arXiv subjects
Publications and source records attributed to Simon J. L. Billinge.
Equations for the reduced structure function and atomic pair distribution function (PDF) of a textured polycrystalline sample are formulated in terms of the orientational distribution function (ODF) and the structure function from a single crystallite. This may be used to determine the sample ODF from experimental data when the structure of the reference crystallite is known.
The temperature dependence of the local structure of PbSe has been investigated using pair distribution function (PDF) analysis of x-ray and neutron powder diffraction data and density functional theory (DFT) calculations. Observation of non-Gaussian PDF peaks at high temperature indicates the presence of significant anharmonicity, which can be modeled as Pb off-centering along [100] directions that grows on warming similar to the behavior seen in PbTe and PbS and sometimes called emphanisis. Interestingly, the emphanitic response is smaller in PbSe than in both PbS and PbTe indicating a non-monotonic response with chalcogen atomic number in the PbQ (Q=S, Se, Te) series. The DFT calculations indicate a correlation between band gap and the amplitude of [100] dipolar distortion, suggesting that emphanisis may be behind the anomalous composition and temperature dependencies of the band gaps in this series.
The improper ferroelectricity in YMnO$_3$ and other related multiferroic hexagonal manganites are known to cause topologically protected ferroelectric domains that give rise to rich and diverse physical phenomena. The local structure and structural coherence across the ferroelectric transition, however, were previously not well understood. Here we reveal the evolution of the local structure with temperature in YMnO$_3$ using neutron total scattering techniques, and interpret them with the help of first-principles calculations. The results show that, at room temperature, the local and average structures are consistent with the established ferroelectric $P6_3cm$ symmetry. On heating, both local and average structural analyses show striking anomalies from $\sim 800$ K up to the Curie temperature consistent with increasing fluctuations of the order parameter angle. These fluctuations result in an unusual local symmetry lowering into a \textit{continuum of structures} on heating. This local symmetry breaking persists into the high-symmetry non-polar phase, constituting an unconventional type of order-disorder transition.
We present time-of-flight neutron total scattering and polarized neutron scattering measurements of the magnetically frustrated compounds NaCaCo$_2$F$_7$ and NaSrCo$_2$F$_7$, which belong to a class of recently discovered pyrochlore compounds based on transition metals and fluorine. The magnetic pair distribution function (mPDF) technique is used to analyze and model the total scattering data in real space. We find that a previously-proposed model of short-range XY-like correlations with a length scale of 10-15 Å, combined with nearest-neighbor collinear antiferromagnetic correlations, accurately describes the mPDF data at low temperature, confirming the magnetic ground state in these materials. This model is further verified by the polarized neutron scattering data. From an analysis of the temperature dependence of the mPDF and polarized neutron scattering data, we find that short-range correlations persist on the nearest-neighbor length scale up to 200 K, approximately two orders of magnitude higher than the spin freezing temperatures of these compounds. These results highlight the opportunity presented by these new pyrochlore compounds to study the effects of geometric frustration at relatively high temperatures, while also advancing the mPDF technique and providing a novel opportunity to investigate a genuinely short-range-ordered magnetic ground state directly in real space.
We present a combined single-crystal x-ray diffuse scattering and ab-initio molecular dynamics study of lead telluride, PbTe. Well-known for its thermoelectric and narrow-gap semiconducting properties, PbTe recently achieved further notoriety following the report of an unusual off-centering of the lead atoms, accompanied by a local symmetry breaking, on heating. This observation, which was named emphanisis, ignited considerable controversy regarding the details of the underlying local structure and the appropriate interpretation of the total scattering experiments. In this study, we demonstrate close agreement between our diffuse scattering measurements and our calculations, which allows us to analyze features such as higher-order correlations that are accessible in the simulations but not experimentally. This allowed us to discover an unusual correlated local dipole formation extending over several unit cells with an associated local reduction of the cubic symmetry in both our x-ray diffuse scattering measurements and our molecular dynamics simulations. Importantly, when averaged spatially or temporally, the most probable positions for the ions are at the centers of their coordination polyhedra. Our results therefore clarify the nature of the local symmetry breaking, and reveal the source of the earlier controversy regarding the existence or absence of off-centering. Finally, we provide an interpretation of the behavior in terms of coupled soft optical and acoustic modes, which is linked also to the high thermoelectric performance of PbTe.
Lead halide perovskites such as methylammonium lead triiodide (MAPI) have outstanding optical and electronic properties for photovoltaic applications, yet a full understanding of how this solution processable material works so well is currently missing. Previous research has revealed that MAPI possesses multiple forms of static disorder regardless of preparation method, which is surprising in light of its excellent performance. Using high energy resolution inelastic X-ray (HERIX) scattering, we measure phonon dispersions in MAPI and find direct evidence for another form of disorder in single crystals: large amplitude anharmonic zone-edge rotational instabilities of the PbI_6 octahedra that persist to room temperature and above, left over from structural phase transitions that take place tens to hundreds of degrees below. Phonon calculations show that the orientations of the methylammonium couple strongly and cooperatively to these modes. The result is a non-centrosymmetric, instantaneous local structure, which we observe in atomic pair distribution function (PDF) measurements. This local symmetry breaking is unobservable by Bragg diffraction, but can explain key material properties such as the structural phase sequence, ultra low thermal transport, and large minority charge carrier lifetimes despite moderate carrier mobility.
We have studied the atomic and magnetic structure of the dilute ferromagnetic semiconductor system (Ba,K)(Zn,Mn)$_2$As$_2$ through atomic and magnetic pair distribution function analysis of temperature-dependent x-ray and neutron total scattering data. We detected a change in curvature of the temperature-dependent unit cell volume of the average tetragonal crystallographic structure at a temperature coinciding with the onset of ferromagnetic order. We also observed the existence of a well-defined local orthorhombic structure on a short length scale of $\lesssim 5$ Å, resulting in a rather asymmetrical local environment of the Mn and As ions. Finally, the magnetic PDF revealed ferromagnetic alignment of Mn spins along the crystallographic $c$-axis, with robust nearest-neighbor ferromagnetic correlations that exist even above the ferromagnetic ordering temperature. We discuss these results in the context of other experiments and theoretical studies on this system.
We present temperature-dependent atomic and magnetic pair distribution function (PDF) analysis of neutron total scattering measurements of antiferromagnetic MnO, an archetypal strongly correlated transition-metal oxide. The known antiferromagnetic ground-state structure fits the low-temperature data closely with refined parameters that agree with conventional techniques, confirming the reliability of the newly developed magnetic PDF method. The measurements performed in the paramagnetic phase reveal significant short-range magnetic correlations on a $\sim$1~nm length scale that differ substantially from the low-temperature long-range spin arrangement. \textit{Ab initio} calculations using a self-interaction-corrected local spin density approximation of density functional theory predict magnetic interactions dominated by Anderson superexchange and reproduce the measured short-range magnetic correlations to a high degree of accuracy. Further calculations simulating an additional contribution from a direct exchange interaction show much worse agreement with the data. The Anderson superexchange model for MnO is thus verified by experiment and confirmed by \textit{ab initio} theory.
Metal-to-insulator transitions (MITs) are a dramatic manifestation of strong electron correlations in solids1. The insulating phase can often be suppressed by quantum tuning, i.e. varying a nonthermal parameter such as chemical composi- tion or pressure, resulting in a zero-temperature quantum phase transition (QPT) to a metallic state driven by quantum fluctuations, in contrast to conventional phase transitions driven by thermal fluctuations. Theories of exotic phenomena known to occur near the Mott QPT such as quantum criticality and high-temperature superconductivity often assume a second-order QPT, but direct experimental evidence for either first- or second-order behavior at the magnetic QPT associated with the Mott transition has been scarce and further masked by the superconducting phase in unconventional superconductors. Most measurements of QPTs have been performed by volume-integrated probes, such as neutron scattering, magnetization, and transport, in which discontinuous behavior, phase separation, and spatially inhomogeneous responses are averaged and smeared out, leading at times to misidentification as continuous second-order transitions. Here, we demonstrate through muon spin relaxation/rotation (MuSR) experiments on two archetypal Mott insulating systems, composition-tuned RENiO3 (RE=rare earth element) and pressured-tuned V2O3, that the QPT from antiferromagnetic insulator to paramagnetic metal is first-order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value across the phase diagram until it is suddenly destroyed at the QPT. These findings call for further investigation into the role of inelastic soft modes and the nature of dynamic spin and charge fluctuations underlying the transition.
Evolution of the average and local crystal structure of Ca-doped LaMnO$_{3}$ has been studied across the metal to insulator (MI) and the orthorhombic to rhombohedral (OR) structural phase transitions over a broad temperature range for two Ca concentrations ($x = 0.18; 0.22$). Combined Rietveld and high real space resolution atomic pair distribution function (PDF) analysis of neutron total scattering data was carried out with aims of exploring the possibility of nanoscale phase separation (PS) in relation to MI transition, and charting the evolution of local Jahn-Teller (JT) distortion of MnO$_{6}$ octahedra across the OR transition at T$_{S}$ $\sim$ 720 K. The study utilized explicit two-phase PDF structural modeling, revealing that away from TMI there is no evidence for nanoscale phase coexistence. The local JT-distortions disappear abruptly upon crossing into the metallic regime both with doping and temperature, with only small temperature-independent signature of quenched disorder being observable at low temperature as compared to CaMnO$_{3}$. The results hence do not support the percolative scenario for the MI transition in La$_{1-x}$Ca$_{x}$MnO$_{3}$ based on PS, and question its ubiquity in the manganites. In contrast to LaMnO3 that exhibits long range orbital correlations and sizeable octahedral distortions at low temperature, the doped samples with compositions straddling the MI boundary exhibit correlations (in the insulating regime) limited to only $\sim$ 1 nm with observably smaller distortions. In $x = 0.22$ sample local JT-distortions are found to persist across the OR transition and deep into the R-phase (up to $\sim$ 1050 K) where they are crystallographically prohibited. Their magnitude and subnanometer spatial extent remain unchanged.
The prototypical phase change material GeTe shows an enigmatic phase transition at Tc ca. 650 K from rhombohedral (R3m) to cubic (Fm-3m) symmetry. While local probes see little change in bonding, in contrast, average structure probes imply a displacive transition. Here we use high energy X-ray scattering to develop a model consistent with both the local and average structure pictures. We detect a correlation length for domains of the R3m structure which shows power law decay upon heating. Unlike a classical soft mode, it saturates at ca. 20 Å above Tc. These nanoclusters are too small to be observed by standard diffraction techniques, yet contain the same local motif as the room temperature structure, explaining previous discrepancies. Finally, a careful analysis of the pair distribution functions implies that the 0.6 % negative thermal expansion (NTE) at the R3m -Fm-3m transition is associated with the loss of coherence between these domains.
An experimental determination of the magnetic pair distribution function (mPDF) defined in an earlier paper (Frandsen, Yang, and Billinge. (2014) Acta Crystallogr. A, 70(1), 3-11) is presented for the first time. The mPDF was determined from neutron powder diffraction data from a reactor and a neutron time-of-flight total scattering source on a powder sample of the antiferromagnetic oxide MnO. A description of the data treatment that allowed the measured mPDF to be extracted and then modelled is provided and utilized to investigate the low-temperature structure of MnO. Atomic and magnetic co-refinements support the scenario of a locally monoclinic ground-state atomic structure, despite the average structure being rhombohedral, with the magnetic PDF analysis successfully recovering the known antiferromagnetic spin configuration. The total scattering data suggest a preference for the spin axis to lie along the pseudocubic [10$\bar{1}$] direction. Finally, $r$-dependent PDF refinements indicate that the local monoclinic structure tends toward the average rhombohedral $R\overline{3}m$ symmetry over a length scale of approximately 100~Å.
The xPDFsuite software program is described. It is for processing and analyzing atomic pair distribution functions (PDF) from X-ray powder diffraction data. It provides a convenient GUI for SrXplanr and PDFgetX3, allowing the users to easily obtain 1D diffraction pattern from raw 2D diffraction images and then transform them to PDFs. It also bundles PDFgui which allows the users to create structure models and fit to the experiment data. It is specially useful for working with large numbers of datasets such as from high throughout measurements. Some of the key features are: real time PDF transformation and plotting; 2D waterfall, false color heatmap, and 3D contour plotting for multiple datasets; static and dynamic mask editing; geometric calibration of powder diffraction image; configurations and project saving and loading; Pearson correlation analysis on selected datasets; written in Python and support multiple platforms.
A long standing puzzle regarding the disparity of local and long range CuO6 octahedral tilt correlations in the underdoped regime of La2-xBaxCuO4 is addressed by utilizing complementary neutron powder diffraction and inelastic neutron scattering (INS) approaches. Long-range and static CuO6 tilt order with orthogonally inequivalent Cu-O bonds in the CuO2 planes in the low temperature tetragonal (LTT) phase is succeeded on warming through the low-temperature transition by one with orthogonally equivalent bonds in the low temperature orthorhombic (LTO) phase. In contrast, the signatures of LTT-type tilts in the instantaneous local atomic structure persist on heating throughout the LTO crystallographic phase on the nanoscale, although becoming weaker as temperature increases. Analysis of the INS spectra for the x = 1/8 composition reveals the dynamic nature of the LTT-like tilt fluctuations within the LTO phase and their 3D character. The doping dependence of relevant structural parameters indicates that the magnitude of the Cu-O bond anisotropy has a maximum at x = 1/8 doping where bulk superconductivity is most strongly suppressed, suggesting that the structural anisotropy might be influenced by electron-phonon coupling and the particular stability of the stripe-ordered phase at this composition. The bond-length modulation that pins stripe order is found to be remarkably subtle, with no anomalous bond length disorder at low temperature, placing an upper limit on any in-plane Cu-O bondlength anisotropy. The results further reveal that although appreciable octahedral tilts persist through the high-temperature transition and into the high temperature tetragonal (HTT) phase, there is no significant preference between different tilt directions in the HTT regime.
Understanding the role played by broken symmetry states such as charge, spin, and orbital orders in the mechanism of emergent properties such as high-temperature superconductivity (HTSC) is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theoretically, but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here we show that the recently discovered BaTi$_2$Sb$_2$O superconductor and its "parent" compound BaTi$_2$As$_2$O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell charge order with $d$-wave symmetry, pointing to the ubiquity of the phenomenon. These findings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide HTSC materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to superconductivity.
This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties when the same image is measured in multiple frames as well as from a single frame. We show the importance of considering the correlation of diffraction points during the integration and the re-sampling process of data analysis. We find that correlations between adjacent pixels in the image can lead to seriously overestimated uncertainties if it is neglected in the integration process. Off-diagonal entries in the variance-covariance (VC) matrix are problematic as virtually all data processing and modeling programs cannot handle the full VC matrix. We show the off-diagonal terms come mainly from the pixel splitting algorithm used as the default integration algorithm in many popular 2D integration programs, as well as from re-binning and re-sampling steps later in the processing. When the full VC matrix can be propagated during the data reduction, it is possible to get accurate refined parameters and their uncertainties at the cost of increasing computational complexity. However, as this is not normally possible, we explore the best approximate methods for data processing in order to estimate uncertainties on refined parameters with the greatest accuracy from just the diagonal variance terms in the VC matrix.
We explore and describe different protocols for calibrating electron pair distribution function (ePDF) measurements for quantitative studies on nano-materials. We find the most accurate approach to determine the camera-length is to use a standard calibration sample of Au nanoparticles from National Institute of Standards and Technology. Different protocols for data collection are also explored, as are possible operational errors, to find the best approaches for accurate data collection for quantitative ePDF studies.
We demonstrate a remarkable equivalence in structure measured by total X-ray scattering methods between very small metallic nanoparticles and bulk metallic glasses (BMGs), thus connecting two disparate fields, shedding new light on both. Our results show that for nanoparticle diameters <5 nm the structure of Ni nanoparticles changes from fcc to the characteristic BMG-like structure, despite them being formed from a single element, an effect we call nano-metallic glass (NMG) formation. However, high-resolution TEM images of the NMG clusters exhibit lattice fringes indicating a locally well-ordered, rather than glassy, structure. These seemingly contradictory results may be reconciled by finding a locally ordered structure that is highly isotropic and we show that local icosahedral packing within 5 atomic shells explains this. Since this structure is stabilized only in the vicinity of a surface which highlights the importance of the presence of free volume in BMGs for stabilizing similar local clusters.