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DOE OSTI2021

Lean-Stratified Combustion System with Miller Cycle for Downsized Boosted Application - Part I

Automotive manufacturers relentlessly explore engine technology combinations to achieve reduced fuel consumption under continued regulatory, societal and economic pressures. For example, technologies enabling advanced combustion modes, increased expansion to effective compression ratio, and reduced parasitics continue to be developed and integrated within conventional and hybrid propulsion strategies across the industry. A high-efficiency gasoline engine capable for use in conventional or hybrid electric vehicle platforms is highly desirable. This paper is the first to two papers describing the development of a combustion system combining lean-stratified combustion with Miller cycle for downsized boosted applications. The work was completed under a multi-year US DOE project. The goal was to define a light-duty engine package capable of achieving a 35% fuel economy improvement at US Tier 3 emission standards over a naturally aspirated stoichiometric baseline vehicle. A multi-mode combustion system was developed enabling highly efficient lean-stratified operation at light-load and stoichiometric Miller-cycle operation at mid- to highloads. Some of the unique challenges in synergistically combining the two concepts are highlighted in this paper. Here, a central direct-injection four-valve layout was designed with high-tumble ports and a bowl-in-piston capable of stable operation under highly dilute (lean plus EGR) mixtures when properly matched to fuel spray characteristics, a multiple-injection strategy, and a high-energy ignition system. Other challenges specific to meeting exhaust emissions requirements with a high-efficiency engine are also explored in this study. In this Part 1 of the paper, the single-cylinder combustion system design, analysis, and testing is described. Multicylinder engine system design, analysis and development is described in Part 2 of the paper.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

A Study of Propane Combustion in a Spark-Ignited Cooperative Fuel Research (CFR) Engine

Liquefied petroleum gas (LPG), whose primary composition is propane, is a promising candidate for heavy-duty vehicle applications as a diesel fuel alternative due to its CO 2 reduction potential and high knock resistance. To realize diesel-like efficiencies, spark-ignited LPG engines are proposed to operate near knock-limit over a wide range of operating conditions, which necessitates an investigation of fuel-engine interactions that leads to end-gas autoignition with propane combustion. This work presents both experimental and numerical studies of stoichiometric propane combustion in a sparkignited (SI) cooperative fuel research (CFR) engine. Engine experiments are initially conducted at different compression ratio (CR) values, and the effects of CR on engine combustion are characterized. A three-pressure analysis (TPA) model based on the two-zone combustion concept is developed in GT-Power and validated using test results to estimate in-cylinder wall temperatures, residual gas fraction, etc. This model is further utilized to examine end-gas chemistry by enabling the SI turbulent flame combustion and unburned gas chemical kinetics modules. Finally, a three-dimensional (3D) computational fluid dynamic (CFD) model of the CFR engine is developed in CONVERGE, where the G-equation and SAGE detailed chemical kinetics models are implemented for combustion modeling. Here, a 153 species reduced chemical kinetics mechanism derived from the detailed NUIGMech1.1 mechanism based on the ignition delay and laminar flame speed (LFS) studies is used to generate an LFS lookup table and to describe end-gas autoignition chemistry. Multi-cycle Reynolds-averaged Navier-Stokes (RANS) simulations are then performed for the tested CRs, and the numerical model is shown to be capable of predicting the propane combustion characteristics, particularly the end-gas autoignition behavior.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2022

Experimental and Numerical Study on the Effect of Nitric Oxide on Autoignition and Knock in a Direct-Injection Spark-Ignition Engine

We report Nitric Oxide (NO) can significantly influence the autoignition reactivity and this can affect knock limits in conventional stoichiometric SI engines. Previous studies also revealed that the role of NO changes with fuel type. Fuels with high RON (Research Octane Number) and high Octane Sensitivity (S = RON – MON (Motor Octane Number)) exhibited monotonically retarding knocklimited combustion phasing (KL-CA50) with increasing NO. In contrast, for a high-RON, low-S fuel, the addition of NO initially resulted in a strongly retarded KL-CA50 but beyond the certain amount of NO, KL-CA50 advanced again. The current study focuses on same high-RON, low-S Alkylate fuel to better understand the mechanisms responsible for the reversal in the effect of NO on KLCA50 beyond a certain amount of NO. Experiments were conducted to measure the responses of KL-CA50 and trace-autoignition CA50, the latter being indicative of CA50 at which end-gas autoignition starts to become measurable from the apparent heat-release rate. Chemical-kinetics simulations were conducted to reveal the role of NO for end-gas autoignition, with a specific focus on sequential autoignition in a thermally stratified end-gas. The simulation results reveal that the magnitude of low-temperature heat release (LTHR) generally increases with NO. However, the relative importance of NO for enhancing LTHR diminishes when the LTHR inherent to a fuel’s chemistry is strong, such as at lower temperatures in a thermal boundary layer. This rendered more uniform LTHR within a hypothetical thermal boundary and led to a more sequential (i.e. slower) autoignition event. It was also revealed that a change in compression ratio influences the importance of intermediate-temperature heat release (ITHR) due to changes of the temperature-pressure history of the end-gas. Together with the condition where end-gas autoignition occurs more sequentially, the shorter time spent in LTHR and ITHR regime can counter the increase in autoignition reactivity at high NO levels and allow KLCA50 to advance

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Simultaneous Reduction of NOx and Fuel Consumption for Off-Road Powertrains

Simultaneously reducing criteria pollutants and fuel consumption is important for clean air and improving vehicle total cost of ownership. The goal of this effort was focused on a 90% NOx reduction and 10% fuel savings for an off-road 407 kW diesel engine. The baseline was a production Fiat Powertrain 13L engine and aftertreatment system meeting 0.4 g/kW-hr NOx. The baseline system was quantified over the NRTC, RMC, new low load cycle and five field cycles. A next generation engine was built incorporating several fuel-efficient design features, including a higher compression ratio, increased fuel-rail pressure, low-friction piston rings, and a high-efficiency variable-geometry turbocharger. Cylinder deactivation and EGR pump technologies were added to this engine as well. The combination was optimized prior to adding advanced aftertreatment systems, showing the trade-off of engine out NOx and exhaust temperature. Two next-generation catalyst technologies were employed into a LO-SCR plus main SCR system, both with and without an electric heater upstream of the LO-SCR. These catalysts were hydrothermally aged to simulate significant field use. Dual SCR dosing with newly developed controls played a critical role in achieving the proper split between the upstream LO-SCR and the downstream main SCR. Adding a next generation mixer for the downstream SCR proved essential in obtaining the final results. The optimal configuration required adding an electric heater to elevate the exhaust temperature at the LO-SCR for early cycle NOx reduction. The final results showed a 94.8% NOx reduction and 15.7% fuel savings on the composite NRTC.

McCarthy, James [Eaton Corporation]↗

DOE OSTI2020

Development of a Physics-Based Combustion Model for Engine Knock Prediction

The objective of this project is to improve the prediction of engine knock by developing a new combustion modeling framework. Engine knock is a limiting factor to constrain the increase of fuel efficiency for spark ignition (SI) engines in most passenger cars. Efforts to increase fuel efficiency, increasing the compression ratio or downsizing, lead to the increase in the tendency of the knock occurrence. The knock is an undesired ignition of the end-gas, unburned fuel/air mixture ahead of the spark-ignited premixed flame, resulting in rapid in-cylinder pressure rises and engine damages. The combustion modeling framework developed in this project can consider turbulence-chemistry interactions during end-gas ignition, while using a reasonably detailed chemical mechanism developed for ignition and combustion reactions under engine relevant conditions, and the subtle characteristics of spark-ignited flame propagation. It is developed in the context of large eddy simulation (LES), which can capture stochastic in-cylinder processes. The developed model is incorporated into a commercial software for engine simulation, CONVERGE CFD, as a user defined function, and validated. Engine knock and knock-free experiments as well as direct numerical simulation (DNS) of end-gas ignition in homogeneous turbulence are performed to help model development and provide data sets for model validation. With further validation, the developed model is expected to advance the predictive capability for engine knock simulations and thus contribute to improving the fuel efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

MULTI-DIMENSIONAL MODELING OF THE CFR ENGINE FOR THE INVESTIGATION OF SI NATURAL GAS COMBUSTION AND CONTROLLED END-GAS AUTOIGNITION

Engine knock and misfire are barriers to pathways leading to high-efficiency Spark-Ignited (SI) Natural Gas engines. The general tendency to knock is highly dependent on engine operating conditions and the fuel reactivity. The problem is further complicated by low emission limits and the wide range of chemical reactivity in pipeline quality natural gas. Depending on the region and the source of the natural gas, its reactivity, described by its methane number (analogous to the octane number for liquid SI fuels) can span from 65 - 95. In order to realize diesel-like efficiencies, SI natural gas engines must be designed to operate at high BMEP near knock limits over a wide range of fuel reactivity. This requires a deep understanding regarding the combustion-engine interactions pertaining to flame propagation and end-gas autoignition (EGAI). However, EGAI, if controlled, provides an opportunity to increase SI natural gas engine efficiency by increasing combustion rate and the total burned fuel, mitigating the effects of the slow flame speeds of natural gas fuels which generally reduce BMEP and increase unburned hydrocarbon emissions. For this reason, in order to study EGAI phenomenon, the present work highlights multi-dimensional computational fluid dynamics (CFD) models of the Cooperative Fuel Research (CFR) engine. The CFR engine models are used to investigate fuel-engine interactions that lead to EGAI with natural gas, including effects of fuel reactivity, engine operating parameters, and exhaust gas recirculation (EGR). A Three-Pressure Analysis, performed with GT-Power, was used to estimate initial and boundary conditions for the three-dimensional CFD model. CONVERGE CFD v2.4 was used for the three-dimensional CFD modeling where the level set G-Equation model and SAGE detailed chemical kinetics solver were used. An assessment of the different modeling approaches is also provided to evaluate their limitations, advantages and disadvantages, and for which situations they are most applicable. Model validation was performed with experimental data taken with a CFR engine over varying compression ratio, CA50, EGR fraction, and IMEP and shows good agreement in Peak Cylinder Pressure (PCP), PCP crank angle, and the location of the 10%, 50%, and 90% mass fraction burned (CA10, CA50, and CA90, respectively). The models can predict the onset crank angle and pressure rise rate for light, medium, and heavy EGAI under a variety of fuel reactivities and engine operating conditions.

Bestel, Diego↗

DOE OSTI2022

The Impact of LPG Composition on Performance, Emissions, and Combustion Characteristics of a Pre-mixed Spark-Ignited CFR Engine

Research on alternative fuels has made significant progress as demands for cleaner and more efficient engine operation intensifies. Liquefied petroleum gas (LPG) can offer a potential alternative fuel route in the Diesel fuel dominated heavy-duty transportation sector due to its low cost, high anti-knock limit relative to gasoline, and reduced emission levels. In this work, experimental investigations are performed to study the effects of LPG compositions on performance, emissions, and combustion behavior of a spark-ignited (SI) cooperative fuel research (CFR) engine under stoichiometric conditions. Four LPG blends (chemically pure propane, a representative US blend, HD-5, and a representative European blend) representing the present LPG market are chosen. The impact of fuel composition is studied under different compression ratios (CR), ranging from 7:1 to 10:1 with one-unit increments, and at constant engine speed, intake manifold air pressure (IMAP) and 50% burn crank angle (CA50). The results show that fuel composition has minimal effect on engine efficiency over the CR range 7:1 to 10:1. Engine-out emissions are substantially affected by fuel compositions with the representative European blend indicating higher unburned hydrocarbon (UHC) emissions, particularly at higher CR. The representative US blend emits the lowest brake specific CO (bsCO) averaged over the tested CR range. With the increase of CR, end-gas autoignition intensifies for all blends and the representative European blend demonstrates the highest knock intensity of all tested blends, due to the presence of the more reactive fuel component, n-butane.

Fosudo, Toluwalase↗

DOE OSTI2021

Impact on Cycle Efficiency of Small CHP Plants from Increasing Firing Temperature Enabled by AM of Turbine Blades

Combined Heat and Power (CHP) systems are gaining popularity because of their potential for high overall thermodynamic efficiency and increased need for distributed power generation. Most CHP systems include a gas turbine for electricity generation and a heat recovery steam generator (HRSG) for steam generation. The steam can be used to power a steam turbine for additional electricity generation or to drive rotating equipment, for space heating, for absorption chillers, etc. A CHP cycle configuration is often driven by the ‘principal’ utility for the facility that it services; steam or electricity. In either case, performance improvements in the gas turbine have the potential to increase the steam and power output from the cycle, which is a direct result of improvements in the gas turbine efficiency and power output. One possible opportunity to improve an existing gas turbine’s performance is to increase the firing temperature with improved turbine cooling and increased compression ratio.<br>In this study, the impact on CHP cycle performance from increasing the turbine firing temperature by 100 °C and improving the turbine blade cooling for a 6-MW scale gas turbine is estimated using an analytical cooled gas turbine model and a steam cycle model. A sensitivity analysis was performed to understand the impact of increasing the internal cooling effectiveness, thermal barrier coating performance and blade material upgrades on gas turbine and CHP cycle efficiency. The impacts of turbine blade cooling improvements were studied for three common CHP cycle configurations identified from the literature. Various definitions for CHP cycle efficiency from the literature are used in the comparisons. The results showed that a 100 °C increase in firing temperature can increase the gas turbine efficiency by 1 percentage point without improving cooling effectiveness and add 2 additional percentage points in efficiency by using advanced turbine blades with higher internal cooling efficiency. Studied engine upgrades showed potential for increasing the CHP cycle efficiency by 3 percentage points while increasing the steam generation rate by 8%.<br>

Uysal, Selcuk Can↗

DOE OSTI2022

System and method for engine control with pressure reactive device to control combustion timing

The present disclosure relates to a system for controlling ignition of an intake charge directed into an internal combustion engine. The system may have a movable component operably associated with at least one of a piston of the engine or a combustion chamber of the engine. The movable component may be tuned to deflect in response to a predetermined pressure being reached in a cylinder in which the piston is housed. The movable component operates to deflect in response to the predetermined pressure being reached in the cylinder as the piston travels toward top dead center during its compression stroke, to change a compression ratio of the engine.

Killingsworth, Nicholas↗

DOE OSTI2024

Next Generation High Efficiency Boosted Engine Concept

This report summarizes a collaborative research project between Ford Motor Company, FEV North America, and Oak Ridge National Laboratory to develop a next-generation, high-efficiency, boosted spark-ignited engine. The goal was to achieve a 23% improvement in fuel economy and a 15% reduction in engine weight compared to a 2016 Ford F150. The team utilized advanced technologies including a high compression ratio, cooled exhaust gas recirculation (EGR), early intake valve closing, and a novel active pre-chamber ignition system. The final engine prototype met the fuel economy goal and demonstrated a 4.3% weight reduction, with further opportunities identified to reach the full 15% target.

Fuel economy↗

DOE OSTI2021

Efficient Data Compression for 3D Sparse TPC via Bicephalous Convolutional Autoencoder

Real-time data collection and analysis in large experimental facilities present a great challenge across multiple domains, including high energy physics, nuclear physics, and cosmology. To address this, machine learning (ML)-based methods for real-time data compression have drawn significant attention. However, unlike natural image data, such as CIFAR and ImageNet that are relatively small-sized and continuous, scientific data often come in as three-dimensional 3D data volumes at high rates with high sparsity (many zeros) and non-Gaussian value distribution. This makes direct application of popular ML compression methods, as well as conventional data compression methods, suboptimal. To address these obstacles, this work introduces a dual-head autoencoder to resolve sparsity and regression simultaneously, called Bicephalous Convolutional AutoEncoder (BCAE). This method shows advantages both in compression fidelity and ratio compared to traditional data compression methods, such as MGARD, SZ, and ZFP. To achieve similar fidelity, the best performer among the traditional methods can reach only half the compression ratio of BCAE. Moreover, a thorough ablation study of the BCAE method shows that a dedicated segmentation decoder improves the reconstruction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

An Algorithm for Atom-Centered Lossy Compression of the Atomic Orbital Basis in Density Functional Theory Calculations

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn–Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. Here, in this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10 –ϵ , by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree–Fock functional and taking the converged density matrix as input suggest that a threshold of 10 –5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10 –7 , while the compression factor is typically between 2 and 2.5.

basis sets↗

DOE OSTI2021

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Initial Design and Experimental Results of a Novel Near-Isothermal Compressor for Heat Pump Applications

In efforts to increase the efficiency of residential and commercial air conditioners and heat pumps, it is found that the compressor has the highest electrical energy usage of the system. Therefore, it is appropriate to try to increase the efficiency of this component to reduce its energy usage. Another challenge with heat pump design is that some compressor types have drawbacks that make modulation difficult. To answer these challenges, we are developing an isothermal liquid compressor. The compressor uses propylene glycol to compress carbon dioxide. In the compression chamber the propylene glycol can enter either from the bottom to create a liquid piston for compression or it can enter through a spray nozzle at the top of the chamber. In the latter case, heat transfer from the gas to be compressed to the liquid droplets is high. This allows near isothermal operation of the compressor, which increases the efficiency by 17% to 30%, compared to adiabatic compression. In addition, the isothermal liquid compressor enables very efficient and simple part load modulation.Experimental results demonstrating the operation of the liquid compressor are presented. Initial data demonstrated a temperature rise of 7 K at pressure ratios of almost 4. For comparison at the same initial pressure, temperature, and pressure ratio, adiabatic compression would result in a temperature increase of approximately 70 K. Plotting data on a P-h diagram demonstrates that the compression started at superheated state and ended in supercritical state. Testing was later performed with repeated compressions in the superheated region of the P-h diagram at liquid flow rates of 2 x 10-3 m3/min and 2 x 10-3 m3/min to understand the limitations of the prototype for use with an actual heat pump system. This work demonstrated a novel cycle on a T-s diagram. Results from this work will be used to develop a second-generation prototype where more rapid cycling is possible.

Kowalski, Steve↗

DOE OSTI2023

Toward continuum gyrokinetic study of high-field mirrors

High-temperature superconducting (HTS) magnetic mirrors under development exploit strong fields with high mirror ratio to compress loss cones and enhance confinement and may offer cheaper, more compact fusion power plant candidates. This new class of devices could exhibit largely unexplored interchange and gradient-driven modes. Such instabilities, and methods to stabilize them, can be studied with gyrokinetics, given the strong magnetization and prevalence of kinetic effects. Our focus here is to (a) determine if oft-used gyrokinetic models for open field lines produce the electron-confining (Pastukhov) electrostatic potential and (b) examine and address challenges faced by gyrokinetic codes in studying HTS mirrors. Here, we show that a one-dimensional limit of said models self-consistently develops a potential qualitatively approaching the analytical Pastukhov level. Additionally, we describe the computational challenges of studying high mirror ratios with open field line gyrokinetic solvers and offer a force softening method to mitigate small time steps needed for time integration in colossal magnetic field gradients produced by HTS coils, providing a 19X speedup.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials

We report the MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ( C ij ) obtained from any ab-initio density-functional theory (DFT) code. The current version of this package reads the output of VASP, ABINIT, and Quantum Espresso codes (but it can be easily generalized to any other DFT code) and performs the appropriate post-processing of elastic constants as per the requirement of the user. This program can also detect the input structure's crystal symmetry and test the mechanical stability of all crystal classes using the Born-Huang criteria. Various useful material-specific properties such as elastic moduli, longitudinal and transverse elastic wave velocities, Debye temperature, elastic anisotropy, 2D layer modulus, hardness, Pugh's ratio, Cauchy's pressure, Kleinman's parameter, and Lame's coefficients, can be estimated using this program. Another existing feature of this program is to employ the ELATE package (2016) [29] and plot the spatial variation of several elastic properties such as Poisson's ratio, linear compressibility, shear modulus, and Young's modulus in three dimensions. Further, the MechElastic package can plot the equation of state (EOS) curves for energy and pressure for a variety of EOS models such as Murnaghan, Birch, Birch-Murnaghan, and Vinet, by reading the inputted energy/pressure versus volume data obtained via numerical calculations or experiments. This package is particularly useful for the high-throughput analysis of elastic and mechanical properties of materials.

2D materials↗

DOE OSTI2022

Molecular insights into the structure-property relationships of 3D printed polyamide reverse-osmosis membrane for desalination

3D-printing is an emerging method for manufacturing polyamide (PA) reserve osmosis (RO) membranes for water treatment and desalination, which can precisely control membrane structural properties, such as thickness, roughness, and resolution. However, the synthesis-structure (i.e., degree of cross-linking (DC), m-phenylenediamine/trimesoyl chloride (MPD/TMC) ratio, and membrane thickness) to property (permeability and water-salt selectivity) relationships for these membranes has not been well understood. At the same time, a microscopic understanding of the physical mechanism of water and salt transport is needed to guide the design of high-performance 3D-printed membranes and improve the printing efficiency. Furthermore, the atomic-scale transport features and energetics of water and salt ions are studied at high pressure for the 3D-printed PA RO membranes with the different DCs and MPD/TMC ratios through non-equilibrium molecular dynamics (NEMD) simulations. Factoring in membrane structure properties, rejection ratio of salt ions and pressure-dependent water flux, 3D-printed PA membranes having an MPD/TMC ratio of 3.0:2.0 and a DC between 80%~90% attains ideal performance: high water flux, high rejection of salt ions, and excellent structural integrity. Mechanistically, water permeability for highly cross-linked PA RO membranes depends on the temporary on-and-off channels that allow water molecules to jump from one cavity to another at high pressure. In addition, higher pressures cause rapid compaction of PA membranes’ free volume and membrane thickness. Membrane failure at high pressure is determined by the DC and MPD/TMC ratios-dependent compressive yield strength. In short, these findings provide physical insights for optimizing existing PA membranes and designing next-generation desalination membranes at the molecular level.

3D-printed PA RO membrane↗

DOE OSTI2025

X-ray diffraction strains in laser-ablated aluminum, nickel, sodium, and invar: Pressures to 475 GPa

Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.

Alloys↗