of MnO₅ in a unit cell, one is Mn2+O₅ pyramid, another one is Mn3+O₅ pyramid. These two kinds of MnO₅ pyramids are arranged in an ordered manner, each Mn2+O₅ pyramid being linked to five Mn3+O₅ pyramids and vice versa, as shown in Figure 14.[15]

In these materials, charge ordering and spin ordering are of great interest. Above the phase-transition temperature, all Mn ions exhibit an intermediate valence state. As the temperature decreases, a charge ordering distribution is stabilized.[16] And the G type ferrimagnetic with checkerboard-type charge order semiconducting state is found to the ground state, as shown in Figure 15.[16] A ferrimagnetic material is one in which the magnetic moment of the atoms on different sublattices are in opposite directions, but the absolute value of these opposing moments are unequal. In YBaMn₂O₅, the directions of the magnetic moment of Mn3+ and Mn2+ are in reverse. Mn3+ has 4 d electrons, while Mn2+ has 5 d electrons. So 2-5/2=-1/2, not equal to zero. So the Charge and spin ordering makes YBaMn₂O₅ a ferrimagnetic material.

Figure 13: Crystal structure of YBaMn₂O₅ in space group P4/mmm. The red atoms are oxygen, the green atoms are barium, the blue atoms are yttrium, and the purple atoms are manganese.

Figure 14: Crystal structure of YBaMn₂O₅ in space group P4/nmm. The red atoms are oxygen, the green atoms are barium, the blue atoms are yttrium, and the purple atoms are manganese.

Figure 15: Schematic diagram showing the checkerborad-type charge ordering and G type spin ordering of YBaMn₂O₅. The red, white and gray atoms are oxygen, Mn2+ and Mn3+, respectively. The plus, minus refer to up and down spins, respectively.

References

[1] Woodward, P.M., Acta. Cryst. 1997, B53, 32-43.

[2] Crystallography and Chemistry of Perovskites, M. Johnsson and P. Lemmens, in “Handbook of Magnetism and Advanced Magnetic Media”,Ed. H. Kronmüller, John Wiley & Sons, New York, (2006), cond-mat/0506606.

[3] Anthony.R.West, "Basic Solid State Chemistry", J.W.& D. Ltd (1999), 55-59;364-366.

[4] Bushmeleva, S.N., et al J. Mag. & Mag. Materials 2006, 205, 491-496.

[5] Gardner, J.S., et al. Physica C 1996, 256, 251-257.

[6] Kiyanagi, R., et al J. Phys. Soc. of Japan 2004, 73, 3, 639-642.

[7] Vousden, P. Acta Cryst. 1951, 4, 373.

[8] Ahtee, M.; Unonius, L. Acta Cryst. 1977, A33, 150-154.

[9] Domen, et. al. Bull. Chem. Soc. Jpn. 2000, 73, 1307-1331.

[10] Porob, D.G.; Maggard, P.A. Journal of Solid State Chemistry. 2006, 179, 1727-1732.

[11] Zhengtao, x. et al. Inorg. Chem. 2003, 42, 2031.

[12] Knutson, J. L.; Martin, J. D.; Mitzi, D.B. Inorg. Chem., 2005, 44, 4699.

[13] Kagan, C. R.; et al. Science 1999, 586, 945.

[14] Chapman, C. P. et al. Angew. Chem. Int. ed. Engl. 1996, 35, 2482.

[15] Millange, F. et al. Materials Research Bulletin 1999, 34, 1.

[16] Vidya, R. et al. Physical Review B. 2002, 65, 144422.