Subsolidus phase equilibria and properties in the system Bi2O3:Mn2O3±x:Nb2O5

Subsolidus phase relations have been determined for the Bi-Mn-Nb-O system in air (750-900 °C). Phases containing Mn²⁺, Mn³⁺, and Mn⁴⁺ were all observed. Ternary compound formation was limited to pyrochlore (A₂B₂O₆O′), which formed a substantial solid solution region at Bi-deficient stoichiometries (relative to Bi₂(Mn,Nb)₂O₇) suggesting that ≈14-30% of the A-sites are occupied by Mn (likely Mn²⁺). X-ray powder diffraction data confirmed that all Bi-Mn-Nb-O pyrochlores form with structural displacements, as found for the analogous pyrochlores with Mn replaced by Zn, Fe, or Co. A structural refinement of the pyrochlore 0.4000:0.3000:0.3000 Bi₂O₃:Mn₂O_3±x:Nb₂O₅ using neutron powder diffraction data is reported with the A and O′ atoms displaced (0.36 and 0.33 Å, respectively) from ideal positions to 96g sites, and with Mn²⁺ on A-sites and Mn³⁺ on B-sites (Bi_1.6Mn²⁺_0.4(Mn³⁺_0.8Nb_1.2)O₇, (?227), a=10.478(1) Å); evidence of A or O′ vacancies was not found. The displacive disorder is crystallographically analogous to that reported for Bi_1.5Zn_0.92Nb_1.5O_6.92, which has a similar concentration of small B-type ions on the A-sites. EELS spectra for this pyrochlore were consistent with an Mn oxidation between 2+ and 3+. Bi-Mn-Nb-O pyrochlores exhibited overall paramagnetic behavior with negative Curie-Weiss temperature intercepts, slight superparamagnetic effects, and depressed observed moments compared to high-spin, spin-only values. At 300 K and 1 MHz the relative dielectric permittivity of Bi_1.600Mn_1.200Nb_1.200O₇ was ≈128 with tan δ=0.05; however, at lower frequencies the sample was conductive which is consistent with the presence of mixed-valent Mn. Low-temperature dielectric relaxation such as that observed for Bi_1.5Zn_0.92Nb_1.5O_6.92 and other bismuth-based pyrochlores was not observed. Bi-Mn-Nb-O pyrochlores were readily obtained as single crystals and also as textured thin films using pulsed laser deposition.     

Local crystal chemistry, structured diffuse scattering and the dielectric properties of (Bi1−xYx)2(MNb)O7 (M=Fe, In) Bi-pyrochlores

Electron diffraction is used to investigate the large amplitude displacive disorder characteristic of the Bi₂(M^IIINb^V)O₇ Bi-pyrochlores, Bi₂InNbO₇ and Bi₂FeNbO₇, as well as of their A site substituted Bi_1.5Y_0.5InNbO₇ and Bi_1.5Y_0.5FeNbO₇ variants. Highly structured diffuse distributions in the form of {110}* sheets of diffuse intensity perpendicular to the six 〈110〉 directions of real space along with 〈111〉* rods of diffuse intensity perpendicular to the four {111} real space planes are observed. The existence of this structured diffuse scattering is interpreted in terms of large amplitude, β-cristobalite-type tetrahedral rotations of the O′A₂ tetrahedral framework sub-structure of the ideal pyrochlore structure type. Bond valence sum calculations are used to understand the local crystal chemistry responsible for such displacive disorder. The frequency-dependent dielectric properties of Bi₂InNbO₇ and Bi₂FeNbO₇ are also investigated along with the effect upon them of A site doping with Y.     

Structural Study of an Unusual Cubic Pyrochlore Bi1.5Zn0.92Nb1.5O6.92

Single-phase pyrochlore-type specimens of Bi_1.5Zn_0.92Nb_1.5O_6.92 were studied using combined electron, X-ray and neutron powder diffraction techniques. Rietveld refinements using neutron powder diffraction data confirmed an average pyrochlore structure A₂B₂O₆O′ (Fd&3macr;m, a=10.5616(1) Å) with both Bi and Zn mixed on the A-sites. However, refinements revealed significant local deviations from the ideal pyrochlore arrangement which were caused by apparent displacive disorder on both the A and O′ sites. The best fit was obtained with a disordered model in which the A-cations were randomly displaced by ∼0.39 Å from the ideal eight-fold coordinated positions. The displacements occur along the six 〈112〉 directions perpendicular to the O′-A-O′ links. In addition, the O′ ions were randomly displaced by ∼0.46 Å along all 12 〈110〉 directions. Crystal-chemical considerations suggest the existence of short-range correlations between the O′ displacements and both the occupancy of the A-sites (i.e., Bi or Zn) and the directions of the A-cation displacements. The combined A-cation and O′ displacements change the coordination sphere of the A-cations from 8 to (5+3); the resulting coordination environment of the A-cations bears similarities to that of the (5+1)coordinated Zn in zirconolite-like Bi₂Zn_2/3Nb_4/3O₇. The observed displacive disorder in the A₂O′ network of the Bi_1.5Zn_0.92Nb_1.5O_6.92 structure involves atoms associated with the lowest-frequency vibrational bending mode, and is likely responsible for both the high dielectric constant and the dielectric relaxation reported for this compound.     

The local crystal chemistry and dielectric properties of the cubic pyrochlore phase in the Bi2O3MONb2O5 (M=Ni and Mg) systems

The composition, dielectric properties and inherent displacive disorder of a Bi-based, misplaced-displacive cubic pyrochlore phase found in two ternary Bi₂O₃M²⁺ONb₂O₅ (M=Ni and Mg) systems has been investigated. The dielectric permittivities (up to 1 MHz) of (Bi_0.825Ni_0.125□_0.05)₂(Ni_0.25Nb_0.75)₂O₇ and (Bi_0.835Mg_0.085□_0.08)₂(Mg_0.235Nb_0.765)₂O₇ at room temperature are found to be 116 and 151, respectively, while the dielectric loss tangents are 0.00065 and 0.00042, respectively, at 100 kHz. A highly structured characteristic diffuse intensity distribution apparent in electron diffraction is reported in both cases and partially interpreted in terms of large amplitude, β-cristobalite-type tetrahedral rotations of the O’A₂ tetrahedral framework sub-structure of the ideal pyrochlore structure type. Bond valence sum calculations are used to investigate the local crystal chemistry responsible for this displacive disorder.     

Phase formation, crystal chemistry, and properties in the system Bi2O3-Fe2O3-Nb2O5

Subsolidus phase relations have been determined for the Bi₂O₃-Fe₂O₃-Nb₂O₅ system in air (900-1075 °C). Three new ternary phases were observed—Bi₃Fe_0.5Nb_1.5O₉ with an Aurivillius-type structure, and two phases with approximate stoichiometries Bi₁₇Fe₂Nb₃₁O₁₀₆ and Bi₁₇Fe₃Nb₃₀O₁₀₅ that appear to be structurally related to Bi₈Nb₁₈O₅₇. The fourth ternary phase found in this system is pyrochlore (A₂B₂O₆O′), which forms an extensive solid solution region at Bi-deficient stoichiometries (relative to Bi₂FeNbO₇) suggesting that ≈4-15% of the A-sites are occupied by Fe³⁺. X-ray powder diffraction data confirmed that all Bi-Fe-Nb-O pyrochlores form with positional displacements, as found for analogous pyrochlores with Zn, Mn, or Co instead of Fe. A structural refinement of the pyrochlore 0.4400:0.2700:0.2900 Bi₂O₃:Fe₂O₃:Nb₂O₅ using neutron powder diffraction data is reported with the A cations displaced (0.43 Å) to 96g sites and O′ displaced (0.29 Å) to 32e sites (Bi_1.721Fe_0.190(Fe_0.866Nb_1.134)O₇, Fd3¯m (#227), ). This displacive model is somewhat different from that reported for Bi_1.5Zn_0.92Nb_1.5O_6.92, which exhibits twice the concentration of small B-type cations on the A-sites as the Fe system. Bi-Fe-Nb-O pyrochlores exhibited overall paramagnetic behavior with large negative Curie-Weiss temperature intercepts, slight superparamagnetic effects, and depressed observed moments compared to high-spin, spin-only values. The single-phase pyrochlore with composition Bi_1.657Fe_1.092Nb_1.150O₇ exhibited low-temperature dielectric relaxation similar to that observed for Bi_1.5Zn_0.92Nb_1.5O_6.92; at 1 MHz and 200 K the relative permittivity was 125, and above 350 K conductive effects were observed.     

Pyrochlore formation, phase relations, and properties in the CaO-TiO2-(Nb,Ta)2O5 systems

Phase equilibria studies of the CaO:TiO₂:Nb₂O₅ system confirmed the formation of six ternary phases: pyrochlore (A₂B₂O₆O′), and five members of the (110) perovskite-slab series Ca_n(Ti,Nb)_nO_3n+2, with n=4.5, 5, 6, 7, and 8. Relations in the quasibinary Ca₂Nb₂O₇−CaTiO₃ system, which contains the Ca_n(Ti,Nb)_nO_3n+2 phases, were determined in detail. CaTiO₃ forms solid solutions with Ca₂Nb₂O₇ as well as CaNb₂O₆, resulting in a triangular single-phase perovskite region with corners CaTiO₃-70Ca₂Ti₂O₆:30Ca₂Nb₂O₇-80CaTiO₃:20CaNb₂O₆. A pyrochlore solid solution forms approximately along a line from 42.7:42.7:14.6 to 42.2:40.8:17.0 CaO:TiO₂:Nb₂O₅, suggesting formulas ranging from Ca_1.48Ti_1.48Nb_1.02O₇ to Ca_1.41Ti_1.37Nb_1.14O₇ (assuming filled oxygen sites), respectively. Several compositions in the CaO:TiO₂:Ta₂O₅ system were equilibrated to check its similarity to the niobia system in the pyrochlore region, which was confirmed. Structural refinements of the pyrochlores Ca_1.46Ti_1.38Nb_1.11O₇ and Ca_1.51Ti_1.32V_0.04Ta_1.10O₇ using single-crystal X-ray diffraction data are reported (Fd3m (#227), a=10.2301(2) Å (Nb), a=10.2383(2) Å (Ta)), with Ti mixing on the A-type Ca sites as well as the octahedral B-type sites. Identical displacive disorder was found for the niobate and tantalate pyrochlores: Ca occupies the ideal 16d position, but Ti is displaced 0.7 Å to partially occupy a ring of six 96g sites, thereby reducing its coordination number from eight to five (distorted trigonal bipyramidal). The O′ oxygens in both pyrochlores were displaced 0.48 Å from the ideal 8b position to a tetrahedral cluster of 32e sites. The refinement results also suggested that some of the Ti in the A-type positions may occupy distorted tetrahedra, as observed in some zirconolite-type phases. The Ca-Ti-(Nb,Ta)-O pyrochlores both exhibited dielectric relaxation similar to that observed for some Bi-containing pyrochlores, which also exhibit displacively disordered crystal structures. Observation of dielectric relaxation in the Ca-Ti-(Nb,Ta)-O pyrochlores suggests that it arises from the displacive disorder and not from the presence of polarizable lone-pair cations such as Bi³⁺.     

The influence of sulfur substitution on the atomic displacement in Bi2Ti2O7

To clarify the role of A₂O′ and B₂O₆ networks on cation displacement observed in Bi₂Ti₂O′O₆, we used density functional theory calculations to examine the effect of sulfur substitution on the O′ and O sites on lone pair formation and resulting atomic displacement observed in Bi₂Ti₂O′O₆. Cation displacement in bismuth titanate is suppressed only when S is substituted on the O′ site. Analysis of the electronic structure shows that S substitution on the O′ site suppresses the formation of the asymmetric p-type lone pair by modifying the Bi-anion hybridization. Lone pair formation is favored in Bi₂Ti₂O′S₆ and the atomic displacement is larger than that observed in Bi₂Ti₂O′O_6. This enhanced displacement is due to weaker Bi-S versus Bi-O interactions leading to significantly stronger hybridization between the Bi and O′ states in Bi₂Ti₂O′S₆. We also induced lone pair formation in a metallic bismuth pyrochlore oxide (Bi₂Ru₂O′O₆) by modifying the Bi-O interactions through S substitution on the B₂O₆ network, indicating atomic displacement on the A₂O′ network may be achieved by modifying the B₂O₆ network.     

Synthesis and structural study of stoichiometric Bi2Ti2O7 pyrochlore

Bi₂Ti₂O₇ has been synthesized using a co-precipitation route from H₂O₂/NH_3(aq) solutions of titanium with aqueous bismuth nitrate. The stoichiometric material crystallizes into a pale yellow cubic pyrochlore phase. A powder X-ray diffraction study showed this crystallization to be very temperature sensitive, the pure phase can only be obtained within a few degrees of 470°C. Time-of-flight powder neutron diffraction studies of Bi₂Ti₂O₇ (Space group , a=10.37949(4) Å at ambient temperature, Z=8, R_p=3.95%, R_wp=4.75%) revealed positional disorder in the bismuth site and in the O′ oxide site both at ambient temperature and at 2 K.     

Thermal expansion and cation disorder in Bi2InNbO7

The structure of the pyrochlore-type oxide Bi₂InNbO₇ has been investigated between room temperature and 700 °C using electron and synchrotron X-ray powder diffraction and at room temperature and 10 K using neutron diffraction methods. Bi₂InNbO₇ exhibits an A₂B₂O₇ cubic pyrochlore-type average structure at all temperatures that is characterized by an apparently random mixing of the In³⁺ and Nb⁵⁺ cations on the octahedral B sites. The Bi cations on the eight-coordinate pyrochlore A sites are displacively disordered, presumably as a consequence of their lone pair electron configuration. Heating the sample does not alter this disorder.     

Chemical twinning of the pyrochlore structure in the system Bi2O3-Fe2O3-Nb2O5

New ternary bismuth iron niobates having structures based on chemical twinning of pyrochlore are described. Bi_5.67Nb₁₀FeO₃₅ has hexagonal symmetry, P6₃/mmc, , , Z=2 and Bi_9.3Nb_16.9Fe_1.1O_57.8 has rhombohedral symmetry, R-3m, , , Z=3. The structures of both phases were determined and refined to R₁=0.04 using single-crystal X-ray data. They can be described as being derived from the pyrochlore structure by chemical twinning on (111)_py oxygen planes. The chemical twin operation produces pairs of corner-connected hexagonal tungsten bronze (HTB) layers as in the HTB structure, so the structures may alternatively be described as pyrochlore:HTB unit-cell intergrowth structures. In the hexagonal phase the pyrochlore blocks have a width of 12 Å, whereas the rhombohedral phase has pyrochlore blocks of two widths, 6 and 12 Å, alternating with HTB blocks. It is proposed that the previously reported binary 4Bi₂O₃:9Nb₂O₅ phase has a related structure containing pyrochlore blocks all of width 6 Å. A feature of the structures is partial occupancy (∼65%) of the Bi sites and displacement of the Bi atoms from the ideal pyrochlore A sites towards the surrounding oxygen atoms, as observed in Bi-containing pyrochlores.     

The disordered structures and low temperature dielectric relaxation properties of two misplaced-displacive cubic pyrochlores found in the Bi2O3-MO-Nb2O5 (M=Mg, Ni) systems

The disordered structures and low temperature dielectric relaxation properties of Bi_1.667Mg_0.70Nb_1.52O₇ (BMN) and Bi_1.67Ni_0.75Nb_1.50O₇ (BNN) misplaced-displacive cubic pyrochlores found in the Bi₂O₃-M^IIO-Nb₂O₅ (M=Mg, Ni) systems are reported. As for other recently reported Bi-pyrochlores, the metal ion vacancies are found to be confined to the pyrochlore A site. The B₂O₆ octahedral sub-structure is found to be fully occupied and well-ordered. Considerable displacive disorder, however, is found associated with the O′A₂ tetrahedral sub-structure in both cases. The A-site ions were displaced from Wyckoff position 16d (, , ) to 96 h (, , ) while the O′ oxygen was shifted from position 8b (, , ) to Wyckoff position 32e (, , ). The refined displacement magnitudes off the 16d and 8b sites for the A and O′ sites were 0.408 Å/0.423 Å and 0.350 Å/0.369 Å for BMN/BNN, respectively.     

A structure, conductivity and dielectric properties investigation of A3CoNb2O9 (A=Ca, Sr, Ba) triple perovskites

The room temperature structures as well as the temperature-dependent conductivity and dielectric properties of the A₃CoNb₂O₉ (A=Ca²⁺, Sr²⁺ and Ba²⁺) triple perovskites have been carefully investigated. A constrained modulation wave approach to Rietveld structure refinement is used to determine their room temperature crystal structures. Correlations between these crystal structures and their physical properties are found. All three compounds undergo insulator to semiconductor phase transitions as a function of increasing temperature. The hexagonal Ba₃CoNb₂O₉ compound acts as an insulator at room temperature, while the monoclinic Ca₃CoNb₂O₉ compound is already a semiconductor at room temperature. The measured dielectric frequency characteristics of the A=Ba compound are excellent.     

Crystal structure refinements of the three-layer Aurivillius ceramics Bi2Sr2−xAxNb2TiO12 (A=Ca,Ba, x=0,0.5,1) using combined X-ray and neutron powder diffraction

Three-layer Aurivillius ceramics Bi₂SrCaNb₂TiO₁₂, Bi₂Sr_1.5Ca_0.5Nb₂TiO₁₂, Bi₂Sr₂Nb₂TiO₁₂, Bi₂Sr_1.5Ba_0.5Nb₂TiO₁₂, and Bi₂SrBaNb₂TiO₁₂ were formed via solid-state synthesis and their structures characterized by combined Rietveld analysis of powder X-ray and neutron diffraction data. Static disorder was observed in the form of mixed cation occupancies between the Bi and the Sr, Ca, or Ba on the A sites in the perovskite block, as well as between the Nb and Ti sites. The degree of site mixing between the Bi site in the (Bi₂O₂)²⁺ layer and the perovskite-block A site increased with increasing average A site cation radius (ACR). Bi₂SrBaNb₂TiO₁₂ displayed the greatest degree of Bi-A site static disorder. Bond valence sum (BVS) calculations showed an increase in A site BVS with average A site cation radius. All compositions except Bi₂SrCaNb₂TiO₁₂ had overbonded A sites and the A site BVS increased nearly linearly with lattice parameter and ACR. A preference was observed for Ca²⁺ to remain on the A site while Ba²⁺ preferred to disorder to the Bi site, indicating that the cation site mixing occurs to reduce strain between the (Bi₂O₂)²⁺ layer and the perovskite block in the structure. Unusually large Ti site BVS and thermal parameter for the equatorial oxygen in the TiO₆ octahedra were observed in structural models that included full oxygen occupancy. However, excellent structure models and more reasonable BVS values were obtained by assuming oxygen vacancies in the TiO₆ octahedra. AC impedance spectroscopy performed on all samples indicate that the total electrical conductivity is on the order of at 900°C.     

Mg2MTaO6 (M=Nd or La): a group of new pyrochlore oxides

Preparation of two novel mixed metal oxide ceramic materials, namely magnesium neodymium tantalum oxide (Mg₂NdTaO₆) and magnesium lanthanum tantalum oxide (Mg₂LaTaO₆) by conventional solid-state reaction method is reported in this paper. The crystal structure of these new compounds, were studied by indexing the X-ray diffraction patterns, powder pattern calculation and profile fitting. They were found to have a defective cubic pyrochlore structure, with the A site being randomly occupied by Mg and La/Nd, while, Ta and Mg are randomly distributed at the B site. The formula assigned were (MgNd)(MgTa)O₆ and (MgLa)(MgTa)O₆. The variation of dielectric constant, dielectric loss and conductivity of sintered pellets of these materials with applied frequencies in the range of 30 Hz-1 MHz were studied at room temperature. These room temperature studies at 1 MHz gave dielectric constant values of 24.8 and 25.35; conductivity values of 7.75×10⁻⁶ and 8.27×10⁻⁶ S/m as well as dielectric loss values of 0.0055 and 0.006 for Mg₂NdTaO₆ and Mg₂LaTaO₆, respectively. These new pyrochlore compounds were found to have dielectric constant, dielectric loss and conductivity values in the range suitable for possible electronic ceramic applications.     

O NMR studies of local structure and phase evolution for materials in the Y2Ti2O7-ZrTiO4 binary system

¹⁷O MAS NMR and XRD studies of precursor-derived Y_1.6Zr_0.4Ti₂O_7.2 and Y_1.2Zr_0.8Ti₂O_7.4 have been performed to investigate the development of local and long-range order in these materials as they evolve from a metastable amorphous state upon heating. Zirconium titanate (ZrTiO₄) was also investigated to help interpret the ¹⁷O NMR spectra of the ternary compositions. Consistent with earlier studies, crystallization was observed at 800 °C to form a fluorite structure and a small amount of rutile; weak broad reflections were also observed which were ascribed to the presence of small pyrochlore-like ordered domains or particles within the fluorite phase. As the temperature was increased further, the sizes of these domains grew along with the concentration of rutile. At the highest temperature studied (1300 °C), the reflections of the thermodynamic phases, pyrochlore and zirconium titanate (ZrTiO₄), dominated the XRD pattern. The ¹⁷O NMR spectra revealed a series of different peaks that were assigned to different 3- and 4-coordinate O local environments. The data were consistent with the formation of a metastable phase Y_2−xZr_xTi_2−yZr_yO_7+x with pyrochlore-like ordering but with Zr substitution on both cation sites of the pyrochlore structure. At low temperatures, doping on the A (Y³⁺) sites predominates (i.e., x>y), consistent with the fact that the pyrochlore develops out of a more disordered fluorite-like, phase. As the temperature is raised, the Zr doping on the A site decreases and the metastable phase at this temperature can now be written as Y_2−x′Zr_x′Ti_2−y′Zr_y′O_7+x′ (i.e., x′<y′); TiO₂ is also observed, consistent with this suggestion. At high temperatures, doping on the B site decreases and the resonances due to the stoichiometric pyrochlore yttrium titanate (Y₂Ti₂O₇) dominate the NMR spectra. Weaker ¹⁷O NMR resonances due zirconium titanate (ZrTiO₄) are also observed.     

Crystal chemistry on a lattice: The case of BZN and BZN-related pyrochlores

This paper uses a diagnostic, highly structured diffuse intensity distribution to investigate the local crystal chemistry of (Bi_1.5Zn_0.5−δ)(Zn_0.5Nb_1.5)O_7−δ (BZN) as well as Sn⁴⁺ and Ti⁴⁺, B site substituted, BZN-related pyrochlore phases. The structured diffuse distribution of the B site substituted material is found to be remarkably similar to that observed for BZN itself. In the special case of (Bi_1.5Zn_0.5)(Ti_1.5Nb_0.5)O₇ (BZNT), the continuous G±〈10l〉* type diffuse streaking characteristic of BZN-related pyrochlores has virtually condensed out to give just G±〈001〉* “satellite reflections” and a P-centred, close to a superstructure phase of average pyrochlore unit cell dimensions. Bond valence sum considerations are used to investigate the local crystal chemistry of this BZNT phase and to derive a plausible model for this superstructure phase. Monte Carlo modelling is used to confirm the plausibility of the model proposed. The underlying crystal chemistry of BZN and BZN-related pyrochlores is shown to result from strong local Bi/Zn ordering rules and associated large amplitude structural relaxation.     

Crystal structure, stoichiometry, and dielectric relaxation in Bi3.32Nb7.09O22.7 and structurally related ternary phases

The crystal structure of the phase previously reported to occur at 4:9 Bi₂O₃:Nb₂O₅ has been determined using single-crystal X-ray and powder neutron diffraction (P6₃/mmc; a=7.4363(1) Å, c=19.7587(5) Å; Z=2). The structural study combined with phase equilibrium analyses indicate that the actual composition is Bi_3.32Nb_7.09O_22.7. This binary compound is the end-member of a family of four phases which form along a line between it and the pyrochlore phase field in the Bi₂O₃:Fe₂O₃:Nb₂O₅ system. The structures are derived from the parent pyrochlore end-member by chemical twinning, and can also be described as unit-cell intergrowths of the pyrochlore and hexagonal tungsten bronze (HTB) structures. The dielectric properties of the three chemically twinned pyrochlore phases, Bi_3.32Nb_7.09O_22.7, Bi_9.3Fe_1.1Nb_16.9O_57.8 and Bi_5.67FeNb₁₀O₃₅, were characterized. All exhibit low-temperature, broad dielectric relaxation similar to that of the Bi-Fe-Nb-O pyrochlore. At 1 MHz and ≈175 K the observed relative permittivites were 345, 240, and 205, respectively, compared to 125 for the Bi-Fe-Nb-O pyrochlore. The higher relative permittivities observed for the chemically twinned pyrochlore derivatives are ascribed to the presence of HTB blocks in their structures: The Bi atoms located in the HTB blocks feature highly asymmetric coordination environments compared to pyrochlore, and the magnitude of the relative permittivity increases with the proportion of Bi located within the HTB portions of the structures.     

Disordered pyrochlore CsMgInF6 at high pressures

High pressure behaviour of disordered pyrochlore CsMgInF₆ (Pnma, Z=4) has been studied with powder and single-crystal X-ray diffraction to 8.0 and 6.94 GPa, respectively, in diamond anvil cells at room temperature. The material is structurally stable to at least 8.0 GPa with no ordering of the In³⁺ and Mg²⁺ cations. The P-V data are fitted by a Birch-Murnaghan equation of state with the zero-pressure bulk modulus B₀=33.4(3) GPa and the unit-cell volume at ambient pressure V₀=603.2(4) Å³ for the first pressure derivative of the bulk modulus B′=4.00. The major contribution to the bulk compressibility arises from the changes in the coordination sphere around the Cs atoms. The effect of hydrostatic pressure on the crystal structure of CsMgInF₆ is comparable to the effect of chemical pressure induced by the incorporation of ions of different sizes into the A and B sites in defect AB²⁺B′³⁺F₆ pyrochlores.     

Anomalous lattice parameter increase in alkali earth aluminium substituted tungsten defect pyrochlores

The structures of the defect pyrochlores AAl_0.33W_1.67O₆ where A=K, Rb or Cs have been investigated using X-ray and neutron powder diffraction methods as well as the ab initio modelling program VASP. The three cubic pyrochlores exhibit a non-linear increase in lattice parameter with respect to ionic radius of the A cation as a consequence of displacive disorder of the A-type cations. Solid state ²⁷Al MAS NMR studies of this pyrochlore system reveal shifts in the δ∼21-22 ppm range that are indicative of pseudo-5 coordinate Al environments and emanate from distorted Al octahedral with one abnormally long Al-O bond. Solid state ³⁹K, ⁸⁵Rb, ⁸⁷Rb and ¹³³Cs MAS and static NMR studies reflect the local cation disorder demonstrated in the structural studies.     

Systematics of the pyrochlore structure type,ideal A2B2X6Y

The geometry of the ideal pyrochlore structure type (⁸A₂⁶B₂⁴X₆⁴Y, Fd3m) has been examined using a data base of 440 synthetic samples. Mean ionic radii of the cubic and octahedral cations together account for 95% of the variation in the cell edge. Nonempirical expressions for calculating the cell edge are also derived, using that the interatomic distances are functions of the cell edge and a single positional parameter, x, of the X anion. This alternative method is equally successful for calculating the cell edge, and additionally provides for the calculation of x. Comparison of calculated x values with 27 experimentally measured values indicates that the stoichiometry, x values, or bond length predicting radii are in error for 20% of these pyrochlores. For 21 observed x values judged to be most accurate, the calculated anion coordinates are within 0.009. In addition, calculated x values are given for 400 pyrochlores for which no values have been previously determined.