In-plane Diffusion Research Articles

Experiments on Tracer Diffusion in Thin Free-Standing Liquid-Crystal Films

Using laser-induced photobleaching of a fluorescent tracer molecule, we study diffusion in free-standing smectic films as thin as two layers. For films four or more layers thick, the in-plane diffusion constant increases in agreement with a hydrodynamic theory outlined here. Two- and three-layer films show different behavior.

Theory of poroelastic plates with in-plane diffusion

A theory is developed for fluid-saturated poroelastic plates made of a material for which diffusion is possible in the in-plane directions only. Both bending and in-plane loading are considered. The plates are isotropic in the plate plane and obey the Kirchhoff hypotheses. Biot's constitutive law is adopted and Darcy's law is used to describe the fluid flow in pores. Quasistatic and transverse vibration problems are investigated. Example solutions are presented and observations are made on the types of deflection/vibration patterns exhibited.

In-Plane Diffusivity of Moisture in Paper

ABSTRACT Any nonuniformity in local moisture content of paper which develops during drying because of locally nonuniform drying rates provides a driving force for in-plane diffusion of moisture, which in turn acts to reduce this moisture nonuniformity. As no data have appeared for the in-plane diffusivity of moisture during desorption from paper over the range of conditions existing during papermachine drying, an investigation was undertaken to obtain this information. Moisture diffusivity was determined to he a very strong function of the extent and state of water in the sheet, increasing exponentially with paper moisture content. The presence or absence of liquid water at the sheet boundary would effect moisture difiusivity when there is water in the pores but the direction of moisture transport in paper was found to be of overriding importance. In-plane moisture diffusivity is very much greater than that in the thickness direction, indicating that the non-isotropic nature of paper structure is a key factor. A microscale view of the mechanism of moisture transport in the thickness and in-plane directions was developed, consistent with the enormous difference in effect of moisture content on diffusivity in the two directions.

Optimized SOFC electrode microstructure

Recent SOFC electrode investigations indicate that the Triple Phase Boundary reaction and the Internal Diffusion reaction should be regarded as occurring over different zones of the electrolyte surface. Under these conditions, an optimization consists of giving the faster process a reaction zone as large as possible. A duplex electrode microstructure composed of an ultra-thin layer of a mixed conductor covered by a porous current-collecting layer made of coarse grains is analyzed in terms of in-plane ohmic drop and diffusion overpotential. Relationships can be defined to optimize this microstructure. With currently available materials, excellent performances can be projected for the medium-temperature SOFC electrodes. A critical parameter for the mixed conducting layer is its electronic conductivity which should be higher than 1 S/cm. Solutions to improve a possibly slow surface oxygen exchange process are also examined.

Mesure de la diffusivité longitudinale de matériaux anisotropes

Measurement of in-plane diffusivity of anisotropic solid samples. Survey of the techniques developed at LEMTA. Three techniques for the measurement of in-plane diffusivity of anisotropic solid samples have been developed at the Laboratory and are presented here : • the two directional heat pulse (flash) method with local contact measurement of two temperatures; • the fin method with local contact or contactless measurement of two temperatures; • the two directional heat pulse method with measurement of the temperature field by an infrared camera and data processing through integral transformations.

Direct measurement of exciton diffusion in quantum wells

We have measured the diffusion of excitons in GaAs quantum wells by using spatial and time-resolved photoluminescence (PL) spectroscopy at liquid helium temperature. A displacement of the detected region (Ø 1.5 μm) with respect to the laser spot allows us to monitor the lateral change of the PL time-dependence. With increasing displacement the maximum of the PL-intensity shifts systematically to later times. For a theoretical description an in-plane diffusion model is applied, with the diffusion constant D as the only fit parameter. We obtain a continuous increase of D from 15 cm 2s −1 to 80 cm 2s −1 for displacements from 0 to 4.2 μm. A measurement with only spatial resolution leads to a diffusion constant of 20 cm 2s −1.

Low- and high-temperature phases of a Pb monolayer on Ge(111) from ab initio molecular dynamics.

We present an ab initio molecular dynamics study of the structure and dynamics of a close-packed monolayer of Pb on the Ge(111) surface, with coverage FTHETA=4/3, at different temperatures. The room-temperature (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 ) structure is characterized by large in-plane fluctuations of the Pb adatoms, and agrees well with recent x-ray standing wave data. At T\ensuremath{\sim}800 K we observe a (1\ifmmode\times\else\texttimes\fi{}1) disordered structure showing in-plane diffusion of the Pb atoms. Disordering is confined to the plane of the overlayer. A strong correlation with the solid Ge substrate is present, leading to preferential residence sites and diffusion paths of the Pb atoms on the surface. The calculated local density of states for the high-temperature phase is found to agree with recent scanning tunnel microscope observations, which show a simply Pb-terminated (1\ifmmode\times\else\texttimes\fi{}1) surface with an apparent coverage FTHETA=1.

Surface anharmonicities and disordering on Ni(100) and Ni(110).

Recent observations on various low-index metallic surfaces of an extraordinary thermal attenuation of diffracted peak intensities suggest that anharmonic effects are important at high temperatures, though such observations have also been interpreted in terms of disordering processes (premelting and roughening). In order to address this problem, we have carried out an extensive molecular-dynamics investigation of the evolution in temperature of the (100) and (110) surfaces of Ni, with the interactions between atoms described using embedded-atom method potentials. We observe both surfaces to suffer an anomalously large thermal expansion, with a concomitant rapid increase of the mean-square amplitudes of vibration; the latter are found in both cases to be larger in the plane of the surface than out of the plane. An analysis of our simulated low-energy electron-diffraction intensities supports the experimental interpretation of the measured ones in terms of enhanced mean-square displacements. Indeed, anharmonicities are found to appear at temperatures well below the onset of disordering, which occurs at 1200 and 1000 K for the (100) and (110) surfaces, respectively (via in-plane diffusion and adatom-vacancy formation). The onset of disordering proceeds differently on the two surfaces: while it involves essentially only the outermost layer on the (100) surface, both the first and second layer participate in the process on the (110) surface. We also calculate the phonon spectra at high-symmetry points of the surface Brillouin zone, which we find to be in good agreement with experimental values at room temperature. We predict, further, that the temperature-dependent frequency shifts are not significantly softened in comparison with bulk phonons, which suggests that surface phonons are affected by anharmonicity in a nontrivial way. Several of the observed properties can be understood in terms of the larger displacements that surface atoms can afford, because of their reduced coordination compared to bulk atoms.

A novel optical study of the tunnelling rate and ambipolar transport characteristics of excitons in superlattices with a variety of barrier thicknesses

We report the use of a time-resolved transient-grating technique to study the in-plane ambipolar diffusion coefficient and interwell tunnelling probability for excitons in a number of multiple quantum well samples. Our specimens were selected with barrier thicknesses ranging from 14 to 141 AA thus giving complete coverage of the transition from isolated quantum well to superlattice behaviour. Two types of MBE growth conditions were used giving rise to samples with low or high surface defect density. The surface defect density had a strong effect on the in-plane mobility but not the tunnelling probability. The samples show surprisingly strong interwell coupling even with the thickest barrier, which we attribute to defect assisted tunnelling.

All-optical measurement of the giant ambipolar diffusion constant in a hetero-nipi reflection modulator

We have measured the in-plane ambipolar diffusion constant in a hetero-nipi reflection modulator using a novel all-optical technique. This technique allows us to monitor the time evolution of an excess carrier population at any point on the sample without the need for electrical contacts. The diffusion is found to be enhanced by almost an order of magnitude over that in bulk material (to values of 45 cm2 s-1) due to the 'giant ambipolar diffusion' mechanism arising from perturbations to the periodic nipi potential. This has important implications in the use of nipi structures as fast optical switching elements as it ensures uniform switching across an individual pixel in a device where the in-plane diffusion dynamics are typically the limiting factor in the switching speed.

Effect of thermal diffusion on the excitonic reflectivity spectra of InGaAs/GaAs quantum wells

We have investigated the effect of intermixing on the excitonic reflectivity spectra of a 100 A thick InGaAs/GAas quantum well (QW). We could resolve both the E 1 -H 1 and E 2 -H 2 excitonic features, up, to LD=80 A. We show that both energy shifts agree well with a simple model which assumes a Fick's law diffusion, with a diffusion coefficient that is independent of the concentration of the cationic species. Next, considering the change (improvement) in signal to noise ratio versus thermal annealing, we suggest that, in our samples, we not only get a broadening of the quantum well as the diffusion proceeds but, also, a diffusion of the lattice constituents in the plane of the well. This in-plane diffusion smoothes the interfaces and reduces the monolayer well width fluctuations

A molecular dynamics simulation of liquid benzene adsorbed on graphite

We study the physisorption of benzene on the basal plane of graphite in the high-temperature fluid phase using the molecular dynamics simulation technique. Intra-adsorbate interactions are modeled using the AMBER potential, whereas the adsorbate-substrate interactions are described via Steele's method in terms of a static external potential acting on the adsorbate. The simulations are carried out for temperatures between 150 and 300 K in the coverage range from 0.5 to 2.0. Our results provide insight into the surface induced structure within the fluid benzene film as a function of separation from the surface. In particular, we obtain results for the temperature and coverage dependence of the molecular position and orientation distribution perpendicular to the substrate. We find that at double layer coverage, the outer benzene layer exhibits structural behavior similar to the bulk fluid. In addition, we calculate the in-plane diffusion coefficient for mono- and submono-layer coverages at various temperatures.

Measurement of the decay of light-induced gratings for characterization of QW heterostructures of type I and II

Using a non-resonant transient grating technique the mobility and recombination lifetime of free carriers in type I and type II QW heterostructures is measured. For the lattice-matched type II Ca xSr 1−xF 2/GaAs structures the diffusion coefficient as well as the diffraction efficiency is found to be affected by carrier separation into different layers. For GaAs/GaAlAs superlattices a strong influence of the barrier parameters on the inplane diffusion of heavy holes is observed.

Giant ambipolar diffusion constant of n-i-p-i doping superlattices.

The analytical expression for the ambipolar in-plane diffusion constant of excess carriers in n-i-p-i doping superlattices is derived. Shockley-Haynes--type experiments quantitatively confirm the predicted huge enhancement of the diffusion constant (in the tested case by factors of about 300) and the long diffusion lengths.

Thermal Diffusivity of Diamond Films Using a Laser Pulse Technique

Polycrystalline diamond films were deposited using a microwave plasma‐enhanced chemical vapor deposition process. A laser pulse technique was developed to measure the thermal diffusivity of diamond films deposited on a silicon substrate. The effective thermal diffusivity of a diamond film on silicon was measured by observing the phase and amplitude of the cyclic thermal waves generated by laser pulses. An analytical model is presented to calculate the effective inplane (face‐parallel) diffusivity of a two‐layer system. The model is used to reduce the effective thermal diffusivity of the diamond/silicon sample to a value for the thermal diffusivity and conductivity of the diamond film. The average effective diffusivity values are and yielding thermal diffusivity values of , respectively, for the two samples; the calculated thermal conductivity values are 13.50 and 13.28 W/cmK, which are better than that of type 1a natural diamond. The phase and amplitude measurements give similar results.

LATERAL MAPPING OF ATOMIC SCALE INTERFACE MORPHOLOGY AND DISLOCATIONS IN QUANTUM WELLS BY CATHODOLUMINESCENCE IMAGING

Our present knowledge of the atomic scale structural, chemical and electronic properties of semiconductor interfaces is inversely proportional to their importance for a whole generation of novel electronic and photonic quantum well devices. It is the purpose of this paper to demonstrate how wavelength- and time-resolved cathodoluminescence imaging (CLI) provides a one-to-one image of the crystallographic island structure of the heterointerfaces which are the boundaries of the quantum well. A detailed description of the fully computer controlled cathodoluminescence (CL) system is given. The accelerating voltage, which is choosen to be 30 kV in our standard CL work, is lowered to 3 kV in order to reduce the diameter of the carrier generation volume resulting in an increase of the lateral CL resolution. The exciting electron beam is digitally scanned over a sample area divided in up to 512 x 400 pixels. The CL signal is detected in the visible and near infrared regime (GaAs quantum wells) by a cooled photomultiplier using the technique of time resolved single photon counting. The total time resolution is better than 250 ps. Our data acquisition technique has the unique advantage that simultaneously up to 14 time Windows can be activated, enabling us to record up to 14 spectra or up to 14 images corresponding to different times with respect to the start of the exciting pulse in a single run. Results on AlGaAs/GaAs/AlGaAs quantum wells are presented as a typical example. Direct images of growth islands differing by one monolayer height (2.8 A) at GaAs/AlGaAs heterointerfaces and of the columnar structure of GaAs QWs are observed. The dependence of the lateral extension of these islands, which for certain growth conditions exceeds 6-7 µm, on the parameters of crystal growth is investigated. A transition from 2 dimensional to 3 dimensional crystal growth due to an increase of the MBE (molecular beam epitaxy) growth temperature from 600° C to 660° C is clearly observed. Spectrally- and time-resolved CLI experiments directly visualize the lateral diffusion of the quasi two dimensional carriers along the quantum well interfaces and provide a measure of the in-plane diffusion velocity in quantum well structures. The CLI detection setup is further extended to the infrared regime, by adapting a Ge-PIN-diode and avalanche photodiodes to the photon counting System. This enables CLI and time resolved CLI investigation of InGaAs quantum wells and related material Systems. Strain induced dislocations in pseudomorphic strained layer quantum wells (e.g. GaAs/InGaAs/GaAs QWs) are directly visualized by infrared CLI. Time resolved experiments yield lifetime images around these dislocations.

Carrier transport property in the amorphous silicon/amorphous silicon carbide multilayer studied by the transient grating technique

The in-plane diffusion coefficient and lifetime of photogenerated carriers in amorphous silicon have been measured by the transient grating technique in amorphous silicon (a-Si)/silicon carbide (a-SiC) multilayered structures, as a function of the a-Si well layer thickness. As the layer thickness is decreased, the diffusion coefficient gradually decreases, while the lifetime drastically increases by more than one order of magnitude than that in thick unlayered a-Si. These behaviors suggest that the carrier transport is determined both by carrier interaction with shallow traps at a-Si/a-SiC interfaces and by quantum-size effect through weakened carrier coupling with deep states.

Remote measurement of in-plane diffusivity components in plates

A method of determining thermal diffusivity in thin plates is presented. The method, using infrared images of evolving thermal patterns previously injected with a laser, is noncontacting, one-sided, and remote. It does not require independent estimates of either the emissivity of the sample or the sample thickness. With a line-segment pattern for thermal input, it yields the in-plane components of the diffusivity tensor in anisotropic materials and also the rate of heat loss to the environment of the plate. Two methods of data analysis are presented, one corresponding to a heating line of general cross section and the other considering a Gaussian cross section, thereby saving considerable computer time. Both methods produce a statistical evaluation of measurement quality as well as estimates of diffusivity and loss rate. Results are shown for plates of metals and graphite-epoxy composite materials. Principal components and orientation for the diffusivity tensor are obtained in the anisotropic graphite-epoxy sample.

In-plane jump diffusion of Li in LiC6.

Li diffusion in ${\mathrm{LiC}}_{6}$ has been measured by high-resolution neutron spectroscopy both in the ordered phase between 630 and 675 K and in the disordered phase at 720 K. The in-plane diffusion constant D at 660 K is 1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ ${\mathrm{cm}}^{2}$/s, which increases to 24\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ ${\mathrm{cm}}^{2}$/s above ${\mathrm{T}}_{\mathrm{c}}$. At all temperatures, a jump-type diffusion mechanism was observed, with jump vectors connecting nearest Li-sublattice sites in the ordered phase, but nearest hexagon centers in the disordered phase.

Structural Energies in Stage-One Graphite Intercalation Compounds

A Thomas-Fermi density-functional theory is developed for structural energies in stage-one alkali-graphite intercalation compounds. Correct trends for lattice constants and elastic moduli are obtained. We compute corrugation energies $\ensuremath{\Delta}E$ and alkali-alkali spring constants $k$, which determine in-plane intercalant diffusion and domain-wall structure. $k$ is determined by electrostatic effects, and is mainly independent of intercalant. $\ensuremath{\Delta}E$ depends strongly on intercalant size; thus Li differs substantially from K, Rb, and Cs.