Long-range Average Structure Research Articles

Tetrahedra Rotational and Displacive Disorder in the Scheelite-Type Oxide CsReO4.

Scheelite-type metal oxides are a notable class of functional materials, with applications including ionic conductivity, photocatalysis, and the safe storage of radioactive waste. To further engineer these materials for specific applications, a detailed understanding of how their properties can change under different conditions is required─not just in the long-range average structure but also in the short-range local structure. This paper outlines a detailed investigation of the metal oxide CsReO4, which exhibits an uncommon orthorhombic Pnma pseudo-scheelite-type structure at room temperature. Using synchrotron X-ray diffraction, the average structure of CsReO4 is found to undergo a transformation from the orthorhombic Pnma pseudo-scheelite-type structure to the tetragonal I41/a scheelite-type structure at ∼440 K. In the X-ray pair distribution function analysis, lattice strain and rotations of the ReO4 tetrahedra are apparent above 440 K despite the increase in long-range average symmetry, revealing a disconnect between the structural models at different length scales. This study demonstrates how the bonding requirements and ionic radii of the A-site cation can induce disorder that is detectable at different length scales, affecting the physical properties of the material.

Influence of processing parameters on the ferroelectric-relaxor crossover in BNT-based piezoelectric ceramics

The effects of sintering time on the ferroelectric to relaxor crossover were systematically investigated for Sr(Hf0.5Zr0.5)O3-modified Bi0.5(Na0.8K0.2)TiO3 ceramics, prepared using the conventional solid-state mixed-oxide route. Scanning electron microscopy indicated a modest increase in grain size from 1.0 ± 0.2 to 2.0 ± 0.5 μm when the sintering time increased from 2 to 24 h. Furthermore, it was observed that the sintering time does not affect the long-range average crystal structure, as x-ray diffraction data suggest the presence of a single pseudocubic phase for all the samples, irrespective of the sintering time. Interestingly, ferroelectric and piezoelectric characterization showed evidence of a ferroelectric to relaxor transition when the sintering time increased from 2 to 6 h. This transition was marked by a sudden decrease in remanent polarization, a loss in negative strain along with a drastic increase in the maximum electromechanical strain. This was further exemplified in the unipolar strain data, which showed a transition from linear to non-linear dependence with electric field when the sintering time increased from 2 to 6 h. The piezoelectric properties were enhanced with further increase in sintering time up to 12 h, with the corresponding normalized strain value (Smax/Emax) d33∗=647pm/V. However, the d33∗ decreased with further increase in sintering time to 24 h. As the sintering time increased, temperature-dependent dielectric data show a decrease in the maximum permittivity along with the slight shift of the Tmax (temperature of maximum permittivity) to a higher temperature. In addition, results from impedance spectroscopy indicate that the DC resistivity increased by approximately two orders of magnitude when the sintering time increased from 2 to 12 h. These results suggest that while sintering time has a minimal impact on either the microstructure or the long-range average structure, it has a strong influence on the ferroelectric to relaxor crossover, which is often associated with enhanced electromechanical properties. This work presents further evidence that the crossover phenomenon is closely tied to the local structure, where disruption of the long-range dipole order results in stabilization of the relaxor state.

Local structural mechanism for phase transition and ferroelectric polarization in the mixed oxide K0.5Na0.5NbO3

$({\mathrm{K}}_{x}{\mathrm{Na}}_{1\ensuremath{-}x}){\mathrm{NbO}}_{3}$ (KNN) and its solid solutions are considered as potential alternatives to traditional Pb-based piezoelectric materials. Recent investigations indicated that the local structure in KNN is much more complex than its long-range average structure. Here, we have undertaken a systematic investigation of the temperature-dependent evolution of local and average structures of KNN5 $[({\mathrm{K}}_{x}{\mathrm{Na}}_{1\ensuremath{-}x}){\mathrm{NbO}}_{3},x=0.5]$ using time of flight neutron scattering. Rietveld analysis of neutron diffraction patterns indicated that the average structure of KNN5 changes from monoclinic to tetragonal to cubic upon heating from 100 to 773 K. In contrast, analysis of neutron pair distribution function (PDF) indicated that the local structure stays monoclinic within the above temperature range. Based on comparative analysis of local and average structures, it is proposed that the average structural phase transitions in KNN5 are partly derived from a local ordering of the polar units, which are correlated over a length of 10 \ensuremath{\sim} 15 \AA{}. A clear indication of order-disorder type transition at 473 K is evident from the temperature-dependent PDF patterns. Additionally, based on local structural analysis, it is shown that large electrical polarization in KNN5 can be attributed to displacements of both A-site and B-site atoms. These structural insights may help in further optimization of electrical properties of Pb-free KNN piezoceramics.

A Structural Study of 0.06LiNbO3-0.94K0.5Na0.5NbO3 from Neutron Total Scattering Analysis

The structure of ferroelectric 0.06LiNbO3-0.94K0.5Na0.5NbO3 (KNNL6) was investigated by the neutron total scattering method in the temperature range of 290–773 K. The Rietveld analysis using the powder neutron diffraction data in the range of 290–773 K indicates transition from a two-phase (monoclinic and tetragonal) mixture at room temperature to tetragonal and cubic phases at higher temperatures. However, characterization of the local structure by the pair distribution function (PDF) method indicates that the local structure (r ≲ 10 Å) stays monoclinic over the same temperature range. Besides, the local oxygen octahedral distortion exhibits smaller changes with temperature than what is observed for the long-range average structure.

High-temperature neutron powder diffraction studies on atomic structure of (1−x)PbTiO3-xBi(Zn0.5Ti0.5)O3

The atomic structure of (1−x)PbTiO3-xBi(Zn0.5Ti0.5)O3 (x=0.1, 0.2, 0.25) is investigated across the tetragonal to cubic phase transition by neutron powder diffraction measurements up to temperature T=750°C. Both the long-range average structure and the local atomic distributions are studied from Rietveld refinements and atomic pair distribution function (PDF) analysis combined with reverse Monte-Carlo (RMC) modeling, respectively. In the tetragonal phase, the average structure is featured with a large shift of oxygen, which is responsible for an off-centering of cations. With increasing concentration x, the shift of the planar oxygen along the c-axis increases further. The increment of the oxygen displacement is larger than that of the Ti/Zn displacement. This makes the off-centering of cations larger at higher x, which enhances the stability of the tetragonal phase with higher transition temperature. On thermal displacements, the heaviest ion Pb/Bi in the structure exhibits the largest value and is also increased by the concentration x in both the tetragonal and cubic phases. The local structure from PDF and RMC modeling shows that the abnormal thermal displacements are due to a large distribution of Pb off-centering and a bond-length mismatch between Ti–O and Zn–O bonds. Based on these complementary local and average structures, a splitting between Ti and Zn displacements is discussed.

Structural characterization of A-site nonstoichiometric (1 − x)Bi0.5Na0.5TiO3–xBaTiO3 ceramics

Lead-free 1 − x(Bi0.5Na0.5TiO3)–xBaTiO3, x = 0.055, 0.06 and 0.07, ceramics [i.e., near the morphotropic phase boundary (MPB)] were modified by varying the A-site cation stoichiometry to induce acceptor and donor doping through the addition of excess Na and Bi, respectively. The role of A-site nonstoichiometry on the crystal structure was investigated by using Raman spectroscopy and high-energy X-ray diffraction (XRD) techniques. The Raman spectra were analyzed via spectral deconvolution, and the resultant fitted data demonstrated deviations in the dominant bands (at 200–400 cm−1 and 400–600 cm−1) which indicated a shift toward tetragonal distortions in all Na-excess samples. High-energy XRD data showed that all the characteristic peaks corresponding to tetragonal P4bm structure became more prominent in Na-excess sample. Rietveld refinement data confirmed the coexistence of rhombohedral (R3c) and tetragonal (P4bm) phases with a significant increase in P4bm phase fraction in Na-excess composition. The clear agreements between Raman spectroscopy and high-energy XRD data suggest that Bi-excess samples (i.e., donor doping) had little or no effect on crystal structure, whereas Na-excess samples (i.e., acceptor doping) had a significant influence on the structure near the MPB such that tetragonal distortions were induced in both the local structure and the long-range average structure.

Local-scale structures across the morphotropic phase boundary in PbZr1-x Ti x O3.

Lead zirconate titanate (PZT) is one of the most widely studied piezoelectric materials, mainly because of its 'mysterious' relationship between the so-called morphotropic phase boundary (MPB) and its strong piezoelectric coupling factor. Using results from a pair distribution function analysis, this paper examines how the complex local structure in PZT affects the long-range average structure across the MPB. A monoclinic M C type structure is discovered in PZT. A first-order transformation between the monoclinic M A and M C components in both the average and local structures explains the sudden change in piezoelectric effect around these compositions. The role of polarization rotation in the enhancement of the piezoelectric properties is discussed with respect to the composition of PZT. The structure-property relationship that is revealed by this study explains the unique properties of PZT, and may be applicable in the design of new MPB-type functional materials.

Nanoscale heterogeneity, premartensitic nucleation, and a new plutonium structure in metastableδfcc Pu-Ga alloys

The scientifically fascinating question of the spatial extent and bonding of the 5$f$ orbitals of Pu and its six different phases extends to its \ensuremath{\delta}-retained alloys and the mechanism by which Ga and a number of other unrelated elements stabilize its low density face-centered-cubic (fcc) structure. This issue of phase stability is also important technologically because of its significance to Science-Based Stockpile Stewardship. Answering these questions requires information on the local order and structure around the Ga and its effects on the Pu. We have addressed this by characterizing the structures of a large number of Pu-Ga and two Pu-In and one Pu-Ce \ensuremath{\delta} alloys, including a set of high purity \ensuremath{\delta} Pu${}_{1\ensuremath{-}x}$Ga${}_{x}$ materials with 1.7 \ensuremath{\le} $x$ \ensuremath{\le} 6.4 at. % Ga that span the low [Ga] portion of the \ensuremath{\delta} region of the phase diagram across the \ensuremath{\sim}3.3 at. % Ga metastability boundary, with extended x-ray absorption fine structure (EXAFS) spectroscopy that probes the element specific local structure, supplemented by x-ray pair distribution function analysis that gives the total local structure to longer distances, and x-ray diffraction that gives the long-range average structure of the periodic component of the materials. Detailed analyses indicate that the alloys at and below a nominal composition of \ensuremath{\sim}3.3 at. % Ga are heterogeneous and in addition to the \ensuremath{\delta} phase also contain up to \ensuremath{\sim}20% of a novel, coexisting ``\ensuremath{\sigma}'' structure for Pu that forms in nanometer scale domains that are locally depleted in Ga. The invariance of the Ga EXAFS with composition indicates that this \ensuremath{\sigma} structure forms in Ga-depleted domains that result from the Ga atoms in the \ensuremath{\delta} phase self-organizing into a quasi-intermetallic with a stoichiometry of Pu${}_{25\ensuremath{-}35}$Ga so that \ensuremath{\delta} Pu-Ga is neither a random solid solution nor the more stable Pu${}_{3}$Ga + \ensuremath{\alpha}. Above this 3.3 at. % Ga nominal composition, the \ensuremath{\delta} Pu-Ga alloy is homogeneous, and no \ensuremath{\sigma} phase is present. These results that demonstrate that collective and cooperative behavior in the interactions between the alloy elements as well as local elastic forces are crucial in determining the properties of complex materials and contradict the conventional mechanism for martensitic transformations, in this case indicating that nucleation is not the rate limiting step.

Intrinsic Nanoscience of δ Pu–Ga Alloys: Local Structure and Speciation, Collective Behavior, Nanoscale Heterogeneity, and Aging Mechanisms

δ Pu–Ga alloys and their response to self-irradiation are important scientifically because of the unique complexity of Pu and technologically because of their importance in Science Based Stockpile Stewardship. The local order and structure and the role of the Ga are crucial to understanding the phase stability and the aging effects. X-ray diffraction that gives the long-range average structure of the periodic component of the materials and pair distribution functions analysis and X-ray absorption fine structure that give the overall and the element specific local structure have been used to examine a variety of new and aged materials, including a set of high purity δ Pu1–xGax alloys with 1.7 ≤ x ≤ 6.4 atom % Ga that span the low [Ga] portion of the δ region of the phase diagram across the ∼3.3 atom % Ga metastability boundary, a ∼1.7 atom % Ga alloy that was enriched with Pu238 to accelerate the aging process, and others. We find that metastable alloys contain tens of percents of a novel, “σ”, Pu structure that we attribute to rearrangement of the Ga-depleted regions after the self-organization of the Ga to form quasi-intermetallic Pu25–35Ga. This collective and cooperative behavior involving the Ga and other defects in terms of a tendency to aggregate into domains with structures that differ from the δ host and the resulting nanoscale heterogeneity also appears to play an important role in the observation of analogous locally ordered structures in aged materials. This description of these materials and their aging is radically different from current conceptual basis derived from other experiments that are insensitive to ordering on the angstrom–nanometer length scale.

Local Crystal Structure of Antiferroelectric Bi2Mn4/3Ni2/3O6 in Commensurate and Incommensurate Phases Described by Pair Distribution Function (PDF) and Reverse Monte Carlo (RMC) Modeling.

The functional properties of materials can arise from local structural features that are not well determined or described by crystallographic methods based on long-range average structural models. The room temperature (RT) structure of the Bi perovskite Bi2Mn4/3Ni2/3O6 has previously been modeled as a locally polar structure where polarization is suppressed by a long-range incommensurate antiferroelectric modulation. In this study we investigate the short-range local structure of Bi2Mn4/3Ni2/3O6, determined through reverse Monte Carlo (RMC) modeling of neutron total scattering data, and compare the results with the long-range incommensurate structure description. While the incommensurate structure has equivalent B site environments for Mn and Ni, the local structure displays a significantly Jahn–Teller distorted environment for Mn3+. The local structure displays the rock-salt-type Mn/Ni ordering of the related Bi2MnNiO6 high pressure phase, as opposed to Mn/Ni clustering observed in the long-range average incommensurate model. RMC modeling reveals short-range ferroelectric correlations between Bi3+ cations, giving rise to polar regions that are quantified for the first time as existing within a distance of approximately 12 Å. These local correlations persist in the commensurate high temperature (HT) phase, where the long-range average structure is nonpolar. The local structure thus provides information about cation ordering and B site structural flexibility that may stabilize Bi3+ on the A site of the perovskite structure and reveals the extent of the local polar regions created by this cation.

RMCProfile: reverse Monte Carlo for polycrystalline materials

A new approach to the reverse Monte Carlo analysis of total scattering data frompolycrystalline materials is presented. The essential new feature is the incorporation of anexplicit analysis of the Bragg peaks using a profile refinement, taking account of theinstrument resolution function. Other new features including fitting data from magneticmaterials, modelling lattice site disorder and new restraint and constraint options. The newmethod is demonstrated by a brief review of studies carried out during its development.The new program RMCProfile represents a significant advance in the analysisof polycrystalline total scattering data, especially where the local structure isto be explored within the true constraints of the long-range average structure.

PDFgetX: a program for obtaining the atomic pair distribution function from X-ray powder diffraction data

For many materials with disorder, the local structure information is important in understanding their physical properties. However, the conventional crystal structure re®nement by the Rietveld method only allows the determination of the long-range average structure. The pair distribution function (PDF), which can be obtained from powder diffraction data, allows one to extract both local and average structural information (Petkov et al., 1999; Billinge & Thorpe, 1998). We present here a program, PDFgetX, for obtaining the PDF from Xray powder diffraction data. A similar program to process neutron powder diffraction data has already been published (Peterson et al., 2000).

A model of local atomic structure in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3

We have developed a model of local atomic structure in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 (PMN) by pair-density function analysis of neutron and x-ray powder diffraction data. We find large static displacements of all atomic species from their ideal cubic perovskite sites producing a long-range average structure consistent with a crystallographic disorder model, however local correlations of these displacements are significant. Two distinctly different B cation environments are found, as are two unique environments for Pb. The model suggests the formation of structurally ordered regions in which the two types of B cation environments are 1:1 ordered. Details of this model for the local atomic structure of PMN and how it was obtained are described.

Local intermolecular correlations in C60.

A neutron-powder-diffraction real-space structural refinement method is applied to study the local intermolecular correlations in bulk ${\mathrm{C}}_{60}$ solid at 10 K. We found that the orientation of the ${\mathrm{C}}_{60}$ molecules often deviates locally from the long-range average structure, and a significant number (30--40 %) of molecules have the sixfold face oriented toward adjacent molecules.