Anion Sublattice Research Articles

Soft Phonon Modes Leading to Ultralow Thermal Conductivity and High Thermoelectric Performance in AgCuTe.

Crystalline solids with intrinsically low lattice thermal conductivity (κL ) are crucial to realizing high-performance thermoelectric (TE) materials. Herein, we show an ultralow κL of 0.35 Wm-1 K-1 in AgCuTe, which has a remarkable TE figure-of-merit, zT of 1.6 at 670 K when alloyed with 10 mol % Se. First-principles DFT calculation reveals several soft phonon modes in its room-temperature hexagonal phase, which are also evident from low-temperature heat-capacity measurement. These phonon modes, dominated by Ag vibrations, soften further with temperature giving a dynamic cation disorder and driving the superionic transition. Intrinsic factors cause an ultralow κL in the room-temperature hexagonal phase, while the dynamic disorder of Ag/Cu cations leads to reduced phonon frequencies and mean free paths in the high-temperature rocksalt phase. Despite the cation disorder at elevated temperatures, the crystalline conduits of the rigid anion sublattice give a high power factor.

Formation and evolution of crystal and local structures in nanostructured Ln2Ti2O7 (Ln = Gd–Dy)

The lanthanide titanates Ln2Ti2O7 (Ln = lanthanide) demonstrate a very broad range of structural, chemical and physical properties. We have studied the whole process of the crystallization and local atomic structure rearrangement in Ln2Ti2O7 (Ln = Gd, Tb, Dy) samples synthesized by combination of sol-gel and coprecipitation methods with the subsequent calcination of Ln-Ti precursors. X-ray absorption spectroscopy (XAFS), X-ray powder diffraction, infrared spectroscopy, Raman spectroscopy, scanning electron microscopy with energy dispersive X-ray spectroscopy and simultaneous thermal analysis were used for the complex analysis of the structural properties. It was shown that crystallization of amorphous precursors directly resulted in the formation of nanocrystalline powders with the pyrochlore structure which is formed in process of ordering of both cationic and anionic sublattices. We have demonstrated that both XAFS and Raman spectroscopy ensure the particularly sensitive markers of changes in local electronic and crystal structure of Ln2Ti2O7 depending on the type of Ln element and the preparation procedure. It was established that splitting of the first Ln-O shell in the FT modulus of L3-Ln EXAFS spectra appears to be the reliable indicator of the ordered pyrochlore structure formation, while the changes in the pre-edge region of the K-Ti XANES spectra reflect the process of the Ln2Ti2O7 electronic structure formation.

A first-principle investigation of the Li diffusion mechanism in the super-ionic conductor lithium orthothioborate Li3BS3 structure

The research of superior ionic conductors is a very active field. Identifying such materials would allow for the design of improved solid-state Li-ion batteries, solving the safety hazard posed by the liquid electrolytes and improving the electrochemical stability and thus the energy efficiency. In this work, we study lithium orthothioborate Li3BS3 by means of first-principle atomistic calculations based on density functional theory. This material is a very promising super ion conductor candidate, as it is a layered compound based on a deformed body-centred structure of the anion sublattice. The minimum energy paths for the diffusion of the lithium ions are identified, and the activation energy are evaluated using the nudged elastic band method. A very fast 1D diffusive channel is found, contained in a Li-rich layer, with an activation energy below 0.1 eV. The other paths connecting these layers and extending the mobility of lithium to the whole structure are found to have activation barriers of 0.25 eV or lower. This bottleneck corresponds to a diffusion coefficient of the order of 10-6 cm2 s−1, thus characterising lithium orthothioborate as an excellent ionic conductor.

On the effect of Ga and In substitutions in the Ca11Bi10 and Yb11Bi10 bismuthides crystallizing in the tetragonal Ho11Ge10 structure type.

The Ga- and In-substituted bismuthides Ca11GaxBi10-x, Ca11InxBi10-x, Yb11GaxBi10-x, and Yb11InxBi10-x (x < 2) can be readily synthesized employing molten Ga or In metals as fluxes. They crystallize in the tetragonal space group I4/mmm and adopt the Ho11Ge10 structure type (Pearson code tI84; Wyckoff sequence n2 m j h2 e2 d). The structural response to the substitution of Bi with smaller and electron-poorer In or Ga has been studied by single-crystal X-ray diffraction methods for the case of Ca11InxBi10-x [x = 1.73 (2); octabismuth undecacalcium diindium]. The refinements show that the In atoms substitute Bi only at the 8h site. The refined interatomic distances show an unconventional - for this structure type - bond-length distribution within the anionic sublattice. The latter can be viewed as consisting of isolated Bi3- anions and [In4Bi820-] clusters for the idealized Ca11In2Bi8 model. Formal electron counting and first-principle calculations show that the peculiar bonding in this compound drives the system toward an electron-precise state, thereby stabilizing the observed bond-length pattern.

Diffusion mechanism in the superionic conductor Li4PS4I studied by first-principles calculations

Li4PS4I was recently discovered as a novel crystalline lithium ion conductor by applying a soft chemistry approach. It adopts a tetragonal structure type suggesting a three-dimensional migration pathway favorable for a high conductivity [S.J. Sedlmaier, Chem. Mater. 29 (2017) 1830]. Especially in view of the highly connected pathways for Li motion within a simple anion sublattice formed by PS43− and iodine anions, the conductivity measured from both impedance spectroscopy and NMR data appears to be rather small, and a negative influence of impurities and of grain boundaries effects was assumed. In order to shed light on the full potential of this material, we performed a theoretical study of Li4PS4I in the framework of density functional theory. After creating a structural model that accurately accounts for the partial occupancies determined by diffraction experiments, we performed molecular dynamics simulations, unraveled the diffusion mechanisms and calculated diffusion coefficients and the activation barrier for diffusion. The results of the theoretical study on both a crystalline and a glassy supercell imply that Li4PS4I is in fact a superionic conductor with a much higher conductivity than reported so far.

Synthesis and characterization of electrical features of bismuth manganite and bismuth ferrite: effects of doping in cationic and anionic sublattice: Materials for applications

The electrical, magnetic, and structural features of bismuth manganite (BM), e.g., BiMnO3, and bismuth ferrite (BF), e.g., BiFeO3, are reviewed. Induced multiferroicity and enhanced magnetoelectric coupling are required for various modern device applications. BM and BF were synthesized using standard high-temperature sintering and processes such as sol–gel, hydrothermal, or wet chemical methods combined with annealing. The size and morphology of the nanoscale particles were controlled, although they were usually inhomogeneous. BF exhibits structurally stable antiferromagnetic (AFM) and ferroelectric (FE) phases in wide temperature ranges. Ferromagnetic (FM) order was induced in a thick shell around the AFM core of the nanoscale BF particles, which was attributed to a size effect related to surface strains and disorder. BM exhibited both structurally stable and unstable phases. The BiMnO3, Bi12MnO20, and BiMn2O5 structures are nonferroelectric. The perovskite BiMnO3 form was synthesized under high hydrostatic pressure. FM order occurs in BM at low temperatures. Bi(MnFe)O3 solid solution samples exhibited competition between AFM and FM ordering. Doping can decrease the content of unavoidable secondary phases. Doping in the Bi ion sublattice can stabilize the crystal lattice owing to local strains caused by the difference in ionic radius between Bi and the dopant. Doping in the Fe and Mn sublattices affects the electrical features. The main achievement of substitution with tetra- and pentavalent ions is compensation of the oxygen vacancies. In turn, leakage current suppression enables switching of FE domains and polarization of the samples. A significant enhancement of magnetoelectric coupling was observed in composites formed from BF and other FE materials. The leakage currents can be diminished when an insulator polymer matrix blocks percolation. The potential applicability is related to enhanced magnetoelectric coupling. The constructed devices meet the size effect limitations for FE and FM ordering. Resistive switching suggests possible use in nonvolatile memories and gaseous sensors. The sensors can be used for hydrophones and for photovoltaic and photoluminescence applications, and they can be constructed from multiphase materials. Bulk multiferroic solid solutions, composites, and nanoheterostructures have already been tested for use in sensors, transducers, and read/write devices for technical purposes.

Probing the ionic dielectric constant contribution in the ferroelectric phase of the Fabre salts

In strongly correlated organic materials it has been pointed out that charge-ordering could also achieve electronic ferroelectricity at the same critical temperature $T_{co}$. A prototype of such phenomenon are the quasi-one dimensional (TMTTF)$_2X$ Fabre-salts. However, the stabilization of a long-range ferroelectric ground-state below $T_{co}$ requires the break of inversion symmetry, which should be accompanied by a lattice deformation. In this work we investigate the role of the monovalent counter-anion $X$ in such mechanism. For this purpose, we measured the quasi-static dielectric constant along the $c^{*}$-axis direction, where layers formed by donors and anions alternate. Our findings show that the ionic charge contribution is three orders of magnitude lower than the intra-stack electronic response. The $c^{*}$ dielectric constant ($\epsilon'_{c^*}$) probes directly the charge response of the monovalent anion $X$, since the anion mobility in the structure should help to stabilize the ferroelectric ground-state. Furthermore, our $\epsilon'_{c^*}$ measurements %conjugated with earlier investigations of the $c^*$ lattice thermal expansion, show that the dielectric response is thermally broaden below $T_{co}$ if the ferroelectric transition occurs in the temperature range where the anion movement begin to freeze in their methyl groups cavity. In the extreme case of the PF$_6$-H$_{12}$ salt, where $T_{co}$ occurs at the freezing point, a relaxor-type ferroelectricity is observed. Also, because of the slow kinetics of the anion sub-lattice, global hysteresis effects and reduction of the charge response upon successive cycling are observed. In this context, we propose that anions control the order-disorder or relaxation character of the ferroelectric transition of the Fabre-salts.

Enhanced oxygen diffusion in nano-structured ceria

Nano-structured polycrystalline СеО2 is proposed to be used as a candidate electrolyte material for solid oxide fuel cells (SOFC) operating at temperatures ≤ 600 °С. Here we show that in this material the diffusion activation energy of oxygen ions is 0.35 eV. The diffusion mechanism corresponds to the “single-file” diffusion mechanism, associated with the presence of one-dimensional channels in the anion sublattice of СеО2. The small grain size of the material ≈ 10 nm, as well as its stoichiometric state (Се2О3), minimize the contribution of the electronic and polaron components of the electrical conductivity of this material, which also contribute to the optimization of SOFC operation.

Об уровне энергии глубокого донора в полупроводниках с вакансиями в анионной решетке

Об уровне энергии глубокого донора в полупроводниках с вакансиями в анионной решетке

Octahedral Distortions at High‐Temperature Superconducting La2CuO4 Interfaces: Visualizing Jahn–Teller Effects

AbstractTuning the octahedral network represents a promising route for achieving new properties and functionalities in perovskite‐based oxide heterostructures. One of the interface‐mediated phenomena occurring in complex oxides is the Jahn—Teller (JT) effect. With the purpose of investigating octahedral distortions at interfaces showing high‐temperature interface superconductivity, atomic layer‐by‐layer oxide molecular‐beam epitaxy grown bilayers consisting of three unit cells, overdoped metallic La1.6M0.4CuO4, and three unit cells undoped insulating La2CuO4, where M represents a divalent dopant (namely, Ba2+, Sr2+, and Ca2+), are studied. The local crystal structure, chemistry, and dopant distribution are probed by analytical spherical‐aberration‐corrected scanning transmission electron microscopy. Here, the interrelation between the cationic size mismatch between dopant (M2+) and host La3+ ions and the local structure are reported, and the impact of the dopant distribution on the structural (CuO6 octahedra elongation) local properties is discussed. A clear correlation between dopant size and local lattice deformations is highlighted. Moreover, a relation between the nature of superconductivity (bulk vs interface) and JT distortions of the anionic sublattice is suggested.

Lanthanide stannate pyrochlores (Ln2Sn2O7; Ln = Nd, Gd, Er) at high pressure

Lanthanide stannate pyrochlores (Ln2Sn2O7; Ln = Nd, Gd, and Er) were investigated in situ to 50 GPa in order to determine their structural response to compression and compare their response to that of lanthanide titanate, zirconate, and hafnate pyrochlores. The cation radius ratio of A3+/B4+ in pyrochlore oxides (A2B2O7) is thought to be the dominant feature that influences their response on compression. The ionic radius of Sn4+ is intermediate to that of Ti4+, Zr4+, and Hf4+, but the 〈Sn–O〉 bond in stannate pyrochlore is more covalent than the 〈B–O〉 bonds in titanates, zirconate, and hafnates. In stannates, based on in situ Raman spectroscopy, pyrochlore cation and anion sublattices begin to disorder with the onset of compression, first measured at 0.3 GPa. The extent of sublattice disorder versus pressure is greater in stannates with a smaller Ln3+ cation. Stannate pyrochlores (Fd-3m) begin a sluggish transformation to an orthorhombic, cotunnite-like structure at ~28 GPa; similar transitions have been observed in titanate, zirconate, and hafnate pyrochlores at varying pressures (18–40 GPa) with cation radius ratio. The extent of the phase transition versus pressure varies directly with the size of the Ln3+ cation. Post-decompression from ~50 GPa, Er2Sn2O7 and Gd2Sn2O7 adopt a pyrochlore structure, rather than the multi-scale defect-fluorite + weberite-type structure adopted by Nd2Sn2O7 that is characteristic of titanate, zirconate, and hafnate pyrochlores under similar conditions. Like pyrochlore titanates, zirconates, and hafnates, the bulk modulus, B0, of stannates varies linearly and inversely with cation radius ratio from 1 1 1 GPa (Nd2Sn2O7) to 251 GPa (Er2Sn2O7). The trends of bulk moduli in stannates in this study are in excellent agreement with previous experimental studies on stannates and suggest that the size of the Ln3+ cation is the primary determining factor of B0. Additionally, when normalized to rA/rB, the bulk moduli of stannates are comparable to those of zirconates and hafnates, which vary from titanates. Our results suggest that the cation radius ratio strongly influences the bulk moduli of stannates, as well as their overall compression response.

Directional dependence of the threshold displacement energies in metal oxides

Molecular dynamics (MD) simulations are performed to investigate the directional dependence and the values of the threshold energies (TDEs) for the displacements of the oxygen and metal atoms and for producing stable Frenkel pairs in five metal oxides of Cr2O3, Al2O3, TiO2, SiO2, and MgO. The TDEs for the Frenkel pairs and atoms displacement are calculated in 66 crystallographic directions, on both the anion and cation sublattices. The performed simulations are for metal and oxygen PKA energies up to 350 and 400 eV, respectively. The calculated probability distributions for the atoms displacement and average number of Frenkel pairs produced in the different oxides are compared. The results revealed unique symmetrical patterns of the TDEs for the displacement of the atoms and the formation of stable Frenkel pairs, confirming the strong dependence on the direction and the crystalline structure of the oxides. Results also showed that the formation of stable Frenkel pairs is associated with the displacements of the PKAs and/or of the SKAs. The probabilities of the TDEs for the displacement of the oxygen and metal PKAs are consistently lower than those of the atoms in the crystal. In SiO2, TDEs for the displacement of oxygen and metal atoms and those for the formation of stable Frenkel pairs are the lowest, while those in TiO2 are among the highest. The results for Cr2O3 and Al2O3, which have the same crystal structure, are similar. The calculated TDEs for MgO, Al2O3 and TiO2 are generally in good agreement with the experimental values and the probability distributions of the TDEs for the PKAs in TiO2 are in good agreement with reported MD simulation results.

(High Temperature Materials Division J. Bruce Wagner, Jr. Award Address) Disorder and Transport in Pyrochlore Oxides

Numerous avenues are currently being explored to enhance ionic conductivity in solid oxide materials, including dopants, nano-structuring, and strain engineering. Their effect on material properties, specifically mobile carrier concentration and mobility, needs to be understood and ultimately exploited to develop advanced functional materials. Crystalline disorder in complex oxides can have a pronounced effect on mass transport, but the role of disorder within the complex landscape of material and microstructural defects is not uniquely understood.In this work, we seek to explore the relationship between intrinsic disorder and oxygen ion conduction. We are using radiation damage, not to study the fundamental damage response, but rather as a tool to induce and control the extent of disorder in oxide materials. The pyrochlore compounds, A2B2O7, consist of both ordered cation and anion sublattices. The introduction of anti-site disorder, where the A and B cations switch positions, is accompanied by increasing disorder on the anion sublattice, and complete randomization of the A- and B-site cations results in the defect fluorite phase. Several workers have previously studied the influence of structural disorder on ionic conductivity by introducing disorder through dopants, temperature, or pressure. It has previously been suggested that disorder increases carrier concentration by freeing the fixed vacancy from the ordered anion sublattice of the pyrochlore structure, while order, on the other hand, may serve to increase mobility by providing a preferential ion transport pathway. This is in contrast to recent modeling results that indicate that both carrier concentration and mobility increase with disorder. In the present work we have chosen to investigate the end members of the Gd2(ZrxTi1-x)2O7 system in order to gain a better understanding of the interplay between disorder and ionic transport. Gd2Zr2O7 is an intrinsic fast-ion conductor that is also very radiation tolerant, whereas Gd2Ti2O7 is a poor ionic conductor that is much more susceptible to amorphization under irradiation than the zirconates. Electrochemical Impedance Spectroscopy is used to measure the conductivity of materials with varying degrees of irradiation-induced structural disorder in order to better understand how the underlying transport mechanisms depend on crystalline disorder. Acknowledgements This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

Theoretical study of divalent samarium defects in lanthanum fluoride crystals

The results from a theoretical study of the electron structure of an impurity rare-earth Sm2+ defect in a LaF3 crystal are presented. The electron energy levels of the rare-earth impurity defect and the transitions between them are studied using the multiconfigurational CASSCF/CASPT2 method. The absorption spectrum obtained during the calculations is consistent with the experimental data. Based on our model, we can state definitively that a vacancy on an anion sublattice serves as a charge compensator for a divalent ion.

Fluorination of Bi1.8Fe1.2SbO7 pyrochlore solid solutions

A technique has been developed for fluorinating the pyrochlore oxide Bi1.8Fe0.2FeSbO7, and a compound with the composition Bi1.8Fe1.2SbO7–x/2Fx has been obtained. The synthesized oxyfluoride also has the pyrochlore structure (sp. gr. Fd3m), with a lattice parameter a = 10.4443(1) A (R wp = 5.2). It has been shown that the charge balance upon fluorine substitution for oxygen is maintained not through partial reduction of Fe3+ to Fe2+ but through the incorporation of fluorine into oxygen vacancies. The magnetic behavior of the fluorinated pyrochlore phase is determined by the persisting frustration of the octahedral sublattice, which is responsible for the development of a spin glass state below T f = 12 K. The fluorination-induced changes in the anion sublattice led to an increase in the antiferromagnetic exchange interaction between neighboring Fe3+ ions and changes in the dynamic properties of the spin glass phase.

Influence of Lattice Polarizability on the Ionic Conductivity in the Lithium Superionic Argyrodites Li6PS5X (X = Cl, Br, I).

In the search for novel solid electrolytes for solid-state batteries, thiophosphate ionic conductors have been in recent focus owing to their high ionic conductivities, which are believed to stem from a softer, more polarizable anion framework. Inspired by the oft-cited connection between a soft anion lattice and ionic transport, this work aims to provide evidence on how changing the polarizability of the anion sublattice in one structure affects ionic transport. Here, we systematically alter the anion framework polarizability of the superionic argyrodites Li6PS5X by controlling the fractional occupancy of the halide anions (X = Cl, Br, I). Ultrasonic speed of sound measurements are used to quantify the variation in the lattice stiffness and Debye frequencies. In combination with electrochemical impedance spectroscopy and neutron diffraction, these results show that the lattice softness has a striking influence on the ionic transport: the softer bonds lower the activation barrier and simultaneously decrease the prefactor of the moving ion. Due to the contradicting influence of these parameters on ionic conductivity, we find that it is necessary to tailor the lattice stiffness of materials in order to obtain an optimum ionic conductivity.

Stabilization of high-temperature disorder of fluorine sublattice by quenching in calcium fluoride crystals

The superionic state of crystals with the fluorite structure caused by disordering of anion sublattice is accompanied by the formation of short-lived clusters due to the correlation between anti-Frenkel defects at the increase of their concentration. The existence of clusters comprising anion vacancies as well as interstitial and displaced anions at high temperatures was deduced from the analysis of neutron scattering. The quenched CaF2 crystals show intense ultraviolet absorption with a long-wavelength tail that can be ascribed to the clusters thus testifying the opportunity of a high-temperature disorder freezing. It was found that the fluorine vacancies introduced into the crystal during preheating in the reduction atmosphere of calcium vapor trigger and intensify the process of cluster formation. The model that takes into account a strong electron-vibration coupling gives rise to the reconstruction of both the valence and conduction bands in the cluster region thereby clarifying the nature of absorption spectra of quenched crystals.

Spatial distribution of optical coloration in single crystalline LiNbO3 after high-temperature H2/air treatments

The paper presents results of investigations of optical absorption spatial changes in congruent bulk LiNbO3 crystals in 300–800 nm spectral region along Х, Y, Z directions caused by high-temperature (400–700 оС) annealing in Н2 and, subsequently, in air. As it is shown, the coloration/discoloration processes are anisotropic: a maximal depth of coloration is observed for Z direction and a minimal one – for X direction. The reversibility of optical properties with respect to the annealing atmosphere changes as well as results of investigations by SIMS and IR spectroscopy methods suggest that the oxygen loss/incorporation. processes play a major role in the coloration/discoloration. The additional absorption spectrum caused by reduction consists of three bands, whose nature is associated with different point defects: 350–410 nm – defects in anion sublattice, 500–520 nm – bipolarons; 700–750 nm – bound polarons. Individual contributions of the bands to the additional absorption spectra depend on the annealing temperature and on the distance from the crystal surface. During reduction lithium oxide is leaving the crystal which leads to the formation of Li2O-depleted structural phase LiNb3O8 in near-surface regions. Experimentally obtained distribution of depth-dependent additional absorption in reduced crystals was successfully approximated basing on the oxygen vacancies diffusion model and solution of differential equations set describing a quasichemical reaction of bipolarons formation due to the oxygen loss in LiNbO3 crystal. On the other hand, this model does not allow to describe accurately the depth-dependent discoloration after oxidizing annealing of previously reduced lithium niobate crystals.

Synthesis, structural study, thermal, optical properties and characterization of the new compound [C6H7N2O2]3TeCl5·2Cl

The new organic-inorganic compound, [C6H7N2O2]3TeCl5·2Cl was synthesized and its structure was determined at room temperature in the triclinic system (P−1) with the following parameters: a=10.5330(11)Å, b=10.6663(11)Å, c=15.9751(16)Å, α=82.090(2)°, β=71.193(2)°, γ=68.284(2)° and Z=2. The final cycle of refinement led to R=0.057 and Rw=0.149. The crystal structure was stabilized by an extensive network of NH⋯Cl and non-classical CH⋯Cl hydrogen bonds between the cation and the anionic group. Several thermal analysis techniques such as thermogravimetric analysis, differential scanning calorimetric analysis and evolved gas analysis were used. We used isoconversional kinetics methods to determine the kinetics parameters. We observe that the decomposition of [C6H7N2O2]3TeCl5·2Cl entails the formation hydrochloric acid of nitroaniline as volatiles. The infrared spectra were recorded in the 4000–400cm−1 frequency region. The Raman spectra were recorded in the external region of the anionic sublattice vibration 50–1500cm−1. The optical band gap was calculated from the UV-Vis absorbance spectra using classical Tauc relation which was found to be 3.12 and 3.67eV.

Crystallography and Growth of Epitaxial Oxide Films for Fundamental Studies of Cathode Materials Used in Advanced Li-Ion Batteries

Li-ion battery systems, synthesized as epitaxial thin films, can provide powerful insights into their electrochemical processes. Crystallographic analysis shows that many important cathode oxides have an underlying similarity: their structures can be considered as different ordering schemes of Li and transition metal ions within a pseudo-cubic sublattice of oxygen anions arranged in a face-center cubic (FCC) fashion. This oxygen sublattice is compatible with SrTiO3 and similar perovskite oxides, thus perovskites can be used as supporting substrates for growing epitaxial cathode films. The predicted epitaxial growth and crystallographic relations were experimentally verified for different oxide films deposited by pulsed laser deposition (PLD) on SrTiO3 or SrRuO3/SrTiO3 of different orientations. The results based on cross-sectional high-resolution TEM of the following films are presented in the paper: (a) trigonal LiCoO2; (b) orthorhombic LiMnO2; (c) monoclinic Li2MnO3; (d) compositionally-complex monoclinic Li1.2Mn0.55Ni0.15Co0.1O2. All results demonstrated the feasibility of epitaxial growth for these materials, with the growth following the predicted cube-on-cube orientation relationship between the cubic and pseudo-cubic oxygen sublattices of a substrate and a film, respectively.