[1] Phase-field simulations with inhomogeneous elasticity: Comparison with an atomic-scale method and application to superalloys

G Boussinot et al

We present a 2D and 3D phase-field analysis of microstructure evolution in the presence of a lattice misfit and with inhomogeneous elastic constants. The method is first critically compared with a Monte Carlo modeling at the atomic scale. We then apply the phase-field model to the Ni–Al system under external load along a cubic axis. We find that the microstructure becomes anisotropic and that the situation qualitatively differs depending on the sign of the applied stress. The microstructure evolution operates mainly by shape changes and alignments of precipitates, but also by splitting of precipitates initially elongated along directions perpendicular to the stress-induced, elastically favorable directions. The final microstructure is finally qualitatively analyzed in terms of a mean field theory in which the elastic inhomogeneity is embedded into an effective eigenstrain. This analysis leads to a simple formulation which can be used to easily predict the coherent microstructural anisotropy induced by any external loading condition.

[2] The hidden link between diffusion-induced recrystallization and ideal strength of metals

G Schmitz et al

Diffusion-induced recrystallization (DIR) is a mechanism which destabilizes thin film multilayers. New grains formed are distinguished by preferred composition levels characteristic for the diffusion couple. By evaluating these concentrations for different material combinations, it is demonstrated that a break of coherency by spontaneous relaxation is the key to understand the DIR process. Based on this, a thermo-elastic model is derived to predict whether diffusion-induced recrystallization can be expected for a given multilayer and to calculate the characteristic concentration levels.

Aluminum Σ3 grain boundary sliding enhanced by vacancy diffusion

N Du et al

Grain boundary sliding is an important deformation mechanism for elevated temperature forming processes. Molecular dynamics simulations are used to investigate the effect of vacancies in the grain boundary vicinity on the sliding of Al bi-crystals at 750 K. The threshold stress for grain boundary sliding was computed for a variety of grain boundaries with different structures and energies. These structures included one symmetrical tilt grain boundary and five asymmetrical tilt grain boundaries. Without vacancies, low energy Σ3 grain boundaries exhibited significantly less sliding than other high energy grain boundaries. The addition of vacancies to Σ3 grain boundaries decreased the threshold stress for grain boundary sliding by increasing the grain boundary diffusivity. A higher concentration of vacancies enhanced this effect. The influence of vacancies on grain boundary diffusivity and grain boundary sliding was negligible for high energy grain boundaries, due to the already high atom mobility in these boundaries.

O Bouaziz et al

We consider strain-hardening of nanostructured materials and propose a physically based interpretation of their low strain-hardening capability in terms of a reduced storage rate of dislocations. The model suggested provides a modification of the Kocks-Mecking-Estrin (KME) evolution law for dislocation storage for nanostructured materials and predicts a critical grain size below which the strain-hardening rate drops off.

## Specific surface area during solidification

### May 11, 2010

Evolution of specific surface area with solid fraction during solidification

L Ratke and A Genau

The specific surface area varies with solid fraction during phase transformation from liquid to solid. The few measurements available show a non-linear dependence of the specific surface area on the solid fraction, with an initial increase as the amount of solid increases, followed by a decrease as the system moves toward complete transformation. We derive a simple model for this behaviour assuming a combination of growth and coalescence. We obtain a relation exhibiting an increase with the square root of fraction solid at low volume fractions, independent of a growth law, and a decrease at higher volume fractions which depends on the model chosen to describe the coalescence of dendrites. By choosing an appropriate constant, the model accurately describes recent data presented by Limodin and co-workers.

## Some recent papers!

### May 6, 2010

[1] Structural and compositional homogeneity of InAlN epitaxial layers nearly lattice-matched to GaN

J M Manuel et al

A group of InAlN films was fabricated by molecular beam epitaxy and investigated by X-ray diffraction, transmission electron microscopy and element nano-analyses. All top In* _{x}*Al

_{1−}

*N layers have compositions around lateral lattice-matching to GaN (*

_{x}*x*≈ 0.18) and are pseudomorphic. For a growth rate of 350 nm h

^{−1}, each InAlN film separated into two sublayers with different In/Al-ratios. Micrographs reveal sharp transitions both at the InAlN/GaN and at the InAlN/InAlN interfaces. In contrast to these separated layers, an optimized epitaxy using an AlN interlayer and a lower growth rate, 100 nm h

^{−1}, enabled the fabrication of a single-phase In

*Al*

_{x}_{1−}

*N layer on GaN, homogeneous on a nanoscopic scale.*

_{x}[2] Microstructural stability in multi-alloy systems: Nanostructured two-phase, dual alloy multilayers

X Pan et al

Interdiffusion and microstructural stability in multilayers consisting of two nanostructured two-phase alloys were investigated using phase field simulations. A prototype ternary system containing a miscibility gap was used as the model system. Alloys with various compositions within the miscibility gap were chosen to form 20 μm bilayer repeating units in the multilayers. The initial microstructures in the alloys were produced by spinodal decomposition, which yielded a uniform distribution of precipitates having an average diameter of about 50 nm. Two types of multilayers were investigated; one in which the alloys in the repeating unit had the same matrix phase and the other in which the alloys had a different matrix phase. In general the microstructural instability measured as the size of the reaction zone increased with the increase in composition difference between the two initial alloys and in atomic mobility difference between the diffusing species. In particular, when the matrix phase was the same a precipitate-free zone (i.e. a single-phase layer) and a coarse interconnected precipitate zone formed at the interface between the two alloys, while when the matrix phase differed two precipitate-free zones formed at the interface. The microstructural instabilities were analyzed in terms of variations in the effective diffusivity with composition, which produced a singularity in the diffusion path at the initial alloy interface. The instability caused the diffusion path to exit the two phase region of the phase diagram and enter the single phase region.

[3] The Shape of Bubble in He Implanted Cu and Au

Q Wei et al

Bubble evolution under thermal annealing has been studied in He implanted Cu and Au by *in situ* transmission electron microscopy (TEM). We show that, under the minimum energy requirement of system, the bubble developed into an octahedron ( or truncated octahedron) shape consisting of {111} planes in the manner predicted by the Wulff construction. Nonspherical shape of bubbles and sessile dislocations along the edges of octahedron provide a barrier to Ostwald ripening and migration of bubbles, leading to the low mobility of bubble under thermal annealing.