Pseudo-cubic Lattice Constant Research Articles

Epitaxial growth of the candidate ferroelectric Rashba material SrBiO3 by pulsed laser deposition

Among oxides, bismuthates have been gaining much interest due to their unique features. In addition to their superconducting properties, they show potential for applications as topological insulators and as possible spin-to-charge converters. After being first investigated in their bulk form in the 1980s, bismuthates have been successfully grown as thin films. However, most efforts have focused on BaBiO3, with SrBiO3 receiving only little attention. Here, we report the growth of epitaxial films of SrBiO3 on both TiO2-terminated SrTiO3 and NdO-terminated NdScO3 substrates by pulsed laser deposition. SrBiO3 has a pseudocubic lattice constant of ∼4.25 Å and grows relaxed on NdScO3. Counter-intuitively, it grows with a slight tensile strain on SrTiO3 despite a large lattice mismatch, which should induce compressive strain. High-resolution transmission electron microscopy reveals that this occurs as a consequence of structural domain matching, with blocks of 10 SrBiO3 unit planes matching blocks of 11 SrTiO3 unit planes. This work provides a framework for the synthesis of high quality perovskite bismuthates films and for the understanding of their interface interactions with homostructural substrates.

Understanding Chemical Expansion in Pr-Based Mixed Conducting Perovskites PrGa0.9Mg0.1O3 and BaPr0.9Y0.1O3

Chemical expansion is a strain induced by a change in stoichiometry, such as oxygen loss, and it can have a significant impact on device performance and lifetime. While large coefficients of chemical expansion (CCE) are needed for high displacements in an actuator, the same, large CCE can be deleterious to device longevity in a fuel cell where large chemical potential gradients exist across very small thicknesses. The breadth of CCE values needed in various devices calls for the development of design rules to tailor CCE for optimal material response, so our work targets the establishment of such structure-property insights.Oxygen-loss-induced, stoichiometric chemical expansion in oxides involves the formation of an oxygen vacancy; when oxygen leaves the lattice, charge compensating electrons are left behind and can localize on nearby multivalent cations. As cations are reduced, their atomic radii and the surrounding lattice expand. An empirical formula describing the pseudo-cubic lattice constant of perovskite materials has been developed [1] which relates the lattice parameter to the ionic radii of cation and anion components. This equation predicts that changes in the B-site cation size will have a larger effect on the lattice parameter than an equal change at the A-site. If the multivalent cation is the only one changing size during redox processes, this equation suggests that its placement on the A or B site will have a significant effect on the magnitude of the overall lattice strain during oxygen loss or gain.In an effort to develop and understand design rules to tailor CCE, two compositions, PrGa0.9Mg0.1O3 (PGM) and BaPr0.9Y0.1O3 (BPY), have been synthesized. These compositions allowed for a comparison between A and B-site multivalent Pr (nominally 3+/4+); however, we found that the empirical model did not adequately predict the differences in CCEs on this basis. Other factors including crystal symmetry, charge localization, and location of charge (anion or cation) were instead found to be significantly impactful for both compositions [2]. Values of CCE have been determined by characterizing isothermal changes in stoichiometry with thermogravimetric analysis (TGA) and corresponding changes in strain with dilatometry and in situ, high temperature XRD (HTXRD) as a function of oxygen partial pressure (pO2). The degree of charge localization has been interpreted from impedance measurements of the temperature dependence of conductivity, and the experimental results have been compared to density functional theory (DFT+U) calculations. Over the pO2 and temperature range studied, PGM and BPY have low CCEs, therefore making them of potential interest for fuel/electrolysis cell electrodes. The effects of the abovementioned design rules are discussed to provide insights into rational material design for tailored CCE.[1] Marrocchelli, D., Perry, N. H., & Bishop, S. R. (2015). Understanding chemical expansion in perovskite-structured oxides. Physical Chemistry Chemical Physics, 17(15), 10028-10039.[2] Ricote, S., Hudish, G., O’Brien, J. R. & Perry, N. H. Non stoichiometry and lattice expansion of BaZr0.9Dy0.1O3-δ in oxidizing atmospheres. Solid State Ionics (2019) doi:10.1016/j.ssi.2018.12.006.

Empirical models of trigonal distortions and polarization in perovskites

AbstractCorrelative models derived from empirical relations describing synthesis‐structure relationships are essential to guiding and improving future research and development of functional materials, yet few models exist for the prediction of structural distortions in perovskites. In this work, a data‐mining approach has been employed to collect structural data for trigonally distorted perovskites in specific model systems. Correlative models were developed which describe the relationship between the c/a ratio and the ratio of the pseudocubic lattice constant (apc) to the B‐X bond length (rBX). General models were then created for the c/a ratio in terms of the modified tolerance factor for trigonal perovskites with symmetry and perovskite‐like compounds with R3c symmetry. These models accurately predict the lattice constants in trigonally distorted perovskites and LiNbO3 type perovskite‐like compounds. In addition, a general model was developed, which accurately predicts polarization in trigonal LiNbO3 type perovskite‐like compounds in space group R3c.

Correlative models for oxygen vacancies in perovskites

Although most commercial perovskite ceramics contain oxygen vacancies, whether intrinsic or extrinsic, few correlative models currently exist to predict their effects on crystal structure or local crystallochemistry. Such predictive models, derived from empirical relationships between synthesis and structural data, can significantly facilitate future research and development. In this work, eight compositions within the CaTi 1- x Fe x O 3- x /2 system and eleven compositions within the SrTi 1- x Fe x O 3- x /2 system were synthesized using a conventional solid-oxide mixing procedure. Using a data-mining approach, these data were supplemented with data from five more published oxygen-deficient systems. Empirical models for all seven systems were developed to calculate both the effective oxygen vacancy size as well as the bond deformation term using only the modified tolerance factor. A general model for the modified tolerance factor itself was also developed which accounts for the effect of oxygen vacancies using only published ionic radii data as inputs. • Developed a general model for the effective anion vacancy size and the bond deformation in oxygen-deficient perovskites. • Developed a general empirical model for the modified tolerance factor in oxygen-deficient perovskites. • Accurately predicted the anion size and pseudocubic lattice constants in oxygen-deficient perovskites using these models.

Tailoring the Coefficient of Chemical Expansion in Perovskite Oxides through A Vs. B-Site Multivalent Cation Placement

Chemical expansion is a strain induced by a change in stoichiometry, such as oxygen loss. It can enable a material to actuate when exposed to different gas environments, and it can significantly impact device longevity when there are large concentration gradients across small material dimensions in multilayer devices. The desired magnitude of chemical expansion depends on the application; typically, the goal is a large expansion in the former and a small expansion in the latter, where compatibility with neighboring materials is of concern. Therefore, design rules for tailoring expansion from oxygen exchange are needed for the multitude of applications in which it is a contributing factor.As oxygen leaves an oxide lattice during reduction, electrons are generated to preserve charge neutrality, which may move to multivalent cations; this process results in significant expansion of the multivalent cation, and the surrounding lattice, as the oxidation state of the multivalent cation decreases. Recently, an empirical formula describing the pseudo-cubic lattice constant of perovskite materials was developed [1], which relates the lattice parameter to the ionic radii of each cationic and anionic component. This equation predicts that changes in the B-site cation size will have a larger effect on the lattice parameter than an equal change at the A-site. If the multivalent cation is the only one changing size during redox processes, this equation suggests that its placement on the A or B site will have a significant effect on the magnitude of the overall lattice strain during oxygen loss or gain.To test this theory, model perovskite bulk ceramic compositions with multivalent Pr(3+,4+) on the A site and on the B site were fabricated: PrGa0.9Mg0.1O2.95+ δ and BaPr0.9Y0.1O2.95- δ, respectively. Strain values from dilatometry and defect concentrations from thermogravimetric analysis were used to calculate the coefficients of chemical expansion (CCE) in both materials, to determine the effect of multivalent cation placement. These measurements were performed under isothermal conditions while varying the pO2 to avoid effects from nonuniform thermal expansion at different stoichiometries. Multiple temperatures were analyzed to observe any temperature-related trends in CCEs and to determine any effects from crystal structure changes. The resulting CCEs will be interpreted not only in terms of multivalent A vs. B site placement but also considering other factors that may impact CCEs: crystallographic distortions, temperature, and charge localization.[1] Marrocchelli, D., Perry, N. H., & Bishop, S. R. (2015). Understanding chemical expansion in perovskite-structured oxides. Physical Chemistry Chemical Physics, 17(15), 10028-10039.

An empirical model for B-site cation ordering in Ba(Mg1/3Ta2/3)O3

Processing-structure models are needed in both the lab and industry; however, few exist for cation ordering in perovskites. The perovskite Ba(Mg1/3Ta2/3)O3 in its ordered form is one of the best known high-Q dielectric materials but requires extended high-temperature annealing to achieve high degrees of order; so an empirical model which describes the ordering as a function of an easily obtainable processing parameter would be useful. In this work, powders of Ba(Mg1/3Ta2/3)O3 were synthesized using a conventional solid-state mixed-oxide method. The as-calcined compound had a cubic (lacking long-range B-site cation order) structure but contained short-range-ordered nanodomains. Upon annealing at 1500 °C for up to 40 h an increasingly ordered arrangement of Mg2+ and Ta5+ on the B site was generated, with the ordering causing a trigonal distortion. Empirical modeling as well as first-principles calculations via density functional theory showed that this ordering process was accompanied by a volume decrease despite the fact that ordered planes stack less efficiently. An empirical model was developed to describe the ordering parameter as a function of either annealing time or effective B-site contraction. The implication of this modeling method is that it may be possible to predict the degree of cation ordering in complex perovskite systems from ionic-radii data and experimentally-derived pseudocubic lattice constants alone. Conversely, it may also be possible to predict the degree of volume expansion/contraction upon ordering, which has implications for functional properties like ionic conduction.

Large-lattice-parameter perovskite single-crystal substrates

The pseudobinary system LaLuO3–LaScO3 was explored in hopes of discovering new perovskite-type substrates with pseudocubic lattice parameters above 4Å. A complete solid solution of the type (LaLuO3)1−x(LaScO3)x forms between the end members LaLuO3 and LaScO3, enabling large single crystals of (LaLuO3)1−x(LaScO3)x to be grown from the melt. A single crystal with x≈0.34 was demonstrated. Considering the maximum thermal load of the iridium crucibles appropriate for Czochralski growth of this solid solution, the theoretically maximum achievable x-value is ~0.67. Based on the phase diagram determined, it is anticipated that single crystals with pseudocubic lattice constants between 4.09 and 4.18Å can be grown in this system by the Czochralski method.

Lattice-constant prediction and effect of vacancies in aliovalently doped perovskites

Processing–structure relationships are at the heart of materials science, and predictive tools are essential for modern technological industries insofar as structure dictates properties. Point defects can have a profound effect on structure and consequently properties, but their effect on crystal chemistry is still not generally known or understood. None of the very few theoretical models which exist for perovskites are suited to the doped and defective ceramics most commonly used in commercial devices; therefore, a new empirical approach is presented here. A predictive model for the effective size of anions as well as cation vacancies and ultimately the pseudocubic lattice constant of such perovskites, based solely on published ionic radii data, has been developed here. The model can also be used to derive ionic radii of cations in twelvefold coordination. Vacancies have an effective size due to both bond relaxation and mutual repulsion of coordinating anions, and as expected this size scales with the host cation radius, but not in a straightforward way. The model is able to predict pseudocubic lattice constants, calculate the effective size of anions and cation vacancies, and identify the effects of both cation ordering and second-order Jahn Teller distortions. A lower limit on the tolerance factor of stable oxide perovskites is proposed.

Effective size of vacancies in aliovalently doped SrTiO3 perovskites

Abstract Point defects like vacancies can have a profound effect on the structure of perovskite ceramics, but the exact mechanisms involved are still unclear. While a few theoretical models exist for some perovskites, none are particularly accurate or at all suited to the impure, doped, or otherwise defective ceramics which abound in commercial devices. A new empirical approach is presented here. A predictive model for the pseudocubic lattice constant of such perovskites, based solely on published ionic radii data, has been developed and adapted as a model for effective tolerance factor. This model shows that the average A-site size generally decreases with increasing vacancy concentration up to [ V ] = 22%, but not as much as would be expected if vacancies were truly zero-dimensional defects. Such vacancies have an effective size due to both bond relaxation and mutual repulsion of coordinating oxygen ions. At compositions corresponding to [ V ] 3 -based perovskites than existing methods and can potentially be expanded to other perovskite systems.

Structure, electrical conducting and thermal expansion properties of Ln0.6Sr0.4Co0.8Fe0.2O3 (Ln=La, Pr, Nd, Sm) ceramics

Ln0.6Sr0.4Co0.8Fe0.2O3 (Ln=La, Pr, Nd, Sm) perovskite-type complex oxides were synthesized using a glycine-nitrate process, and the structure, electrical conducting and thermal expansion properties of the resulting ceramics were examined with regard to the nature of the lanthanide cations. The results indicated that the La, Pr and Nd specimens had a rhombohedral symmetry, while an orthorhombic structure was determined for the Sm specimen. The pseudo-cubic lattice constant decreased with smaller lanthanide cations. It was found that the electrical conducting properties declined with decreasing lanthanide cation size. Fortunately, all the compositions remained rather high electrical conductivities exceeding 650 Ω−1·cm−1 in the intermediate temperature range (600–800 °C). An appreciable thermal expansion increase at high temperatures was detected for all the compositions. Decreasing the size of the lanthanide cations resulted in an increase of thermal expansion. With respect to the high electrical conductivities, the Ln0.6Sr0.4Co0.8Fe0.2O3 oxides are considered to be acceptable as mixed conducting component in composite cathode designs together with doped ceria electrolytes.

Properties of rare-earth scandate single crystals (Re=Nd−Dy)

Rare-earth (RE) scandate single crystals ranging from NdScO 3 to DyScO 3 were grown by the conventional Czochralski technique. The crystals were found to have a non-stoichiometric composition caused by RE-deficiency on the A-site of the distorted perovskite structure. Their pseudocubic lattice constants lie between 3.95 and 4.01 Å and their average thermal expansion coefficients are between 8.2×10 −6 and 10.9×10 −6 K −1. The pseudocubic lattice constants of the RE scandates vary in about 0.01 Å steps as the RE series is traversed, enabling the growth of substrates appropriate for the strain engineering of perovskite thin films. The crystalline perfection and homogeneity of the DyScO 3 and GdScO 3 single crystals are characterized by a full-width at half-maximum of the 220 reflection of the substrates of about 20–25 arcsec in ω and a very small fluctuation margin of about ±3 arcsec over the whole wafer surface. The average dislocation density of the RE scandate crystals was 10 3–10 5 cm −2. These characteristics make RE scandate single crystals some of the best available substrates for the epitaxial growth of perovskite thin films.

Structure, electrical conducting and thermal expansion properties of Ln 0.6Sr 0.4Co 0.2Fe 0.8O 3 (Ln = La, Pr, Nd, Sm) perovskite-type complex oxides

Fine and uniform Ln 0.6Sr 0.4Co 0.2Fe 0.8O 3 (Ln = La, Pr, Nd, Sm) powders with a perovskite phase were produced using a glycine–nitrate process. The structure, electrical conducting and thermal expansion properties of the resulting ceramics were investigated. The results indicate that replacing La 3+ by smaller lanthanide cations led to a change in crystal structure from rhombohedral to orthorhombic symmetry and a decrease of the pseudo-cubic lattice constant. It was found that the electrical conducting properties decrease with reducing lanthanide cation size. Compared with La 0.6Sr 0.4Co 0.2Fe 0.8O 3, the degradation of the electrical conducting properties in Pr 0.6Sr 0.4Co 0.2Fe 0.8O 3 and Nd 0.6Sr 0.4Co 0.2Fe 0.8O 3 is not pronounced, whereas the electrical conducting properties of Sm 0.6Sr 0.4Co 0.2Fe 0.8O 3 decline to an unsatisfactory level. There is an evident increase in thermal expansion at high temperatures for all the compositions. This is attributed to a chemically induced lattice expansion due to oxygen lose and formation of oxygen vacancies. Pr 0.6Sr 0.4Co 0.2Fe 0.8O 3 and Nd 0.6Sr 0.4Co 0.2Fe 0.8O 3 present relatively low thermal expansion coefficient values of 14.2 × 10 −6 and 13.2 × 10 −6 K −1 averaged between 100–750 and 100–700 °C, respectively.

Crystal structure, thermal expansion and electrical conductivity of Nd 0.7Sr 0.3Fe 1− xCo xO 3 (0≤ x≤0.8)

The crystal structure, thermal expansion and electrical conductivity of the solid solution Nd 0.7Sr 0.3Fe 1− x Co x O 3 for 0≤ x≤0.8 were investigated. All compositions had the GdFeO 3-type orthorhombic perovskite structure. The lattice parameters were determined at room temperature by X-ray powder diffraction (XRPD). The pseudo-cubic lattice constant decreased continuously with x. The average linear thermal expansion coefficient (TEC) in the temperature range from 573 to 973 K was found to increase with x. The thermal expansion curves for all values of x displayed rapid increase in slope at high temperatures. The electrical conductivity increased with x for the entire temperature range of measurement. The calculated activation energy values indicate that electrical conduction takes place primarily by the small polaron hopping mechanism. The charge compensation for the divalent ion on the A-site is provided by the formation of Fe 4+ ions on the B-site (in preference to Co 4+ ions) and vacancies on the oxygen sublattice for low values of x. The large increase in the conductivity with x in the range from 0.6 to 0.8 is attributed to the substitution of Fe 4+ ions by Co 4+ ions. The Fe site has a lower small polaron site energy than Co and hence behaves like a carrier trap, thereby drastically reducing the conductivity. The non-linear behaviour in the dependence of log σT with reciprocal temperature can be attributed to the generation of additional charge carriers with increasing temperature by the charge disproportionation of Co 3+ ions.

Variation du parametre cristallin de l'oxyde de nickel a l'etat divise

Samples of finely divided NiO, obtained from Ni(OH) 2, showing a continuous variation in porosity and deviation from stoichiometry, have been studied by means of X-Ray diffraction. The pseudo-cubic lattice constant has been measured. The crystallite size and the strain value have been inferred from the line broadening analysis. The crystallite size of the most divided of these samples is about 10 nm. The corresponding strain value is ϵ = 17.10 −3 and the relative increase of the lattice constant is 4.10 −3 with reference to a standard sample of bulk NiO. The decrease of the lattice parameter and of the strain value and the increase of the crystallite size have been followed as the development of texture proceeds with increasing temperature. The high strain value observed is related to the crystal mosaic structure of NiO. The variation of the lattice constant may be related to the high surface-volume ratio or the non-stoichiometry of NiO.

Oxidation of W(110): I. LEED study of the oxide formation at 1000 K

Oxidation of the (110) surface of a tungsten crystal in 2 × 10 −3 torr of oxygen at 1000 K for 80 sec has revealed a LEED pattern which exhibits a complex variation with incident electron energy. A kinematic analysis has shown that the LEED patterns result from three pairs of twin related WO 3(111̄) nuclei, each facetted to pyramids exposing three well developed (100) type surfaces. Detailed analysis of the pattern has shown that the nuclei exhibit the same monoclinic symmetry at the surface as that existing in bulk WO 3. A pseudo-cubic lattice constant of 7.58 ± 0.1 Å was estimated from the electron energies at which Laue back reflexion beams were excited.