## Papers from acta!

### August 10, 2010

E Efstathiou et al

This paper presents a method – based on high-energy synchrotron X-ray diffraction data and a crystal-based finite element simulation formulation – for understanding grain scale deformation behavior within a polycrystalline aggregate. We illustrate this method by using it to determine the single-crystal elastic moduli of β21s, a body-centered cubic titanium alloy. We employed a polycrystalline sample. Using in situ loading and high-energy X-rays at the Advanced Photon Source beamline 1-ID-C, we measured components of the lattice strain tensor from four individual grains embedded within a polycrystalline specimen. We implemented an optimization routine that minimized the difference between the experiment and simulation lattice strains. Sensitivity coefficients needed in the optimization routine are generated numerically using the finite element model. The elastic moduli that we computed for the β21s are C11 = 110 GPa, C12 = 74 GPa and C44 = 89 GPa. The resulting Zener anisotropic ratio is A = 5.

[2] Elastic strain around needle-shaped particles embedded in Al matrix

J Douin et al

Precise measurements of strain fields around precipitates embedded in a crystalline matrix were performed, and simple but accurate models were deduced from the observations. The measurements were carried out in an aged aluminum alloy containing needle-shaped particles. The displacement and strain fields around rod-shaped and lath-shaped particles were obtained from high-resolution electron micrographs using geometric phase analysis. The measurements reveal that strain field of a rod-shaped particle is well described by the classical Eshelby analytical elastic solution. For the more complex case of lath precipitates, it is shown that the strain field in the matrix can be simply approximated by a dislocations dipole. The methods developed are generally applicable to the characterization of strain in nano-structured materials, including those with complex or unknown structures.

[3] Measurement of grain boundary triple line energy in copper

B Zhao et al

Recent studies have demonstrated that grain boundary triple junctions are crystal defects with specific thermodynamic and kinetic properties. In this study we address the energy of triple lines. Previously, a geometrical model was proposed to determine the grain boundary line tension. The current study introduces a thermodynamically correct approach which allows direct and precise measurement of the triple line energy. The experimental technique utilizes the measurement of the surface topography of a crystal in the vicinity of a triple junction by atomic force microscopy. The grain boundary triple line tension source of a random triple line in a copper tricrystal was measured to be 6.3 ± 2.8 × 10−9 J m–1.

[4] Effects of elastic interactions on the aggregation of nanostructures

Y Lou and J L Bassani

Externally imposed fields can directly affect microstructural evolution arising from diffusional phase separation in binary mixtures and potentially can be utilized to form highly ordered nanostructures. The effects of elastic fields on phase separation and coarsening are investigated in this paper using a Cahn–Hilliard-type phase-field model. Periodic traction distributions are shown to lead to patterned microstructures. The kinetics and morphology of aggregation are found to depend significantly on the transformation strain, contrast in moduli between phases and the magnitude of externally applied tractions (mechanical fields). The trends observed in simulations are analyzed in detail in terms of Eshelby-type estimates for elastic interaction energies, and the correlations are shown to be remarkably accurate. Predictions based solely upon interaction energies can provide very useful guidelines to develop strategies to control the morphology of aggregation.

M Ohno and K Matsuura

A quantitative phase-field model for two-phase solidification processes is developed based on the anti-trapping current approach with the free energy functional formulated to suppress the formation of an extra phase at the interface. This model appropriately recovers the free boundary problem for the motion of interface in the thin-interface limit and, importantly, it is applicable to the solidification process in binary alloy systems with arbitrary values of the solid diffusivities and interfacial energies. The performance of the present model is investigated for the peritectic reaction process in carbon steel. The present model exhibits excellent convergence behavior with respect to the interface thickness.

[6] The energetics of magnetoelastic actuators is analogous to phase transformations in materials

R L Snyder et al

A ferrogel is a composite system comprised of a polymeric matrix and magnetic filler particles. The elastic properties of the polymer can be coupled with the magnetic properties of the particles to create novel soft actuators. Understanding the mechanical behavior of ferrogels in an external magnetic field is essential to optimize actuator performance. The energetics of the mechanical behavior of cylindrical ferrogel specimens was found to be analogous to the energetics of chemical phase transformations in materials. Depending on the sample geometry, the elongation mechanism of ferrogel cylinders in an external magnetic field was identified as either a continuous or discontinuous deformation, analogous to a second- or first-order phase transformation, respectively. In analyzing mechanical strain as a function of magnetic field, the first and second derivatives of energy can be used to predict metastability and transitions in ferrogel deformation behavior.

[7] Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy

D J Rowenhorst et al

While considerable efforts have been made to model the effects of grain coarsening, there has been little experimental verification of these models. Using serial sectioning techniques, the full 3-D morphology of 2098 β-titanium grains in Ti–21S are analyzed and directly compared to grain coarsening theories. The experimental grain size distribution and the distribution in the number of grain faces are shown to have a close comparison to the predictions of the steady-state size distribution from a number of simulations and analytical theories. The geometric factor of the growth rates is determined by measuring the mean curvature of the grain faces. It is found that, on average, the grains with an average of 15.5 faces have a zero integral mean curvature of the grain faces, higher than the predicted value of 13.4 faces. This difference is suggested to be due to the non-random nearest-neighbor effects within the grain network.

[8] Atomistic simulation of hillock growth

T Frolov et al

This paper explores the mechanisms of hillock and whisker growth in stressed polycrystalline films by molecular dynamics simulations. The initial geometry consists of three grains with a triple line aligned perpendicular to a free surface, plus a fourth pyramidal-shaped grain implanted between the triple line and the surface. This simulated grain geometry corresponds to that observed in experiments during hillock and whisker growth, with the fourth grain serving as a seed for hillock growth. The simulations, performed under an applied in-plane biaxial compression, reveal an upward motion and growth of the seed grain. The growth occurs by stress-driven grain boundary diffusion from below the seed grain onto some of its internal faces. Accretion of atoms to those faces pushes the seed grain upwards and sideways. The different diffusion and accretion rates at different boundaries also give rise to internal stresses, which can be partially accommodated by grain boundary motion coupled to shear deformation. The hillock growth is countered by surface diffusion, which can slow the growth or even suppress it completely. Other mechanisms involved in hillock growth are also discussed.

H Wang et al

Departing from the volume-averaging method, the equiaxed solidification model was extended to describe the overall solidification kinetics of undercooled single-phase solid-solution alloys. In this model, a single grain, whose size is given assuming site saturation, is divided into three phases, i.e. the solid dendrite, the inter-dendritic liquid and the extra-dendritic liquid. The non-equilibrium solute diffusion in the inter-dendritic liquid and the extra-dendritic liquid, as well as the heat diffusion in the extra-dendritic liquid, is considered. The growth kinetics of the solid/liquid interface is given by the solute or heat balance, where a maximal growth velocity criterion is applied to determine the transition from thermal-controlled growth to solutal-controlled growth. A dendrite growth model, in which the nonlinear liquidus and solidus, the non-equilibrium interface kinetics, and the non-equilibrium solute diffusion in liquid are considered, is applied to describe the growth kinetics of the grain envelope. On this basis, the solidification path is described.

[10] Modeling the overall solidification kinetics for undercooled single-phase solid-solution alloys. II. Model application

H Wang et al

An overall solidification kinetic model was applied to undercooled Ni–15 at.% Cu alloy. A good agreement between the model predictions and the measured cooling curves was obtained by adopting a “phenomenological” heat boundary condition. Applying numerical calculations, it was demonstrated that solute is uniformly distributed at the purely thermal-controlled growth stage; a transition from non-equilibrium to near-equilibrium solidification occurs at the mainly thermal-controlled growth stage only if sufficiently high initial undercooling is available; and a transition from recalescence to post-recalescence occurs at the solutal-controlled growth stage wherein the current model reduces to Scheil’s equation. The volume fraction solidified during recalescence is the same as the ratio of the initial undercooling to the hypercooling limit, and solidification should end generally at a temperature between the prediction of Scheil’s equation and that of the Lever rule if back diffusion is considered.