Atomistic computer simulation studies of Sr2RuO4 and Ca2RuO4

Atomistic static computer simulation techniques have been applied to investigate the energetics of defects and dopants in Sr₂RuO₄ (SRO) and Ca₂RuO₄ (CRO). Interatomic potentials have been derived which reproduced the crystal structures of these systems. Solution energies are calculated for different dopant ions to ascertain the site occupied by the dopant ion in the host lattice. Monovalent and divalent ions are predicted to substitute preferentially at the alkaline-earth site in both the systems. Trivalent cations of smaller ionic radii substitute at the Ru sites while those having larger ionic radii prefer to substitute at the Sr or Ca sites in SRO or CRO systems, respectively. In addition, there is a possibility of self-compensation, where a trivalent cation can substitute at both Sr(Ca) and Ru sites. Tetravalent dopants are found to substitute at the ruthenium sites in both systems.     

An NMR crystallographic approach to monitoring cation substitution in the aluminophosphate STA-2

The substitution of the divalent cations Mg²⁺ and Zn²⁺ into the aluminophosphate (AlPO) framework of STA-2 has been studied using an “NMR crystallographic” approach, combining multinuclear solid-state NMR spectroscopy, X-ray diffraction and first-principles calculations. Although the AlPO framework itself is inherently neutral, the positive charge of the organocation template in an as-made material is usually balanced either by the coordination to the framework of anions from the synthesis solution, such as OH⁻ or F⁻, and/or by the substitution of aliovalent cations. However, the exact position and distribution of the substituted cations can be difficult to determine, but can have a significant impact upon the catalytic properties a material exhibits once calcined.For as-made Mg substituted STA-2, the positive charge of the organocation template is balanced by the substitution of Mg²⁺ for Al³⁺ and, where required, by hydroxide anions coordinated to the framework [27] Al MAS NMR spectra show that Al is present in both tetrahedral and five-fold coordination, with the latter dependent on the amount of substituted cations, and confirms the bridging nature of the hydroxyl groups, while high-resolution MQMAS spectra are able to show that Mg appears to preferentially substitute on the Al1 site. This conclusion is also supported by first-principles calculations. The calculations also show that ³¹P chemical shifts depend not only on the topologically-distinct site in the SAT framework, but also on the number of next-nearest-neighbour Mg species, and the exact nature of the coordinated hydroxyls (whether the P atom forms part of a six-membered ring, P(OAl)₂OH, where OH bridges between two Al atoms). The calculations demonstrate a strong correlation between the ³¹P isotropic chemical shift and the average 〈P–O–M〉 bond angle. In contrast, for Zn substituted STA-2, both X-ray diffraction and NMR spectroscopy show less preference for substitution onto Al1 or Al2, with both appearing to be present, although that into Al1 appears slightly more favoured.     

Emission Mössbauer studies of the magnetoresistive compound, La0.7Sr0.3MnO3

The magnetic behavior of the Sr_0.3 manganite is studied using a local microprobe, ⁵⁷Co. In contrast with Ca substituted manganites, a much larger fraction of the material exhibits short-range order with superparamagnetic-like behavior even at 80 K. The differences in behavior are attributed to the large mismatch between the ionic radii of La⁺³ and the divalent substituent Sr⁺², which introduces anharmonicity in local vibrations. In common with all other compounds exhibiting negative bulk magnetoresistivity, the Sr_0.3 compound also exhibits very marked softening of lattice as one approaches T_c from below. Application of an external magnetic field results in coalescing of nanosized magnetic clusters to form larger ones with better alignment of spins.     

Preparation and properties of polycrystalline divalent-cation β″-alumina

Using ion exchange from an appropriate molten salt, the divalent cations Ca, Sr, Ba, Zn, Cd, Sn and Pb have been substituted for Na in polycrystalline Li₂O-stabilized Na-β″-alumina samples. The Ca-, Sr-, and Cd-β″ alumina specimens were dense, crack-free bodies. Preparation procedures for the substitutions, lattice parameters for the substituted structure, and Raman spectra are given for the various divalent-cation β″-aluminas. Raman data aided in determining whether or not exchange of one ion by another had occured.     

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.     

The effect of doping LiMn2O4 spinel on its use as a cathode in Li-ion batteries: neutron diffraction and electrochemical studies

A series of compounds Li_1+yMn_2−xM′_xO₄ (x≤0.1;y≤0.02), have been synthesised by doping the parent LiMn₂O₄ spinel with various metal ions of variable oxidation state. Powder neutron diffraction data has been collected on these samples alongside a series of electrochemical experiments in order to elucidate the relationship between structure on the performance of these systems as Li batteries. Doping the LiMn₂O₄ spinel with a small amount of metal ions has a remarkable effect on the electrochemical properties. Whereas the capacity of the spinels doped with trivalent ions is much greater, the cycling fading properties are much enhanced with using divalent ions as dopants. The underlying reasons for this are discussed, and it is suggested that the occupancy of the tetrahedral site with divalent ions to form a more compact structure offers an improved structural stability to support greater Li insertion/extraction, but which ultimately prevents the free movement of Li also sited on the tetrahedral site of the lattice.     

Half-metallic ferromagnetism in I2-VI compounds with non-magnetic dopants

First-principles calculations based on the tight-binding linear muffin-tin orbital (TB-LMTO) method were performed to investigate the occurrence of spin polarization in the alkali metal oxides (M₂O) [M: Li, Na, K, Rb] in antifluorite (anti- CaF₂-type) structure with non-magnetic (N, P, As, Sb and Bi) dopants. The calculations reveal that non-magnetic substitutional doping at anion site can induce stable half-metallic ferromagnetic ground state in I₂-VI compounds. Total energy calculations show that the antifluorite ferromagnetic state is energetically more stable than the antifluorite non-magnetic state at equilibrium volume. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The calculated magnetic moment is found to be 1.00 μ_B per dopant atom. The magnetic moment is mainly contributed by p orbitals of dopant atom.     

Synthesis and physical properties of negative thermal expansion materials Zr1−xMxW2O8−y (M=Sc, In, Y) substituted for Zr(IV) sites by M(III) ions

Zr_1−xM_xW₂O_8−y (M=Sc, In and Y) solid solutions substituted up to x=0.04 for Zr(IV) sites by M(III) ions were synthesized by a solid-state reaction. X-ray diffraction experiments from 90 to 560 K revealed that all solid solutions had a cubic crystal structure and showed negative thermal expansion coefficients. The lattice parameters of Zr_1−xM_xW₂O_8−y were smaller than that of ZrW₂O₈ probably due to oxygen defects, though the ionic radii of substituted M³⁺ ions were larger than that of Zr⁴⁺. Order-disorder phase transition temperatures of the substituted samples drastically decreased in the order of Y, In and Sc compared to the percolation theory, and decreased with increasing M content.     

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.     

Effect of Ca and Sr alkaline earth ions on luminescence properties of BaAl12O19:Eu nanophosphor

Nanosized barium aluminate materials was doped by divalent cations (Ca²⁺, Sr²⁺) and Eu²⁺ having nominal compositions Ba_1−xMxAl₁₂O₁₉:Eu (M=Ca and Sr) (x=0.1-0.5), were synthesized by the combustion method. These phosphors were characterized by XRD, scanning electron microscopy-energy-dispersive spectrometry (SEM-EDS) and photoluminescence measurement. The photoluminescence characterization showed the presence of Eu ion in divalent form which gave emission bands peaking at 444 nm for the 320 nm excitation (solid-state lighting excitation), while for 254 nm it gave the same emission wavelength of low intensity (1.5 times) compared to 320 nm excitation. It was also observed that alkaline earth metal (Ca²⁺ and Sr²⁺) dopants increase the intensity of Eu²⁺ ion in BaAl₁₂O₁₉ lattice, thus this phosphor may be useful for solid-state lighting.     

Crystallographic study of the phase transition in (Me4P)2ZnBr4

The compound (Me₄P)₂ZnBr₄, a member of the β-K₂SO₄ structure class, undergoes a phase transition at 84°C from the room temperature space group P12₁/c1 to the parent Pmcn structure. The room temperature structure corresponds to a ferrodistortive transition of B_1g symmetry at the zone center. At room temperature, the compound has lattice constants a=9.501(1), b=16.055(2), c=13.127(2) Å and β=90.43(1)°. For the high temperature phase, the orthorhombic cell has dimensions a=9.466(2), b=16.351(3) and c=13.284(2) Å. The structures consist of two crystallographically independent Me₄P⁺ cations and the ZnBr₄²⁻ anions. In the room temperature phase, all three ionic species show substantial displacement from the mirror plane perpendicular to the a-axis that exists in the high temperature phase, as well as rotations out of that plane. The thermal parameters of the cations are indicative of substantial librational motion. Measurements of lattice parameters have been made at 2-5°C intervals over the temperature range 40-140°C. The changes in the lattice constants appear continuous at T_c (within experimental limits) indicating that the phase transition is likely second-order. The a lattice constant shows an anomalous shortening as T_c is approached. Thermal expansion coefficients are calculated from this data. An application of Landau theory is used to derive the temperature dependencies of spontaneous shear strain and corresponding elastic stiffness constants associated with the primary order parameter.     

Surface cation ratios of binary oxide solid solutions

The cation ratios in the (100) surface of cubic oxides of bulk composition A_0.99B_0.01O, in which A and B are divalent cations were calculated using a monolayer model. Divalent cations including Ni, Co, Mn, Fe and Mg were studied. The cations were represented by a shell model, and the surface compositions were calculated by minimizing the total Gibbs free energy of the solid. The bulk energy change on surface segregation was evaluated by minimizing the energy change on substituting one bulk cation by another in an infinitely dilute solid solution and the surface energy was evaluated by a statistical method to accommodate the possibility that both cations can exist at non-negligible densities at the surface. The bulk energy change on surface segregation was found to be dominant in most cases. The surface energy change, the entropy change, and the change in crystal field stabilization energy were all secondary. Thus, except when the difference in ionic radii is very small, the larger cation is always more preferred at the surface. This conclusion appears to be in agreement with available experimental data.     

Prediction of defect structure in lithiated tin- and titanium-doped α-Fe2O3 using atomistic simulation

The defect structure of lithiated tin- and titanium-doped α-Fe₂O₃ has been assessed using interatomic potential calculations. Of the models considered for lithiation, a model in which Li⁺ occupies an interstitial site balanced by the reduction of Fe³⁺ to Fe²⁺ on an Fe³⁺ site was found to be more favourable than the substitution of Li⁺ on an Fe³⁺ octahedral site balanced by an O²⁻ vacancy. Insertion of lithium into the interstitial site between two adjacent M⁴⁺ ions was particularly favourable. The calculated lattice parameters decrease on lithiation as has been observed experimentally.     

Ground state and lattice dynamical study of ionic conductors CaF2, SrF2 and BaF2 using density functional theory

The present paper reports a comprehensive and complementary study on structural, electronic and phonon properties of face centered cubic fluorites, namely CaF₂, BaF₂ and SrF₂, using first principles density functional calculations within the generalized gradient approximation. The calculated lattice constants and bulk modulus are in good agreement with available experimental data. The analysis of band structure and density of states confirms the ionic character for all the three fluorides. The phonon dispersion curves and corresponding phonon density of states obtained in the present work are consistent with the available experimental and other theoretical data. The LO-TO splitting is maximum for CaF₂, which confirms that the ionicity is maximum in the case of CaF₂. The phonon properties for SrF₂ have been calculated for the first time.     

Structural, electronic, elastic and thermal properties of Mg2Si

First-principles calculations of the lattice parameter, electron density maps, density of states and elastic constants of Mg₂Si are reported. The lattice parameter is found to differ by less than 0.8% from the experimental data. Calculations of density of states and electron density maps are also performed to describe the orbital mixing and the nature of chemical bonding. Our results indicate that the bonding interactions in the Mg₂Si crystal are more covalent than ionic. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the plane-wave pseudopotential method, is applied to study the elastic, thermal and vibrational effects. The variations of bulk modulus, Grüneisen parameter, Debye temperature, heat capacity C_v, C_p and entropy with pressure P up to 7 GPa in the temperature interval 0-1300 K have been systemically investigated. Significant differences in properties are observed at high pressure and high temperature. When T<1300 K, the calculated entropy and heat capacity agree reasonably with available experimental data. Therefore, the present results indicate that the combination of first-principles and quasi-harmonic Debye model is an efficient approach to simulate the behavior of Mg₂Si.     

Combined Rietveld refinement of BaMgAl10O17:Eu using X-ray and neutron powder diffraction data

The phosphor, BaMgAl₁₀O₁₇:Eu²⁺, showing a blue emission band at about 450 nm was prepared by a normal solid-state reaction using BaCO₃, Al₂O₃, MgO and Eu₂O₃ as starting materials with AlF₃ as a flux. The study of combined Rietveld refinement and photoluminescence spectra was carried out to determine the structural parameters, such as lattice constants, the valence state of Eu, the site preference of Mg and site fractions of Mg and Eu. The occupancies of Eu and Mg were 0.022 and 0.526, respectively. The valence state of Eu was the divalent state because there was only one broad line at about 450 nm in the photoluminescence spectrum. The site preference of Mg atoms was the tetrahedral site of Al atoms surrounded by oxygen atoms in the spinel block. Lattice parameters decreased due to the difference of two ionic radii, Eu²⁺(1.09 Å) and Ba²⁺(1.34 Å), compared with those of BaMgAl₁₀O₁₇.     

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.     

Structure refinements of cadmium substituted lead fluoroapatites by powder X-ray pattern fitting

Solid solutions of cadmium and lead fluoroapatite [Pb_(10−x)Cd_x(PO₄)₆F₂ (0?x?5)] were synthesized by a wet process in a basic medium. Replacement of lead by cadmium induces a linear variation of the crystallographic parameters “a” and “c” according to Végard's law. The cadmium content, as obtained from the refinement, is in agreement with the chemical analysis. The distribution of the lead and cadmium ions between two non-equivalent crystallographic sites, M(1) and M(2), was determined by the Rietveld method. The site-occupancy factors of atoms clearly indicate a preference of cadmium for site M(1) in the apatite structure in agreement with its smaller ionic radii. A progressive shift of the F⁻ ion toward the center of the triangles formed by the site M(2) metals has been observed with increasing cadmium content.     

Doping strategies for increased performance in BiFeO3

Investigation of crystal structure, dielectric, magnetic and local ferroelectric properties of the diamagnetically substituted Bi_1−xA_xFeO_3−x/2 (A=Ca, Sr, Pb, Ba; x=0.2, 0.3) polycrystalline samples has been carried out. It has been shown that the heterovalent A²⁺ substitution result in the formation of oxygen vacancies in the host lattice. The solid solutions have been found to possess a rhombohedrally distorted perovskite structure described by the space group R3c. Piezoresponse force microscopy has revealed signs of existence of the ferroelectric polarization in the samples at room temperature. Magnetization measurements have shown that the magnetic state of these compounds is determined by the ionic radius of the substituting elements. A-site substitution with the biggest ionic radius ions has been found to suppress the spiral spin structure of BiFeO₃ giving rise to the appearance of room-temperature weak ferromagnetism.     

Half-metallic ferromagnetism in (C, Si, Ge, Sn and Pb)-doped I2-VI compounds: An ab initio study

First-principles calculations were performed to investigate the stability, electronic structure and magnetism in Group IV elements-doped alkali-metal oxides (M₂O) [M: Li, Na, K, Rb] in antifluorite structure using the linear muffin-tin orbital method in its tight-binding representation (TB-LMTO). The calculations reveal that non-magnetic dopants can induce stable half-metallic ferromagnetic ground state in I₂-VI compounds. Total energy calculations show that the ferromagnetic state is energetically more stable than the non-magnetic state at equilibrium volume. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The magnetic moment is found to be 2.00 μ_B per dopant atom.