Grain boundary behavior in metallic solid solutions as deduced from diffusion and segregation experiments

Grain boundary diffusion and segregation experiments have been carried out in the same metallic solid solutions by means of radio-isotopes and Auger techniques. It was shown that the mass transport parameters could only be understood by assuming the formation of “2D phases” in “segregated grain boundaries” where the main bonds between atoms were identical to those which limit the bulk solid solubility of the solutes.     

Simultaneous enhancement in coercivity and remanence of Nd2Fe14B permanent magnet by grain boundary diffusion process using NdHx

We have successfully developed a Dy-free grain boundary diffusion process with neodymium hydride (NdH_x) alloy to the permanent magnet Nd₂Fe₁₄B powders using hydrogenation – disproportionation – desorption – recombination (HDDR) method. All the diffusion treatments were performed at 700–800 °C for various annealing time under the high vacuum with rotating diffusion method that effectively control the abnormal grain growth. The coercivities of Dy-treated Nd₂Fe₁₄B powders were varied from 9.5 kOe to 13.2 kOe but the remanence was decreased to 8.1 kG (10% reduction) depending on dysprosium hydride (DyH_x) content and diffusion treated time. However, the coercivity and remanence of Dy-free diffusion treated powder have been increased to 12.2 kOe (28.5% enhancement) and 11.1 kG (22% enhancement) at the optimal diffusion treatment (800 °C for 3 h), respectively. This unique simultaneous enhancement is to isolate the magnetic coupling between Nd₂Fe₁₄B grains by creating non-magnetic Nd grain boundaries and enhance the alignment of the Nd₂Fe₁4B hard magnetic phase, fabricated by optimal diffusion conditions.     

Comparison of implantation and diffusion behavior of Ti, Sb and N in ion-implanted single crystal and polycrystalline ZnO: A SIMS study

Implantation and diffusion behavior of Sb, Ti and N in ZnO single crystal and sputter deposited thin films were studied through secondary ion mass spectrometric studies on ion-implanted and thermally annealed samples. Sb was implanted and Ti and N were co-implanted into ZnO single crystals and polycrystalline thin films on Si substrates at room temperature. The implanted samples were then annealed at 800 °C. Depth profiles of implant distributions before and after annealing were examined by Secondary Ion Mass Spectrometry (SIMS). As expected, implant range is sensitive to the mass of the dopants; and the dopant distribution is broadened as implanted elements migrate deeper into the film on thermal annealing. While diffusion of N in the ZnO thin film is not significant, Ti tends to diffuse deeper into the sample during annealing. For Ti and N co-implanted single crystal, annealing induced diffusion causes more redistribution of the lighter N than Ti. In general, implanted dopants diffuse more easily in thin films compared to the single crystal due to the presence of grain boundaries in the latter.     

Grain boundary interdiffusion in the case of concentration-dependent grain boundary diffusion coefficient

The grain boundary diffusion in a binary system which exhibits a grain boundary phase transition is considered in the framework of Fisher's model. The kinetic law of the growth of the grain boundary phase and the distribution of the diffusant near the grain boundary are calculated. The method of determining of the concentration dependence of the grain boundary diffusion coefficient from the experimentally measured penetration profiles of the diffusant along the grain boundaries is suggested. The experimental results on Zn diffusion in Fe(Si) bicrystals, Ni diffusion in Cu bicrystals and grain boundary grooving in Al in the presence of liquid In are discussed in light of the suggested model.     

The thermodynamic factors for cation diffusion in AO,p-type oxides doped with a trivalent impurity

The thermodynamic factors for cation diffusion in p-type semiconducting oxides of the formula AO doped with a trivalent impurity are evaluated, assuming a known structure of defects of the base oxide. It is shown that these parameters are not only functions of the oxygen activity and of the dopant concentration, but also strongly depend on the ratio between the gradients of these two variables. Limiting expressions corresponding to the presence of only one of these gradients are derived and evaluated by means of suitable approximations under conditions of very small or very large impurity concentrations. A general relationship between the two thermodynamic factors is obtained by means of the Gibbs-Duhem equation as applied to the relevant ternary system. Finally, the thermodynamic factors for cation diffusion are evaluated numerically for the case of NiO doped with a trivalent impurity at 1000°C, using a convenient detailed model to represent its defect structure.     

The stability of triple junctions during the grain boundary diffusion process

The grain boundary diffusion in a system with triple junctions is considered in such a geometry, in which the flows of diffusing atoms meet at the triple line. The solutions of the diffusion equation is given in the frameworks of Fisher's model and under the assumption of quasi-stationary distribution of the diffusing atoms along the grain boundaries. The change of the mechanical equilibrium at the triple junction due to the increase of the concentration of solute atoms is considered. It is shown that under some circumstances the triple junction looses its stability with respect to migration in the direction to the diffusion source. The stability diagrams in the segregation-diffusivity parameter space are plotted.     

Interfacial diffusion relaxation of internal stresses in solids

The relaxation of internal stresses due to interfacial diffusion in a two-phase solid is studied theoretically with the help of the onsageristic approach of irreversible thermodynamics. In this note we derive an expression for the rate at which internal stresses associated with misfit caused by bonding a flat surface of one material to a rough surface of another. The two phases are treated as isotropic clastic substances. It is assumed that the components of only of the solids are capable of leaving their positions of migrating along the interface. The driving force for this process is minimization of total energy-clastic plus interfacial energy. We show that the time constant for relaxing these stresses is proportional to the cube of the wavelength of the roughness.     

The effect of duration of diffusion on Ag diffusion coefficients in YBa2Cu3O7

The Ag diffusion in superconducting YBa₂Cu₃O₇ (YBaCuO) ceramic has been studied over the duration of the diffusion range 5-24 h in the temperature range 700-850 °C by the energy-dispersive X-ray fluorescence (EDXRF) technique. For the excitation of silver atoms, an annular Am-241 radioisotope source (50 mCi) emitting 59.543 keV photons was used. The temperature dependences of silver diffusion coefficients in grains (D₁) and over the grain boundaries in the range 700-850 °C (D₂) are described by the relations D₁=1.4×10⁻² exp[−(1.18±0.10)/kT] and D₂=3.1×10⁻⁴ exp[−(0.87±0.10)/kT].     

Application of laser beam deflection technique to study the diffusion process in electrolyte solutions

A simple method based on laser beam deflection to study the variation of diffusion coefficient with concentration in a solution is presented. When a properly fanned out laser beam is passed through a rectangular cell filled with solution having concentration gradient, the emergent beam traces out a curved pattern on a screen. By taking measurements on the pattern at different concentrations, the variation of diffusion coefficient with concentration can be determined.     

Acquisition of pure-phase diffusion spectra using oscillating-gradient spin echo

Oscillating-gradient spin echo (OGSE) diffusion experiments have long been used to measure the short-time apparent diffusion coefficient, D(app)(t), in the presence of restricted diffusion, as well as the spectrum of the slow-motion velocity autocorrelation function. In this work, we focus on two previously unexplored aspects of OGSE experiments: convection compensation and acquisition of pure-phase diffusion spectra in the presence of homonuclear scalar couplings. We demonstrate that convection compensation afforded by single-echo OGSE compares well with that in double-echo convection-compensated PGSE experiments. We also show that, in the presence of homonuclear scalar couplings, setting the OGSE echo time to 1/2J enables acquisition of pure-phase diffusion spectra and yields more reliable D estimates than mixed-phase PGSE or OGSE spectra. Pure-phase OGSE acquisition is also compatible with measurements of the apparent diffusion coefficient at an arbitrary diffusion time. These features of OGSE can be valuable in diffusion measurements of scalar-coupled small-molecule probes in cellular and other heterogeneous systems.     

Oxygen ion diffusion measurements in Bi0.775La0.225O1.5

The oxygen transport properties of the Bi_0.775La_0.225O_1.5 electrolyte material have been investigated. Isotopic exchange depth profiling (IEDP) technique with secondary ion mass spectrometry (SIMS) was used in order to measure the oxygen tracer diffusion coefficient D. The activation energy for oxygen tracer diffusion was found to be 115 ± 2 kJ/mol (1.19 ± 0.02 eV). The measured D values were converted using the Nernst-Einstein relationship to conductivity and compared with data from AC Impedance. The agreement of the two sets of data implies that the material is an oxygen ion conductor.     

Influence of grain sizes on the ionic conductivity and the chemical diffusion coefficient in copper selenide

Ionic conductivity and chemical diffusion coefficient have been studied for superionic polycrystalline Cu_1.75Se copper selenide within the temperature interval 300–500 K. An increase in ionic conductivity with an grain size increase is observed. In our opinion, this fact is caused by lower activation energy for the bulk diffusion than that for the grain boundary diffusion.     

Experimental determination of solid-liquid interfacial energy for solid Sn in the Sn-Mg system

The equilibrated grain boundary groove shapes for solid Sn in equilibrium with the Sn-9 at.% Mg eutectic liquid were directly observed annealing a sample at the eutectic temperature for about 5 days with a radial heat flow apparatus. The thermal conductivities of the solid phase, κ_S, and the liquid phase, κ_L, for the groove shapes were measured. From the observed grain boundary groove shapes, the Gibbs-Thomson coefficient, the solid-liquid interfacial energy and grain boundary energy for solid Sn in equilibrium with the Sn-9 at.% Mg eutectic liquid have been determined to be (7.35 ± 0.36) × 10⁻⁸ Km, (136.41 ± 13.64) × 10⁻³ J m⁻² and (230.95 ± 25.40) × 10⁻³ J m⁻², respectively.     

Apparent diffusion coefficient of line scan diffusion image in normal prostate and prostate cancer—comparison with single-shot echo planner image

Purpose

This retrospective study was designed to evaluate the apparent diffusion coefficient (ADC) of line scan diffusion images (LSDI) in normal prostate and prostate cancer. Single-shot echo planner images (SS-EPI) were used for comparison.

Materials and Methods

Twenty prostate tumors were examined by conventional MRI in 14 patients prior to radical prostatectomy. All patients were examined with a 1.5-T MR imager (Signa CV/i ver. 9.1 GE Medical System Milwaukee, WI, USA). Diffusion-weighted MR imaging (DWI) using LSDI was performed with a pelvic phased-array coil, with b values of 5 and 800 s/mm². DWI using SS-EPI was performed with a body coil, with b values of 0 and 800 s/mm². The ADCs of each sequence for 14 normal prostate and 20 prostate cancers were histopathologically assessed. Signal-to-noise ratio (SNR) on DWI was estimated and compared for each sequence.

Results

The mean ADCs (±S.D.) of normal peripheral zones (PZ), transition zones (TZ) and cancer (in 10⁻³ mm²/s) that used LSDI were 1.42±0.12, 1.23±0.10 and 0.79±0.19, respectively. Those that used SS-EPI were 1.76±0.26, 1.38±0.20 and 1.05±0.27, respectively. Using unpaired t test (P<.05), we found a significant difference in each sequence between normal tissue (both PZ and TZ) and the cancer. Paired t test (P<.05) also registered a significant difference between LSDI and SS-EPI. Mean SNR for DWI using LSDI was 16.49±5.03, while the DWI using SS-EPI was 18.85±9.26. The difference between the SNR of each sequence was not statistically significant by paired t test.

Conclusion

We found that ADCs using LSDI and SS-EPI showed similar tendencies in the same patients. However, in all regions, LSDI ADCs had smaller standard deviations than SS-EPI ADCs.     

Measurement of solid-liquid interfacial energy for solid Zn in the Zn-Cd eutectic system

The equilibrated grain boundary groove shapes for the Zn solid solution in Zn-Cd liquid solutions were directly observed. From the observed grain boundary groove shapes, the Gibbs-Thomson coefficient for solid Zn (Zn-15 wt.% Cd) in Zn-Cd liquid solutions has been determined to be (2.5 ± 0.1) × 10⁻⁸ Km by a direct method. The solid-liquid interfacial energy between solid Zn and Zn-Cd liquid solution has been obtained to be (165.5 ± 19.0) mJ/m² from the Gibbs-Thomson equation. The grain boundary energy for the same alloy has been determined as (317.8 ± 39.9) mJ/m². The thermal conductivities of the solid and liquid phases at the eutectic composition and temperature have also been measured.     

Vacancy diffusion in Cu∑ = 5[0 0 1] twist grain boundary

Both the formation energies and the diffusive activation energy of a single vacancy migrating intra- and inter-layer in the first four atomic planes near Cu∑ = 5[0 0 1] twist GB have been investigated by means of MD in conjunction with MAEAM. The effects of the GB on the vacancy formation and migration are only to the third layer. The vacancy is favorable to be formed on the un-coincident site in the first, second and third layers near the GB plane and this case is enhanced successively following the third, second and first layers. A single vacancy either on un-coincident site or on coincident site in the forth, third and second layers is favorable to migrate to un-coincident site (its first-nearest-neighbor) in its adjacent layer near the GB. But for the first layer, the favorable migration path of the vacancy on the un-coincident site is between un-coincident sites of the first layer or to its nearest-neighbor of the first layer in the rotating grain, which is not the case for the vacancy on the coincident site ‘1’ that is migrated difficultly. So, there are collective tendency of the vacancy in the GB.     

The effect of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame

The influence of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame was investigated by numerical simulation using three different transport property calculation methods. One simulation included preferential diffusion and the other two neglected preferential diffusion. The results show that the neglect of preferential diffusion or the use of unity Lewis number for all species results in a significant underprediction of soot volume fraction. The peak soot volume fraction is reduced from 8.0 to 2.0 ppm for the studied flame when preferential diffusion is neglected in the simulation. Detailed examination of numerical results reveals that the underprediction of soot volume fraction in the simulation neglecting preferential diffusion is due to the slower diffusion of some species from main reaction zone to PAH and soot formation layer. The slower diffusion of these species causes lower PAH formation rate and thus results in lower soot inception rate and smaller particle surface area. The smaller surface area further leads to smaller surface growth rate. In addition, the neglect of preferential diffusion also leads to higher OH concentration in the flame, which causes the higher specific soot oxidation rate. The lower inception rate, smaller surface growth rate and higher specific oxidation rate results in the lower soot volume fraction when preferential diffusion is neglected. The finding of the paper implies the importance of preferential diffusion for the modeling of not only laminar but maybe also some turbulent flames.     

Research on the effective gas diffusion coefficient in dry porous media embedded with a fractal-like tree network

A theoretical model for the relative gas diffusion coefficient in dry porous media embedded with a Y-shaped fractal-like tree network is presented under the combination of bulk diffusion and Knudsen diffusion. The proposed model is expressed as a function of the length ratio, the diameter ratio, the branching level, the branching angle and the relative areal porosity. The effect of the structural parameters of the medium and the tortuosity on gas diffusion is analyzed in detail. Model predictions are compared with available experimental data, and a fair agreement between them is found.     

Different effects of grain boundary scattering on chargeand heat transport in polycrystalline platinum and goldnanofilms

The in-plane electrical and thermal conductivities of several polycrystalline platinum and gold nanofilms with different thicknesses are measured in a temperature range between the boiling point of liquid nitrogen (77K) and room temperature by using the direct current heating method. The result shows that both the electrical and thermal conductivities of the nanofilms reduce greatly compared with their corresponding bulk values. However, the electrical conductivity drop is considerably greater than the thermal conductivity drop, which indicates that the influence of the internal grain boundary on heat transport is different from that of charge transport, hence leading to the violation of the Wiedemann--Franz law. We build an electron relaxation model based on Matthiessen's rule to analyse the thermal conductivity and employ the Mayadas & Shatzkes theory to analyse the electrical conductivity. Moreover, a modified Wiedemann--Franz law is provided in this paper, the obtained results from which are in good agreement with the experimental data.     

On the relationship between the apparent diffusion coefficient and extravascular extracellular volume fraction in human breast cancer

MRI techniques have been developed that can noninvasively probe the apparent diffusion coefficient (ADC) of water via diffusion-weighted MRI (DW-MRI). These methods have found much application in cancer where it is often found that the ADC within tumors is inversely correlated with tumor cell density, so that an increase in ADC in response to therapy can be interpreted as an imaging biomarker of positive treatment response. Dynamic contrast enhanced MRI (DCE-MRI) methods have also been developed and can noninvasively report on the extravascular extracellular volume fraction of tissues (denoted by v_e). By conventional reasoning, the ADC should therefore also be directly proportional to v_e. Here we report measurements of both ADC and v_e obtained from breast cancer patients at both 1.5 and 3.0 T. The 1.5-T data were acquired as part of normal standard of care, while the 3.0-T data were obtained from a dedicated research protocol. We found no statistically significant correlation between ADC and v_e for the 1.5- or 3.0-T patient sets on either a voxel-by-voxel or a region-of-interest (ROI) basis. These data, combined with similar results from other disease sites in the literature, may indicate that the conventional interpretation of either ADC, v_e or their relationship is not sufficient to explain experimental findings.