Kinetic equations for concurrent size and shape coarsening by the ledge mechanism

The kinetic equations describing concurrent size and shape coarsening of plate-and rod-shaped particles having shapes that deviate from equilibrium are presented. In the derivations, the assumption is made that some of the interfaces are fully or partially coherent and migrate by the ledge mechanism. Three different interfacial character combinations are considered. The analysis also assumes a small and constant volume fraction of particles so that the average matrix composition can be estimated from knowledge of the particle size distribution, the surface area available for atomic attachment/detachment, and the diffusion distance. The resultant flux equations are then used in a computer model to predict the coarsening behavior of an ensemble of nonequilibrium-shaped particles. Comparison of these results with those obtained from the traditional coarsening theory of Lifshitz and Slyosov¹ and Wagner² (LSW) show significant discrepancies. These differences are attributed to the invalidity of many assumptions made in the LSW theory when applied to solid:solid coarsening systems. Formerly Graduate Student, Michigan. Technological University. Formerly Graduate Student, University of Utah. Formerly Graduate Student, University of Utah, Salt Lake City, UT. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Influence of particle size distribution on coarsening

This study has examined the evolution of the particle size distribution and the effect of the initial and transient distributions on coarsening kinetics and the path of evolution. A numerical procedure has been employed to simulate the coarsening process statistically. It was found that the distribution passes through a continuous range of forms from the initial distribution towards the asymptotic state, with initially narrow distributions widening and wide distributions narrowing. Experimental studies using liquid phase sintered Cu-20 Co alloy with different initial distribution widths agreed with the above simulation results qualitatively. The simulated coarsening rate was found to be related to the width and shape of particle size distribution. A rate constant has been derived relating the instantaneous coarsening rate and the transient moments of the distribution. The effect of the initial distribution on coarsening rate was found to be particularly significant in the early stage of coarsening when rapid distribution changes occur. After these early rapid transients but still far from the asymptotic state, the instantaneous coarsening rate was closely related to the instantaneous geometric standard deviation of the distribution.     

Simultaneous recovery of size and radioactivity concentration of small spheroids with PET data

Quantification of tumor activity is used to predict prognosis and discriminate benign from malignant lesions identified by PET. Accurate quantitation of small lesions requires correction for the partial volume effects. Such a correction is often based on the recovery coefficient (RC), which depends on the lesion size, the object-to-background ratio (OBR) and physical properties of the media. The purpose of this investigation was to determine whether a model-based optimization method to simultaneously recover the size and the activity concentration of small spheroids could improve estimates of lesion radioactivity when object size is unknown. For reference, we compared our method with a widely used approach, RC correction, that requires the object size to be known. METHODS: A three-dimensional, spatially varying, object size- and contrast-dependent Gaussian model of the point spread function (PSF) of an ECAT EXACT was developed. The observed dependence of the PSF on random coincidences and measured-peak/background activity were included in the PSF using three adjusting factors. Size and radioactivity concentration of a spheroid were estimated by adjusting size and concentration until model output best matched the image data. Elliptic and circular phantoms both containing seven hot spheroids, with OBRs ranging from 5.6 to 0 background, were evaluated. RESULTS: The proposed quantification method reduced the activity error by 11%-63% of the error obtained without correction. The greatest error reduction occurred for small spheroids. The average error in radius estimation ranged from 2% to 48%, wherein the smallest spheroid produced the largest errors. For spheroids with diameters from 8 to 22 mm, Student t test (paired, one-tail) showed the proposed method significantly improved accuracy (P < 0.05) in comparison with the RC method and also in comparison with optimization without the three adjusting factors. CONCLUSION: The model-based optimization method improved estimation of radioactivity concentration over that corrected by the RC method and that made without any correction. It also provided accurate estimation of size for spheroids larger than 6 mm in diameter.     

Effect of size distribution on the kinetics of normal grain growth and of particle coarsening

A simple model is presented to describe the kinetics of normal grain growth. The final expression incorporates a factor which depends on the grain size distribution but no assumption is made on the distribution function. A similar expression is also derived for particle coarsening.     

Measuring the shape and size of microcracks in bone

Microcracks in bone are normally measured from two-dimensional, transverse sections but this provides incomplete information about their three-dimensional shape and size. The methods of stereology can usefully be applied in such a case. This problem has been addressed using a theoretical model and a numerical simulation. Results show that the data are consistent with a crack shape which is elliptical, with axis ratio approximately 4.5:1 and with size variation (expressed as the ratio of standard deviation to mean length) of at least 0.1. Measured lengths will, on average, be smaller and have more scatter than true lengths. Errors caused by omitting small cracks are relatively unimportant. Knowledge of the true crack dimensions, and their variability, is important for the analysis of damage, stress fracture, remodelling and adaptation.     

Diffusion coarsening of the lamellar structure in two-phase Ti-47.5 at.% Al intermetallic alloy

Diffusion coarsening of the lamellar structure in two-phase γ-α₂ intermetallic Ti-47.5 at.% Al alloy is treated as caused by hole-like macro-defects growth. A model of unlimited diffusion-controlled growth of such defects and an approach to the experimental data processing are considered. Based on this model, experimental investigations of coarsening kinetics have been carried out in TiAl alloy in the temperature range 1073–1373 K. The low value of the activation enthalpy Q_m = 63.8 kJmol⁻¹ has been found. The stability of the γ-α₂ lamellar structure in the studied TiAl intermetallic alloy is compared with the stability of the γ-γ′ raft structure in Ni-base superalloy single crystals.     

The effect of biopsy-hole shape and size on bone strength

The erythrocyte cholesterol, total phospholipid and individual phospholipids content have been determined in patients with chronic renal failure, resulting from glomerulonephritis and pyelonephritis. The rise in total phospholipid, confined predominantly to the sphingomyelin and lecithin classes was found. It was often accompanied by decrease in the phosphatidylethanol-amine content. The cholesterol/phospholipid ratio was found to be reduced. The excessive lipid loss during incubation of erythrocytes in glucose-rich medium has been observed in some patients.     

Is blood pressure related to kidney size and shape?

OBJECTIVE: To examine the relationship between blood pressure and the size and shape of the kidneys in healthy volunteers from the community. DESIGN: A cross-sectional community-based study of normal volunteers in Portsmouth City, Hampshire, UK. SUBJECTS: Subjects numbered 185 (99 female), aged 19-66 years. RESULTS: Blood pressure was higher in men, and in those with higher body mass index. Both systolic and diastolic blood pressure were correlated with the derived kidney volume. However, when corrected for age, sex and BMI the relationship was not statistically significant. Blood pressure correlated inversely with the width : length ratio of the left kidney. CONCLUSIONS: Blood pressure was not correlated with kidney size in this group of adults.     

Grain shape and its influence on the experimental measurement of grain size

A procedure for determining grain size,N _V , from measurable two-dimensional parameters is presented. A variety of microstructures (ferritic, austenitic, and ferrite-pearlitic steels and zinc) are considered and all tend to obey the following relation:N _V = 122.23 (N _L /K _S )³, whereN _L is the average number of grains per unit length of the test line, and KS is the shape factor of the grains. A shape factor is proposed which can be used to examine quantitatively the influence of grain shape, and an analysis is made of possible errors resulting from the approximate equations used in the literature for theN _V determination. The presence of a nonnegligible percentage of nonequiaxial grains and the curvature of the surfaces of each grain make the variety and complexity of shape distribution in grains greater than could be expected from their topological features.     

A unified model of microsegregation and coarsening

Using a coordinate transform in a standard microsegregation model it is shown that the effect of coarsening on the dilution of the liquid phase can be accounted for by adding a dimensionless parameter α ^c to the back-diffusion Fourier number. Through theory, for the case of parabolic growth, and numerical experiments for the constant cooling rate, it is shown that a constant value of α ^c =0.1 is a sound choice across a wide range of casting and alloy conditions. This finding allows for the development of a unified model for microsegregation and coarsening. In particular, previous approximate microsegregation models can be readily modified to account for coarsening.     

Investigation of iron ore particle size and shape on green pellet quality

ABSTRACT

Particle size and shape of iron ore concentrate are effective parameters in the production of quality green pellets. In this research, the effect of particle morphology on green pellet quality was studied. It was concluded that pellet quality improved with increasing specific surface area. Drop number and green compression strength of pellets ground by HPGR were found to be superior over those ground in the ball mill. The chief reasons were related to particle shape and the fraction of fine particles. Smaller particle size results in a higher order of bonding between particles and therefore the formation of a stronger system. Also, the rougher and less circular shape of particles resulted in higher strength. According to the breakage model in the particle-moisture system, pellet failure occurs because of crack propagation in the solid–liquid interface. The effects of roughness on capillary force and wettability have been explained mathematically. In addition, the effects of roughness and aspect ratio on breakage path and increase of required energy for pellet failure have been modelled.     

Readily releasable pool size changes associated with long term depression

We have estimated, for hippocampal neurons in culture, the size of the autaptic readily releasable pool before and after stimulation of the sort that produces culture long term depression (LTD). This stimulation protocol causes a decrease in the pool size that is proportional to the depression of synaptic currents. To determine if depression in this system is synapse specific rather than general, we have also monitored synaptic transmission between pairs of cultured hippocampal neurons that are autaptically and reciprocally interconnected. We find that the change in synaptic strength is restricted to the synapses on the target neuron that were active during LTD induction. When viewed from the perspective of the presynaptic neuron, however, synapse specificity is partial rather than complete: synapses active during induction that were not on the target neuron were partially depressed.