## Transformation kinetics, anisotropic sintering stress, growth kinetics, grain boundary energies in fcc materials, and thermodynamics of grain boundary premelting

### June 5, 2009

[1] Transformation kinetics for nucleus clusters

E Villa and P R Rios

A rigorous mathematical approach based on stochastic geometry concepts is presented to extend previous Johnson–Mehl, Avrami, Kolmogorov treatment of transformation kinetics to situations in which nuclei are not homogeneously located in space but are located in clusters. An exact analytical solution is presented here for the first time assuming that nucleation sites follow a Matérn cluster process. The influence of Matérn cluster process parameters on subsequent growth kinetics and the microstructural path are illustrated by means of numerical examples. Moreover, using the superposition principle, exact analytical solutions are also obtained when nucleation takes place by a combination of a Matérn cluster process and an inhomogeneous Poisson point process. The new solutions presented here significantly increase the number of exactly solvable cases available to formal kinetics.

[2] Anisotropic sintering stress for sintering of particles arranged in orthotropic symmetry

F Wakai and Y Shinoda

Many sintering bodies shrink in an anisotropic manner when the particle packing is not isotropic. The thermodynamic driving force for the anisotropic shrinkage, i.e. the sintering stress tensor, is determined numerically for an open pore structure with orthotropic symmetry in three dimensions. The sintering stress tensor is calculated rigorously by the energy method, the force balance method and the volume averaging method. The deviatoric component of sintering stress is approximately proportional to the logarithm of the aspect ratio of the orthorhombic volume element, and acts so as to deform the elongated particles to be more isotropic in most cases.

[3] Phase field study of precipitate growth: Effect of misfit strain and interface curvature (Note: self-promotion!)

R Mukherjee et al

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

[4] Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

D L Olmsted et al

The energies of a set of 388 distinct grain boundaries have been calculated based on embedded-atom method interatomic potentials for Ni and Al. The boundaries considered are a complete catalog of the coincident site lattice boundaries constructible in a computational cell of a prescribed size. Correlations of the boundary energy with other boundary properties (disorientation angle, *Σ* value, excess boundary volume and proximity of boundary normals to 1 1 1) are examined. None of the usual geometric properties associated with grain boundary energy are useful predictors for this data set. The data set is incorporated as supplementary material to facilitate the search for more complex correlations. The energies of corresponding boundaries in Ni and Al are found to differ by approximately a scaling factor related to the Voigt average shear modulus or C_{44}. Crystallographically close boundaries have similar energies; hence a table of grain boundary energies could be used for interpolation.

[5] Thermodynamics of grain boundary premelting in alloys. I. Phase-field modeling

Y Mishin et al

The rich nature of the premelting transition of grain boundaries in solid solutions is analyzed. Part I of this paper uses a multi-phase field model, whereas Part II employs atomistic Monte Carlo simulations. To enable comparison, Cu-rich Cu–Ag solid solutions are chosen for study. In the phase-field model, a system composed of two grains and a liquid phase is treated with three phase field parameters and with a realistic bulk thermodynamic description of Cu–Ag alloys obtained with the CALPHAD approach. Several different computation methods are employed, both rigorous and approximate, to examine the premelting behavior and relate it to the so-called “disjoining potential” between the solid–liquid interfaces in the grain boundary region. Depending on the grain boundary energy, temperature and grain composition chosen, several different classes of premelting transitions have been detected. As the grain concentration approaches the solidus line, one class shows a premelted layer whose thickness diverges continuously to infinity (complete wetting). Another class shows a discontinuity of the premelted layer thickness, exhibiting a first-order thin-to-thick transition prior to continuous thickening to infinity at the solidus line. In other cases, a metastable grain boundary state can exist above the solidus line, indicating the possibility of superheating/supersatuation of the grains together with the grain boundary. The possibility of such transitions has been predicted previously for generic thermodynamics by many authors. The results of the current investigation are compared with the atomistic calculations for the Cu–Ag system in Part II of this work.