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At least 919 records · Page 51

Experimental validation of thermodynamic mixture rules at extreme pressures and densities

Accurate modeling of a mixed material Equation of State (EOS) at high pressures (~1 to 100 Mbar) is critical for simulating inertial confinement fusion and high energy density systems. Here, this paper presents a comparison of two mixing rule models to the experiment to assess their applicability in this regime. The shock velocities of polystyrene, aluminum, and nickel aluminide (NiAl) were measured at a shock pressure of ~3 TPa (~30 Mbar) on the Omega EP laser facility (Laboratory for Laser Energetics, University of Rochester, New York). The resultant shock velocities were compared to those derived from the RAGE (Eulerian) hydrodynamics code to validate various mixing rules used to construct an EOS for NiAl. The simulated shock transit time through the sample (Al or NiAl) matched the measurements to within the ±45ps measurement uncertainty. The law of partial volume (Amagat) and the law of partial pressure (Dalton) mixture rules provided equally good matches to the NiAl shock data. Other studies showed that the Amagat mixing rule is superior, and we recommend it since our results also show a satisfactory match. In conclusion, the comparable quality of the simulation to data for the Al and NiAl samples implies that a mixture rule can supply an EOS for plasma mixtures with adequate fidelity for simulations where mixing takes place, such as advective mix in an Eulerian code or when two materials are mixed together via diffusion, turbulence, or other physical processes.

36 MATERIALS SCIENCE↗

Cinematic reflectometry using QIKR, the quite intense kinetics reflectometer

The Quite Intense Kinetics Reflectometer (QIKR) will be a general-purpose, horizontal-sample-surface neutron reflectometer. Reflectometers measure the proportion of an incident probe beam reflected from a surface as a function of wavevector (momentum) transfer to infer the distribution and composition of matter near an interface. The unique scattering properties of neutrons make this technique especially useful in the study of soft matter, biomaterials, and materials used in energy storage. Exploiting the increased brilliance of the Spallation Neutron Source Second Target Station, QIKR will collect specular and off-specular reflectivity data faster than the best existing such machines. It will often be possible to collect complete specular reflectivity curves using a single instrument setting, enabling “cinematic” operation, wherein the user turns on the instrument and “films” the sample. Samples in time-dependent environments (e.g., temperature, electrochemical, or undergoing chemical alteration) will be observed in real time, in favorable cases with frame rates as fast as 1 Hz. Cinematic data acquisition promises to make time-dependent measurements routine, with time resolution specified during post-experiment data analysis. This capability will be deployed to observe such processes as in situ polymer diffusion, battery electrode charge–discharge cycles, hysteresis loops, and membrane protein insertion into lipid layers.

47 OTHER INSTRUMENTATION↗

Understanding the mechanisms of amorphous creep through molecular simulation

Significance The individual and collective molecular displacements in an amorphous solid undergoing plastic deformation are simulated by an atomistic method that allows incremental motions to be observed over a time window of fractions of seconds. Because the timescale matches well with the conditions of experimental measurements, simulation details provide dynamical evidence for the fundamental mechanisms of amorphous creep. In particular, knowledge of the interplay between diffusion (flow) and mechanical deformation processes enables us to explain the stress and temperature behavior of the experimental data as well as the validity of model descriptions of molecular mechanisms in terms of spatially and temporally heterogeneous fluctuations.

42 ENGINEERING↗

Pseudoelasticity at Large Strains in Au Nanocrystals

Pseudoelasticity in metals is normally associated with phase transformations (e.g., shape memory alloys) but has recently been observed in sub-10 nm Ag nanocrystals that rapidly recovered their original shape after deformation to large strains. The discovery of pseudoelasticity in nanoscale metals dramatically changes the current understanding of the properties of solids at the smallest length scales, and the motion of atoms at surfaces. However, it remains unclear whether pseudoelasticity exists in different metals and nanocrystal sizes. The challenge of observing deformation at atomistic to nanometer length scales has prevented a clear mechanistic understanding of nanoscale pseudoelasticity, although surface diffusion and dislocation-mediated processes have been proposed. We further the understanding of pseudoelasticity in nanoscale metals by using a diamond anvil cell to compress colloidal Au nanocrystals under quasihydrostatic and nonhydrostatic pressure conditions. Nanocrystal structural changes are measured using optical spectroscopy and transmission electron microscopy and modeled using electrodynamic theory. Here, we reveal that 3.9 nm Au nanocrystals exhibit pseudoelastic shape recovery after deformation to large uniaxial strains of up to 20%, which is equivalent to an ellipsoid with an aspect ratio of 2. Nanocrystal absorbance efficiency does not recover after deformation, which suggests that crystalline defects may be trapped in the nanocrystals after deformation.

36 MATERIALS SCIENCE↗

Iron- and aluminium-induced depletion of molybdenum in acidic environments impedes the nitrogen cycle: Mo depletion by Fe/Al precipitation at ORR

Anthropogenic nitrate contamination is a serious problem in many natural environments. Nitrate removal by microbial action is dependent on the metal molybdenum (Mo), which is required by nitrate reductase for denitrification and dissimilatory nitrate reduction to ammonium. The soluble form of Mo, molybdate (MoO 4 2- ), is incorporated into and adsorbed by iron (Fe) and aluminium (Al) (oxy) hydroxide minerals. In this paper, we used Oak Ridge Reservation (ORR) as a model nitrate-contaminated acidic environment to investigate whether the formation of Fe- and Al-precipitates could impede microbial nitrate removal by depleting Mo. We demonstrate that Fe and Al mineral formation that occurs as the pH of acidic synthetic groundwater is increased, decreases soluble Mo to low picomolar concentrations, a process proposed to mimic environmental diffusion of acidic contaminated groundwater. Analysis of ORR sediments revealed recalcitrant Mo in the contaminated core that co-occurred with Fe and Al, consistent with Mo scavenging by Fe/Al precipitates. Nitrate removal by ORR isolate Pseudomonas fluorescens N2A2 is virtually abolished by Fe/Al precipitate-induced Mo depletion. Lastly, the depletion of naturally occurring Mo in nitrate- and Fe/Al-contaminated acidic environments like ORR or acid mine drainage sites has the potential to impede microbial-based nitrate reduction thereby extending the duration of nitrate in the environment.

54 ENVIRONMENTAL SCIENCES↗

US-UK Collaboration on Fossil Energy Advanced Materials: Task 1—Steam Oxidation

This presentation goes over the following from the US-UK collaboration on Fossil Energy Advanced Materials: Task 1, Steam Oxidation: US-led or co-led deliverables, Phase II products (US), 2011-present, Phase III products, Phase III Plan, an explanation of sCO 2 compared with sH 2 O, an explanation of Ni-base Alloys, an explanation of 300 Series (18Cr-8Ni)/E-Brite, an explanation of the typical Microchannel HX Fabrication process, and an explanation of diffusion bonded Ni-base superalloys.

02 PETROLEUM↗

Advancing Understanding of Fission Gas Behavior in Nuclear Fuel through Leadership Class Computing

This report describes the outcome of the pilot SciDAC project jointly funded by the DOE Office of Nuclear Energy and the DOE Office of Science, Advanced Scientific Computing Research to advance understanding of fission gas behavior in nuclear fuel. The computational approach involved utilizing both a bottom up and top down multiscale materials modeling to evaluate the processes of xenon fission gas diffusion, xenon clustering and precipitation and the mechanisms of fission gas resolution by energetic fission fragments in uranium dioxide nuclear fuel. The computer science and applied mathematics research activities were focused on optimizing the uranium – oxygen – xenon interatomic potential implementation in the LAMMPS molecular dynamics code for large-scale simulations of fission gas resolution, in addition to improvements in visualization of accelerated molecular dynamics simulations and performance optimization of the Xolotl continuum cluster dynamics with a new grouping scheme to reduce the computational cost of modeling very large fission gas bubbles containing more than 10,000 xenon atoms. The most impactful result from this project stems from a systematic series of atomistic molecular dynamics to evaluate fission gas resolution from xenon bubbles that, combined with the fission product yields and consideration of electron-phonon coupling, informed a first principles model that predicts the magnitude of fission gas resolution in good agreement with empirical estimates.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

ION INJECTION AT QUASI-PARALLEL SHOCKS SEEN BY THE CLUSTER SPACECRAFT

Collisionless shocks in space plasma are known to be capable of accelerating ions to very high energies through diffusive shock acceleration (DSA). This process requires an injection of suprathermal ions, but the mechanisms producing such a suprathermal ion seed population are still not fully understood. We study acceleration of solar wind ions resulting from reflection off short large-amplitude magnetic structures (SLAMSs) in the quasi-parallel bow shock of Earth using in situ data from the four Cluster spacecraft. Nearly specularly reflected solar wind ions are observed just upstream of a SLAMS. The reflected ions are undergoing shock drift acceleration (SDA) and obtain energies higher than the solar wind energy upstream of the SLAMS. Our test particle simulations show that solar wind ions with lower energy are more likely to be reflected off the SLAMS, while high-energy ions pass through the SLAMS, which is consistent with the observations. The process of SDA at SLAMSs can provide an effective way of accelerating solar wind ions to suprathermal energies. Therefore, this could be a mechanism of ion injection into DSA in astrophysical plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparison of plug flow and multi-node stratified tank modeling approaches regarding computational efficiency and accuracy

Residential water heaters contain water stratified by temperature-driven density differences. This implies that a water tank can reach a state in which the top and bottom sections have different temperatures, unless mixing happens. A high degree of thermal stratification can improve the efficiency of some water heaters, by saving the amount of energy required for the heat-up process. Studies of stratification became popular in the 1970s and it remains an active research topic today. The research has led to the development of different models and techniques to better predict and define a stratified tanks behavior. By comparing these models and techniques used previously to describe thermal stratification, the phenomenon could be better understood, exploited, and used to increase efficiency and thermal energy capacity in modern water tanks. From the existing models, we found the one-dimensional standard plug-flow and a multi node model to be appropriate for analyzing the processes of the heat up and cool-down in a water tank. These two models are based on energy balances. This work involved comparing the accuracy and computational effort needed to implement these models. To assess accuracy, we compared both types of existing models to experimental data (also collected in this work) which included a heat up process using an external heat pump. This external process included a layering process that has an eddy diffusivity at five times the rate of thermal diffusion. For this project, we implemented the models in MATLAB, the multi-paradigm numerical computing environment. We quantified model accuracy using the root mean squared error between modeled data and experimental data for six measured tank temperatures. Comparing the accuracy and the computational time taken to run the simulation provides a method to contrast the performance of each model and a way to rate it. The multi node model was run using from 6 to 96 spatial nodes; the plug flow model was run using 1 to 0.001 º C temperature bin sizes. Additionally, timesteps were varied from 4 to 236 s. The results quantify the tradeoff between accuracy and computational time, providing guidance for simulations to intelligently select the best model type and simulation parameters. This research can be used to validate the pre-existing models and possibly improve the modern water tank.

Bulnes, Fernando Karg↗

Slides for MS&T2022: Carbon-Carbon Composites from 3D Printed Preforms Graphitized by Electric Field Assisted Sintering

Formation of Carbon-Carbon (C-C) composite materials requires putting a carbon fiber preform through a cycle of densification, carbonization, and graphitization. This cycle is then repeated until the desired properties are achieved. The graphitization phase is particularly energy demanding as it involves heating the components to in excess of 2000°C. In traditional furnaces this is also quite time consuming as typical heating rates are low, and the actual heat treatment may be limited by component dimensions, as heat is conducted throughout the part primarily by thermal diffusion. Joule heating by means of Electric Field Assisted Sintering (EFAS) systems enables high heating rates and causes the part to be heated from the inside, which eliminates the thermal diffusion time constraint. In our process, C-C composites are formed by pyrolyzation of 3D-printed carbon fiber preforms, vacuum infiltration of naphthalene based mesophase pitch, and carbonization. The part is then graphitized in the EFAS system. By this method graphitization of the composite matrix was achieved in less than an hour. A part density of greater than 1.6g/cc (up to 1.9g/cc demonstrated) was achieved after only two rounds of infiltration and a single graphitization. Overall the process took less than a week which is significantly faster than traditional methods. Optical microscopy and XRD results are discussed to elucidate the internal porosity and characterize the degree of graphitization. Testing was performed showing the impact on fiber direction to electrical and thermal properties of the final part.

36 MATERIALS SCIENCE↗

Radiological Performance Modeling: Platform Comparison

Zapadnoe Uranium Mill Tailings Site, Pridneprovsky Chemical Plant Ukraine: Two exposure scenarios were utilized to develop performance assessment models in GoldSim and NORMALYSA. The first scenario is an onsite worker exposed to radioactivity through external ground irradiation as well as radon and radioactive dust inhalation. The second being an offsite Resident 300 years after institutional control exposed through the ingestion of garden vegetables irrigated by contaminated ground water, ingestion of fish from Konoplyanka River, and agricultural activities in contaminated garden. NORMALYSA utilizes a modular interface to connect extensive pre-created modules to develop contaminant transport and risk assessment models for safety assessments and performance assessments at NORM and legacy sites. Developed by Facilia AB, the program was tested with the creation of the Zapadnoe model under the International Atomic Energy Agency MODARIA Il Working Group 1 (WG1). Default values are provided for input parameters where site specific data and distributions lack. Probabilistic simulations and inputs are limited to parameters with assigned Gaussian probability functions. Similar results for transient worker inhalation dose were found in comparison with the Zapadnoe GoldSim model. However, the NORMALYSA model has results larger by an order of magnitude for external radiation in the transient worker and for aquatic food ingestion, inhalation, and garden food ingestion to the resident. Performance Assessment Modeling: Radiological performance models promote good management and support in remediation and environmental decision making by optimizing radioactive waste disposal site performance. a performance assessment model of the Zapadnoe uranium mill tailings site and a model for calculating authorized limits at Los Alamos National Laboratory are created to demonstrate and highlight the respective capabilities of three modeling platforms: GoldSim, NORMALYSA, and RESRAD-Onsite. GoldSim is a general-purpose modeling platform with the ability to simulate site-specific FT radionuclide transport and risk assessment using a graphical interface to create and link elements that act as indivisible building blocks of the model. The Zapadnoe performance assessment model created in GoldSim is composed of input parameters collected from site specific parameters from WG1 as well as standard assumptions seen in the Generic PA Model from Neptune and Company. The multivariate Zapadnoe simulation contains both deterministic and probabilistic simulation capabilities with the ability to quantitatively represent the uncertainty and associated risks of the site via the Monte Carlo simulation method. Model parameters, documentation, and assumptions are built directly into the model creating a transparent, reproducible, and more purposeful site specific model. To demonstrate this, an ingestion of water pathway was included in addition to the exposure pathways included in the NORMALYSA model. GoldSim offers a wide variety of probability distributions to choose from as well as many tools to visualize the uncertainty of the models and explore which pathways and radionuclides dominate dose. In contrast to the NORMALYSA model, the GoldSim model uses dynamic simulation to calculate tritium concentrations. Authorized limits support the evaluation of radiological health effects from radionuclides present in bulk contaminated soil in order to assist in the process of clearing land for release under different uses. Calculations of authorized limits in RESRAD-Onsite and GoldSim models support the evaluation for 15 radionuclides using a residential exposure scenario, indoor and outdoor inhalation of dust and vapor phase radionuclides (tritium), incidental soil ingestion, and ingestion grown fruits and Vegetables. RESRAD-Onsite, developed by Argonne National Laboratory is a dedicated computer code for calculating radiation doses and cancer risks to an individual located on top of radioactively contaminated soils. It can also be used to provide guidelines for deriving radionuclide soil levels corresponding to a specific dose criterion. The menu driven user interface facilitates selection of radionuclides and soil concentrations, as well as defines parameter values related to materials, environmental factors, and exposure pathways. The program contains radionuclide-specific data such as dose conversion factors and risk coefficients, as well as soil-water partition coefficients and transfer factors for biotic media. The GoldSim model successfully emulates the RESRAD-Onsite code using identical radiological decay and ingrowth factors, radiation dose conversion factors, and other input parameters. DE EEDE ETS Each model supports dynamic modeling of radionuclide ingrowth and decay over time, and integrate this capability with the transport of radionuclides in the environment via processes such as advection and/or diffusion in fluids, or within porous solid media, The applicability of each program is heavily dependent on project context. In the context of developing Authorized Limits, RESRAD-Onsite may be a more desirable option as it was developed for this particular application. For simple disposal or legacy sites or sites that do not need site-specific model structure, NORMALYSA may be a desirable modeling platform, GoldSim can be used to model any problem for which RESRAD or NORMALYSA is applicable, but its strength lies in its flexibility, analytical, and probabilistic capabilities.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Density Effects on Lock Exchange Flow During a DCC

The High Temperature Test Facility (HTTF) is a scaled, electric model at Oregon State University (OSU) of the Modular High Temperature Gas Reactor (MHTGR) by General Atomics. There are a few major differences between the design and the OSU facility. In the HTTF the reactor pressure vessel and the reactor cavity are in two separate tanks connected by a crossover duct similar to the crossover duct that would be seen between the reactor core and the steam generator in the MHTGR. This feature allows for the facility to open two main break valves simulating a Double-Ended Guillotine Break (DEGB) of the cross over duct, synonymous to a crossover duct break in the MHTGR. The density gradient driven flow phenomena in the HTTF duct can then be studied further. This break would cause a depressurization of the reactor and a loss of flow. It is called the Depressurized Loss of Forced Convection Accident (D-LOFC), also known as the Depressurized Conduction Cool-Down Event for High Temperature Gas Reactors (HTGRs) because heat removal is by conduction through the core and radiation out of the vessel. The HTTF was built and scaled to maintain the highest accuracy for the DCC. Prototypical temperatures with an inlet temperature of 259 deg. C and an outlet temperature of 687 deg. C are maintained in the HTTF. The temperature profile is also maintained in the smaller volume by using a ceramic core. The HTTF uses graphite heaters because the resistive heat produced does not change significantly with temperature . In order to produce a facility of similar temperatures within the allotted budget, sacrifices had to be made in other areas. The HTTF is scaled one-fourth in diameter, one-fourth in height and one-eighth in pressure of the MHTGR. There are also a few limitations for the HTTF. While in the MHTGR, the cavity is filled with air, the HTTF uses highly pure Nitrogen and does not have the ability to simulate a full depressurization. The DCC event is traditionally comprised of multiple stages: depressurization, molecular diffusion and natural circulation. However, this traditional interpretation ignores lock exchange flow which will occur immediately following depressurization and could have significant consequences in the reactor. It was found that the traditional model underestimates the amount of air ingress by at least 660 times according to Oh and Kim in their theoretical research of air ingress. Molecular diffusion also decreases with stratification. Any model that specifies the gases are stratified has further underestimated the air ingress of the DCC event. In addition, molecular diffusion is a much slower process, allowing the reactor to shut down and cool off considerably from operating temperatures. Thus, understanding lock exchange flow, the air ingress concentrations and the time scale is critical to MHTGR research and licensing. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗

Structural Evolution of Layered Manganese Oxysulfides during Reversible Electrochemical Lithium Insertion and Copper Extrusion

The electrochemical lithiation and delithiation of the layered oxysulfide Sr 2 MnO 2 Cu 4-δ S 3 has been investigated by using a combination of in situ powder X-ray diffraction and ex situ neutron powder diffraction, X-ray absorption and 7 Li NMR spectroscopy, together with a range of electrochemical experiments. Sr 2 MnO 2 Cu 4-δ S 3 consists of [Sr 2 MnO 2 ] perovskite-type cationic layers alternating with highly defective antifluorite-type [Cu 4-δ S 3 ] (δ ≈ 0.5) anionic layers. It undergoes a combined displacement/intercalation (CDI) mechanism on reaction with Li, where the inserted Li replaces Cu, forming Li 4 S 3 slabs and Cu + is reduced and extruded as metallic particles. For the initial 2-3% of the first discharge process, the vacant sites in the sulfide layer are filled by Li; Cu extrusion then accompanies further insertion of Li. Mn 2.5+ is reduced to Mn 2+ during the first half of the discharge. The overall charging process involves the removal of Li and re-insertion of Cu into the sulfide layers with re-oxidation of Mn 2+ to Mn 2.5+ . However, due to the different diffusivities of Li and Cu, the processes operating on charge are quite different from those operating during the first discharge: charging to 2.75 V results in the removal of most of the Li, little reinsertion of Cu, and good capacity retention. A charge to 3.75 V is required to fully reinsert Cu, which results in significant changes to the sulfide sublattice during the following discharge and poor capacity retention. This detailed structure-property investigation will promote the design of new functional electrodes with improved device performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Percolating porosity in ultrafine grained copper processed by High Pressure Torsion

Defect structures in copper of different purity (nominally 99.99 and 99.999 wt. %) deformed via High Pressure Torsion (HPT) with varying processing parameters are investigated utilizing the radiotracer diffusion technique. While the degree of deformation is kept constant, the effects of applied quasi-hydrostatic pressure, processing temperature, post-deformation annealing treatments, and of the impurity concentration on the deformed samples are analyzed in terms of the formation of interconnected internal porosity. Furthermore, the anisotropy of the developing porosity network is examined. The porosity channels occurred to be interconnected along the direction parallel to the surface normal with a volume fraction of the order of a few ppm while no long-range penetration along the internal porosity could be detected when measured along the azimuthal or radial directions of a HPT processed sample.

36 MATERIALS SCIENCE↗

Unveiling the Origin of Morphological Instability in Topologically Complex Electrocatalytic Nanostructures

Coarsening and degradation phenomena in metals have largely focused on thermally driven processes, such as bulk and surface diffusion. However, dramatic coarsening has been reported in high-surface-area, nanometer-sized Pt-based catalysts during potential cycling in an electrolyte at room temperature─a temperature too low for the process to be explained purely by surface mobility values measured in both vacuum and electrolytes (∼10 –22 and ∼10 –18 cm 2 /s, respectively). This morphological evolution must be due to a different mechanism for mass transport that is sensitive to electrochemical conditions (e.g., electrolyte composition, potential limits, and scan rate). However, there have been no notable studies of electrochemically induced coarsening in nanometer-sized electrocatalysts. Here, we unveil the origins of coarsening in an electrolyte through coupled in situ experiments and atomistic kinetic Monte Carlo (kMC) simulations. Our work demonstrates electrochemical coarsening is driven by two concurrent mechanisms that can be explained at the atomistic level: (i) dissolution/redeposition during the reduction of an oxidized species and (ii) rapid surface diffusion of undercoordinated atoms.

gold↗

LUNUS, Version 0.1a

LUNUS software for generating 3D maps of diffuse scattering from macromolecular X-ray crystallography diffraction images. A set of tools needed for advanced refinement of crystal structures and crystallographic charge density models. Includes tools for processing X--ray diffraction images, charge density maps, and structure factors for analysis of diffuse X-ray scattering and charge density variations in crystallography. Specific methods include: elementary algebraic operations on images and 3D lattices; fourier transform of images and 3D lattices; image processing to measure diffuse intensity; crystallographic refinement; and 3D integration of diffuse intensity.

Wall, Michael↗

LUNUS, Version 0.1a

LUNUS software for generating 3D maps of diffuse scattering from macromolecular X-ray crystallography diffraction images. A set of tools needed for advanced refinement of crystal structures and crystallographic charge density models. Includes tools for processing X--ray diffraction images, charge density maps, and structure factors for analysis of diffuse X-ray scattering and charge density variations in crystallography. Specific methods include: elementary algebraic operations on images and 3D lattices; fourier transform of images and 3D lattices; image processing to measure diffuse intensity; crystallographic refinement; and 3D integration of diffuse intensity.

Wall, Michael↗