Search NASA⌕ Search

SEARCH · Search NASA

Results for “Percolation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 721 records · Page 40

Mn doped InSb studied at the atomic scale by cross-sectional scanning tunneling microscopy

We present an atomically resolved study of metal-organic vapor epitaxy grown Mn doped InSb. Both topographic and spectroscopic measurements have been performed by cross-sectional scanning tunneling microscopy (STM). The measurements on the Mn doped InSb samples show a perfect crystal structure without any precipitates and reveal that Mn acts as a shallow acceptor. The Mn concentration of the order of ∼10{sup 20 }cm{sup −3} obtained from the cross-sectional STM data compare well with the intended doping concentration. While the pair correlation function of the Mn atoms showed that their local distribution is uncorrelated beyond the STM resolution for observing individual dopants, disorder in the Mn ion location giving rise to percolation pathways is clearly noted. The amount of clustering that we see is thus as expected for a fully randomly disordered distribution of the Mn atoms and no enhanced clustering or second phase material was observed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Random center vortex lines in continuous 3D space-time

We present a model of center vortices, represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a cuboid with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configuration, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. Using the model, we study both vortex percolation and the potential V(R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We have found three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature. The model reproduces the qualitative features of confinement physics seen in SU(2) Yang-Mills theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A self-consistent first-principle based approach to model carrier mobility in organic materials

Transport through thin organic amorphous films, utilized in OLEDs and OPVs, has been a challenge to model by using ab-initio methods. Charge carrier mobility depends strongly on the disorder strength and reorganization energy, both of which are significantly affected by the details in environment of each molecule. Here we present a multi-scale approach to describe carrier mobility in which the materials morphology is generated using DEPOSIT, a Monte Carlo based atomistic simulation approach, or, alternatively by molecular dynamics calculations performed with GROMACS. From this morphology we extract the material specific hopping rates, as well as the on-site energies using a fully self-consistent embedding approach to compute the electronic structure parameters, which are then used in an analytic expression for the carrier mobility. We apply this strategy to compute the carrier mobility for a set of widely studied molecules and obtain good agreement between experiment and theory varying over several orders of magnitude in the mobility without any freely adjustable parameters. The work focuses on the quantum mechanical step of the multi-scale workflow, explains the concept along with the recently published workflow optimization, which combines density functional with semi-empirical tight binding approaches. This is followed by discussion on the analytic formula and its agreement with established percolation fits as well as kinetic Monte Carlo numerical approaches. Finally, we skatch an unified multi-disciplinary approach that integrates materials science simulation and high performance computing, developed within EU project MMM@HPC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Microscopic origin of read current noise in TaO{sub x}-based resistive switching memory by ultra-low temperature measurement

TaO{sub x}-based resistive random access memory (RRAM) attracts considerable attention for the development of next generation nonvolatile memories. However, read current noise in RRAM is one of the critical concerns for storage application, and its microscopic origin is still under debate. In this work, the read current noise in TaO{sub x}-based RRAM was studied thoroughly. Based on a noise power spectral density analysis at room temperature and at ultra-low temperature of 25 K, discrete random telegraph noise (RTN) and continuous average current fluctuation (ACF) are identified and decoupled from the total read current noise in TaO{sub x} RRAM devices. A statistical comparison of noise amplitude further reveals that ACF depends strongly on the temperature, whereas RTN is independent of the temperature. Measurement results combined with conduction mechanism analysis show that RTN in TaO{sub x} RRAM devices arises from electron trapping/detrapping process in the hopping conduction, and ACF is originated from the thermal activation of conduction centers that form the percolation network. At last, a unified model in the framework of hopping conduction is proposed to explain the underlying mechanism of both RTN and ACF noise, which can provide meaningful guidelines for designing noise-immune RRAM devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolution and sign control of square-wave-like anisotropic magneto-resistance in spatially confined La{sub 0.3}Pr{sub 0.4}Ca{sub 0.3}MnO{sub 3}/LaAlO{sub 3}(001) manganite thin films

We investigated magneto-transport properties of a compressively strained spatially confined La{sub 0.3}Pr{sub 0.4}Ca{sub 0.3}MnO{sub 3} (LPCMO) thin film micro-bridge deposited on LaAlO{sub 3}. Angular dependence of the magneto-resistance R(θ) of this bridge, where θ is the angle between the magnetic field and the current directions in the film plane, exhibits sharp positive and negative percolation jumps near T{sub MIT}. The sign and the magnitude of these jumps can be tuned using the magnetic field. Such behavior has not been observed in LPCMO micro-bridges subjected to tensile strain, indicating a correlation between the type of the lattice strain, the distribution of electronic domains, and the anisotropic magneto-resistance in spatially confined manganite systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DC bias effect on alternating current electrical conductivity of poly(ethylene terephthalate)/alumina nanocomposites

Polymer nanocomposites based on metal oxide (ceramic) nanoparticles are a new class of materials with unique properties and designed for various applications such as electronic device packaging, insulation, fabrication and automotive industries. Poly(ethylene terephthalate) (PET)/alumina (Al{sub 2}O{sub 3}) nanocomposites with filler content between 1 wt% and 5 wt% were prepared by melt compounding method using co-rotating twin screw extruder and characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and precision LCR meter techniques. The results revealed that proper uniform dispersion at lower content up to 2 wt% of nano-alumina observed by using TEM. Aggregation of nanoparticles was observed at higher content of alumina examined by using SEM and TEM. The frequency dependences of the alternating current (AC) conductivity (σ{sub AC}) of PET/alumina nanocomposites on the filler content and DC bias were investigated in the frequency range of 20Hz - 1MHz. The results showed that the AC and direct current (DC) conductivity increases with increasing DC bias and nano-alumina content upto 3 wt%. It follows the Jonscher’s universal power law of solids. It revealed that σ{sub AC} of PET/alumina nanocomposites can be well characterized by the DC conductivity (σ{sub DC}), critical frequency (ω{sub c}), critical exponent of the power law (s). Roll of DC bias potential led to an increase of DC conductivity (σ{sub DC}) due to the creation of additional conducting paths with the polymer nanocomposites and percolation behavior achieved through co-continuous morphology.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

High-throughput shadow mask printing of passive electrical components on paper by supersonic cluster beam deposition

We report the rapid prototyping of passive electrical components (resistors and capacitors) on plain paper by an additive and parallel technology consisting of supersonic cluster beam deposition (SCBD) coupled with shadow mask printing. Cluster-assembled films have a growth mechanism substantially different from that of atom-assembled ones providing the possibility of a fine tuning of their electrical conduction properties around the percolative conduction threshold. Exploiting the precise control on cluster beam intensity and shape typical of SCBD, we produced, in a one-step process, batches of resistors with resistance values spanning a range of two orders of magnitude. Parallel plate capacitors with paper as the dielectric medium were also produced with capacitance in the range of tens of picofarads. Compared to standard deposition technologies, SCBD allows for a very efficient use of raw materials and the rapid production of components with different shape and dimensions while controlling independently the electrical characteristics. Discrete electrical components produced by SCBD are very robust against deformation and bending, and they can be easily assembled to build circuits with desired characteristics. The availability of large batches of these components enables the rapid and cheap prototyping and integration of electrical components on paper as building blocks of more complex systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A study of the oriented composites with the conductive segregated structure obtained via solid-phase processing of the UHMWPE reactor powder mixed with the carbon nanofillers

Electrically conductive oriented polymer nano-composites of different compositions, based on the reactor powder of ultra-high-molecular-weight polyethylene (UHMWPE) with a special morphology, filled with particles of nanostructured graphite (NG), multi-walled carbon nanotubes (MWCNTs), and electrically conductive carbon black (CB), were investigated. Polymer composites were obtained via compaction of the mechanical mixture of the polymer and filler powder, followed by uniaxial deformation of the material under homogeneous shear (HS) conditions (all of the processing stages were conducted at room temperature). Resulted composites possess a high tensile strength, high level of the electrical conductivity and low percolation threshold, owing it to the formation of the segregated conductive structure, The influence of the type of nanosized carbon filler, degree of the deformation under HS condition, temperature and etc. on the electrical conductivity and mechanical properties of strengthened conductive composites oriented under homogeneous shear conditions was investigated. Changes in the electrical conductivity of oriented composite materials during reversible “tension–shrinkage” cycles along the orientation axis direction were studied. A theoretical approach, describing the process of transformation of the conductive system as a response on polymer phase deformation and volume change, was proposed, based on the data received from the analysis of the conductivity behavior during the uniaxial deformation and thermal treatment of composites.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

3D numerical modeling of the carrier transport and radiative efficiency for InGaN/GaN light emitting diodes with V-shaped pits

In this paper, influence of a V-pit embedded inside the multiple quantum wells (MQWs) LED was studied. A fully three-dimensional stress-strain solver and Poisson-drift-diffusion solver are employed to study the current path, where the quantum efficiency and turn-on voltage will be discussed. Our results show that the hole current is not only from top into lateral quantum wells (QWs) but flowing through shallow sidewall QWs and then injecting into the deeper lateral QWs in V-pit structures, where the V-pit geometry provides more percolation length for holes to make the distribution uniform along lateral MQWs. The IQE behavior with different V-pit sizes, threading dislocation densities, and current densities were analyzed. Substantially, the variation of the quantum efficiency for different V-pit sizes is due to the trap-assisted nonradiative recombination, effective QW ratio, and ability of hole injections.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

A quasi-classical model of ionization equilibrium in the p-type diamond between hydrogen-like acceptors (boron atoms which substitute carbon atoms in the crystal lattice) and holes in the valence band (v-band) is proposed. The model is applicable on the insulator side of the insulator–metal concentration phase transition (Mott transition) in p-Dia:B crystals. The densities of the spatial distributions of impurity atoms (acceptors and donors) and of holes in the crystal are considered to be Poissonian, and the fluctuations of their electrostatic potential energy are considered to be Gaussian. The model accounts for the decrease in thermal ionization energy of boron atoms with increasing concentration, as well as for electrostatic fluctuations due to the Coulomb interaction limited to two nearest point charges (impurity ions and holes). The mobility edge of holes in the v-band is assumed to be equal to the sum of the threshold energy for diffusion percolation and the exchange energy of the holes. On the basis of the virial theorem, the temperature T{sub j} is determined, in the vicinity of which the dc band-like conductivity of holes in the v-band is approximately equal to the hopping conductivity of holes via the boron atoms. For compensation ratio (hydrogen-like donor to acceptor concentration ratio) K ≈ 0.15 and temperature T{sub j}, the concentration of “free” holes in the v-band and their jumping (turbulent) drift mobility are calculated. Dependence of the differential energy of thermal ionization of boron atoms (at the temperature 3T{sub j}/2) as a function of their concentration N is calculated. The estimates of the extrapolated into the temperature region close to T{sub j} hopping drift mobility of holes hopping from the boron atoms in the charge states (0) to the boron atoms in the charge states (−1) are given. Calculations based on the model show good agreement with electrical conductivity and Hall effect measurements for p-type diamond with boron atom concentrations in the range from 3 × 10{sup 17} to 3 × 10{sup 20 }cm{sup −3}, i.e., up to the Mott transition. The model uses no fitting parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interface structure in nanoscale multilayers near continuous-to-discontinuous regime

Interfacial atomic diffusion, reaction, and formation of microstructure in nanoscale level are investigated in W/B{sub 4}C multilayer (ML) system as functions of thickness in ultrathin limit. Hard x-ray reflectivity (XRR) and x-ray diffuse scattering in conjunction with x-ray absorption near edge spectroscopy (XANES) in soft x-ray and hard x-ray regimes and depth profiling x-ray photoelectron spectroscopy (XPS) have been used to precisely evaluate detailed interfacial structure by systematically varying the individual layer thickness from continuous-to-discontinuous regime. It is observed that the interfacial morphology undergoes an unexpected significant modification as the layer thickness varies from continuous-to-discontinuous regime. The interfacial atomic diffusion increases, the physical density of W layer decreases and that of B{sub 4}C layer increases, and further more interestingly the in-plane correlation length decreases substantially as the layer thickness varies from continuous-to-discontinuous regime. This is corroborated using combined XRR and x-ray diffused scattering analysis. XANES and XPS results show formation of more and more tungsten compounds at the interfaces as the layer thickness decreases below the percolation threshold due to increase in the contact area between the elements. The formation of compound enhances to minimize certain degree of disorder at the interfaces in the discontinuous region that enables to maintain the periodic structure in ML. The degree of interfacial atomic diffusion, interlayer interaction, and microstructure is correlated as a function of layer thickness during early stage of film growth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Impact of water dilution and cation tail length on ionic liquid characteristics: Interplay between polar and non-polar interactions

The recalcitrance of lignocellulosic biomass poses a major challenge that hinders the economical utilization of biomass for the production of biofuel, plastics, and chemicals. Ionic liquids have become a promising solvent that addresses many issues in both the pretreatment process and the hydrolysis of the glycosidic bond for the deconstruction of cellulosic materials. However, to make the use of ionic liquids economically viable, either the cost of ionic liquids must be reduced, or a less expensive solvent (e.g., water) may be added to reduce the overall amount of ionic liquid used in addition to reducing the viscosity of the binary liquid mixture. In this work, we employ atomistic molecular dynamics simulations to investigate the impact of water dilution on the overall liquid structure and properties of three imidazolium based ionic liquids. It is found that ionic liquid-water mixtures exhibit characteristics that can be grouped into two distinct regions, which are a function of the ionic liquid concentration. The trends observed in each region are found to correlate with the ordering in the local structure of the ionic liquid that arises from the dynamic interactions between the ion pairs. Simulation results suggest that there is a high level of local ordering in the molecular structure at high concentrations of ionic liquids that is driven by the aggregation of the cationic tails and the anion-water interactions. It is found that as the concentration of ionic liquids in the binary mixture is decreased, there is a point at which the competing self and cross interaction energies between the ionic liquid and water shifts away from a cation-anion dominated regime, which results in a significant change in the mixture properties. This break point, which occurs around 75% w/w ionic liquids, corresponds to the point at which water molecules percolate into the ionic liquid network disrupting the ionic liquids’ nanostructure. It is observed that as the cationic alkyl tail length increases, the changes in the binary mixtures’ properties become more pronounced.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Largely enhanced dielectric properties of carbon nanotubes/polyvinylidene fluoride binary nanocomposites by loading a few boron nitride nanosheets

The ternary nanocomposites of boron nitride nanosheets (BNNSs)/carbon nanotubes (CNTs)/polyvinylidene fluoride (PVDF) are fabricated via a combination of solution casting and extrusion-injection processes. The effects of BNNSs on the electrical conductivity, dielectric behavior, and microstructure changes of CNTs/PVDF binary nanocomposites are systematically investigated. A low percolation value (f{sub c}) for the CNTs/PVDF binary system is obtained due to the integration of solution and melting blending procedures. Two kinds of CNTs/PVDF binary systems with various CNTs contents (f{sub CNTs}) as the matrix are discussed. The results reveal that compared with CNTs/PVDF binary systems at the same f{sub CNTs}, the ternary BNNSs/CNTs/PVDF nanocomposites exhibit largely enhanced dielectric properties due to the improvement of the CNTs dispersion state and the conductive network. The dielectric constant of CNTs/PVDF binary nanocomposite with 6 vol. % CNTs (f{sub CNTs} < f{sub c}) shows a 79.59% enhancement from 49 to 88 after the incorporation of 3 vol. % BNNSs. For the other CNTs/PVDF system with 8 vol. % CNTs (f{sub CNTs} > f{sub c}), it displays a 43.32% improvement from 1325 to 1899 after the addition of 3 vol. % BNNSs. The presence of BNNSs facilitates the formation of the denser conductive network. Meanwhile, the ternary BNNSs/CNTs/PVDF systems exhibit a low dielectric loss. The adjustable dielectric properties could be obtained by employing the ternary systems due to the microstructure changes of nanocomposites.

36 MATERIALS SCIENCE↗

Understanding the unique sorption of alkane- α , ω -diols in silicalite-1

Adsorption equilibria of alkane-α, ω-diols (propane-1,3-diol, butane-1,4-diol, pentane-1,5-diol, and hexane-1,6-diol) from aqueous solution onto an all-silica zeolite of the type mordenite framework inverted (MFI, also known as silicalite-1) are obtained by simulations and experiments at T = 323 K and also for pentane-1,5-diol (C5) at 348 and 383 K. After an initial slow rise, isotherms at T = 323 K exhibit steep changes in loading, reaching saturation at 10, 9, 8, and 7 molec/uc as the number of carbon atoms of the diols increases from 3 to 6. The abrupt change in loading corresponds to a minimum in the free energy of adsorption (from vapor to zeolite) that is associated with a rapid rise in the number of hydrogen bonds per sorbate molecule due to the formation of large clusters. For C5 at low loading, the centers-of-mass primarily occupy the channel intersections with oxygens oriented along the straight channels where intermolecular hydrogen bonds are formed. At saturation loading, the C5 centers-of-mass instead occupy the straight and zig-zag channels, and nearly all C5 molecules are involved in a percolating hydrogen-bonding network (this also occurs for C6). With increasing temperature, the C5 isotherm decreases in steepness as the minimum in free energy of adsorption decreases in depth and a less-ordered structure of the adsorbed molecules results in a lower number of diol–diol hydrogen bonds. However, the C5 isotherm does not shift significantly in concentration of the adsorption onset, as the free energies of solvation and adsorption increase by similar and compensating amounts. At T = 323 and 348 K, the steep change for the C5 adsorption isotherm is found to be a phase transition (as indicated by a bimodal distribution of unit cell occupancies at intermediate loading) from a less-dense phase with only small hydrogen-bonded clusters to an ordered solid phase with loadings of 8 molec/uc. At T = 383 K, the sorbates are less ordered, the distribution of occupancies becomes unimodal at intermediate loading, and the loading rises more gradually with concentration. Lastly, several different enhanced sampling methods are utilized for these simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Monte Carlo simulation of cylinders with short-range attractions

Cylindrical or rod-like particles are promising materials for the applications of fillers in nanocomposite materials and additives to control rheological properties of colloidal suspensions. Recent advances in particle synthesis allows for cylinders to be manufactured with short-ranged attractions to study the gelation as a function of packing fraction, aspect ratio and attraction strength. In order to aid in the analysis of small-angle scattering experiments of rod-like particles, computer simulation methods were used to model these particles with specialized Monte Carlo algorithms and tabular superquadric potentials. The attractive interaction between neighboring rods increases with the amount of locally-accessible surface area, thus leading to patchy-like interactions. We characterize the clustering and percolation of cylinders as the attractive interaction increases from the homogenous fluid at relatively low attraction strength, for a variety of aspect ratios and packing fractions. Comparisons with the experimental scattering results are also presented, which are in agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Structure and phase behavior of polymer-linked colloidal gels

Low-density “equilibrium” gels that consist of a percolated, kinetically arrested network of colloidal particles and are resilient to aging can be fabricated by restricting the number of effective bonds that form between the colloids. Valence-restricted patchy particles have long served as one archetypal example of such materials, but equilibrium gels can also be realized through a synthetically simpler and scalable strategy that introduces a secondary linker, such as a small ditopic molecule, to mediate the bonds between the colloids. Here, we consider the case where the ditopic linker molecules are low-molecular-weight polymers and demonstrate using a model colloid–polymer mixture how macroscopic properties such as the phase behavior as well as the microstructure of the gel can be designed through the polymer molecular weight and concentration. The low-density window for equilibrium gel formation is favorably expanded using longer linkers while necessarily increasing the spacing between all colloids. Furthermore, we show that blends of linkers with different sizes enable wider variation in microstructure for a given target phase behavior. Our computational study suggests a robust and tunable strategy for the experimental realization of equilibrium colloidal gels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermal conductivity of two-dimensional disordered fibrous materials defined by interfiber thermal contact conductance and intrinsic conductivity of fibers

A general framework for the theoretical analysis and numerical calculations of the effective thermal conductivity of two-dimensional homogeneous and isotropic disordered fibrous materials is developed in this work based on the model of random contacts between soft-core spherocylinders. The analysis accounts for the interfiber contact conductance and intrinsic conductivity of fibers and is performed in a wide space of governing parameters that includes the fiber aspect ratio, Biot number calculated for a single thermal contact between fibers, and material density ranging from values corresponding to the percolation threshold up to those characteristic of dense fiber networks. For dense networks, exact theoretical equations for the thermal conductivity of materials composed of spherocylinders with an arbitrary aspect ratio and Biot number are derived. The effect of the intrinsic conductivity of fibers on the thermal transport in fibrous materials is found to depend on the density of contacts and can be significant in sufficiently dense fiber networks even if the Biot number for a single thermal contact is small. Semiempirical corrections to the theoretical equations are derived for small and moderate fiber densities. The power law exponent describing the approximate dependence of the conductivity on the density parameter is found to vary from values close to 1 up to values exceeding 2 when evaluated within different finite ranges of the density parameter. This finding explains the variability of scaling laws for thermal conductivity of fibrous materials suggested in the literature based on numerical simulations performed in different regions of the space of material parameters.

36 MATERIALS SCIENCE↗

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and $\langle$100$\rangle$ dumbbell interstitials in Ni–Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy’s non-monotonic behavior. In contrast, the difference between formation energies of Ni–Ni, Ni–Fe, and Fe–Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition—based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one—is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

36 MATERIALS SCIENCE↗