[1] L2 droplet interaction with α-Al during solidification of hypermonotectic Al–8 wt.% Bi alloys

P L Schaffer, R H Mathiesen and L Arnberg

Studies of Al-based hypermonotectics have so far focused mainly on droplet motion and coagulation dynamics, with limited attention given to the interaction between droplets and the advancing solidification front which is decisive for the final distribution of the second phase within the α-Al matrix. The current work presents results from directional solidification experiments with Al–8 wt.% Bi alloys. It was found that droplets with large radii were frequently pushed and small droplets were engulfed. This is contradictory to the many models that have been proposed to explain pushing/engulfment of solid particles and can in part be ascribed to the fact that while solid-particle models only consider single, non-interacting particles that remain unaffected by solutal gradients ahead of the advancing solidification front, droplet–droplet interaction and local solute gradients have been found to be critical for droplet pushing/engulfment behaviour in hypermonotectic alloys.

P C Millett, and Y U Wang

A novel mesoscale simulation approach to modeling the collective interactions of charged colloidal particles allowing investigation of complex self-assembly processes is presented. Diffuse interface field variables are used to describe the shape, size, location and orientation of each individual particle within the computational domain. In addition, these field variables are used to determine the spatially resolved particle charge density distributions as well as the magnitude and direction of the electric field throughout the medium. Individual particle positions and rotations are updated in time as a result of long-range electrostatic and short-range repulsive forces and torques. Illustrative results of the model’s capability to evolve both monodisperse and binary distributions of charged particles of various shapes and charge characteristics are presented.

[3] Kinetics of diffusion-controlled transformations: Application of probability calculation

H Wang et al

An analytical model has been developed to describe the overall kinetics of diffusion-controlled transformations assuming site saturation or continuous nucleation, in combination with one-dimensional growth. On the basis of linear approximation of the concentration gradient, the method of probability calculation is adopted to model the transformed fraction. First, the so-called geometrical model was re-derived, assuming that the diffusion-controlled growth, according to the parabolic growth law, stops due to geometrical impingement of grains plus their diffusion fields. Then, the transformation kinetics subjected to soft impingement was described, following an analogous approach. The effect of soft impingement, depending on the degree of supersaturation, has been interpreted by evolution of the transformed fraction and the growth exponent. The model was applied to describe the isothermal austenite–ferrite transformation of 0.37C–1.45Mn–0.11 V microalloyed steel, and a good agreement between model predictions and experimental results has been obtained.

[4] Pattern formation in constrained dendritic growth with solutal buoyancy

I Steinbach

Competing self-organization between the solidification pattern and the convection pattern in a directional solidification environment is investigated theoretically and by phase-field simulations. Melt flow introduces a mode of transport with broken symmetry dependent on the direction of growth relative to the vector of gravity. A stable and an unstable regime can be distinguished. The interaction between spacing selection and convection leads to a new type of scaling that explains results from phase-field simulations and solidification experiments under enhanced gravity.

[5] Study of twinned dendrite growth stability

M A Salgado-Ordorica, J Vallonton and M Rappaz

Under certain thermal conditions (G ≈ 1 × 104 K m−1, νs ≈ 1 × 10−3 m s−1), left angle bracket1 1 0right-pointing angle bracket twinned dendrites appear in aluminum alloys and can overgrow regular columnar dendrites, provided that some convection is also present in the melt. In order to check the stability of such morphologies, directionally solidified twinned samples of Al–Zn were partially remelted in a Bridgman furnace and then resolidified under controlled conditions, with minimal convection. It was found that, although twin planes remain stable during partial remelting, non-twinned dendrites regrow during solidification. They have a crystallographic orientation given by those of the twinned and untwinned “seed” regions, and grow along preferred directions that tend to be those of normal specimens.

[6] Atomistic considerations of stressed epitaxial growth from the solid phase

N G Rudawski and K S Jones

A dual-timescale model of stressed solid-phase epitaxial growth is developed to provide a basis for the atomistic interpretation of experiments where the macroscopic growth velocity of (0 0 1) Si was studied as a function of uniaxial stress applied in the plane of the growth interface. The model builds upon prior empirical modeling, but is a significant improvement as it provides solid physical bases as to the origin of growth being dual-timescale and more accurately models growth kinetics.

## 2D foam rheology

### April 4, 2009

A simple analytical theory of localisation in 2D foam rheology

D Weaire, R J Clancy and S Hutzler

A very simple derivation is given for the dependence of localisation length on boundary velocity and various model parameters, in the continuum theory of 2D foam shear localisation. It is pointed out that the existence of distinct yield and limit stresses can complicate this theory for low boundary velocities, by introducing another mechanism for localisation, which does not depend on wall drag.

[1] Pattern formation in constrained dendritic growth with solutal buoyancy

I Steinbach

Competing self-organization between the solidification pattern and the convection pattern in a directional solidification environment is investigated theoretically and by phase-field simulations. Melt flow introduces a mode of transport with broken symmetry dependent on the direction of growth relative to the vector of gravity. A stable and an unstable regime can be distinguished. The interaction between spacing selection and convection leads to a new type of scaling that explains results from phase-field simulations and solidification experiments under enhanced gravity.

[2] A new class of metrics for the macroscopic crystallographic space of grain boundaries

D L Olmsted

The macroscopic description of a defect-free, flat grain boundary in a pure material requires five degrees of freedom. There is a need to define the distance between boundaries in this five-dimensional space, because boundaries that are close together crystallographically should have similar properties. Morawiec has recently proposed such a metric, defined in terms of the misorientation of the two grains and their boundary normals. This approach has the disadvantage that there is no unique way of weighting the importance of the difference in disorientation compared to the difference in boundary normals, as was pointed out by Cahn and Taylor. In this work a metric is developed using a less familiar description of the crystallographic space which avoids this problem. Two technical results are proven, and a sample application to grain boundary properties is offered.

A couple of papers from the latest PNAS:

[1] Solution to the problem of the poor cyclic fatigue resistance of bulk metallic glasses

M E Launey et alThe recent development of metallic glass-matrix composites represents a particular milestone in engineering materials for structural applications owing to their remarkable combination of strength and toughness. However, metallic glasses are highly susceptible to cyclic fatigue damage, and previous attempts to solve this problem have been largely disappointing. Here, we propose and demonstrate a microstructural design strategy to overcome this limitation by matching the microstructural length scales (of the second phase) to mechanical crack-length scales. Specifically, semisolid processing is used to optimize the volume fraction, morphology, and size of second-phase dendrites to confine any initial deformation (shear banding) to the glassy regions separating dendrite arms having length scales of ≈2 μm, i.e., to less than the critical crack size for failure. Confinement of the damage to such interdendritic regions results in enhancement of fatigue lifetimes and increases the fatigue limit by an order of magnitude, making these “designed” composites as resistant to fatigue damage as high-strength steels and aluminum alloys. These design strategies can be universally applied to any other metallic glass systems.

[2] Instability of stationary liquid sheets

A M Ardekani and D D Joseph

The rupture of a 3D stationary free liquid film under the competing effects of surface tension and van der Waals forces is studied as a linearized stability problem in a purely irrotational analysis utilizing the dissipation method. The results of the foregoing analysis are compared with a 2D long-wave approximation that has given rise to an extensive literature on the rupture problem. The irrotational and long-wave approximations are here compared with the exact 2D solution. The exact solution and the two approximate theories give the same results for infinitely long waves. The problem considered depends on two dimensionless parameters, the Hamaker number and the Ohnesorge number. The Hamaker number is a dimensionless number defined as a measure of the ratio of van der Waals forces to surface tension. The exact solution and the two approximate solutions differ by < 1% when the Hamaker number is small for all values of the Ohnesorge number. When the Ohhnesorge number is close to one, as in the case of water films separated by distance 100 Å, the long-wave approximation overestimates and the potential flow approximation underestimates the exact solution by similar small amounts. The high accuracy of the dissipation method shows that the effects of vorticity are small for small to moderate Hamaker numbers.