Disorder In Solids Research Articles

On Topological Order and Disorder in Solids and Liquids

On Topological Order and Disorder in Solids and Liquids

Hidden chemical order in disordered Ba7Nb4MoO20 revealed by resonant X-ray diffraction and solid-state NMR

The chemical order and disorder of solids have a decisive influence on the material properties. There are numerous materials exhibiting chemical order/disorder of atoms with similar X-ray atomic scattering factors and similar neutron scattering lengths. It is difficult to investigate such order/disorder hidden in the data obtained from conventional diffraction methods. Herein, we quantitatively determined the Mo/Nb order in the high ion conductor Ba7Nb4MoO20 by a technique combining resonant X-ray diffraction, solid-state nuclear magnetic resonance (NMR) and first-principle calculations. NMR provided direct evidence that Mo atoms occupy only the M2 site near the intrinsically oxygen-deficient ion-conducting layer. Resonant X-ray diffraction determined the occupancy factors of Mo atoms at the M2 and other sites to be 0.50 and 0.00, respectively. These findings provide a basis for the development of ion conductors. This combined technique would open a new avenue for in-depth investigation of the hidden chemical order/disorder in materials.

Variability of mesoscopic mechanical disorder in disordered solids

Quantifying mechanical disorder in solids, either disordered crystals or glassy solids, and understanding its range of variability are of prime importance, e.g. for discovering structure–properties relations. The bounds on the degree of mechanical fluctuations in disordered solids and how those depend on solids formation history remain unknown. Here, we study a broadly applicable quantifier of mesoscopic mechanical disorder χ, defined via the dimensionless fluctuations of the shear modulus, over a wide variety of disordered computer solids and upon varying different control parameters. χ is intimately related to basic properties of disordered solids, such as elastic constants and plastic deformability, and can be experimentally extracted by wave-attenuation measurements. We find that a large variety of self-organized glassy solids, where disorder is an emergent property, appear to satisfy a generic lower bound on χ. On the other hand, we show that χ is unbounded from above, and may diverge in systems driven towards the critical unjamming point. These results highlight basic properties of disordered solids and set the ground for systematically quantifying mechanical disorder across different systems.

Unified quantifier of mechanical disorder in solids.

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

A Practical Review of NMR Lineshapes for Spin-1/2 and Quadrupolar Nuclei in Disordered Materials.

NMR is a powerful spectroscopic method that can provide information on the structural disorder in solids, complementing scattering and diffraction techniques. The structural disorder in solids can generate a dispersion of local magnetic and electric fields, resulting in a distribution of isotropic chemical shift δiso and quadrupolar coupling CQ. For spin-1/2 nuclei, the NMR linewidth and shape under high-resolution magic-angle spinning (MAS) reflects the distributions of isotropic chemical shift, providing a rich source of disorder information. For quadrupolar nuclei, the second-order quadrupolar broadening remains present even under MAS. In addition to isotropic chemical shift, structural disorder can impact the electric field gradient (EFG) and consequently the quadrupolar NMR parameters. The distributions of quadrupolar coupling and isotropic chemical shift are superimposed with the second-order quadrupolar broadening, but can be potentially characterized by MQMAS (multiple-quantum magic-angle spinning) spectroscopy. We review analyses of NMR lineshapes in 2D DQ–SQ (double-quantum single-quantum) and MQMAS spectroscopies, to provide a guide for more general lineshape analysis. In addition, methods to enhance the spectral resolution and sensitivity for quadrupolar nuclei are discussed, including NMR pulse techniques and the application of high magnetic fields. The role of magnetic field strength and its impact on the strategy of determining optimum NMR methods for disorder characterization are also discussed.

Direct coupling of first-principles calculations with replica exchange Monte Carlo sampling of ion disorder in solids

We demonstrate the feasibility of performing sufficient configurational sampling of disordered oxides directly from first-principles without resorting to the use of fitted models such as cluster expansion. This is achieved by harnessing the power of modern-day cluster supercomputers using the replica exchange Monte Carlo method coupled directly with structural relaxation and energy calculation performed by density functional codes. The idea is applied successfully to the calculation of the temperature-dependence of the degree of inversion in the cation sublattice of MgAl2O4 spinel oxide. The possibility of bypassing fitting models will lead to investigation of disordered systems where cluster expansion is known to perform badly, for example, systems with large lattice deformation due to defects, or systems where long-range interactions dominate such as electrochemical interfaces.

Disorder in the early universe

Little is known about the microscopic physics that gave rise to inflation in our universe. There are many reasons to wonder if the underlying description requires a careful arrangement of ingredients or if inflation was the result of an essentially random process. At a technical level, randomness in the microphysics of inflation is closely related to disorder in solids. We develop the formalism of disorder for inflation and investigate the observational consequences of quenched disorder. We find that a common prediction is the presence of additional noise in the power spectrum or bispectrum. At a phenomenological level, these results can be recast in terms of a modulating field, allowing us to write the quadratic maximum likelihood estimator for this noise. Preliminary constraints on disorder can be derived from existing analyses but significant improvements should be possible with a dedicated treatment.

Damage profile and ion distribution of slow heavy ions in compounds

Slow heavy ions inevitably produce a significant concentration of defects and lattice disorder in solids during their slowing-down process via ion-solid interactions. For irradiation effects research and many industrial applications, atomic defect production, ion range, and doping concentration are commonly estimated by the stopping and range of ions in matter (SRIM) code. In this study, ion-induced damage and projectile ranges of low energy Au ions in SiC are determined using complementary ion beam and microscopy techniques. Considerable errors in both disorder profile and ion range predicted by the SRIM code indicate an overestimation of the electronic stopping power, by a factor of 2 in most cases, in the energy region up to 25 keV/nucleon. Such large discrepancies are also observed for slow heavy ions, including Pt, Au, and Pb ions, in other compound materials, such as GaN, AlN, and SrTiO3. Due to the importance of these materials for advanced device and nuclear applications, better electronic stopping cross section predictions, based on a reciprocity principle developed by Sigmund, is suggested with fitting parameters for possible improvement.

Characterizing Slight Structural Disorder in Solids by Combined Solid-State NMR and First Principles Calculations

A general approach for structural interpretation of local disorder in partially ordered solids is proposed, combining high-resolution two-dimensional (2D) nuclear magnetic resonance (NMR) and first principles calculations. We show that small chemical shift variations of the order of a ppm can be interpreted in detailed structural terms with advanced density functional theory methods. Focusing on a model system of bisphosphinoamine, we demonstrate that the existence and the spatial range of small amplitude disorder can be probed using quantitative statistical analyses of 2D NMR line shapes obtained from through-space correlation experiments collected using variable mixing times. We show how low-energy vibration modes calculated from first principles can be conveniently used not as a cause of disorder but, instead, to generate a basis set of physically plausible local distortions to describe candidate static distributions of local geometries. Calculations of (31)P NMR isotropic chemical shifts are then used for the first time to simulate 2D correlation lineshapes associated with these distortions, which permit their evaluation as a potential source of disorder by comparison to experimental 2D cross-peaks between phosphorus sites. This new type of structural constraints allows the identification of changes in the bonding geometry that most likely contribute to the local structural disorder. We thus identify at least one type of structural deformation that is compatible with the experimental 2D NMR data and is also within the order of magnitude of the "thermal ellipsoids" associated with the uncertainties on the atomic positions of the X-ray diffraction structure.

Symmetry-adapted configurational modelling of fractional site occupancy in solids

A methodology is presented, which reduces the number of site-occupancy configurations tobe calculated when modelling site disorder in solids, by taking advantage of the crystalsymmetry of the lattice. Within this approach, two configurations are considered equivalentwhen they are related by an isometric operation; a trial list of possible isometrictransformations is provided by the group of symmetry operators in the parent structure,which is used to generate all configurations via atomic substitutions. We haveadapted the equations for configurational statistics to operate in the reducedconfigurational space of the independent configurations. Each configuration in this space ischaracterized by its reduced energy, which includes not only its energy but also acontribution from its degeneracy in the complete configurational space, via an entropicterm. The new computer program SOD (site-occupancy disorder) is presented,which performs this analysis in systems with arbitrary symmetry and any size ofsupercell. As a case study we use the distribution of cations in iron antimony oxideFeSbO4, where we also introduce some general considerations for the modelling of site-occupancydisorder in paramagnetic systems.

The physics and chemistry of materials

Preface. List of Tables. Introduction. STRUCTURE OF MATERIALS. Structure of Crystals. Bonding in Solids. Diffraction and the Reciprocal Lattice. Order and Disorder in Solids. PHYSICAL PROPERTIES OF MATERIALS. Phonons. Thermally Activated Processes, Phase Diagrams, and Phase Transitions. Electrons in Solids: Electrical and Thermal Properties. Optical Properties of Materials. Magnetic Properties of Materials. Mechanical Properties of Materials. CLASSES OF MATERIALS. Semiconductors. Metals and Alloys. Ceramics. Polymers. Dielectric and Ferroelectric Materials. Superconductors. Magnetic Materials. Optical Materials. SURFACES, THIN FILMS, INTERFACES, AND MULTILAYERS. Surfaces. Thin Films, Interfaces, and Multilayers. SYNTHESIS AND PROCESSING OF MATERIALS. Synthesis and Processing of Materials. Characterization of Materials. Appendix WA: Thermodynamics. Appendix WB: Statistical Mechanics. Appendix WC: Quantum Mechanics. Materials Index. Index.

86 P - Usefulness of color doppler in assessing breast intracystic or intraductal solid lesions

The visualization of solid, echogenic content within a cystic lesion or a dilated duct poses the diagnostic problem of differentiating debris and clots versus a solid disorder. We used Color Doppler (CD) to asses vascular abnormalities within intracystic and intraductal lesions. Between January and November 1995 we encountered 48 complex cystic lesions and 9 dilated ducts with echogenic material. We used high frequency US probes (10 or 13 MHz) to assess the lesions and we also performed CD with low PRF (500Hz) to detect slow flow. All the patients underwent US guided aspiration biopsy of the complex cistic lesion with the tip of the needle carefully directed within the echogenic portion. In 39 cases the CD was negative as well as the cytological exam. Nine CD-positive cases were associated with 7 papillomas and 2 carcinomas and underwent surgery. Blood flow signal had been detected in 3 of the 4 cases with papilloma, while one was falsely negative. Two small cystic lesions (diameter less than 7mm) showed a clear CD signal, due to an artefactual intralesion projection of a nerby running vessel: the cytology was negative. We think that CD should always be performed in the assesment of intracystic and intraductal solid projections, but a better sensitivity to flow in small blood vessels is still needed.

Crystal-field induced dipoles in heteropolar crystals II: Physical significance

The significance of dipole moments induced by crystal fields in heteropolar crystals is discussed with respect to some aspects of solid state physics. Experimental results from structural analyses that provide data on induced dipoles are summarized. The concept of ionic radii is reconsidered, and a new tabulation scheme is proposed in terms of deformed charge distributions. It is shown that spontaneous polarization as well as the pyro- and piezoelectric coefficients are not independent sets of crystallographic constants, but are accounted for by the structural parameters, the ionic polarizabilities and the elastic constants. The dipole concept is extended to statistically induced or random dipoles. They can account for an important part of the binding energy of substitutionally disordered and non-stoichiometric compounds and, therefore, are concluded to stabilize disorder in solids.

The absence of localization in certain statically disordered solids

We present statically disordered electronic system in which under certain circumstances an initially localized particle necessarily becomes delocalized at long times regardless of the spatial dimension and the magnitude of the disorder. The model is based on correlations between diagonal and off-diagonal matrix elements and is shown to be applicable to structurally-induced disorder in solids. Numerical and analytical calculations in 1-dimension indicate that transport is superdiffusive with the mean-square displacement growing in the time as 3 2 , regardless of the magnitude of the disorder.

Diffusion and Disorder in Solids

Diffusion and Disorder in Solids

An example of conformational disorder in solids: X-ray crystallographic and 13C CPMAS NMR studies of dibenzo and dicyclohexano-13-crown-4 ethers and some lithium complexes

For the cis–anti–cis isomer of dicyclohexano-13-crown-4 ether, disorder has been detected in the crystal structure, with two conformations being present in the ratio of ca. 3:2. Crystal structures for two Li+ complexes of the cis–syn–cis isomer have also been determined. Representative 13C solid phase NMR spectra are presented and discussed for these systems and the related dibenzo substituted compounds. Keywords: crown ethers, solids, NMR, conformation.

On the Electrochemical Transformation of Adsorbates, and the Nature of the Disorder of Solids

On the Electrochemical Transformation of Adsorbates, and the Nature of the Disorder of Solids

Absence of localization in certain statically disordered lattices in any spatial dimension.

We present a statically disordered electronic system in which under certain circumstances an initially localized particle necessarily becomes delocalized at long times regardless of the spatial dimension and the magnitude of the disorder. The model is based on correlations between diagonal and off-diagonal matrix elements and is shown to be applicable to structurally induced disorder in solids. Numerical and analytical calculations in one dimension indicate that transport is superdiffusive, with the mean-square displacement growing in time as ${t}^{3/2}$, regardless of the magnitude of the disorder. Transport is shown to arise in this model from a set of measure-zero unscattered states at a particular energy in the parent-ordered band. It is argued that, when the Fermi level coincides with the energy of the unscattered states, an enhancement of transport should obtain. In addition, it is shown that superdiffusive motion persists for a wide range of correlations between the diagonal and off-diagonal matrix elements when the disorder is structurally induced and chosen from a bivalued distribution. The relevance of these results to transport experiments is discussed.

The use of calorimetric data for estimation of the point defect concentration in solids

Calorimetric methods which allow estimation of the point defect concentration in solids are reviewed. Special attention is paid to the calculation of defect parameters based on the analysis of excessive heat capacity, and to correlations between the thermodynamic parameters of melting and the energetic parameters of point defect formation. The applicability of the thermodynamic approach to the study of intrinsic disorder in solids is demonstrated.

Tunneling-induced disorder in solids

A variety of otherwise well ordered crystals exhibit tunneling-induced disorder at zero temperature, but there seem to be two distinct classes of such materials: hindered rotors, such as H2, D2, and CH4, which have their tunneling suppressed by external pressure, and hydrogen-bonded ferroelectrics, such as KH2PO4 (KDP), which have tunneling promoted by pressure. With the aid of a simple model which explicitly includes the effect of lattice dynamics on the barriers to tunneling, this paper is able to show that both kinds of behavior may be thought of as largely identical. In addition, the same discretized path integral methods used to study this model in mean-field theory turn out to permit the incorporation of a fluctuation correction. The correction reveals that the combination of lattice dynamics and fluctuation effects dramatically shifts the predicted critical pressure—perhaps by enough to account for some recently emphasized discrepancies between theory and experiment for H2 and D2.