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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Compressed Expanded Natural Graphite (CENG) Processing for PCM Composites

The use of phase change materials (PCMs) in thermal energy storage applications has received considerable attention in recent decades. Organic PCMs are popular due to their high latent heat of fusion, noncorrosive properties, and relative stability over many charge and discharge cycles. A primary limitation of these materials is their low thermal conductivity. This has led researchers to develop various methods to increase thermal conductivity by seeding PCM with or impregnating them into more conductive materials. One method is to impregnate PCMs into compressed expanded natural graphite (CENG) matrices, which can improve thermal conductivity by a factor of 100. CENG matrices have received particular interest due to their low cost, high porosity, small (nano/micro) pore size, high pore density, high thermal conductivity, and ability to be compressed into many geometries. PCM/CENG matrix composites have been extensively studied; however, the effect that CENG processing has on PCM saturation and the overall matrix thermal conductivity has not been well investigated. This processing includes four major steps including graphite intercalation, thermal shock, compression, and PCM saturation. Intercalation involves soaking graphite flakes in sulfuric and/or nitric acid to intercalate the acids between the graphene layers. The graphite flakes are then subjected to a high-temperature thermal shock, during which the intercalated acid is gasified rapidly, pushing the graphene layers apart, resulting in accordion-shaped graphite "worms". The "worms" are then compacted to a desired bulk density and then soaked with molten PCM until fully saturated. The properties of the produced CENG matrix, and its ability to allow PCM permeation, are sensitive to the processing parameters, namely, the thermal shock temperature and exposure time, as well as the matrix apparent density or porosity. Here, we study the effect of the thermal shock conditions necessary to expand intercalated graphite flakes on PCM saturation and the expanded graphite's thermal conductivity and morphology. We found that the thermal shock temperature exhibits the greatest influence. At greater shock temperatures, SEM images showed that expanded graphite worms exhibited greater density of pores, thus increasing total surface area within the matrices. Increasing thermal shock temperature yielded greater overall PCM saturation, as well as an increased rate of saturation. Improvements in PCM saturation rate and overall saturation are obtained as the shock temperature is increased. Longer exposure to thermal shock also improves initial saturation rates and is beneficial if a shortened impregnation time is needed. Thermal shock conditions did not impact thermal conductivity; however, conductivity was largely affected by matrix porosity. A local maximum in axial thermal conductivity was observed at around 83% porosity, which is similar to that observed in previous studies.

compressed expanded natural graphite↗
DOE OSTI2023

High-performance strategies for the recent MRSF-TDDFT in GAMESS

Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. Here, this paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

The paper reports development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), a new relativistic quantum-chemical method for treating spin-orbit coupling in molecules. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. In conclusion, to demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO+ is reported.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Superfluid condensate fraction and pairing wave function of the unitary Fermi gas

The unitary Fermi gas is a many-body system of two-component fermions with zero-range interactions tuned to infinite scattering length. Despite much activity and interest in unitary Fermi gas and its universal properties, there have been great difficulties in performing accurate calculations of the superfluid condensate fraction and pairing wave function. In this paper, we present auxiliary-field lattice Monte Carlo simulations using a lattice interaction which accelerates the approach to the continuum limit, thereby allowing for robust calculations of these difficult observables. As a benchmark test, we compute the ground-state energy of 33 spin-up and 33 spin-down particles. As a fraction of the free Fermi gas energy $E_{\text{FG}}$, we find $E_0/E_{\text{FG}}$ = 0.369(2), 0.372(2), using two different definitions of the finite-system energy ratio, in agreement with the latest theoretical and experimental results. We then determine the condensate fraction by measuring off-diagonal long-range order in the two-body density matrix. We find that the fraction of condensed pairs is α = 0.43(2). Further, we also extract the pairing wave function and find the pair correlation length to be $ζ_pk_F$ = 1.8(3)ℏ, where $k_F$ is the Fermi momentum. Provided that the simulations can be performed without severe sign oscillations, the methods we present here can be applied to superfluid neutron matter as well as more exotic $\textit{P}$-wave and $\textit{D}$-wave superfluids.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1997

Microphysical Retrievals Over Stratiform Rain Using Measurements from an Airborne Dual-Wavelength Radar-Radiometer

The need to understand the complementarity of the radar and radiometer is important not only to the Tropical Rain Measuring Mission (TRMM) program but to a growing number of multi-instrumented airborne experiment that combine single or dual-frequency radars with multichannel radiometers. The method of analysis used in this study begins with the derivation of dual-wavelength radar equations for the estimation of a two-parameter drop size distribution (DSD). Defining a "storm model" as the set of parameters that characterize snow density, cloud water, water vapor, and features of the melting layer, then to each storm model there will usually correspond a set of range-profiled drop size distributions that are approximate solutions of the radar equations. To test these solutions, a radiative transfer model is used to compute the brightness temperatures for the radiometric frequencies of interest. A storm model or class of storm models is considered optimum if it provides the best reproduction of the radar and radiometer measurements. Tests of the method are made for stratiform rain using simulated storm models as well as measured airborne data. Preliminary results show that the best correspondence between the measured and estimated radar profiles usually can be obtained by using a moderate snow density (0.1-0.2 g/cu cm), the Maxwell-Garnett mixing formula for partially melted hydrometeors (water matrix with snow inclusions), and low to moderate values of the integrated cloud liquid water (less than 1 kg/sq m). The storm-model parameters that yield the best reproductions of the measured radar reflectivity factors also provide brightness temperatures at 10 GHz that agree well with the measurements. On the other hand, the correspondence between the measured and modeled values usually worsens in going to the higher frequency channels at 19 and 34 GHz. In searching for possible reasons for the discrepancies, It is found that changes in the DSD parameter Mu, the radar constants, or the path-integrated attenuation can affect the high frequency channels significantly. In particular, parameters that cause only modest increases in the median mass diameter of the snow, and which have a minor effect on the radar returns or the low frequency brightness temperature, can produce a strong cooling of the 34 GHz brightness temperature.

Meneghini, Robert↗
DOE OSTI2022

Synthesis and Characterization of Polymeric Pore Former Microspheres using Modified Polymer Resin

Porosity in polymer parts is often desired to improve mechanical properties. Individual pores must be small enough that bulk mechanical properties are retained but significant enough to reduce the density of the material. Filler materials can be incorporated into polymer matrices and subsequently removed to create voids. The materials used to create the voids are known as pore-formers. The present research aims to create spherical pores in a silicone matrix by inserting and removing core materials or fillers post-cure. A method was developed to incorporate pore formers into an uncured polymer resin and remove the materials from the matrix. Polyethylene Glycol (PEG) and Polylactic Acid (PLA) microspheres are created and incorporated into silicone matrices as pore formers. Microspheres with controllable size distributions are formed via ultrasonic spray pyrolysis and emulsion formation. Microspheres are removed from the matrix by solvent extraction and calcination. PLA microspheres were modified by hydroxyl addition to the surface to study their solubility in water. PEG-PLA block copolymers are also synthesized and investigated, comparing their physical and chemical properties to the monomers to identify whether the block copolymer microspheres will be more easily removable than their monomeric microspheres. Moreover, other properties including thermal stability, rheology, and mechanical response are studied. The present dissertation provides a comprehensive understanding of the synthesis and characterization of PEG and PLA-based pore formers, toward the future development of feedstock for additive manufacturing porous structures.

Damptey, Ransford↗
DOE OSTI2022

Hubbard-corrected oxide formation enthalpies without adjustable parameters

A density functional theory (DFT) approach to computing transition metal oxide heat of formation without adjustable parameters is presented. Different degrees of d-electron localization in oxides are treated within the DFT+U approach with site-dependent, first-principles Hubbard U-parameters obtained from linear response theory, and delocalized states in the metallic phases are treated without Hubbard corrections. Comparison of relative stabilities of these differently treated phases is enabled by a local d-electron density matrix-dependent model, which was found by genetic programming against experimental reference formation enthalpies. This mathematically simple model does not explicitly depend on the Hubbard-corrected ionic species and is shown to reproduce the heats of formation of the Mott insulators Ca 2 RuO 4 and Y 2 Ru 2 O 7 within ~3% of experimental results, where the experimental training data did not contain Ru oxides. This newly developed method thus absolves from the need for element-specific corrections fitted to experiments in existing Hubbard-corrected approaches to the prediction of reaction energies of transition metal oxides and metals. The absence of fitting parameters opens up here the possibility to predict relative thermodynamic stabilities and reaction energies involving d-states of varying degree of localization at transition metal oxide interfaces and defects, where site-dependent U-parameters will be particularly important and devising a fitting scheme against experimental data with predictive power would be exceedingly difficult.

transition metal oxides↗
NASA NTRS2003

Thermal Response of Cooled Silicon Nitride Plate Due to Thermal Conductivity Effects Analyzed

Lightweight, strong, tough high-temperature materials are required to complement efficiency improvements for next-generation gas turbine engines that can operate with minimum cooling. Because of their low density, high-temperature strength, and high thermal conductivity, ceramics are being investigated as materials to replace the nickelbase superalloys that are currently used for engine hot-section components. Ceramic structures can withstand higher operating temperatures and a harsh combustion environment. In addition, their low densities relative to metals help reduce component mass (ref. 1). To complement the effectiveness of the ceramics and their applicability for turbine engine applications, a parametric study using the finite element method is being carried out. The NASA Glenn Research Center remains very active in conducting and supporting a variety of research activities related to ceramic matrix composites through both experimental and analytical efforts (ref. 1). The objectives of this work are to develop manufacturing technology, develop a thermal and environmental barrier coating (TBC/EBC), develop an analytical modeling capability to predict thermomechanical stresses, and perform a minimal burner rig test on silicon nitride (Si3N4) and SiC/SiC turbine nozzle vanes under simulated engine conditions. Moreover, we intend to generate a detailed database of the material s property characteristics and their effects on structural response. We expect to offer a wide range of data since the modeling will account for other variables, such as cooling channel geometry and spacing. Comprehensive analyses have begun on a plate specimen with Si3N4 cooling holes.

Baaklini, George Y.↗
DOE OSTI2021

Statistical learning for predicting density–matrix-based electron dynamics

In this study, we consider the problem of learning density-dependent molecular Hamiltonian matrices from time series of electron density matrices, all in the context of Hartree–Fock theory. Prior work developed a solution to this problem for small molecular systems with density and Hamiltonian matrices of size at most 6 × 6. Here, using a battery of techniques, we scale prior methods to larger molecular systems with, for example, 29 × 29 matrices. This includes systems that either have more electrons or are expressed in large basis sets such as 6-311++G**. Scaling the method to larger systems enhances its relevance for realistic applications in chemistry and physics. To achieve this scaling, we apply dimensionality reduction, ridge regression and analytic computation of Hessians. Through the combination of these techniques, we are able to learn Hamiltonians by minimizing an objective function that encodes local propagation error. Importantly, these learned Hamiltonians can then be used to predict electron dynamics for thousands of steps: When we use our learned Hamiltonians to numerically solve the time-dependent Hartree–Fock equation, we obtain predicted dynamics that are in close quantitative agreement with ground truth dynamics. This includes field-off trajectories similar to the training data and field-on trajectories outside of the training data.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Identifying Bounds of Inorganic Content in Solventless Processing of Hybrid Solid Electrolytes

Solid-state lithium batteries require safe, robust electrolytes to enable higher energy densities and improved safety over conventional cells. Hybrid polymer–ceramic electrolytes are a promising solution, combining the processability of polymers with the high ionic conductivity and mechanical strength of inorganic fillers. In this work, we demonstrate a solventless, UV-curing method to produce hybrid solid electrolytes using a poly(ethylene glycol) dimethyl ether (PEGDME)-based photocurable matrix incorporating Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 (LAGP) or Li 7 La 3 Zr 2 O 12 (LLZO) ceramic electrolyte. Inorganic filler loadings up to ∼55 wt.% could be successfully incorporated via this process which was the highest inorganic content at which the slurry remains processable and cured into a uniform film. The resulting UV-cured composite electrolytes remain flexible and exhibit room-temperature ionic conductivities on the order of 10 −4 S·cm −1 , along with notably improved lithium-ion transference numbers compared to conventional polymer electrolytes. Similar performance and processing limits were observed for both LAGP and LLZO, indicating that ceramic filler chemistry does not significantly affect the UV-curing process or the electrolyte's ion transport properties in this regime. Eliminating solvents from fabrication not only simplifies processing and mitigates environmental concerns but also enables higher solid contents that enhance mechanical strength and help suppress lithium dendrite formation. In conclusion, this scalable approach thus paves the way for manufacturing robust composite solid electrolytes for next-generation solid-state batteries (SSBs).

Batteries↗
DOE OSTI2024

Separation of Lipoproteins for Quantitative Analysis of 14 C-Labeled Lipid-Soluble Compounds by Accelerator Mass Spectrometry

To date, 14 C tracer studies using accelerator mass spectrometry (AMS) have not yet resolved lipid-soluble analytes into individual lipoprotein density subclasses. The objective of this work was to develop a reliable method for lipoprotein separation and quantitative recovery for biokinetic modeling purposes. The novel method developed provides the means for use of small volumes (10–200 µL) of frozen plasma as a starting material for continuous isopycnic lipoprotein separation within a carbon- and pH-stable analyte matrix, which, following post-separation fraction clean up, created samples suitable for highly accurate 14 C/ 12 C isotope ratio determinations by AMS. Manual aspiration achieved 99.2 ± 0.41% recovery of [5- 14 CH 3 ]-(2R, 4'R, 8'R)-α-tocopherol contained within 25 µL plasma recovered in triacylglycerol rich lipoproteins (TRL = Chylomicrons + VLDL), LDL, HDL, and infranatant (INF) from each of 10 different sampling times for one male and one female subject, n = 20 total samples. Small sample volumes of previously frozen plasma and high analyte recoveries make this an attractive method for AMS studies using newer, smaller footprint AMS equipment to develop genuine tracer analyses of lipophilic nutrients or compounds in all human age ranges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

Water vapor profile retrieval simulation studies for the HIRS/MSU and AMTS/MSU sounders

A combined physical statistical method for the retrieval of atmospheric water vapor column densities has been developed at the Goddard Laboratory for Atmospheric Sciences. In this method differences between observed and calculated clear column brightness temperatures are used in a regression formalism to obtain estimates of integrated column densities in given atmospheric layers. The physics of the radiative transfer problem is contained in the calculated clear column brightness temperatures and in accounting for the effects of clouds on the observed radiances. The regression matrix is equivalent to a set of empirical sensitivity factors.

Reuter, D.↗
NASA NTRS2005

E-Beam Processing of Polymer Matrix Composites for Multifunctional Radiation Shielding

Aliphatic polymers were identified as optimum radiation shielding polymeric materials for building multifunctional structural elements for in-space habitats. Conceptual damage tolerant configurations of polyolefins have been proposed, but many manufacturing issues relied on methods and materials which have sub-optimal radiation shielding characteristics (for example, epoxy matrix and adhesives). In the present approach, we shall investigate e-beam processing technologies for inclusion of high-strength aliphatic polymer reinforcement structures into a highly cross-linked polyolefin matrix. This paper reports the baseline thermo-mechanical properties of low density polyethylene and highly crystallized polyethylene.

Hou, Tan-Hung↗
NASA NTRS2001

Retrieval of Polar Stratospheric Cloud Microphysical Properties From Lidar Measurements: Dependence on Particle Shape Assumptions

Knowledge of particle sizes and number densities of polar stratospheric clouds (PSCs) is highly important, because they are critical parameters for the modeling of the ozone chemistry of the stratosphere. In situ measurements of PSC particles are rare. the main instrument for the accumulation of PSC data are lidar systems. Therefore the derivation of some microphysical properties of PSCS from the optical parameters measured by lidars would be highly beneficial for ozone research. Inversion of lidar data obtained in the presence of PSCs formed from crystalline particles type 11 and the various nitric acid tri Ydrrate (NAT) types cannot be easily accomplished, because a suitable scattering theory for small faceted crystals has not been readily available tip to now. As a consequence, the T-matrix method is commonly used for the interpretation of these PSC lidar data. Here the assumption is made that the optical properties of an ensemble of spheroids resemble those of crystalline PSCs, and microphysical properties of the PSC are inferred from the optical signatures of the PSC at two or more wavelengths. The problem with the T-matrix approach is that the assumption of spheroidal instead of faceted particles can lead to dramatically wrong results: Usually cloud particle properties are deduced from analysis of lidar profiles of backscatter ratio and depolarization ratio. The particle contribution to the backscatter ratio is given by the product of the particle number density and the backscattering cross section. The latter is proportional to the value of the particle's scattering phase function at 180 degrees scattering angle. At 180 degrees however, the phase functions of rough, faceted crystals and of spheroids with same maximum dimension differ by a factor of 6. From this it follows that for a PSC consisting of faceted crystals, the particle number density is underestimated by roughly the same factor if spheroidal particles are unrealistically assumed. We are currently developing a retrieval technique for determining the microphysical parameters of crystalline PSCs that takes into account the faceted shape of the PSC particles. This approach utilizes finite-difference time-domain (FDTD) calculations of particle optical properties. The accuracy and the free choice of the shape of the scattering particle make the FDTD technique a promising tool for the inversion of PSC lidar data. A first comparison of FDTD and T-matrix calculations will be presented.

Reichardt, Susanne↗
DOE OSTI2020

Dual-cone variational calculation of the two-electron reduced density matrix

The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher $\textit{N}$-representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. Further, we apply the method to computing the energies and properties of strongly correlated electrons—including atomic charges, electron densities, dipole moments, and orbital occupations—in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Radiance, polarization, and ellipticity of the radiation in the earth's atmosphere

The complete radiation field including polarization is calculated for a model of the real atmosphere by the matrix operator method. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0; 0.15 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution which is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 deg and 160 deg for transmitted and reflected photons respectively.

Hitzfelder, S. J.↗
NASA NTRS1989

Microgravity processing of particulate reinforced metal matrix composites

The elimination of such gravity-related effects as buoyancy-driven sedimentation can yield more homogeneous microstructures in composite materials whose individual constituents have widely differing densities. A comparison of composite samples consisting of particulate ceramics in a nickel aluminide matrix solidified under gravity levels ranging from 0.01 to 1.8 G indicates that the G force normal to the growth direction plays a fundamental role in determining the distribution of the reinforcement in the matrix. Composites with extremely uniform microstructures can be produced by these methods.

Morel, Donald E.↗