The sintering behavior of close-packed spheres

The sintering behavior and microstructural evolution of a powder compact is influenced strongly by initial properties, such as the relative density, the particle and pore size distribution, and the powder packing. While the influence of the former parameters on the microstructural evolution has been investigated in some detail, the impact of the initial packing of the powder has been mostly overlooked. However, research has shown that the sintering behavior of a powder can be significantly improved if the powder is regularly packed. This has been shown for monodisperse spherical TiO2 particles [1], which sintered 10 times faster and exhibited almost no grain growth compared to ordinary TiO2. Similar observations has been made for homogeneously packed Al2O3 [2], SiO2 [3], as well as a number of other materials [4]. Monodispersed spherical TiO2 particles have been shown to order in face-centered cubic (fcc) arrays, while the SiO2 powder forms stacked planes of hexagonal close-packed (hcp) particles. Close packing of monodispersed silica has also been observed [5]. Sintering of two-dimensional close packing cylinders has also been demonstrated experimentally [6–8] and numerically modeled [9,10], and the sintering of particle clusters in three dimensions has also been studied [11]

Strain in the mesoscale kinetic Monte Carlo model for sintering

Shrinkage strains measured from microstructural simulations using the mesoscale kinetic Monte Carlo (kMC) model for solid state sintering are discussed. This model represents the microstructure using digitized discrete sites that are either grain or pore sites. The algorithm used to simulate densification by vacancy annihilation removes an isolated pore site at a grain boundary and collapses a column of sites extending from the vacancy to the surface of sintering compact, through the center of mass of the nearest grain. Using this algorithm, the existing published kMC models are shown to produce anisotropic strains for homogeneous powder compacts with aspect ratios different from unity. It is shown that the line direction biases shrinkage strains in proportion the compact dimension aspect ratios. A new algorithm that corrects this bias in strains is proposed; the direction for collapsing the column is determined by choosing a random sample face and subsequently a random point on that face as the end point for an annihilation path with equal probabilities. This algorithm is mathematically and experimentally shown to result in isotropic strains for all samples regardless of their dimensions. Finally, the microstructural evolution is shown to be similar for the new and old annihilation algorithms.Comment: 6 pages, 6 figure

On the nitrogen-induced lattice expansion of a non-stainless austenitic steel, Invar 36®, under triode plasma nitriding

Chromium, as a strong nitride-forming element, is widely regarded to be an “essential” ingredient for the formation of a nitrogen-expanded lattice in thermochemical nitrogen diffusion treatments of austenitic (stainless) steels. In this article, a proprietary “chrome-free” austenitic iron-nickel alloy, Invar® 36 (Fe-36Ni, in wt pct), is characterized after triode plasma nitriding (TPN) treatments at 400 °C to 450 °C and compared with a “stainless” austenitic counterpart RA 330® (Fe-19Cr-35Ni, in wt pct) treated under equivalent nitriding conditions. Cr does indeed appear to play a pivotal role in colossal nitrogen supersaturation (and hence anisotropic lattice expansion and superior surface hardening) of austenitic steel under low-temperature (≤ 450 °C) nitrogen diffusion. Nevertheless, this work reveals that nitrogen-induced lattice expansion occurs below the nitride-containing surface layer in Invar 36 alloy after TPN treatment, implying that Cr is not a necessity for the nitrogen-interstitial induced lattice expansion phenomenon to occur, also suggesting another type of γN

A Numerical Approach for Non-Linear Moisture Flow in Porous Materials with Account to Sorption Hysteresis

A numerical approach for moisture transport in porous materials like concrete is presented. The model considers mass balance equations for the vapour phase and the water phase in the material together with constitutive equations for the mass flows and for the exchange of mass between the two phases. History-dependent sorption behaviour is introduced by considering scanning curves between the bounding desorption and absorption curves. The method, therefore, makes it possible to calculate equilibrium water contents for arbitrary relative humidity variations at every material point considered. The scanning curves for different wetting and drying conditions are constructed by using third degree polynomial expressions. The three coefficients describing the scanning curves is determined for each wetting and drying case by assuming a relation between the slope of boundary sorption curve and the scanning curve at the point where the moisture response enters the scanning domain. Furthermore, assuming that the slope of the scanning curve is the same as the boundary curve at the junction point, that is, at the point where the scanning curve hits the boundary curve once leaving the scanning domain, a complete cyclic behaviour can be considered. A finite element approach is described, which is capable of solving the non-linear coupled equation system. The numerical calculation is based on a Taylor expansion of the residual of the stated problem together with the establishment of a Newton-Raphson equilibrium iteration scheme within the time steps. Examples are presented illustrating the performance and potential of the model. Two different types of measurements on moisture content profiles in concrete are used to verify the relevance of the novel proposed model for moisture transport and sorption. It is shown that a good match between experimental results and model predictions can be obtained by fitting the included material constants and parameters