## KMC, capillarity driven growth and thermal expansivity of 2d lattices

### January 26, 2011

Pareige et al

An atomic scale analysis of phase separation in a thermally aged Fe–25 at.% Cr alloy at 500 °C using 3-D atom probe (3DAP) and atomistic kinetic Monte Carlo (AKMC) simulation is presented. Treatment of the simulation data with the Lifshitz–Slyozov–Wagner and Huse laws shows that, whereas diffusion along the interfaces and through the bulk both occur at early stages, diffusion through the matrix quickly controls the growth of domains whereas the structure is still interconnected. Comparison of AKMC results with experimental ones showed that AKMC simulation in the two-band model approximation on a rigid lattice is able to reproduce the behaviour of the concentration field and of the width of the domains observed with 3DAP. This comparison also strongly support that, in real Fe–Cr alloys, as well as in simulated systems, diffusion is predominantly through the bulk and controls the growth of domains, while the structure is still interconnected.

We have investigated the retraction of a single-crystalline Ge wedge in epitaxial contact with a bicrystalline Au film using in situ electron microscopy. The rate of retraction was close to that predicted for capillarity-driven surface diffusion, following kinetics proportional to tn, with n = 0.22–0.35, but crystal anisotropy caused migration to be significantly faster along left angle bracket1 0 0right-pointing angle bracket directions than along left angle bracket1 1 0right-pointing angle bracket. The bicrystalline Au substrate was not inert, but underwent abnormal grain growth in the area swept by the receding Ge wedge. Cross-sections made from plan-view transmission electron microscopy samples revealed that this was related to ridge formation during the retraction process. In situ observations of the process in an inclined orientation showed direct evidence of substrate grain boundaries being dragged by the receding Ge wedge. The results can be understood in the framework of capillarity models for isotropic solid-state wedges and reactive wetting in high-temperature liquid–solid experiments.

Palumbo et al

The coefficient of thermal expansivity (CTE), α, of a 2-D dual-material lattice and the effects of varying the constituent materials and geometry were explored in a parametric study. The lattices had geometries similar to those found in lightweight structures in many transport applications including aerospace and spacecraft. The aim was to determine how to reduce the CTE of such structures to near zero, by using two constituent materials with contrasting CTEs, without incurring penalties in terms of other elastic and failure properties, mass and manufacturability. The results are scale independent and so generic to all such lattices. Lattice CTE was primarily driven by the geometry of the lattice and the mismatch in the constituent’s CTE and elastic moduli, with zero CTE attainable if (i) the relative lengths of internal members a and b were in the range of 1.4–1.6, and (ii) the contrast between αb and αa was at least 4. Large negative CTEs could be obtained easily if in addition the ratio of moduli Eb and Ea was more than 10. It was shown that pairings of commonly used materials, in lattices with commonly used geometries, can give near-zero and negative CTEs. It was shown that this dual-material mechanism effectively exchanges distortion for internal stress. With carefully chosen material pairings there were either small or no penalties for the reduced CTE in terms of other key mechanical performance indices, e.g. premature failure. Two lattices were manufactured, one monolithic and one dual-material (grade 2 titanium and aluminium 6082). Their thermal expansivity was measured and found to match closely the analytical model’s prediction.

## De-alloying and percolation, non-equilibrium melting, shear thinning, and discovery of local hidden symmetries

### July 15, 2009

Artymowicz et al

The parting limit or de-alloying threshold for electrolytic dissolution of the more reactive component from a homogeneous fcc binary alloy is usually between 50 and 60 at%. The system that has been most studied, dissolution of Ag from Ag-Au, shows a parting limit close to 55 at% Ag. Here, Kinetic Monte Carlo (KMC) simulations of ‘Ag-Au’ alloys and geometric percolation modeling are used to study the relationship between this parting limit and the high-density site percolation thresholds pc(m) for an fcc lattice, subject to the rule that atoms with coordination greater than nine are prevented from dissolution. The value of pc(9) is calculated from geometric considerations to be 59.97 ± 0.03%. In comparison, using KMC simulations with no surface diffusion and no dissolution allowed for ‘Ag’ atoms with more than nine total neighbors, the parting limit is found to be slightly lower (58.4 ± 0.1%). This slight discrepancy is explained by consideration of the local atomic configurations of ‘Ag’ atoms – a few of these configurations satisfy the percolation requirement but do not sustain de-alloying, while a larger number show the converse behavior. There is still, however, an underlying relationship between the parting limit and the percolation threshold, because being at pc(9) guarantees a percolation path in which successive ‘Ag’ atoms share at least one other ‘Ag’ neighbor. With realistic kinetics of surface diffusion for ‘Au’, the parting limit drops to 54.7 ± 0.3% because a few otherwise inaccessible dissolution paths are opened up by surface diffusion of ‘Au’.

E Villanova-vidal et al

A novel and flexible experiment is reported for investigation of the non-equilibrium melting behaviour of model crystals made from charged colloidal spheres. In a slit geometry, polycrystalline material formed in a low salt region is driven by hydrostatic pressure up an evolving gradient in salt concentration and melts at large salt concentration. Depending on particle and initial salt concentration, driving velocity and the local salt concentration, complex morphologic evolution is observed. Crystal-melt interface positions and the melting velocity are obtained quantitatively from time-resolved Bragg and polarisation microscopic measurements. A simple theoretical model predicts the interface to first advance, then for balanced drift and melting velocities to become stationary at a salt concentration larger than the equilibrium melting concentration. It also describes the relaxation of the interface to its equilibrium position in a stationary gradient after stopping the drive in different manners. The influence of the gradient strength on the resulting interface morphology and a shear-induced morphologic transition from polycrystalline to oriented single crystalline material before melting are discussed.

V Lubchenko

We compute, on a molecular basis, the viscosity of a deeply supercooled liquid at high shear rates. The viscosity is shown to decrease at growing shear rates, owing to an increase in the structural relaxation rate as caused by the shear. The onset of this non-Newtonian behavior is predicted to occur universally at a shear rate significantly lower than the typical structural relaxation rate, by approximately two orders of magnitude. This results from a large size—up to several hundred atoms—of the cooperative rearrangements responsible for mass transport in supercooled liquids and the smallness of individual molecular displacements during the cooperative rearrangements. We predict that the liquid will break down at shear rates such that the viscosity drops by approximately a factor of 30 below its Newtonian value. These phenomena are predicted to be independent of the liquid’s fragility. In contrast, the degree of nonexponentiality and violation of the Stokes–Einstein law, which are more prominent in fragile substances, will be suppressed by shear. The present results are in agreement with existing measurements of shear thinning in silicate melts.

P Wochner et al

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states.

## Elastic energy contribution from core tractions to dislocations

### June 20, 2009

Elastic energy of a straight dislocation and contribution from core tractions

E Clouet

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in lcub110rcub planes are more stable than those gliding in lcub112rcub planes.

## Dislocation dipoles and grain boundary pre-melting

### May 22, 2009

H Wang et al

Transformations of vacancy dipoles of dissociated edge dislocations are analyzed in Cu, Ni and γ-TiAl by molecular dynamics. Dipole heights up to 20 {1 1 1} interplanar distances are investigated at temperatures ranging from 0 K to near the melting points of Cu and Ni and slightly below the upper boundary of the single phase γ-TiAl domain. Three model configurations, hollows, vertical compact and inclined dipoles, are considered and their relative stabilities compared. Except for dipoles one interplanar distance high, hollows are either metastable or unstable and they are never formed by mutually approaching dipolar dislocations. The three configurations transform into a variety of height- and temperature-dependent layouts including cores containing ordered free volumes, zigzagged faulted dipoles and agglomerated stacking-fault tetrahedra (SFT). At the highest temperatures, small individual SFTs are formed by short-range pipe-diffusion along the dipole cores. There is no critical height below which small-height dipoles or their debris would just simply disappear.

P L Williams and Y Mishin

We apply the semi-grand-canonical Monte Carlo method with an embedded-atom potential to study grain boundary (GB) premelting in Cu-rich Cu–Ag alloys. The Σ5 GB chosen for this study becomes increasingly disordered near the solidus line while its local chemical composition approaches the liquidus composition at the same temperature. This behavior indicates the formation of a thin layer of the liquid phase in the GB when the grain composition approaches the solidus. The thickness of the liquid layer remains finite and the GB can be overheated/oversaturated to metastable states slightly above the solidus. The premelting behavior found by the simulations is qualitatively consistent with the phase-field model of the same binary system presented in Part I of this work [Mishin Y, Boettinger WJ, Warren JA, McFadden GB. Acta Mater, in press]. Although this agreement is encouraging, we discuss several problems arising when atomistic simulations are compared with phase-field modeling.

## Grain boundaries and glass forming liquids

### May 13, 2009

Polycrystalline materials are composites of crystalline particles or “grains” separated by thin “amorphous” grain boundaries (GBs). Although GBs have been exhaustively investigated at low temperatures, at which these regions are relatively ordered, much less is known about them at higher temperatures, where they exhibit significant mobility and structural disorder and characterization methods are limited. The time and spatial scales accessible to molecular dynamics (MD) simulation are appropriate for investigating the dynamical and structural properties of GBs at elevated temperatures, and we exploit MD to explore basic aspects of GB dynamics as a function of temperature. It has long been hypothesized that GBs have features in common with glass-forming liquids based on the processing characteristics of polycrystalline materials. We find remarkable support for this suggestion, as evidenced by string-like collective atomic motion and transient caging of atomic motion, and a non-Arrhenius GB mobility describing the average rate of large-scale GB displacement.

## Structure and mobility of dislocations in BCC iron using MD

### January 11, 2009

Structure and mobility of the $\frac{1}{2} \langle 11\bar{1} \rangle \{112\}$ edge dislocation in BCC iron studied by molecular dynamics

G Monnet and D Terentyev

In this paper, we carried out atomistic calculations to investigate in detail the core structure and motion mechanism of the $\frac{1}{2} \langle 11\bar{1} \rangle \{112\}$ edge dislocation in α-iron. First, molecular statics simulations are used to characterise the dislocation-core structure in the framework of the Peierls–Nabarro model. It is shown that the accommodation of the distortion due to the insertion of the extra half-planes is not equivalent in the planes above and below the dislocation slip plane and that the relative atomic-displacement profile in the dislocation-core region is asymmetrical. Then, molecular dynamics simulations are used to study the mechanism of the dislocation motion at different temperatures. At low temperature, the dislocation is found to move by nucleation and propagation of kink-pairs along its line. Independently of temperature, when loading is performed in the twinning direction, the critical stress is found to be lower than the one corresponding to the antitwinning loading direction.

## Liquid metal embrittlement in Al-Ga systems

### January 8, 2009

Effect of material properties on liquid metal embrittlement in the Al–Ga system

H-S Nam and D J Srolovitz

There are many examples in which a liquid metal in contact with a polycrystalline solid develops a deep liquid groove at the intersections of the grain boundaries and the solid–liquid interface. In the Al–Ga system, liquid Ga quickly penetrates deep into the solid along grain boundaries resulting in brittle intergranular fracture under even modest stresses, a process known as liquid metal embrittlement. This is a complex phenomenon, involving several different types of simultaneous processes associated with diverse interfacial properties of materials. We have performed molecular dynamics simulations on idealized sets of conditions to emphasize certain effects. We report how Ga propagates into grain boundaries in Al as a function of some important external parameters such as applied stress, temperature, grain boundary type/structure, grain size and liquid properties. Our simulation results are very consistent with both the dislocation-climb model and general trends gleaned from experimental studies in the literature.