Prediction of lattice constant in cubic perovskites

Regularities of lattice constant in ideal perovskites are investigated by using a total of 132 ABX₃-type compounds, including oxides and halides. Two atomic properties; the sum of ionic radius of B and X atoms and the well known ‘tolerance factor’ (which is a function of ionic radius of A, B and X), were found very effective in reproducing the measured lattice constant through a linear combination of these two parameters (R²=0.995). It is further indicated that these two parameters are linked to the crystal features of perovskite. The average error limits in predicting lattice constant, by using this empirical equation, are expected within 0.63%. It may be useful to design new substrates/buffer materials for compound semiconductor epitaxy, in which there is a requirement of lattice match between them and adjacent layers.     

Modeling of lattice constant and their relations with ionic radii and electronegativity of constituting ions of A2XY6 cubic crystals (A=K, Cs, Rb, Tl; X=tetravalent cation, Y=F, Cl, Br, I)

In the present paper a new empirical model is proposed to describe and predict the lattice constants for a series of cubic crystals, all of which have the A₂XY₆ composition (A=K, Cs, Rb, Tl; X=tetravalent cation, Y=F, Cl, Br, I). The model is based on a thorough analysis of structural properties of 85 representative crystals from this group. It was shown that the lattice constant is a linear function of the ionic radii and electronegativity of the constituting ions. A simple empirical equation was obtained as a result of the performed analysis. It gives very good agreement between the experimental and modeled values of the lattice parameters, with an average error of 1.05%. The developed approach can be efficiently used for a simple, fast, and reliable prediction of lattice constants and interionic distances in isostructural materials having a similar composition.     

Formability of ABO3 cubic perovskites

In this study, 223 binary oxide systems (of which, 34 systems can form cubic perovskites) are collected to explore the regularity of cubic perovskites formability. It is found that the octahedral factor (r_B/r_O) take the same important role as the tolerance factor (t) to form cubic perovskites in complex oxide system. Regularities governing cubic perovskites formability are obtained by using empirical structure map constructed by these two parameters, on this structure map, sample points representing systems of forming (cubic structure) and non-forming are distributed in distinctively different regions. Prediction criteria for the formability of cubic perovskites are squeezed out, which may be applied to design new substrate or buffer materials with cubic perovskite structure in compound semiconductor epitaxy.     

Prediction of lattice constant in perovskites of GdFeO3 structure

Lattice constants in GdFeO₃-type ABO₃ perovskites are correlated to their constituent elemental properties by using linear regression (LR) and artificial neural networks (ANN) techniques and a sample set of 157 known GdFeO₃-type ABO₃ perovskites. LR models are first obtained using two elemental ionic radii only and ANN models, using five elemental properties; ionic radii, electronegativities of cation A and B, and the valence of ion A, are further developed to improve the model predictability, which reaches an error limits of less than 2%. It is shown that lattice constants of these compounds only roughly correlate to their ionic radii, and for a good prediction model 3 more elemental properties (electronegativity and valence) are necessary. In new materials research, where lattice constant is one of the key design target, the developed LR and ANN models may be used to screen and shortlist promising perovskites from a large pool of all possible candidates. These selected compounds may undergo further test using relatively more expensive experiments or quantum mechanics computations.     

The structure and optical properties of AlN nanocrystals prepared by Schlenk techniques at atmospheric pressure and low temperature

AlN nanocrystals were prepared in organic solvent at atmospheric pressure and low temperature by the Schlenk technique. Both hexagonal and cubic AlN nanocrystals were obtained. The hexagonal nano-AlN powder possessed a wurtzite structure with a=3.124 Å, c=5.024 Å, the average grain size was about 2 nm. The lattice constant of the cubic nano-AlN was a=9.171 Å, the average grain size was about 4 nm. The structural and optical properties of the obtained AlN were analyzed. The emission related to deep-level defects was investigated by using temperature-dependent photoluminescence.     

Single crystal and powder EPR study of trivalent gadolinium in Cs2NaBiCl6 in the 30-300 K interval

A crystalline electric field cubic symmetry site has been reported for Gd³⁺ in Cs₂NaBiCl₆ at room temperature. This host exhibits an apparent structural transformation below 100 K that is completely reversible. However, an EPR examination for a powdered sample of Cs₂NaBiCl₆:Gd³⁺ clearly demonstrates that there are no new large crystalline electric field symmetry sites arising between the transition temperature (100 K) and 30 K, suggesting, therefore, that the site symmetry remains predominantly cubic even at temperatures close to 30 K. In order to substantiate this statement, a computer EPR powder simulation was performed using the single-crystal-spin-Hamiltonian parameters obtained from the three different sites that emerge from the original site while observed at 30 K. A remarkable agreement is observed while comparing the computer-simulated data with that of powdered experimental data. It is important to mention here that several attempts were done trying to fit the observed new spectra to lower crystalline field symmetries, however, our best analytical adjustment was obtained with the cubic spin-Hamiltonian.Below 30 K, new structural transitions are present and the lattice loses its original cubic nature. However, at 10 K the EPR spectrum of the crystal again shows only seven lines that are very broad. This new spectrum cannot be fitted with previously used cubic spin-Hamiltonian parameters.     

First-principle calculations of structural, electronic and optical properties of BaTiO3 and BaZrO3 under hydrostatic pressure

A theoretical study of structural, electronic and optical properties of cubic BaTiO₃ and BaZrO₃ perovskites is presented, using the full-potential linear augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. In this approach the local density approximation (LDA) is used for the exchange-correlation (XC) potential. Results are given for lattice constant, bulk modulus, its pressure derivative, band structure, density of states, pressure coefficients of energy gaps and refractive indices. The results are compared with previous calculations and experimental data.     

Spontaneous organisation of ZnS nanoparticles into monocrystalline nanorods with highly enhanced dopant-related emission

A natural self-assembly process of semiconductor nanoparticles leading to the formation of doped, monocrystalline nanorods with highly enhanced dopant-related luminescence properties is reported. ∼4 nm sized, polycrystalline ZnS nanoparticles of zinc-blende (cubic) structure, doped with Cu⁺-Al³⁺ or Mn²⁺ have been aggregated in the aqueous solution and grown into nanorods of length ∼400 nm and aspect ratio ∼12. Transmission electron microscopic (TEM) images indicate crystal growth mechanisms involving both Ostwald-ripening and particle-to-particle oriented-attachment. Sulphur-sulphur catenation is proposed for the covalent-linkage between the attached particles. The nanorods exhibit self-assembly mediated quenching of the lattice defect-related emission accompanied by multifold enhancement in the dopant-related emission. This study demonstrates that the collective behavior of an ensemble of bare nanoparticles, under natural conditions, can lead to the formation of functionalized (doped) nanorods with enhanced luminescence properties.     

The evolution of octahedral rotations of orthorhombic LaVO3 in superlattices with cubic SrVO3

We have studied the octahedral rotations in LaVO₃/SrVO₃ superlattices, keeping the thickness of the orthorhombic LaVO₃ layers constant and increasing the thickness of cubic SrVO₃ layers. We have found that for a small thickness of SrVO₃, the octahedral rotations in LaVO₃ are maintained, while for an increasing thickness, these rotations are suppressed. This observation cannot be explained by purely elastic effects due to the lattice mismatch between the two materials, but the absence of rotations in SrVO₃ is a crucial ingredient, illustrating the concept of interface engineering of octahedral rotations.     

Lattice dynamics of BiFeO<Subscript>3</Subscript>: The untypical behavior of the ferroelectric instability under hydrostatic pressure

Within a nonempirical model of an ionic crystal with the inclusion of the dipole and quadrupole ion polarizations, the lattice vibrational frequencies, high-frequency dielectric constant, Born dynamic charges, and the elasticity moduli of the BiFeO₃ crystal have been calculated and their dependencies on the hydrostatic pressure in the cubic, rhombic, and rhombohedral phases have been determined. The results indicate the presence of the ferroelectric instability, which depends weakly on the pressure in all of the phases investigated. The dependence of the crystal lattice dynamics on the applied pressure for the cubic phases of BiAlO₃, BaTiO₃, and PbTiO₃ has been calculated for comparison.     

Relationships between lattice energy and electronic polarizability of AB crystals

The correlations between the electronic polarizability, determined from Clausius-Mosotti equation based on dielectric constant ε, and the lattice energy density u have been established for A^NB^8-N crystals, such as the systems of rock salt crystals (group I-VII, II-VI) and tetrahedral coordinated crystals (group II-VI, III-V). For the A^NB^8-N crystals systems, our present conclusions suggest that lattice energy density u decreases exponentially with increasing electronic polarizability, and the normal mathematical expression between lattice energy density u and electronic polarizability is u = pα^q, p and q depend on the type of crystals. For the same cation binary A^NB^8-N crystals systems, curve fitting equations have been obtained, and the relevant squares of the correlation coefficient R² are larger than 0.99, which show all lattice energy density u are in good exponential relation with electronic polarizability. These empirical equations will give more information on calculating lattice energy or electronic polarizability. New data of lattice energy have been calculated on the above equation u = pα^q, and a good linear trend in the calculating values along with the Zhang’s values has been obtained.     

Structural, magnetic and electrical properties of NiCuZn ferrites prepared by microwave sintering method suitable for MLCI applications

Polycrystalline NiCuZn soft ferrites with stoichiometric iron were prepared by a novel microwave sintering method. The powders were calcined, compacted and sintered at 950 °C for 30 min in a microwave sintering furnace. X-ray diffraction patterns confirm the formation of single phase cubic spinel structure. The grain size was estimated using SEM micrographs. The lattice constant is found to increase with increase in zinc concentration. The sintered ferrites have been investigated for their physical, magnetic and electrical properties such as bulk density, X-ray density, porosity, anisotropy constant, initial permeability, saturation magnetization, DC resistivity, dielectric constant and dielectric loss as a function of zinc concentration. Permeability, saturation magnetization, dielectric constant and dielectric loss were found to increase while DC resistivity was found to decrease with the replacement of Zn with Ni. The present series of ferrites are found to posses properties that are suitable for the core materials in multilayer chip inductors.     

Ab initio study of structural and electronic properties of BiAlO3 and BiGaO3

The first principles within the full potential linearized augmented plane wave (FP-LAPW) method was applied to study the structural and electronic properties of cubic perovskite-type compounds BiAlO₃ and BiGaO₃. The lattice constant, bulk modulus, its pressure derivative, band structure and density of states were obtained. The results show that BiGaO₃ should exhibit higher hardness and stiffness than BiAlO₃. The Al–O or Ga–O bonds are typically covalent with a strong hybridizations as well as Bi–O ones that have a significant ionic character. Both materials are weakly ionic and exhibit wide and indirect band gaps, which are typical of insulators.     

First principle study of the structural and optoelectronic properties of cubic perovskites CsPbM3 (M=Cl, Br, I)

The highly accurate all electrons full potential linearized augmented plane wave method is used to calculate structural, electronic, and optical properties of cubic perovskites CsPbM₃ (M=Cl, Br, I). The theoretically calculated lattice constants are found to be in good agreement with the experimentally measured values. It is found that all of these compounds are wide and direct bandgap semiconductors with bandgap located at R-symmetry point, while the bandgap decreases from Cl to I. The electron densities reveal strong ionic bonding between Cs and halides but strong covalent bonding between Pb and halides. Optical properties of these compounds like real and imaginary parts of dielectric functions, refractive indices, extinction coefficients, reflectivities, optical conductivities, and absorption coefficients are also calculated. The direct bandgap nature and high absorption power of these compounds in the visible-ultraviolet energy range imply that these perovskites can be used in optical and optoelectronic devices working in this range of the spectrum.     

Experimental and theoretical studies on bis(glycine) lithium nitrate (BGLiN): A physico-chemical approach

Good quality and bulk size single crystal (size: 20×13×8 mm³) of bis(glycine) lithium nitrate (BGLiN) was grown by a slow evaporation solution technique from the aqueous solutions at constant temperature i.e. 27 °C using synthesized materials. Crystal system and lattice parameters were determined by single crystals as well as powder X-ray diffraction analysis. The lattice parameters of the titled compound are a=10.0223 Å, b=5.0343 Å, c=17.0510 Å, and V=860.312 Å³ and it crystallized in an orthorhombic system with space group Pca2₁ obtained by single crystal XRD. Elemental composition was confirmed by energy dispersive X-ray spectroscopic analysis. Optical absorption spectrum was recorded and various optical parameters such as optical transmission (~60%), and optical band gap (4.998 eV) were calculated. Photoluminescence study shows that the grown crystal is free from major defects. Crystalline perfection of the grown crystal was assessed and found good. Ground state optimized geometry has been obtained by using DFT with 6-31G(d,p) basis set. HOMO and LUMO energy gap was found to be 6.01 eV and dipole moment was 1.65 D.     

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.     

Zone-center soft mode behavior in the cubic phase of NaNbO3

The temperature dependence of the zone-center polar lattice vibrations, including a soft mode, in the cubic phase of NaNbO₃ as observed by infrared reflectivity spectroscopy, is reported. Data are analysed and discussed in the light of results previously obtained in other oxidic perovskites.     

Impurities in noncubic crystals: stabilization mechanisms for Jahn-Teller ions in layered perovskites

Mechanisms responsible for the local geometry around Jahn-Teller impurities in K2NiF4 type lattices are shown to be different from those generating the warping in cubic crystals. The present density functional theory calculations reveal that the elastic anisotropy of the host lattice (visible for closed shell impurities) and the electric field created by the rest of lattice ions upon active electrons make it possible to have d(9) ions in an elongated geometry but with a A(1g) ground state. The puzzling difference between equilibrium geometries for Cu2+ and Ni+ in layered perovskites can reasonably be understood.     

General behavior of longitudinal optical phonons in cubic diatomic crystals

A general relationship for longitudinal optical (LO) phonons in diatomic cubic crystals is introduced. The analysis of spectroscopic data of diatomic cubic crystals reveals that LO frequencies correlate directly with bulk moduli in a nearest-neighbor fashion. The proportionality constant is found to be dependent only on lattice geometries. Transverse effective charges can be obtained when the Lyddane-Sachs-Teller is incorporated into the model. Our calculations are in excellent agreement with experimental values and theoretical calculations. Some interesting implications of the model are discussed.     

Heat capacity of ZnO with cubic structure at high temperatures

The heat capacities at constant pressure and constant volume, and thermal expansivity are calculated for ZnO with rocksalt-type and zinc-blende-type cubic structures over a wide range of temperatures using molecular dynamics simulations with interactions due to effective pair-wise potentials which consist of the Coulomb, dispersion, and repulsion interaction. It is shown that the calculated structural and thermodynamic parameters including lattice constant, thermal-expansion coefficient, isothermal bulk modulus and its pressure derivative at ambient condition are in good agreement with the available experimental data and the latest theoretical results. At extended pressure and temperature ranges, lattice constant and heat capacity have also been predicted. The structural and thermodynamic properties of ZnO with cubic structure are summarized in the 300-1500 K temperature ranges and up to 100 kbar pressure.