## Papers of interest from Acta and Scripta

### April 17, 2010

[1] A new ultrahigh-strength stainless steel strengthened by various coexisting nanoprecipitates

W Xu et al

A general computational alloy design approach based on thermodynamic and physical metallurgical principles and coupled with a genetic optimization scheme is presented. The model is applied to develop a new ultrahigh-strength maraging stainless steel. The alloy composition and heat treatment parameters are integrally optimized so as to achieve microstructures of fully lath martensite matrix strengthened by multiple precipitates of MC carbides, Cu particles and Ni3Ti intermetallics. The combined mechanical properties, corrosion resistance and identification of actual strengthening precipitates in the experimental prototype produced on the basic of the model predictions provide a strong justification for the alloy design approach.

[2] An investigation of the effect of structural order on magnetostriction and magnetic behavior of Fe–Ga alloy thin films

A Javed et al

This paper reports results from a comprehensive study of Fe–Ga films fabricated over a wide range of growth conditions. Polycrystalline Fe100−xGax films (14 less-than-or-equals, slant x less-than-or-equals, slant 32) were deposited (using three different combinations of growth parameters) on Si(1 0 0) using a co-sputtering and evaporation technique. The growth parameters (sputter power, Ga evaporation rate and chamber pressure) were used primarily to control the Fe:Ga ratio in the films. X-ray diffraction showed that all films had left angle bracket1 1 0right-pointing angle bracket crystallographic texture normal to the film plane. The lattice parameter increased with % Ga up to x = 22 and was independent of growth parameters. Conversion electron Mössbauer spectroscopy studies showed a predominance of the disordered A2 phase in all films. It appears that the use of vacuum deposition with appropriate parameters can effectively suppress the D03 ordered phase. Systematic studies of the effective magnetostriction constant as a function of composition support this conclusion. It was found that films of high effective saturation magnetostriction constant and low stress could be fabricated using low Ar pressure, irrespective of sputter power or evaporation rate, giving properties useful for application in microelectromechanical systems.

[3] Coarsening of a multimodal nickel-base superalloy

K Coakley et al

The coarsening of γ′-Ni3Al precipitates in the nickel superalloy Ni115 has been examined and compared to the results of a numerical model based on LSW coarsening theory. Ni115 has a γ′ fraction of around 60%, and at the coarsening temperatures of interest the γ′ distribution is bimodal, with two populations not, vert, similar5 nm and not, vert, similar90 nm in radius. It is found that during the initial transient (around 2000 h at 800 °C), the fine γ′ dissolve, leading to a rapid increase in the mean radius followed by a plateau. At long times, the expected steady-state unimodal t1/3 coarsening is observed. The model reproduces these features in form and approximately in magnitude, a first for LSW model-experiment comparisons in nickel superalloys.

[4] Growth morphologies in peritectic solidification of Fe–C: A phase-field study

A Choudhury et al

We use a thermodynamically consistent multi-phase, multi-component phase-field model, where the evolution equations for the different fields are derived from an entropy functional, for simulating peritectic growth structures in two and three dimensions. Different solidification morphologies are obtained in the computations and the characteristic properties of the growth forms are discussed. The phase-field method allows for a prediction of the surface energies in the three-phase system δ-ferrite, γ-austenite and liquid based on comparison between experimentally observed and simulated structures. Additionally an investigation of possible nucleation sites in evolving domains is presented and its dependence on the solid–solid surface energy is examined.

[5] Topological characteristics of plane sections of polycrystals

G S Rohrer and H M Miller

Homology metrics have been used to assess the connectivity of grain boundary networks in plane sections of polycrystals. The analysis is based on orientation maps, and four characteristic microstructure types were examined: SrTiO3 microstructures with normal and bimodal grain size distributions and two Ni microstructures with different concentrations of Σ3 grain boundaries. The inverse connectivity, defined as the ratio of the number of independent pieces of the network to the number of closed loops, is proposed as a metric for the extent to which certain types of grain boundaries are connected. The variation in inverse connectivity with disorientation threshold, below which boundaries are excluded from the network, produces distinct signatures for the different microstructures.

[6] Controlling Ag whisker growth by using very-thin metallic films

H Tohmyoh et al

The selective growth of Ag nano-whiskers on polycrystalline films has been realized by introducing an additional artificial layer onto the films. Ag nano-whiskers with diameters of about 200 nm and lengths of around 3 μm have been successfully generated from Ag films covered with a 1 nm-thick SiO2 layer. On the other hand, the formation of Ag whiskers/hillocks on the top surface of the film could be suppressed by using thick SiO2 layers or ductile Au layers.

## Abnormal grain growth

### July 17, 2009

Abnormal grain growth in Al–3.5Cu

J Dennis et al

Significant abnormal grain growth has been observed in an Al–3.5 wt.% Cu alloy at temperatures where the volume fraction of small CuAl2 particles was less than about 0.01. The initial fine-grained material had a weak crystallographic texture and there was no indication that any special boundaries were involved in the abnormal growth. Island grains isolated within the abnormal grains also showed no indication of special orientation relationships with their surrounding grains. Measurements indicated that the island grains initially had a size advantage over other matrix grains. The fraction of pinning phase was much lower at abnormal grain boundaries than at boundaries in the fine-grained matrix into which they were growing. A variety of simulations were made, including attempts to model that difference in pinning phase distribution, but none of these were successful in predicting abnormal grain growth.

## Maximally fast algorithm for Cahn-Hilliard equation

### March 18, 2007

Here is a follow-up paper on the unconditionally stable time step for diffuse interface methods.

Paper: Maximally fast coarsening algorithms

Authors: Mowei Cheng and Andrew D. Rutenberg

Abstract:We present maximally fast numerical algorithms for conserved coarsening systems thatare stable and accurate with a growing natural time step . We compare the scaling structure obtained from our maximally fast conserved systems directly against the standard fixed time-step Euler algorithm, and find that the error scales as —so arbitrary accuracy can be achieved. For non-conserved systems, only effectively finite time steps are accessible for similar unconditionally stable algorithms.

Paper: Fast and accurate coarsening simulation with an unconditionally stable time step

Authors: Benjamin P. Vollmayr-Lee and Andrew D. Rutenberg

Abstract:We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre’s theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. For the Cahn-Hilliard case, we show that accuracy can be controlled with an unbounded time step that grows with time as . We develop a classification scheme for the step exponent and demonstrate that a class of simple linear algorithms gives . For this class the speedup relative to a fixed time step grows with , the linear size of the system, as . With conservative choices for the parameters controlling accuracy and finite-size effects we find that an lattice can be integrated 300 times faster than with the Euler method.

The Eyre’s theorem referred to in the abstract is described in this report (ps file).

## A review of domain coarsening using phase field models

### March 16, 2007

Here is a review of Cahn-Hilliard and Allen-Cahn models with specific reference to coarsening studies:

Author:Bray, A.J.

Source:Advances In Physics, Volume 43, Number 3, May/June 1994, pp. 357-459 (103)

Abstract:The theory of phase-ordering dynamics, that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these different systems

The review collects all the important results pertaining to the mathematical aspects of the problem and describes them in a very lucid fashion, making it a very pleasant read indeed.