Pyrochlore Materials Research Articles

Order out of a Coulomb Phase and Higgs Transition: Frustrated Transverse Interactions of Nd_{2}Zr_{2}O_{7}.

The pyrochlore material Nd_{2}Zr_{2}O_{7} with an "all-in-all-out" (AIAO) magnetic order shows novel quantum moment fragmentation with gapped flat dynamical spin ice modes. The parametrized spin Hamiltonian with a dominant frustrated ferromagnetic transverse term reveals a proximity to a U(1) spin liquid. Here we study the magnetic excitations of Nd_{2}Zr_{2}O_{7} above the ordering temperature (T_{N}) using high-energy-resolution inelastic neutron scattering. We find strong spin ice correlations at zero energy with the disappearance of gapped magnon excitations of the AIAO order. It seems that the gap to the dynamical spin ice closes above T_{N} and the system enters a quantum spin ice state competing with and suppressing the AIAO order. Classical MonteCarlo simulations, molecular dynamics, and quantum boson calculations support the existence of a Coulombic phase above T_{N}. Our findings relate the magnetic ordering of Nd_{2}Zr_{2}O_{7} with the Higgs mechanism and provide explanations for several previously reported experimental features.

Fluorescent Thermal Feedback in Ho3+/Yb3+ Doped Y2Ti2O7 Electrospun Nanofibers

One-dimensional (1D) Y2Ti2O7 (YTO): Ho3+/Yb3+ nanofibers with diameters ranging from 300 to 400 nm were synthesized by an electrospinning technology and the structure of YTO nanofibers was identified as face-centered cubic pyrochlores. The detected green and red signals in the upconversion emission spectra under 980 nm laser excitation are due to the radiative transitions (5F4, 5S2) → 5I8 and 5F5 → 5I8 of Ho3+ ions, respectively. YTO: Ho3+/Yb3+ nanofibers have the characteristics of porosity, three-dimensional braidability, high specific surface area and controllable structure, which improves the performance of optical temperature sensing. Furthermore, the nanofiber membranes consisting of YTO: Ho3+/Yb3+ with temperature sensing performance can work steadily at medium temperature range in view of its fast responses and high stability, moreover, a maximum sensitivity about 0.18% K−1 at 423 K, which indicates that the nanofibers have good thermal sensitivity. 1D nanostructure rare earth ion-doped cubic pyrochlore material was proven to obtain excellent upconversion luminescence properties, which provides a new route for the development of sensitive optical temperature-sensing materials.

Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr4O8 and LiGaCr4O8, a spiral spin liquid with two-dimensional degeneracy for CuInCr4Se8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr4S8, LiGaCr4S8, and CuInCr4S8. The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.

Competing orders in pyrochlore magnets from a Z2 spin liquid perspective

The pyrochlore materials have long been predicted to harbor a quantum spin liquid, an intrinsic long-range-entangled state supporting fractionalized excitations. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled ${\mathbb{Z}}_{2}$ spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic spinons. For each spin liquid, we construct a mean-field Hamiltonian that can be used to describe phase transitions out of the spin liquid via spinon condensation. Studying these phase transitions, we establish phase diagrams for our mean-field Hamiltonians that link magnetic orders to specific spin liquids. In general, we find that seemingly unrelated magnetic orders are intertwined with each other and that the conventional spin orders seen in the experiments are accompanied by more exotic hidden orders. Our critical theories are categorized into $z=1$ and $z=2$ types, based on their spinon dispersion and Hamiltonian diagonalizability, and are shown to give distinct signatures in the heat capacity and the spin structure factor. This study provides a clear map of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.

Size, structure, and luminescence of Nd2Zr2O7 nanoparticles by molten salt synthesis

Pyrochlore materials with novel properties are in demand with multifunctional applications such as optoelectronics, scintillator materials, and theranostics. Many reports have already indicated the importance of the synthesis technique for Nd2Zr2O7 (NZO) nanoparticles (NPs); however, no explanation has been provided for the reason behind the nature of its phase selectivity. Here, we have explored the structural and optical properties of the NZO NPs synthesized by a molten salt synthesis method. We have synthesized size-tunable NZO NPs and correlated the particle size with their structural behavior and optical performance. All NZO NPs are stabilized in defect fluorite phase. Neutron diffraction provided insight on the behavior of oxygen in the presence of heavy atoms. We have collected bright amalgam of blue and green emission on UV irradiation due to the presence of oxygen vacancies from these NPs. We have carried out in situ XRD and Raman investigations to observe the temperature-induced phase transformation in a controlled argon environment. Interestingly, we have not observed phase change for the molten salt synthesized fluorite NZO NPs; however, we observed phase transformation from a precursor stage to pyrochlore phase by in situ XRD directly. These observations provide a new strategy to synthesize nanomaterials phase-selectively for a variety of applications in materials science.

Investigations of atomic disorder and grain growth kinetics in polycrystalline La2Zr2O7

In the present study, we investigated the impact of annealing temperature and time on grain growth and atomic order/disorder in La2Zr2O7 pyrochlore. Experimental results showed that the sample remains in the pyrochlore phase at higher annealing temperature (1500 °C) for a longer time (96 h). The influence of grain growth and atomic order/disorder on the structural properties could be effective in designing and tailoring the pyrochlore materials for energy applications. La2Zr2O7 with different degrees of atomic order was prepared by isothermal annealing at different temperatures (1200 °C, 1300 °C and 1500 °C) for various annealing time (24, 48, and 96 h). Structural and microstructural properties of La2Zr2O7 were investigated using the X-ray diffraction, and Raman spectroscopy techniques. The degree of cation–anion order increases with increasing annealing temperature and time. The curvature-driven grain coarsening of the small grains favored the formation of larger grains. The grain-growth kinetics is studied using the Arrhenius equation $$G_{t}^{n} - G_{0}^{n} = k_{0} \exp \left( { - \frac{{E_{\text{a}} }}{RT}} \right)t^{q}$$ and activation energy for grain growth is found to be 590 ± 21 kJ/mol. A quantitative analysis has been presented to investigate the cation/anion order and microstructural evolution in pure phase polycrystalline La2Zr2O7.

Potassium zirconium oxalate a new precursor for the preparation of perovskite, pyrochlore and Nasicon type materials

A new precursor, potassium zirconium oxalate pentahydrate, K4[Zr(C2O4)4]·5H2O, was used for the preparation of zirconium containing perovskite, pyrochlore and Nasicon type materials. Perovskites (BaZrO3, CaZrO3, SrZrO3 and PbZrO3) were prepared by the thermal decomposition of a mixture of potassium zirconium oxalate pentahydrate and MCl2 (M = Ba, Ca, Pb and Sr). Pyrochlore type materials, Ln2Zr2O7 (Ln = Pr, Nd and Gd) were synthesized by heating a mixture of potassium zirconium oxalate pentahydrate and LnCl3. Nasicon type composition, KZr2(PO4)3 was obtained using potassium zirconium oxalate pentahydrate and phosphoric acid by hydrothermal method. Hydrothermal treatment of potassium zirconium oxalate pentahydrate in basic, neutral and acidic medium gave different products. A compound, ZrO(C2O4)·xH2O (x = 1.2–1.8), was obtained from hydrothermal heating of parent potassium zirconium oxalate pentahydrate in acid medium. The TGA profile of ZrO(C2O4)·xH2O was recorded. All the prepared compositions were characterized by powder X-ray diffraction technique. The composition ZrO(C2O4)·xH2O was characterized by Fourier-transform infrared spectroscopy, elemental analysis, XPS and powder XRD techniques. The advantages of this precursor over other zirconium containing compounds and reasons for the formation of final products are discussed.

Influence of Α-Site Cations on Performance of Α2Ir2O7 Pyrochlore Oxygen Evolution Catalysts in Acidic Condition

The acidic nature of proton exchange membrane (PEM) electrolysis coupled with the highly oxidizing conditions of the oxygen evolution reaction (OER) greatly limits viable options for catalysts that are both active and stable. Precious metal catalysts, such as IrOx, are high performing OER materials, but scarcity and high cost may limit widespread implementation. Pyrochlore catalysts of the form A2B2O7 (where A is typically a rare-earth or alkaline-earth metal and B is a transition metal) have emerged as promising active candidates with reduced precious metal content and intriguing stability. For example, Y2Ir2O7 has demonstrated excellent activity and stability under acidic OER conditions despite some leaching of the Y cation, potentially leading to the in situ formation of a new active phase during catalysis1. In this work, the influence of the A-site cation on the activity and stability of Ir-based pyrochlore materials (A2Ir2O7) was systematically explored. Using a series of rare-earth metals, activity and stability were experimentally correlated with changes in the physical, chemical, and electronic properties to better understand the origin of the enhanced performance. This experimental work was supported by density functional theory (DFT) calculations. The fundamental insight gained will help to design OER catalysts with improved activity and reduced precious metal content, all without compromising stability. Cyclic voltammetry, chronoamperometry, chronopotentiometry, and double layer capacitance were used to determine the electrochemical performance of the catalysts. Inductively coupled plasma mass spectrometry (ICP-MS) was used to quantify leaching of the A-site cations and Ir under acidic OER conditions and establish a relationship between the loss of material and the change in catalytic performance. This relationship was further investigated with DFT calculations. Additionally, the crystal structure, surface composition, and morphology of the catalysts before and after electrochemical testing were probed using x-ray diffraction (XRD), x-ray photoelectron spectroscopy (XPS), and scanning electron microscopy (SEM).

Dynamical Structure Factor of the Three-Dimensional Quantum Spin Liquid Candidate NaCaNi_{2}F_{7}.

We study the dynamical structure factor of the spin-1 pyrochlore material NaCaNi_{2}F_{7}, which is well described by a weakly perturbed nearest-neighbour Heisenberg Hamiltonian, Our three approaches-molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory-reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence with the exception of the lowest energies. We discuss two surprising aspects and their implications for quantum spin liquids in general: the complete lack of sharp quasiparticle excitations in momentum space and the success of the linear spin wave theory in a regime where it would be expected to fail for several reasons.

Simultaneous three‐dimensional elemental mapping of Hollandite and Pyrochlore material phases in ceramic waste form materials

AbstractDifferential X‐ray absorption contrast tomography was performed on model ceramic composite systems to image the 3D spatial distributions of Ga and Nd containing phases. The model material systems were fabricated such that they contained two constituent phases. Ga–doped Ba hollandite (Ba1.33Ga2.66Ti5.34O16), and pyrochlore (Nd2Ti2O7) which are under consideration as nuclear waste immobilization matrices. Two complementary techniques have been used to characterize the 3D distribution of phases. The analysis suggests that the 3D spatial distributions of hollandite and pyrochlore can be readily identified through the distributions Ga and Nd, respectively. These results represent a critical development towards characterizing the complex microstructure inherent to practical materials such as multiphase ceramic composite waste forms. Moreover, these methods can be applied to elucidate microstructural features that fundamentally determine the performance and properties of complex systems, which is central to the design of durable waste forms as well as many other real materials such fuel cells, batteries, ultra‐high temperature ceramics.

The spin-1/2 Heisenberg ferromagnet on the pyrochlore lattice: A Green's function study

We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Green's function technique within the random-phase (or Tyablikov) approximation as well as the linear spin-wave theory and quantum Monte Carlo simulations. We compare our results to the ones obtained recently by other methods to corroborate our findings. Finally, we contrast our results with the ones for the simple-cubic-lattice case: both lattices are identical at the mean-field level. We demonstrate that thermal fluctuations are more efficient in the pyrochlore case (finite-temperature frustration effects). Our results may be of use for interpreting experimental data for ferromagnetic pyrochlore materials.

High-Performance Praseodymium Doped Pyrochlore-Type Yttrium Ruthenate Electrocatalysts for Proton Exchange Membrane Water Electrolysis

Proton exchange membrane water electrolysis (PEMWE) is an advanced and effective solution to the primary energy storage which allows for direct production of hydrogen from water. Due to the harsh electrochemical environment (e.g., high anodic overpotential, the presence of strong oxidants, low PH) and the sluggish electrode processes, precious metal compounds have been chosen as electrocatalysts in PEMWE [1]. The development of low-cost, highly active and stable oxygen evolution reaction (OER) catalysts remains an important challenge. Pyrochlore yttrium ruthenate (Y2Ru2O7−δ) has significantly enhanced performance over conventional IrO2 electrocatalyst towards OER and high stability in acid media [2]. However, Y2Ru2O7−δ is limited by its low electrical conductivity related to the n-type semiconducting behavior [3]. Doping the A site of the pyrochlore structure (A2B2O7−δ) is a strategy to improve the electrical conductivity of pyrochlore materials. In this work, novel yttrium–ruthenates compositions doped with Pr were synthesized by sol-gel method. Electrochemical measurements in acidic media showed that Pr doped yttrium pyrochlore catalysts possess high OER activity and stability. The OER overpotentials of Y2Ru2O7−δ and Y1.8Pr0.2Ru2O7−δ are 310 mV and 300 mV at 10 mA/cm2, which is lower than that of IrO2 (340 mV). The Tafel slopes for Y2Ru2O7−δ and Y1.8Pr0.2Ru2O7−δ are 40 mV/dec and 36 mV/dec, respectively, in comparison with 42 mV/dec for IrO2. The superior activity of Y2Ru2O7−δ and Y1.8Pr0.2Ru2O7−δ measured by current density remained largely unchanged even after 2000 cyclic voltammograms (CVs) cycles, only decreasing by 17% and 5.6%, respectively. In contrast, IrO­2 catalyst lost 46% of its activity. Figure 1. OER performance of pyrochlore Y2Ru2O7, Y1.8Pr0.2Ru2O7 and reference IrO2 electrocatalysts. (a) CVs cycles from 1st to 2 000th. Inset shows the comparison of current densities for yttrium ruthenate and IrO2 at 1.52 V versus RHE. (b) Tafel plots. [1] Q. Feng, X.Z. Yuan, G. Liu, B. Wei, Z. Zhang, H. Li, H. Wang, Journal of Power Sources, 366 (2017) 33-55. [2] J. Kim, P.C. Shih, K.C. Tsao, Y.T. Pan, X. Yin, C.J. Sun, H. Yang, J Am Chem Soc, 139 (2017) 12076-12083. [3] C. Abate, V. Esposito, K. Duncan, J.C. Nino, D.M. Gattia, E.D. Wachsman, E. Traversa, Journal of the American Ceramic Society, (2010). Figure 1

Competing phases and topological excitations of spin-1 pyrochlore antiferromagnets

Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments. We here study the spin-one local moments on the pyrochlore lattice, and propose a generic interacting spin model on a pyrochlore lattice. Our spin model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii-Moriya interaction and the single-ion spin anisotropy. We develop a flavor wave theory and combine with a mean-field approach to study the global phase diagram of this model and establish the relation between different phases in the phase diagram. We find the regime of the quantum paramagnetic phase where a degenerate line of the magnetic excitations emerges in the momentum space. We further predict the critical properties of the transition out of the quantum paramagnet to the proximate orders. The presence of quantum order by disorder in the parts of the ordered phases is then suggested. We point out the existence of degenerate and topological excitations in various phases. We discuss the relevance with fluoride pyrochlore material NaCaNi$_2$F$_7$ and explain the role of the spin-orbit coupling and the magnetic structures of the Ru-based pyrochlore A$_2$Ru$_2$O$_7$ and the Mo-based pyrochlore A$_2$Mo$_2$O$_7$.

Weyl magnons in pyrochlore antiferromagnets with an all-in-all-out order

We investigate novel topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials and has not be experimentally observed so far. We further show that breathing pyrochlores with AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings apply to any pyrochlore material supporting AIAO orders, irrespective of the forms of interactions. Specifically, we show that the Weyl magnons are robust against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the ubiquitous AIAO orders in pyrochlore magnets including R$_2$Ir$_2$O$_7$, and experimentally achievable external strain and magnetic field, our predictions provide promising arena to witness the Weyl magnons in quantum magnets.

Orange-red emitting Gd2Zr2O7:Sm3+: Structure-property correlation, optical properties and defect spectroscopy

Local structure analysis of dopant ion, understanding host to dopant energy transfer dynamics and defects characterization in a doped material which plays an important role in the designing a highly efficient opto-electronic material. In this connection a new Sm3+ doped Gd2Zr2O7 pyrochlore material was synthesized using gel-combustion technique and was characterized systematically using X-ray diffraction (XRD), time resolved photoluminescence spectroscopy (TRPLS), positron annihilation lifetime spectroscopy (PALS) and density functional theory (DFT) based ab-initio calculation. Based on DFT site selective energetics calculation and luminescence decay measurement, it was observed that the Sm3+ was distributed at both Gd3+ and Zr4+ site with higher Sm3+ fraction at the Gd3+ site. PALS was used to probe the presence of defects in the phosphor. In this work intense orange-red emission is realized through manipulating the energy transfer from host defect emission (oxygen vacancies) to Sm3+ which allows color emission from green in undoped to orange-red in doped samples. Effect of dopant concentration and annealing temperature was probed using TRPLS and PALS. These all information is highly important for researcher looking to achieve pyrochlore based phosphor materials with high quantum yield.

The Numerical Modeling of Thermal Stress Distribution in Thermal Barrier Coatings

Abstract The paper presents the results of numerical calculations of temperature and thermal stress distribution in thermal barrier coatings deposited by thermal spraying process on the nickel based superalloy. An assumption was made to apply conventional zirconium oxide modified with yttrium oxide (8YSZ) and apply pyrochlore type material with formula La2Zr2O7. The bond coat was made of NiCoCrAlY. Analysis of the distribution of temperature and stresses in ceramic coatings of different thicknesses was performed in the function of bond-coat thickness and the type of ceramic insulation layer. It was revealed that the thickness of NiCrAlY bond-coat has not significant influence on the stress distribution, but there is relatively strong effect on temperature level. The most important factor influenced on stress distribution in TBC system is related with type and properties of ceramic insulation layer.

Characterization of calcination temperature on a Ni-substituted lanthanum-strontium-zirconate pyrochlore

A lanthanum strontium zirconate pyrochlore material was substituted with Ni, and the effect of calcination temperature on important catalytic properties was evaluated. The introduction of the Ni into the pyrochlore decreased the BET surface as compared to non-Ni containing materials due to enhanced sintering. The presence of Ni dispersed in the precursor material produced oxygen vacancies which improved solid state diffusion of the pyrochlore cations, and lowered the onset of crystallization by almost 100°C compared to the baseline material without Ni. Furthermore, only a small amount of Ni was found to be soluble in the structure up to 1000°C, at which point almost no Ni occupies lattice positions in the pyrochlore crystal structure. The Ni was found to exsolve to the surface and grain boundary regions of the pyrochlore and reside on the surface as NiO. Heating to temperatures greater than 800°C also led to the formation of a La2ZrNiO6 perovskite phase. Surface composition, as measured by XPS, showed a decrease in Ni concentration at the surface as the calcination temperature was increased. This was likely due to the formation of larger Ni particles with increasing temperature, as well as the migration of the Ni into the bulk through the formation of the La2ZrNiO6 phase. Temperature programmed reduction results showed that increasing the calcination temperature resulted in particle growth of the NiO and a weaker interaction with the pyrochlore surface, which made the NiO more reducible at lower temperatures. Multiple reduction-oxidation TPR/TPO cycles showed that the results were not reproducible from cycle-to-cycle for the lowest calcination temperature material (700°C) due to an amorphous La-Zr-O phase initially present. However, materials calcined at all other temperatures showed an almost identical TPR/TPR profiles after the second cycle.

“Energy Selection Channels” for High-Performance Electrolyte: Anion-Frenkel Defect Pair as Dominant Source for O Ion Conductions in Pyrochlore-type Lanthanide Hafnium Oxides SOFC

The excellent ion conductivities of pyrochlore-type materials are believed to be based on oxygen anion transportations caused by the intrinsic defects, in which the anion Frenkel (a-Fr) pair (VO+IO) defect is the most stable one that lacks detailed study. The partially disordered pyrochlore with formation of the a-Fr pair defect will result in more disorder in local pyrochlore structure and increase number of possible migration paths for oxygen anions, which could further improve the ion conductivities of materials. Hence, we studied the formation of a-Fr defect pairs in La2Hf2O7 as a representative pyrochlore structure by density functional theory (DFT) calculations. Three types of defect migration sites were discovered with the ability to incorporate interstitial oxygen atoms from 48f sites and form a-Fr defect pairs (IO+VO(48f)). Besides the most stable vacant 8a sites with lowest defect formation energy of 3.49 eV/pair, two other novel migration sites have been first reported with ability to form a-Fr pair defect with formation energies of 6.53 and 8.49 eV/pair, respectively. These two new types of migration path, as intermediate sites, could construct a diffuse channel with vacant 8a site for interstitial oxygen anions diffusion in the lattice and significantly decrease the distance and barrier of each jump for oxygen atoms. In contrast with the oxygen interstitial defects, the formation of a-Fr pair defect shows higher priority because of much lower formation energies. Since oxygen anions could be easier to generate and diffuse in the pyrochlore structure, the a-Fr pair defect can be explained as the origin of excellent ion conductivities of pyrochlore materials. This work provides a detailed understanding of relationship between intrinsic defects and electronic properties, which enable us to predict electronic properties of other pyrochlore-type materials in the future study.

Single-ion properties of theSeff=12XY antiferromagnetic pyrochloresNaA′Co2F7(A′=Ca2+, Sr2+)

The antiferromagnetic pyrochlore material NaCaCo$_2$F$_7$ is a thermal spin liquid over a broad temperature range (~ 140 K down to $T_F = 2.4 $K), in which magnetic correlations between Co$^{2+}$ dipole moments explore a continuous manifold of antiferromagnetic XY states. The thermal spin liquid is interrupted by spin freezing at a temperature that is ~ 2 % of the mean field interaction strength, leading to short range static XY clusters with distinctive relaxation dynamics. Here we report the low energy inelastic neutron scattering response from the related compound NaSrCo$_2$F$_7$, confirming that it hosts the same static and dynamic spin correlations as NaCaCo$_2$F$_7$. We then present the single-ion levels of Co$^{2+}$ in these materials as measured by inelastic neutron scattering. An intermediate spin orbit coupling model applied to an ensemble of trigonally distorted octahedral crystal fields accounts for the observed transitions. The single-ion ground state of Co$^{2+}$ is a Kramers doublet with a strongly XY-like $g$-tensor ($g_{xy}/g_{z}$ ~ 3). The local disorder inherent from the mixed pyrochlore $A$ sites (Na$^{+}$/Ca$^{2+}$ and Na$^{+}$/Sr$^{2+}$) is evident in these measurements as exaggerated broadening of some of the levels. A simple model that reproduces the salient features of the single-ion spectrum produces approximately 8.4 % and 4.1 % variation in the $z$ and $xy$ components of the $g$-tensor, respectively. This study confirms that an $S_{eff} =1/2$ model with XY antiferromagnetic exchange and weak exchange disorder serves as a basic starting point in understanding the low temperature magnetic behavior of these strongly frustrated magnets.

Composition dependent order-disorder transition in NdxZr1−xO2−0.5x pyrochlores: A combined structural, calorimetric and ab initio modeling study

The order-disorder phase transition in the NdxZr1−xO2−0.5x system is studied by complementary techniques which include wet chemical synthesis of a series of compositions with various Nd/Zr ratios with the final annealing at 1873 K, X-ray diffraction, oxide melt solution calorimetry and ab initio thermodynamic modeling. Our structural data indicate the transition from ordered to disordered pyrochlore at x ∼0.31 at a temperature of 1873 K. Our calorimetric data show a transition enthalpy of ∼30 kJ/mol, which corresponds to an entropy of disordering of ∼16 J/K/mol. The latter value is significantly smaller than the configurational entropy of transition computed under the assumption of complete disorder in a fluorite phase, indicating a substantial degree of order remaining in the fluorite phase at the temperature of synthesis. The considered phases are computed ab initio using a series of special quasi-random structures that emulate the complete or partial disorder. The results of our calculations and thermodynamic modeling are in good agreement with the measured lattice parameters, the Nd content at the order-disorder transition, and the measured formation and transformation enthalpies. Thus our combined experimental and modeling results provide valuable insight into the disordering of this pyrochlore phase and of other pyrochlore materials.