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Fundamentals of Condensed Matter Physics Marvin L. Cohen and Steven G. Louie

This graduate level textbook on Condensed Matter Physics is written lucidly by two leading luminaries in this field. The volume draws its material from the graduate course in condensed matter physics that has been offered by the authors for several decades at the University of California, Berkeley. Cohen and Louie have done an admirable job of guiding the reader gradually from elementary concepts to advanced topics. The book is divided into four main parts that have four chapters each. Chapter 1 presents models of solids in terms of interacting atoms, which is appropriate for the ground state, and excitations to describe collective effects. Chapter 2 deals with the properties of electrons in crystalline materials. The authors introduce the Born-Oppenheimer approximation and then proceed to the periodic potential approximation. Chapter 3 discusses energy bands in materials and covers concepts from the free electron model to the tight binding model and periodic boundary conditions. Chapter 4 starts with fixed atomic cores and introduces lattice vibrations, phonons, and the concept of density of states. By the end of this part, the student should have a basic understanding of electrons and phonons in materials. Part II presents electron dynamics and the response of materials to external probes. Chapter 5 covers the effective Hamiltonian approximation and the motion of the electron under a perturbation, such as an external field. The discussion moves to many-electron interactions and the exchange-correlation energy in Chapter 6, the widely-used Density Functional Theory (DFT) in chapter 7, and the dielectric response function in Chapter 8. The next two parts of the book cover advanced topics. Part III begins with a discussion of the response of materials to photons in Chapter 9. Chapter 10 goes into the details of electron-phonon interactions in different materials and introduces the polaron. Chapter 11 presents electron dynamics in a magnetic field and Chapter 12 discusses electrical and thermal transport in materials. Part IV takes the reader further into many body effects, superconductivity, and nanoscale materials. The authors introduce Feynman diagrams and many-body perturbation theory in Chapter 13, theories of superconductivity in Chapter 14, magnetism in Chapter 15, and low dimensional systems in Chapter 16. The first two parts are required reading for the beginner planning to perform DFT calculations. The advanced student interested in conducting research in condensed matter physics will benefit from continuing on to the last two parts. There is a set of problems at the end of each part. The narrative is aided by equations and detailed figures. References at the end of the book direct the reader to relevant books and review articles for each chapter. The inside covers include a periodic table and a useful list of fundamental physical constants. The authors present the underlying mathematics elegantly, which makes the textbook quite readable for those with a good mathematical background. Students lacking a firm footing in math will find the terrain rough after Chapter 1. This field has seen many good undergraduate textbooks including those by Kittel and by Ashcroft and Mermin. This volume fills the need for a rigorous graduate level textbook, and is a required addition to the bookshelf of every condensed matter physicist. Cohen and Louie have brought refreshing clarity to a challenging subject and made it eminently accessible to the motivated student.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Alternatives to argon for gas stopping volumes in the B194 neutron imager

In a recent experiment at Lawrence Berkeley National Laboratory, the 40Ar(d,p)41Ar excitation function between 3-7 MeV was measured, confirming a previous estimation that there may be an intolerable radiation dose from 41Ar production by slowing to rest 6.74 MeV deuterons in the gas cell of the neutron imaging facility being constructed in B194. Gas alternatives to argon are considered, including helium, nitrogen (N2), neon, sulfur hexafluoride (SF6), krypton, and xenon, as well as high atomic number solid backings such as tantalum.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Multiscale characterization of irradiation behaviour of ion-irradiated SiC/SiC composites

Here, the irradiation tolerance of SiC/SiC composites was studied using 10 MeV Au ion irradiations at 350 °C, for surface doses between 1 and 50 displacements per atom (dpa). Atomic force microscopy and optical profilometry revealed irradiation-induced axial and radial shrinkage of SiC-fibers. At 50 dpa, net fiber shrinkage reached 2.8 ± 0.3%. We conclude that the primary cause of SiC-fiber shrinkage in SiC/SiC composites is the irradiation-induced loss of pre-existing carbon packets, which had occupied 2–3% fiber volume in unirradiated state. A compelling evidence of the carbon packet loss was revealed using a combination of state-of-art conventional transmission electron microscopy (TEM), high resolution TEM, energy-filtered TEM and electron energy loss spectroscopy. Additionally, the carbon packet volume fraction decreased with increasing dose, reaching near-complete loss after 50 dpa. Carbon packet loss was further confirmed using Raman spectroscopy where the carbon D and G peaks disappeared after irradiation. In contrast, irradiation-induced swelling of 1 ± 0.5% was observed in the matrix after 50 dpa. The study also shows that up to 50 dpa, the multilayer pyrolytic-carbon (PyC) interface in the composite is highly irradiation tolerant as it maintained its morphology, graphitic nature and showed no signs of amorphization. Additionally, Raman spectroscopy revealed a saturation of TEM invisible disorder at 1 dpa for both ultra-fine grains of the fiber and the larger SiC-matrix grains. However, TEM visible extended defect formation such as dislocation loops were only detected in the larger matrix grains, thereby revealing a potential role of grain size on defect accumulation in SiC.

36 MATERIALS SCIENCE↗

Determining the influence of temperature and pressure on the structural stability in a polyurea elastomer

The structural response of amorphous elastomers to applied pressure and temperature is of significant interest given their potential for blast and impact protection applications. While understanding disordered structures is often challenging, this study focuses on the ordered correlations that are present at the atomic level even in amorphous materials. This local order was characterized in polyurea elastomers with two molecular weights up to 6 GPa and ~280 °C using in situ energy dispersive X-ray diffraction at the Advanced Photon Source via total scattering techniques. The resulting structure factors and pair distribution functions indicate that the applied pressure reduced the free volume but had little effect on covalent bonds for both molecular weights. Temperature-induced order-disorder transitions that occur readily at ambient pressures within the temperature range studied here were not observed, their onset likely delayed by the limited chain mobility associated with the free volume reduction. In conclusion, this study demonstrates that total scattering offers insights into the high-pressure structure of disordered polymers that are otherwise inaccessible using more conventional X-ray scattering techniques.

42 ENGINEERING↗

Structural analysis, optical and dielectric function of [Ba{sub 0.9}Ca{sub 0.1}](Ti{sub 0.9}Zr{sub 0.1})O{sub 3} nanocrystals

This work presents the identification of inter-band transitions in the imaginary part of the dielectric function (ε{sub 2}) derived from the Kramers–Kronig analysis for [Ba{sub 0.9}Ca{sub 0.1}](Ti{sub 0.9}Zr{sub 0.1})O{sub 3} (BCZT) nanocrystals synthesized by the modified Pechini method. The analysis started with the chemical identification of the atoms that conform BCZT in the valence loss energy region of a high energy-resolution of electron energy loss spectroscopy. The indirect band energy (E{sub g}) was determined in the dielectric response function. This result is in agreement with the UV-Vis technique, and it obtained an optical band gap of 3.16 eV. The surface and volume plasmon peaks were observed at 13.1 eV and 26.2 eV, respectively. The X-ray diffraction pattern and the Rietveld refinement data of powders heat treated at 700 °C for 1 h suggest a tetragonal structure with a space group (P4 mm) with the average crystal size of 35 nm. The average particle size was determined by transmission electron microscopy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The solvent component of macromolecular crystals

On average, the mother liquor or solvent and its constituents occupy about 50% of a macromolecular crystal. Ordered as well as disordered solvent components need to be accurately accounted for in modelling and refinement, often with considerable complexity. The mother liquor from which a biomolecular crystal is grown will contain water, buffer molecules, native ligands and cofactors, crystallization precipitants and additives, various metal ions, and often small-molecule ligands or inhibitors. On average, about half the volume of a biomolecular crystal consists of this mother liquor, whose components form the disordered bulk solvent. Its scattering contributions can be exploited in initial phasing and must be included in crystal structure refinement as a bulk-solvent model. Concomitantly, distinct electron density originating from ordered solvent components must be correctly identified and represented as part of the atomic crystal structure model. Herein, are reviewed (i) probabilistic bulk-solvent content estimates, (ii) the use of bulk-solvent density modification in phase improvement, (iii) bulk-solvent models and refinement of bulk-solvent contributions and (iv) modelling and validation of ordered solvent constituents. A brief summary is provided of current tools for bulk-solvent analysis and refinement, as well as of modelling, refinement and analysis of ordered solvent components, including small-molecule ligands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Investigating the Role of Defects in α-Pu Phase Transitions using Density Functional Theory

Before reaching its relatively low melting point of 913 K, plutonium undergoes six solid state phases: simple monoclinic alpha, body-centered monoclinic beta, face-centered orthorhombic gamma, face centered cubic delta, body-centered tetragonal delta-prime, and body-centered cubic epsilon phases. Due to their low symmetry, the monoclinic alpha and beta phases have not been studied extensively, however it has been previously hypothesized that the transition between alpha and beta is caused by defects in the lattices due to the incommensurate number of atoms. Additionally, the martensitic delta to alpha phase transformation in plutonium-gallium alloys induces an expanded alpha lattice known as alpha prime, most likely due to the insoluble gallium impurity atom. This work explores how defects such as plutonium interstitials and gallium interstitials and substitutionals may affect the alpha plutonium lattice, providing a better understanding of the mechanisms for the alpha-beta and martensitic phase transformations through density functional theory (DFT). Results indicate that plutonium interstitials within the alpha lattice induce beta features structurally and electronically, such as volume expansion and bonding changes, and gallium interstitials and substitutionals within the alpha lattice induce volume changes as observed experimentally in alpha prime.

36 MATERIALS SCIENCE↗

Dielectric constant of liquid alkanes and hydrocarbon mixtures

The complex dielectric constants of n-alkanes with two to seven carbon atoms have been measured. The measurements were conducted using a slotted-line technique at 1.2 GHz and at atmospheric pressure. The temperature was varied from the melting point to the boiling point of the respective alkanes. The real part of the dielectric constant was found to decrease with increasing temperature and correlate with the change in the molar volume. An upper limit to all the loss tangents was established at 0.001. The complex dielectric constants of a few mixtures of liquid alkanes were also measured at room temperature. For a pentane-octane mixture the real part of the dielectric constant could be explained by the Clausius-Mosotti theory. For the mixtures of n-hexane-ethylacetate and n-hexane-acetone the real part of the dielectric constants could be explained by the Onsager theory extended to mixtures. The dielectric constant of the n-hexane-acetone mixture displayed deviations from the Onsager theory at the highest fractions of acetone. The dipole moments of ethylacetate and acetone were determined for dilute mixtures using the Onsager theory and were found to be in agreement with their accepted gas-phase values. The loss tangents of the mixtures exhibited a linear relationship with the volume fraction for low concentrations of the polar liquids.

NASA Program Exobiology↗

Strained Hydrocarbons as Potential Hypergolic Fuels

A storable combination of high-energy hypergolic fuel and oxidizer is advantageous to the future of reusable launch vehicles (RLVs). The combination will allow an increase in energy per unit volume of fuel and eliminate the need for an external ignition system. Strained systems have been studied as potential high-density fuels. Adding hypergolic functional groups, such as amino groups, to these hydrocarbons will potentially allow auto ignition of strained systems with hydrogen peroxide. Several straight chain amines and their strained counterparts containing an equivalent number of carbon atoms have been purchased and synthesized. These amines provide initial studies to determine the effects of fuel vapor pressure, strain energy, fuel miscibility, and amine substitution upon fuel ignition time and hypergolicity with hydrogen peroxide as an oxidizer.

Source record↗

Bellerophon Environment for Analysis of Materials (BEAM)

Improvements in scientific instrumentation allow imaging at mesoscopic to atomic length scales, many spectroscopic modes, and now--with the rise of multimodal acquisition systems and the associated processing capability--the era of multidimensional, informationally dense data sets has arrived. Technical issues in these combinatorial scientific fields are exacerbated by computational challenges best summarized as a necessity for drastic improvement in the capability to transfer, store, and analyze large volumes of data. The Bellerophon Environment for Analysis of Materials (BEAM) platform provides material scientists the capability to directly leverage the integrated computational and analytical power of High Performance Computing (HPC) to perform scalable data analysis and simulation and manage uploaded data files via an intuitive, cross-platform client user interface. This framework delivers authenticated, "push-button" execution of complex user workflows that deploy data analysis algorithms and computational simulations utilizing compute-and-data cloud infrastructures and HPC environments like Titan at the Oak Ridge Leadershp Computing Facility (OLCF).

Lingerfelt, Eric J↗

An Fe-Ni-Cr embedded atom method potential for austenitic and ferritic systems: An Fe-Ni-Cr embedded atom method potential for austenitic and ferritic systems

Fe-Ni-Cr stainless-steels are important structural materials because of their superior strength and corrosion resistance. Atomistic studies of mechanical properties of stainless-steels, however, have been limited by the lack of high-fidelity interatomic potentials. Here in this paper, using density functional theory as a guide, we have developed a new Fe-Ni-Cr embedded atom method potential. We demonstrate that our potential enables stable molecular dynamics simulations of stainless-steel alloys at high temperatures, accurately reproduces the stacking fault energy—known to strongly influence the mode of plastic deformation (e.g., twinning vs. dislocation glide vs. cross-slip)—of these alloys over a range of compositions, and gives reasonable elastic constants, energies, and volumes for various compositions. The latter are pertinent for determining short-range order and solute strengthening effects. Our results suggest that our potential is suitable for studying mechanical properties of austenitic and ferritic stainless-steels which have vast implementation in the scientific and industrial communities.

36 MATERIALS SCIENCE↗

Tomographic detection of photon pairs produced from high-energy X-rays for the monitoring of radiotherapy dosing

Measuring the radiation dose reaching a patient’s body is difficult. Here we report a technique for the tomographic reconstruction of the location of photon pairs originating from the annihilation of positron–electron pairs produced by high-energy X-rays travelling through tissue. We used Monte Carlo simulations on pre-recorded data from tissue-mimicking phantoms and from a patient with a brain tumour to show the feasibility of this imaging modality, which we named ‘pair-production tomography’, for the monitoring of radiotherapy dosing. We simulated three image-reconstruction methods, one applicable to a pencil X-ray beam scanning through a region of interest, and two applicable to the excitation of tissue volumes via broad beams (with temporal resolution sufficient to identify coincident photon pairs via filtered back projection, or with higher temporal resolution sufficient for the estimation of a photon’s time-of-flight). In addition to the monitoring of radiotherapy dosing, we show that image contrast resulting from pair-production tomography is highly proportional to the material’s atomic number. The technique may thus also allow for element mapping and for soft-tissue differentiation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Bulk formation of a metallic glass - Pd40Ni40P20

Molten spheroids of Pd40Ni40P20, of up to 0.53-cm minor diameter, were slowly cooled (1.4 K/s) on a fused silica surface under 10 to the -6 torr vacuum to a form which was entirely glassy except for some superficial crystallinity comprising less than 0.5% of the volume. The occurrence of crystallization was eliminated by subjecting the specimens to surface etching followed by a succession of heating and cooling cycles. The absence of crystallization in bulk was confirmed by X-ray diffraction, transmission electron microscopy, and calorimetry. Using the last technique, the heat of crystallization of the glass was measured to be 5.3 + or - 0.3 kJ/g atom.

Drehman, A. J.↗

Phosphate (U-Th)/He Thermochronology of Apollo 14 Melt Breccia 14311

Our ability to confidently characterize the impact history of the inner solar system is limited by discrepancies in radiometric dates and age interpretations for lunar rocks, impact melts, and recovered meteorites. It is therefore important to explore different thermally sensitive radiometric systems to unravel the timing and extent of the long term impact flux. Low-temperature thermochronology of lunar samples has the potential to provide more complementary geochronological datasets and further test dynamical models related to the evolution of the inner solar system (e.g., [1]). (U-Th)/He dating is based on the production of 4He atoms by radioactive alpha decay of U and Th (and to a lesser extent, Sm) in a crystal and the thermally activated volumetric diffusion of those 4He nuclides. At high temperatures, the crystal is an open system from which 4He can escape; at lower temperatures, 4He may be retained. This retention temperature depends on factors such as crystal structure and volume fraction of radiation damage in the crystal (e.g., [2, 3]), but is significantly lower for phosphate minerals compared to the diffusion of the radiogenic daughter products in other widely used chronometric systems (e.g., ~75°C in terrestrial apatite (U-Th)/He vs. ~500°C in apatite U-Th-Pb vs. ~900°C in zircon U-Th-Pb chronometry). Phosphate (U-Th)/He dating has been used to decipher peak temperatures and cooling rates related to terrestrial impact events (e.g., [4]). Pairing a low-temperature thermochronometer with higher-temperature approaches (i.e., a combined 207Pb-206Pb and (U-Th)/He approach), can therefore resolve multiple impact ages within a given sample or even grain. However, despite its potential, phosphate (U-Th)/He dating has not been reported on any lunar samples. Here we present the first lunar phosphate (U-Th)/He thermochronology on an Apollo 14 impact melt-breccia.

C A Diaz↗

Damped Ly α absorbers and atomic hydrogen in galaxies: the view of the GAEA model

ABSTRACT Using the GAEA semi-analytic model, we analyse the connection between Damped Ly α systems (DLAs) and H i in galaxies. Our state-of-the-art semi-analytic model is tuned to reproduce the local galaxy H i mass function, and that also reproduces other important galaxy properties, including the galaxy mass–gas metallicity relation. To produce catalogues of simulated DLAs we throw 105 random lines of sight in a composite simulated volume: dark matter haloes with log$(\frac{M_{200}}{ {\rm M}_{\odot }}) \ge 11.5$ are extracted from the Millennium Simulation, while for $9.2 \le \log (\frac{M_{200}}{ \mathrm{M}_{\odot }})\lt 11.5$ we use the Millennium II, and for $8 \le \log (\frac{M_{200}}{\mathrm{M}_{\odot }}) \lt 9.2$ a halo occupation distribution model. At 2 < z < 3, where observational data are more accurate, our fiducial model predicts the correct shape of the column density distribution function, but its normalization falls short of the observations, with the discrepancy increasing at higher redshift. The agreement with observations is significantly improved increasing both the H i masses and the disc radii of model galaxies by a factor of 2, as implemented ‘a posteriori’ in our 2M−2R model. In the redshift range of interest, haloes with $M_{200} \ge {10}^{11} \, \mathrm{M}_{\odot }$ give the major contribution to ΩDLA, and the typical DLA host halo mass is $\sim \!{10}^{11} \, \mathrm{M}_{\odot }$. The simulated DLA metallicity distribution is in relatively good agreement with observations, but our model predicts an excess of DLAs at low metallicities. Our results suggest possible improvements for the adopted modelling of the filtering mass and metal ejection in low-mass haloes.

Di Gioia, Serafina↗

A laser-based sizing/velocimetry technique to investigate the secondary atomization of aluminum gel propellants

A laser-based, forward-scatter diagnostic technique, employing a single laser sheet, has been developed to simultaneously measure the size and velocity of individual 10-150 micron droplets in a dilute polydisperse droplet stream (less than 1000 particles/cc) and to detect the presence of burning aluminum in these same droplets. Spectral emission from aluminum vapor in the 390-400 nm wavelength region is used as an indication of burning aluminum. The technique utilizes a 4-mm uniformly illuminated probe volume, eliminating trajectory-dependent particle sizing and size-dependent system detection bias. Particle sizing is based on a correlation of particle size with near-forward scattered light intensity. Calculations show average particle sizing variation to be within 3.5% over the expected range of refractive indices. Calibrations using a range of optical pinholes (10-100 micron) were used to verify the above sizing correlation.

Mueller, D. C.↗

Imaging Phase Segregation in Nanoscale Li x CoO 2 Single Particles

Li x CoO 2 (LCO) is a common battery cathode material that has recently emerged as a promising material for other applications including electrocatalysis and as electrochemical random access memory (ECRAM). During charge– discharge cycling LCO exhibits phase transformations that are significantly complicated by electron correlation. While the bulk phase diagram for an ensemble of battery particles has been studied extensively, it remains unclear how these phases scale to nanometer dimensions and the effects of strain and diffusional anisotropy at the single-particle scale. Understanding these effects is critical to modeling battery performance and for predicting the scalability and performance of electrocatalysts and ECRAM. Here we investigate isolated, epitaxial LiCoO 2 islands grown by pulsed laser deposition. After electrochemical cycling of the islands, conductive atomic force microscopy (c-AFM) is used to image the spatial distribution of conductive and insulating phases. Above 20 nm island thicknesses, we observe a kinetically arrested state in which the phase boundary is perpendicular to the Li-planes; we propose a model and present image analysis results that show smaller LCO islands have a higher conductive fraction than larger area islands, and the overall conductive fraction is consistent with the lithiation state. Thinner islands (14 nm), with a larger surface to volume ratio, are found to exhibit a striping pattern, which suggests surface energy can dominate below a critical dimension. When increasing force is applied through the AFM tip to strain the LCO islands, significant shifts in current flow are observed, and underlying mechanisms for this behavior are discussed. The c-AFM images are compared with photoemission electron microscopy images, which are used to acquire statistics across hundreds of particles. Finally, the results indicate that strain and morphology become more critical to electrochemical performance as particles approach nanometer dimensions.

25 ENERGY STORAGE↗

First principles calculations in support of Pu aging: calculating the effects of lattice imperfections on thermodynamics

Plutonium (Pu) has, in theory, well defined crystal structures: its atoms are arranged in regular spatial patterns. But Pu is radioactive, and as its nuclei decay those regular spatial patterns are interrupted. The interruptions are lattice imperfections, which are known to affect how materials respond to their environment. To adequately model Pu, we need to know which lattice imperfections are present, how they interact with each other, and how they affect the material’s response to its environment. The work presented here aims to use density functional theory (DFT) calculations to begin to answer the latter, in particular, how individual lattice imperfections affect measurable effects including thermal expansion (the change in volume in response to a change in temperature), heat capacity (the amount of thermal energy needed to change a material’s temperature), and elastic moduli (a material’s resistance to applied stresses). Pu poses many computational challenges. The $\textit{f}$ electrons require special attention. Of all the elements, Pu has the largest number of electrons that must be included in the calculations. Thermal effects require calculating the phonons (the lattice vibrations), which for systems containing lattice imperfections demand large, complex computational cells - but computational resources limit the size and complexity. With careful restructuring of how the calculations are performed, all these challenges have been met to enable calculations that provide insight into how lattice imperfections affect Pu’s response to its environment. Reported here are the computational challenges and the advances developed to meet them, along with the first results showing the strong effect that one prototype lattice imperfection (an interstitial Pu atom in a delta-phase Pu lattice) has on Pu’s response to its environment.

36 MATERIALS SCIENCE↗