Does Local Disorder Occur in the Pyrochlore Zirconates?

Surface thermodynamics of yttrium titanate pyrochlore nanomaterials

Nanocrystalline pyrochlore materials have been investigated for their enhanced radiation tolerance as ceramic nuclear waste hosts. In this work, we study the thermodynamic driving force of nano-scale materials for radiation resistance. The size dependent thermodynamic properties of a series of Y2Ti2O7 nanoparticles were investigated. Samples were synthesized by a sol-gel method and characterized by synchrotron X-ray diffraction, BET analysis, and thermogravimetric analysis. The surface and interface enthalpies of Y2Ti2O7 were determined by high temperature oxide melt drop solution calorimetry to be 4.07 J m-2 and 3.04 J m-2, respectively. The experimentally obtained surface energy is in good agreement with computationally derived average surface energies for yttrium and other rare-earth titanate pyrochlores. Theoretical links between nanoparticle stability, surface energy, and radiation resistance of pyrochlore materials were then explored.

Decoding ionic conductivity and reordering in cation-disordered pyrochlores

The ordered structure A₂B₂O₆O' in pyrochlores engenders twin rows of inequivalent anion sublattices each centred on alternating cations. While it is known that cation antisite disorder augments the ionic conductivity by several orders of magnitude, the local cation environment around the anions and the dynamic anion reordering during the cation disordering are not well-elucidated. Using atomistic simulations on Gd₂Zr₂O₇, we first show that the anions engage in concerted hops to the neighbouring tetrahedral sites mostly along with the 〈1 0 0〉 direction while completely avoiding the octahedral sites. While the initially vacant 8a sites start accommodating oxygen ions with increasing cation disorder, they show noticeable reluctance even at significant levels of disorder. We have also tracked both the distribution of available oxygen sites following random cation disorder, which is dependent only on cation disordering, and the probability of occupation of these sites. Interestingly, the available oxygen sites show a non-monotonic dependence on the number of B ions in the nearest neighbouring shell while the occupation probability of all the available oxygen sites increases monotonically. A tetrahedral oxygen site thus has a better probability of being occupied when it has a greater number of second neighbour B ions. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Modeling Disorder in Pyrochlores and Other Anion-Deficient Fluorite Structural Derivative Oxides

Their very flexible chemistry gives oxide materials a richness in functionality and wide technological application. A specific group of oxides that have a structure related to fluorite but with less oxygen, termed anion-deficient fluorite structural derivatives and with pyrochlores being the most notable example, has been shown to exhibit a diversity of useful properties. For example, the possibility to undergo a transition from an ordered to disordered state allows these oxides to have high radiation tolerance. Atomistic-scale calculations in the form of molecular dynamics (MD) and density functional theory (DFT) have been extensively used to understand what drives this order/disorder transition. Here we give a brief overview of how atomistic-scale calculations are utilized in modeling disorder in pyrochlores and other anion-deficient fluorite structural derivatives. We discuss the modeling process from simple point defects to completely disordered structures, the dynamics during the disordering process, and the use of mathematical models to generate ordered solid-solution configurations. We also attempt to identify the challenges in modeling short range order and discuss future directions to more comprehensive models of the disordered structures.

Magnetic ordering in the Ising antiferromagnetic pyrochlore Nd2ScNbO7

The question of structural disorder and its effects on magnetism is relevant to a number of spin liquid candidate materials. Although commonly thought of as a route to spin glass behaviour, here we describe a system in which the structural disorder results in long-range antiferromagnetic order due to local symmetry breaking. Nd₂ScNbO₇is shown to have a dispersionless gapped excitation observed in other neodymium pyrochlores belowT_N= 0.37 K through polarized and inelastic neutron scattering. However the dispersing spin waves are not observed. This excited mode is shown to occur in only 14(2)% of the neodymium ions through spectroscopy and is consistent with total scattering measurements as well as the magnitude of the dynamic moment 0.26(2)μ_B. The remaining magnetic species order completely into the all-in all-out Ising antiferromagnetic structure. This can be seen as a result of local symmetry breaking due disordered Sc⁺³and Nb⁺⁵ions about theA-site. From this work, it has been established thatB-site disorder restores the dipole-like behaviour of the Nd⁺³ions compared to the Nd₂B₂O₇parent series.

Effect of Long- and Short-Range Disorder on the Oxygen Ionic Conductivity of Tm2(Ti2-xTmx)O7-x/2 "Stuffed" Pyrochlores

The long-range average and short-range local structures in the Tm₂(Ti_2-xTm_x)O_7-x/2 (x = 0.00-0.67) series were studied using a combination of diffraction and spectroscopic techniques. The long-range average structure, established from synchrotron X-ray and neutron powder diffraction data, shows the development of multiphase regions from x = 0.134 and the formation of antisite cation disorder from x = 0.402. The crystal field splitting of the Ti⁴⁺ ions, as derived from the Ti L₃-edge X-ray absorption near-edge structure (XANES) spectroscopy, decreases gradually from 2.17 to 1.92 eV with increasing Tm³⁺ content (x), reflecting the increase in coordination number from 6 to predominantly 7. This is consistent with a gradual evolution of the short-range local disorder from x = 0.00 to 0.67. These results suggest that local disorder develops gradually throughout the entire composition range, whereas changes in the long-range disorder occur more suddenly. Electrochemical impedance spectroscopic results show an increase in oxygen ionic conductivity at 1000 °C, by a factor of 4 upon doping at x = 0.268. This suggests that inducing small amounts of disorder into the pyrochlore structure, by stuffing, may lead to applications of this material as a solid electrolyte in solid-oxide fuel cells.

Structural Evolution and Magnetic Properties of Gd2Hf2O7 Nanocrystals: Computational and Experimental Investigations

Structural evolution in functional materials is a physicochemical phenomenon, which is important from a fundamental study point of view and for its applications in magnetism, catalysis, and nuclear waste immobilization. In this study, we used x-ray diffraction and Raman spectroscopy to examine the Gd₂Hf₂O₇ (GHO) pyrochlore, and we showed that it underwent a thermally induced crystalline phase evolution. Superconducting quantum interference device measurements were carried out on both the weakly ordered pyrochlore and the fully ordered phases. These measurements suggest a weak magnetism for both pyrochlore phases. Spin density calculations showed that the Gd³⁺ ion has a major contribution to the fully ordered pyrochlore magnetic behavior and its cation antisite. The origin of the Gd magnetism is due to the concomitant shift of its spin-up 4f orbital states above the Fermi energy and its spin-down states below the Fermi energy. This picture is in contrast to the familiar Stoner model used in magnetism. The ordered pyrochlore GHO is antiferromagnetic, whereas its antisite is ferromagnetic. The localization of the Gd-4f orbitals is also indicative of weak magnetism. Chemical bonding was analyzed via overlap population calculations: These analyses indicate that Hf-Gd and Gd-O covalent interactions are destabilizing, and thus, the stabilities of these bonds are due to ionic interactions. Our combined experimental and computational analyses on the technologically important pyrochlore materials provide a basic understanding of their structure, bonding properties, and magnetic behaviors.

Disorder in Ho2Ti2-x Zr x O7: pyrochlore to defect fluorite solid solution series

Pyrochlore (A₂B₂O₇) is an important, isometric structure-type because of its large variety of compositions and structural derivatives that are generally related to different disordering mechanisms at various spatial scales. The disordering is key to understanding variations in properties, such as magnetic behavior or ionic conduction. Neutron and X-ray total scattering methods were used to investigate the degree of structural disorder in the Ho₂Ti_2-x Zr _x O₇ (x = 0.0-2.0, Δx = 0.25) solid solution series as a function of the Zr-content, x. Ordered pyrochlores (Fd3̄m) disorder to defect fluorite (Fm3̄m) via cation and anion disordering. Total scattering experiments with sensitivity to the cation and anion sublattices provide unique insight into the underlying atomic processes. Using simultaneous Rietveld refinement (long-range structure) and small-box refinement PDF analysis (short-range structure), we show that the series undergoes a rapid transformation from pyrochlore to defect fluorite at x ≈ 1.2, while the short-range structure exhibits a linear increase in a local weberite-type phase, C222₁, over the entire composition range. Enthalpies of formation from the oxides determined using high temperature oxide melt solution calorimetry support the structural data and provide insight into the effect of local ordering on the energetics of disorder. The measured enthalpies of mixing are negative and are fit by a regular solution parameter of W = -31.8 ± 3.7 kJ mol^-1. However, the extensive short-range ordering determined from the structural analysis strongly suggests that the entropies of mixing must be far less positive than implied by the random mixing of a regular solution. We propose a local disordering scheme involving the pyrochlore 48f to 8a site oxygen Frenkel defect that creates 7-coordinated Zr sites contained within local weberite-type coherent nanodomains. Thus, the solid solution is best described as a mixture of two phases, with the weberite-type nanodomains triggering the long-range structural transformation to defect fluorite after accumulation above a critical concentration (50% Ti replaced by Zr).

High-Pressure Routes to New Pyrochlores and Novel Magnetism

The pyrochlore structure (A2B2O7) has been an object of consistent study by materials scientists largely due to the stability of the cubic lattice with respect to a wide variety of chemical species on the A or B sites. The criterion for stability under ambient conditions is controlled by the ratio of these cations, which is empirically 1.36 < RA/RB < 1.71. However, under applied pressure synthesis conditions, the pyrochlore lattice is stable up to RA/RB ∼ 2.30, opening up possibilities for new compounds. In this review, we will highlight recent work in exploring new rare-earth pyrochlores such as the germanates RE2Ge2O7 and platinates RE2Pt2O7. We highlight recent discoveries made in these pyrochlores such as highly correlated spin ice behavior, spin liquid ground states, and exotic magnetic ordering.

Metastable Bi2Zr2O7 with Pyrochlore-like Structure: Stabilization, Oxygen Ion Conductivity, and Catalytic Properties

Equimolar concentrations of Zr⁴⁺ and Bi³⁺ were chelated with ethylenediaminetetraacetic acid ligand with the purpose of using it as a precursor to generate pyrochlore-like Bi₂Zr₂O₇. When the X-ray amorphous precursor was calcined at 750 °C for 3 h in air, pyrochlore-like product with superstructure reflections was identified by powder X-ray diffraction (PXRD) along with one minor reflection due to β-Bi₂O₃. This phase was found to be metastable from additional experiments conducted by varying calcination conditions. Structural refinement of PXRD pattern by Le Bail method in Fd3̅ m space group yielded cubic lattice constant of 10.8421(27) Å. Flower-petal-like morphology of the sample was evident in its field-emission scanning electron microscopy image and energy-dispersive X-ray analysis performed at various locations of the specimen confirmed nearly equal concentration of zirconium and bismuth. Six bands at 260, 320, 448, 531, 597, and 828 cm^-1 were observed for this sample in its Raman spectrum and supported our claim of pyrochlore-like structure. Indexation of bright spots present in selected area electron diffraction pattern and observed distances of lattice fringes in high-resolution transmission electron microscopy image were in conformity with the results from PXRD measurements. Absorbance maxima at 312, 372, and 423 nm with a broad tailing stretching up to visible region was noticed in the UV-visible spectrum of this sample. Direct band gap of 2 eV was estimated for this sample from Tauc plot. The oxygen ion conductivity of the sample in the temperature range of 333-773 K was examined, and the highest conductivity at 773 K was 3.071 × 10^-6 S/cm. From activation energy estimation and dielectric loss analysis, thermally activated process related to the mobility of oxygen ion vacancy was found responsible for the observed ionic conductivity. A similar conclusion was reached after careful analysis of dielectric spectroscopy data of this sample. High surface area (125.04 m²/g) and mesoporosity (pore diameter of 3.81 nm) were possessed by this sample, which paved way for studying its catalytic role in the reduction of nitroaromatics and carcinogenic Cr⁶⁺. Cyclability experiments showed the retainment of catalytic activity up to five cycles by the sample without undergoing any structural change.

A Critical Review of Existing Criteria for the Prediction of Pyrochlore Formation and Stability

Depending on intrinsic (e.g., radius ratio rule r_Ln/ r_Zr) and extrinsic factors (e.g., processing conditions), pyrochlore-type Ln₂Zr₂O₇ oxides achieve variable degrees of structural disorder. We report on a systematic study of the structural and microstructural characteristics of the Gd_{2- x}Ln _xZr₂O₇ system, exploring the effect of replacing Gd with a wide range of homovalent lanthanide ions (Ln = Nd, Sm, Dy, Ho, Y, and Er; x = 0.20 and 0.80). All compositions were prepared via a mechanochemical reaction between the corresponding oxides and characterized by X-ray diffraction (standard and synchrotron sources) using the Rietveld method, as well as by Raman spectroscopy. Irrespective of chemical composition, this study reveals that all compositions exhibit a fluorite-like structure. Furthermore, by firing each sample at 800 and 1400 °C, we are able to analyze the transition to pyrochlore-like structures, featuring different degrees of disorder, in all but Gd_1.20Y_0.80Zr₂O₇, which retains the fluorite structure even after heating. The structural data are used to assess the existing criteria for predicting the formation and stability of the pyrochlore structure; according to this analysis, the simple radius ratio rule ( r_Ln/ r_Zr), provides a useful and sufficiently robust criterion. Because the pyrochlore structure has a strong tendency to disorder, it is not possible to define an empirical index similar to the Goldschmidt tolerance factor for perovskite.

Fingerprint of local disorder in long range ordered isometric pyrochlores

The detailed characterization of local order and disorder in isometric A₂B₂O₇ crystalline pyrochlores is of significant importance in view of their wide range and sensitive technological applications. Nevertheless, much remains to be understood concerning their atomic scale structures. Here we specifically pinpoint local order and disorder in four stoichiometric Ln₂Zr₂O₇ (Ln = La, Nd, Sm and Eu) pyrochlores using a combination of three standard easily available laboratory techniques: XRD, ¹⁷O solid-state MAS NMR and Raman spectroscopy. The evolution of the oxygen sub-lattice identifies specific features (extra ¹⁷O NMR signals and Raman bands) which undoubtedly reveal local oxygen order and disorder in these stoichiometric long range ordered crystalline pyrochlores. These results complete the understanding of the atomic scale in these stoichiometric pyrochlores necessitating the need for new microscopic structural models.

Intricate disorder in defect fluorite/pyrochlore: a concord of chemistry and crystallography

Intuitively scientists accept that order can emerge from disorder and a significant amount of effort has been devoted over many years to demonstrate this. In metallic alloys and oxides, disorder at the atomic scale is the result of occupation at equivalent atomic positions by different atoms which leads to the material exhibiting a fully random or modulated scattering pattern. This arrangement has a substantial influence on the material’s properties, for example ionic conductivity. However it is generally accepted that oxides, such as defect fluorite as used for nuclear waste immobilization matrices and fuel cells, are the result of disorder at the atomic scale. To investigate how order at the atomic scale induces disorder at a larger scale length, we have applied different techniques to study the atomic composition of a homogeneous La₂Zr₂O₇ pyrochlore, a textbook example of such a structure. Here we demonstrate that a pyrochlore, which is considered to be defect fluorite, is the result of intricate disorder due to a random distribution of fully ordered nano-domains. Our investigation provides new insight into the order disorder transformations in complex materials with regards to domain formation, resulting in a concord of chemistry with crystallography illustrating that order can induce disorder.

Chemical ordering in substituted fluorite oxides: a computational investigation of Ho2Zr2O7 and RE2Th2O7 (RE=Ho, Y, Gd, Nd, La)

Fluorite-structured oxides find widespread use for applications spanning nuclear energy and waste containment, energy conversion, and sensing. In such applications the host tetravalent cation is often partially substituted by trivalent cations, with an associated formation of charge-compensating oxygen vacancies. The stability and properties of such materials are known to be influenced strongly by chemical ordering of the cations and vacancies, and the nature of such ordering and associated energetics are thus of considerable interest. Here we employ density-functional theory (DFT) calculations to study the structure and energetics of cation and oxygen-vacancy ordering in Ho₂Zr₂O₇. In a recent neutron total scattering study, solid solutions in this system were reported to feature local chemical ordering based on the fluorite-derivative weberite structure. The calculations show a preferred chemical ordering qualitatively consistent with these findings, and yield values for the ordering energy of 9.5 kJ/mol-cation. Similar DFT calculations are applied to additional RE₂Th₂O₇ fluorite compounds, spanning a range of values for the ratio of the tetravalent and trivalent (RE) cation radii. The results demonstrate that weberite-type order becomes destabilized with increasing values of this size ratio, consistent with an increasing energetic preference for the tetravalent cations to have higher oxygen coordination.

Probing disorder in isometric pyrochlore and related complex oxides

There has been an increased focus on understanding the energetics of structures with unconventional ordering (for example, correlated disorder that is heterogeneous across different length scales). In particular, compounds with the isometric pyrochlore structure, A2B2O7, can adopt a disordered, isometric fluorite-type structure, (A, B)4O7, under extreme conditions. Despite the importance of the disordering process there exists only a limited understanding of the role of local ordering on the energy landscape. We have used neutron total scattering to show that disordered fluorite (induced intrinsically by composition/stoichiometry or at far-from-equilibrium conditions produced by high-energy radiation) consists of a local orthorhombic structural unit that is repeated by a pseudo-translational symmetry, such that orthorhombic and isometric arrays coexist at different length scales. We also show that inversion in isometric spinel occurs by a similar process. This insight provides a new basis for understanding order-to-disorder transformations important for applications such as plutonium immobilization, fast ion conduction, and thermal barrier coatings.

Predicting the lattice constants of the ternary pyrochlores A₂B₂O₆O'

The pyrochlores A2B2O6O' attract much attention because of their physical properties. Several models which relate chemical compositions of ternary pyrochlores with lattice constants have been proposed. Analysis of these models shows that some of them are statistically inadequate and cannot be used. Statistical models to predict lattice constants of ternary pyrochlores A2B2O6O' have been derived using multiple linear regression analysis.

An unconventional method for measuring the Tc L3-edge of technetium compounds

Tc L3-edge XANES spectra have been collected on powder samples of SrTcO3 (octahedral Tc(4+)) and NH4TcO4 (tetrahedral Tc(7+)) immobilized in an epoxy resin. Features in the Tc L3-edge XANES spectra are compared with the pre-edge feature of the Tc K-edge as well as other 4d transition metal L3-edges. Evidence of crystal field splitting is obvious in the Tc L3-edge, which is sensitive to the coordination number and oxidation state of the Tc cation. The Tc L3 absorption edge energy difference between SrTcO3 (Tc(4+)) and NH4TcO4 (Tc(7+)) shows that the energy shift at the Tc L3-edge is an effective tool for studying changes in the oxidation states of technetium compounds. The Tc L3-edge spectra are compared with those obtained from Mo and Ru oxide standards with various oxidation states and coordination environments. Most importantly, fitting the Tc L3-edge to component peaks can provide direct evidence of crystal field splitting that cannot be obtained from the Tc K-edge.

Studying the effects of Zr-doping in (Bi0.5Na0.5)TiO3via diffraction and spectroscopy

The phase transformation in the (Bi_0.5Na_0.5)Ti_1−xZr_xO₃ are characterized using XRD and XANES.