Comment on “Prediction of lattice constant in cubic perovskites”

In a recent work by Jiang et al. [Prediction of lattice constant in cubic perovskites, J. Phys. Chem. Solids 67 (2006) 1531-1536], the interrelationship between lattice constant, ionic radii and tolerance factor of cubic perovskites has been established and an empirical equation was obtained. However, the assumption of incorrect ionic coordination led to an incorrect mathematical expression even though the average relative errors between predicted and observed lattice constants of 132 materials were below 1%. Here, corrected coefficients for that empirical expression are obtained, which would likely be useful for investigation of general perovskite materials.     

Leakage current, ferroelectric and structural properties in Pb1−xBaxTiO3 thin films prepared by chemical route

Single-phase perovskite structure Pb_1−xBa_xTiO₃ thin films (x=0.30, 0.50 and 0.70) were deposited on Pt/Ti/SiO₂/Si substrates by the spin-coating technique. The dielectric study reveals that the thin films undergo a diffuse type ferroelectric phase transition, which shows a broad peak. An increase of the diffusivity degree with the increasing Barium contents was observed, and it was associated to a grain decrease in the studied composition range. The temperature dependence of the phonon frequencies was used to characterize the phase transition temperatures. Raman modes persist above tetragonal to cubic phase transition temperature, although all optical modes should be Raman inactive. The origin of these modes was interpreted in terms of breakdown of the local cubic symmetry by chemical disorder. The absence of a well-defined transition temperature and the presence of broad bands in some interval temperature above FE-PE phase transition temperature suggested a diffuse type phase transition. This result corroborates the dielectric constant versus temperature data, which showed a broad ferroelectric phase transition in these thin films. The leakage current density of the PBT thin films was studied at different temperatures and the data follow the Schottky emission model. Through this analysis the Schottky barrier height values 0.75, 0.53 and 0.34 eV were obtained to the PBT70, PBT50 and PBT30 thin films, respectively.     

Study on the local structure of (CrO6) complex in garnet crystals by optical and EPR spectrum

The local lattice structure distortions for YAG and YGG systems doped with Cr³⁺ have been investigated by the d³ configuration complete energy matrices which contain the Zeeman energy besides the electron–electron interaction, the trigonal crystal field as well as the spin–orbit coupling interaction. The local lattice structure parameters R and θ of (CrO₆)⁹⁻ complex are determined for Cr³⁺ in YAG and YGG systems, respectively. The calculated results show that the local lattice structures have expansion distortions, which almost tend to the same after distortions. Meanwhile, the EPR parameter D, g factors (g_||, g) and optical spectrum of these systems have been interpreted uniformly by quantitative calculation. It is shown that the effect of the orbit reduction factor k on g factors (g_||, g) cannot be ignored.     

Electronic structure and structural phase stability of CuAlX2 (X=S, Se, Te) under pressure

The electronic and structural properties of chalcopyrite compounds CuAlX₂ (X=S, Se, Te) have been studied using the first principle self-consistent Tight Binding Linear Muffin-Tin Orbital (TBLMTO) method within the local density approximation. The present study deals with the ground state properties, structural phase transition, equations of state and pressure dependence of band gap of CuAlX₂ (S, Se, Te) compounds.Electronic structure and hence total energies of these compounds have been computed as a function of reduced volume. The calculated lattice parameters are in good agreement with the available experimental results. At high pressures, structural phase transition from bct structure (chalcopyrite) to cubic structure (rock salt) is observed. The pressure induced structural phase transitions for CuAlS₂, CuAlSe₂, and CuAlTe₂ are observed at 18.01, 14.4 and 8.29 GPa, respectively. Band structures at normal as well as for high-pressure phases have been calculated. The energy band gaps for the above compounds have been calculated as a function of pressure, which indicates the metallic character of these compounds at high-pressure fcc phase. There is a large downshift in band gaps due to hybridatization of the noble-metal d levels with p levels of the other atoms.     

The phase stability of Ca2TiO4 and related Ruddlesden–Popper phases

The Ruddlesden–Popper phases of the Ca–Ti–O system, Ca_n+1Ti_nO_3n+1, are investigated by means of atomistic simulations employing empirical pair potentials. The stability of the phases is examined in terms of various reaction schemes: the formation from the binary oxides, the addition of the perovskite oxide to a given phase, and the reaction between perovskite and rock-salt oxides. The energies of these reactions are compared with results previously obtained for the Ruddlesden–Popper phases of the Sr–Ti–O system. The importance of the disproportionation reaction of the various R–P phases in both Ca and Sr systems is also emphasized. The results obtained are in good agreement with experimental observations regarding both systems.     

Melting curve of silicon to 15 GPa determined by two-dimensional angle-dispersive diffraction using a Kawai-type apparatus with X-ray transparent sintered diamond anvils

The melting curve of silicon has been determined up to 15 GPa using a miniaturized Kawai-type apparatus with second-stage cubic anvils made of X-ray transparent sintered diamond. Our results are in good agreement with the melting curve determined by electrical resistivity measurements [V.V. Brazhkin, A.G. Lyapin, S.V. Popova, R.N. Voloshin, Nonequilibrium phase transitions and amorphization in Si, Si/GaAs, Ge, and Ge/GaSb at the decompression of high-pressure phases, Phys. Rev. B 51 (1995) 7549] up to the phase I (diamond structure)—phase II (β-tin structure)—liquid triple point. The triple point of phase XI (orthorhombic, Imma)—phase V (simple hexagonal)—liquid has been constrained to be at 14.4(4) GPa and 1010(5) K. These results demonstrate that the combination of X-ray transparent anvils and monochromatic diffraction with area detectors offers a reliable technique to detect melting at high pressures in the multianvil press.     

Preparation and thermal decomposition studies of l-tyrosine intercalated MgAl, NiAl and ZnAl layered double hydroxides

l-Tyrosine (represented as l-Tyr) intercalated MgAl, NiAl and ZnAl layered double hydroxides (LDHs) have been obtained by the method of coprecipitation. In situ FT-IR, in situ HT-XRD and TG-DTA measurements allow a detailed understanding of the thermal decomposition process for the three intercalated composites. In situ HT-XRD reveals that the layered structure of l-Tyr/MgAl-LDH collapses completely at 450 °C with the first appearance of reflections of a cubic MgO phase, while the corresponding temperature for l-Tyr/NiAl-LDH is some 50 °C lower. In contrast, there is a major structural change in l-Tyr/ZnAl-LDH at 250 °C as shown by the disappearance of its (0 0 6) and (0 0 9) reflections at this temperature accompanied by the appearance of reflections of ZnO. In situ FT-IR experiments give information about the decomposition of the interlayer -Tyr ions. The decomposition temperature of l-Tyr in the ZnAl host is about 50 °C lower than the corresponding values for the MgAl and NiAl hosts. TG-DTA curves show a significant weight loss step (170-260 °C) in l-Tyr/ZnAl-LDH which is due to the dehydroxylation of the host layers, with a corresponding weak endothermic peak at 252 °C. This temperature range is much lower than that observed for MgAl and NiAl hosts, indicating that the ZnAl-LDH layers are relatively unstable. The data indicate that the order of thermal stability of the three intercalates is: l-Tyr/MgAl-LDH > l-Tyr/NiAl-LDH > l-Tyr/ZnAl-LDH.     

Local properties of the electronic structure of cubic SrTiO3, BaTiO3 and PbTiO3 crystals, analysed using Wannier-type atomic functions

The electronic structure of the cubic perovskites SrTiO₃, BaTiO₃ and PbTiO₃ is calculated by Hartree-Fock and density functional theory methods. Wannier-type atomic orbitals (WTAOs) are obtained from symmetrized combinations of Bloch states of some occupied and vacant bands by a variational method. Population analysis, based on the WTAOs, attributes a mixed ionic-covalent type of bonding with partly covalent Ti-O bonds to the perovskites under study. The atomic charges thus calculated are then compared to those obtained by the traditional Mulliken population analysis.     

Phase transitions in BaCeO3: neutron diffraction and Raman studies

Polycrystalline samples and small single crystals of the perovskite BaCeO₃ were studied by neutron diffraction and Raman spectrometry between 300 and 1200 K. The controversy about the phase transitions originally deduced from our previous Raman study and those observed since by neutron diffraction by Knight has stimulated this work. Pretransitional effects which are detected by Raman much before long-range ordering takes place can partly explain the above disagreement. A continuous monitoring of the structural changes by neutron diffraction and by Raman spectroscopy including polarization analysis has allowed discussion of the transition mechanisms: The first transition Pnma–Imma takes place at 573 K and is of second order. Although some modes soften when the temperature is raised as in many of these perovskite compounds the transition is likely partly displacive partly order–disorder. The Raman modes which disappear transform in modes at the X point of the Brillouin zone of the Imma phase. The second transition Imma–R c takes place at 673 K and is first order. The last transition R c–Pm3m occurs above 1200 K and the transition temperature which can be deduced by extrapolation to zero Raman intensity is in good agreement with neutron results. This second order transition is progressive and begins at about 400 K, the intermediate R c structure appearing as an attempt for slowing down the structural evolution toward the cubic perovskite form.     

Relative stability of cubic and different hexagonal forms of boron nitride

Boron nitride in the cubic form has a hardness approaching that of diamond. It is synthesized from a hexagonal graphitic phase. The physical behavior of the hexagonal phase depends upon the nature of layer stacking. This stacking is investigated using density functional approaches with the local density approach being far more successful than the generalized gradient approach. Various forms of the AaAa… stacking are predicted to be stable suggesting the existence of slightly different phases of the material. At the same time the energy differences between the stacking geometries is small and associated with small changes in the inter-layer spacing. This could have implications for the h-BN to c-BN transformation.     

In situ neutron diffraction study (300-1273 K) of non-stoichiometric strontium ferrite SrFeOx

The high-temperature cubic phase of non-stoichiometric strontium ferrite SrFeO_x (2.5≤x≤3.0) has been studied by in situ neutron powder diffraction in air over the temperature range 300-1273 K. The composition of SrFeO_x changes within the range 2.56≤x≤2.81 from 1273 to 673 K, respectively.Rietveld refinements of the diffraction patterns show that the high-temperature cubic phase of SrFeO_x is consistent with a face-centred Fm3c structure. This structure leads to agreement with previous density measurements. This cell allows the high-temperature structure of SrFeO_x to be described in terms of a solid solution of the composition end members. Cubic SrFeO_x at high temperature is found to closely obey Vegard's law. The density of cubic SrFeO_x is also found to exhibit a linear relationship with composition.     

Relating tracer and chemical diffusion coefficients in intermetallic compounds taking the DO3 and A15 structures

In this article we employ computer simulation to explore the validity of the Darken/Manning relation between the chemical diffusion coefficient and the tracer diffusion coefficients of the components in stoichiometric intermetallic compounds A₃B taking the DO₃ and A15 structures at vanishingly small vacancy contents. The analysis centres on the validity of Manning’s random alloy expression for the vacancy wind factor. The models for both the DO₃ and A15 structures use eight atom-vacancy exchange frequencies. For the DO₃ structure it is found that the actual vacancy wind factor is usually somewhat larger than that predicted by Manning but overall the agreement is good. At worst the use of Manning’s expression would underestimate this factor by about 30 or 40%. For the A15 structure a similar result is found except when diffusion along the chains in the structure is rapid. Then Manning’s expression fails badly when a constant geometrical tracer correlation factor is employed. In both the structures if the geometrical correlation factor is varied to reflect the structure actually explored by the atoms (mainly the majority atoms A) the agreement is improved very dramatically.     

The p–T phase diagram of KNbO3 by a dielectric constant measurement

A dielectric constant measurement was carried out on perovskite-type ferroelectrics KNbO₃ over a wide range of temperature under high pressure. The temperature- and pressure-dependence of the dielectric constant clarified that all temperatures of the transitions from the ferroelectric rhombohedral to orthorhombic, to tetragonal and then to the paraelectric cubic phase, decrease with increasing pressure. These results indicate that the orthorhombic–tetragonal transition takes place at 8.5 GPa and the tetragonal–cubic transition at 11 GPa, at room temperature.     

Theoretical study of metal-insulator transition in rhombohedral vanadium sesquioxide

The electronic structure and the metal-insulator transition (MIT) of V₂O₃ are investigated in the framework of density functional theory and GGA+U. It is found that, both the insulating and metallic phases can be realized in rhombohedral structure by varying the on-site Coulomb interaction, and the MIT in V₂O₃ can take place without any structure phase transition. Our calculated energy gap (0.63 eV) agrees with experimental result very well. The metallic phase exhibits high spin (S=1) character, but it becomes S=1/2 in insulating phase. According to our analysis, the Mott-Hubbard and the charge-transfer induce the MIT together, and it supports the mechanism postulated by Tanaka (2002) [11].     

A study of structural, compositional and optical properties of spray-deposited non-stoichiometric (Zn,Fe)S thin films

Non-stoichiometric ternary chalcogenides (Zn,Fe)S were prepared in the film form by pyrolytic spray deposition technique, using air/nitrogen as the carrier gas. The precursor solution comprised of ZnCl₂, FeCl₂ and thiourea. The depositions were carried out under optimum conditions of experimental parameters viz. carrier gas (air/nitrogen) flow rate, concentration of precursor constituents, nozzle substrate distance and temperature of quartz substrate. The deposited thin films were later sintered in argon at 1073 K for 120 min.The structural, compositional and optical properties of the sintered thin films were studied. X-ray diffraction studies of the thin films indicated the presence of (Zn,Fe)S solid solution with prominent cubic sphalerite phase while surface morphology as determined by scanning electron microscopy (SEM) revealed a granular structure.The chemical composition of the resulting thin films as analyzed by energy dispersive X-ray analysis (EDAX) reflected the composition of the precursor solutions from which the depositions were carried out with Fe at% values ranging from 0.4 up to 33.SEM micrographs of thin films reveal that the grain sizes of the thin films prepared using air as carrier gas and N₂ as carrier gas are in the vicinity of 300 and 150 nm, respectively.The diffuse transmittance measurements for thin films, as a function of wavelength reveal the dependence of direct optical band gap on Fe content and type of phase.     

On the criteria of formation and lattice distortion of perovskite-type complex halides

The famous Goldschmidt's tolerance factor gives us a necessary but not sufficient condition for the formation of perovskite-type compounds (ABX₃). In this work, computerized data analysis has been used to find some complementary criteria for the formation and lattice distortion of perovskite-type complex halides. It has been found that the radius ratio (R_A/R_X) and (R_B/R_X), affecting the stability of BX₆ octahedra and AX₁₂ cubo-octahedra (they are basic units of perovskite structure), are also dominating factors for the formation and lattice distortion of perovskite-type compounds. Besides, it has been found that the transition between the perovskite structure (with corner-sharing BX₆ octahedra) to BaNiO₃ structure (with face-sharing BX₆ octahedra) can be predicted by a criterion based on the relative magnitude of ionic radii and electronegativity. Based on multivariate data analysis, several complementary criteria for the formation and lattice distortion of perovskite-type complex halides have been obtained, and some empirical equations expressing the relationships between the ionic radii (R_A,R_B,R_X) and the lattice constants of perovskite-type complex halides have been found. The physical meaning of these empirical relationships has been discussed based on Pauling's rules of the crystal lattice stability of complex ionic compounds.     

High temperature XRD studies of nanoscale AgI-CuI solid solutions

A preliminary high-temperature X-ray diffraction (HT-XRD) study of the nanometer-sized solid solution phases in the AgI-CuI system is reported through an extended range of temperatures (300-723K) covering phase transitions in both AgI and CuI. A major feature of this work is the observation of the coexistence of the zincblende and base-centred cubic phases of AgI over an extended range of temperatures the temperature width being a function of Cu content in the binary. The lattice parameters derived from HT-XRD data reflect systematics of phase transitions with progressive Cu substitution of AgI. The present results are discussed together with our earlier ionic conductivity, dilatometry and DSC data which have helped deduce phase diagrams for both the Ag-rich and Cu-rich regions of the binary.     

Effects of annealing temperature on structure and magnetic properties of amorphous Fe61Co27P12 nanowire arrays

Arrays of Fe₆₁Co₂₇P₁₂ nanowire with an aspect ratio about 70 were prepared in anodic aluminum oxide templates by electrodeposition. The influences of annealing temperature on structure and magnetic properties of Fe₆₁Co₂₇P₁₂ nanowires were studied. When the specimens were annealed below 400 °C, there are no obvious changes in structure except relaxation. With the annealing temperature increasing from 400 to 600 °C, the Fe-Co phase is detected by X-ray diffraction and Mössbauer spectra. The crystalline fraction and hyperfine field can be derived from Mössbauer spectra. The room temperature magnetic hysteresis loops show that the coercivity and squareness of the nanowire arrays in parallel to the wire axis increase with the increasing of annealing temperature, which mainly attributes to the strengthening of anisotropy.     

Phase stability in the LnCa2Mn2O7 (Ln=Pr, Nd, Sm and Gd) Ruddlesden-Popper series

The synthesis of the Ruddlesden-Popper series, LnCa₂Mn₂O₇, (Ln=Pr, Nd, Sm and Gd) is described and their structure and electronic properties investigated. The reduction in size of the A-site cation causes an increase in the distortion of their orthorhombic structures (space group Cmcm). All of these compounds form with a perovskite impurity, the amount of which increases on reduction of the cation size. The synthesis temperature also alters the amount of perovskite impurity in the phase, but only to a lower limit, implying the perovskite phase is intrinsic to the material and that a phase equilibrium exists between the layered Ruddlesden-Popper and perovskite phases, which is controlled by the cation size. The magnetic susceptibility show transitions characteristic of the perovskite phase, therefore little direct information can be obtained about the Ruddlesden-Popper phases, except that ferromagnetism is not observed in any of these materials.     

Crystal structure and compressibility of a high-pressure Ti-rich oxide, (Ti0.50Zr0.26Mg0.14Cr0.10)O1.81, isomorphous with cubic zirconia

A Ti-rich oxide, (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)_∑=1.0O_1.81, was synthesized at 8.8 GPa and 1600 °C using a multi-anvil apparatus. Its crystal structure at ambient conditions and compressibility up to 10.58 GPa were determined with single-crystal X-ray diffraction. This high-pressure phase is isomorphous with cubic zirconia (fluorite-type) with space group Fm3¯m and unit-cell parameters a=4.8830(5) Å and V=116.43(4) Å³. Like stabilized cubic zirconia, the structure of (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)O_1.81 is also relaxed, with all O atoms displaced from the (, , ) position along 〈1 0 0〉 by 0.319 Å and all cations from the (0, 0, 0) position along 〈1 1 1〉 by 0.203 Å. No phase transformation was detected within the experimental pressure range. Fitting the high-pressure data (V vs. P) to a third-order Birch-Murnaghan EOS yields K₀=164(4) GPa, K′=4.3(7), and V₀=116.38(3) Å³. The bulk modulus of (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)O_1.81 is significantly lower than that (202 GPa) determined experimentally for cubic TiO₂ or that (~210 GPa) estimated for cubic ZrO₂. This study demonstrates that cubic TiO₂ may also be obtained by introducing various dopants, similar to the way cubic zirconia is stabilized below 2370 °C. Furthermore, (Ti_0.50Zr_0.26Mg_0.14Cr_0.10)O_1.81 has the greatest ratio of Ti⁴⁺ content vs. vacant O²⁻ sites of all doped cubic zirconia samples reported thus far, making it a more promising candidate for the development of electrolytes in solid oxide fuel cells.