Lecture notes which are under preparation (by Prof. Prita Pant and me) are available for download here (as and when they become ready).

Deformation mechanisms, length scales and optimizing the mechanical properties of nanotwinned metals

Wu et al

Refinement of microstructural length scales and modification of interface character offer opportunities for optimizing material properties. While strength and ductility are commonly inversely related, nanotwinned polycrystalline copper has been shown to possess simultaneous ultrahigh strength and ductility. Interestingly, a maximum strength is found at a small, finite twin spacing. We study the plastic deformation of nanotwinned polycrystalline copper through large-scale molecular dynamics simulations. The simulations show that plastic deformation is initiated by partial dislocation nucleation at grain boundary triple junctions. Both pure screw and 60° dislocations cutting across twin boundaries and dislocation-induced twin boundary migration are observed in the simulation. Following twin boundary cutting, 60° dislocations frequently cross-slip onto {0 0 1} planes in twin grains and form Lomer dislocations. We further examine the effect of twin spacing on this Lomer dislocation mechanism through a series of specifically designed nanotwinned copper samples over a wide range of twin spacings. The simulations show that a transition in the deformation mechanism occurs at a small, critical twin spacing. While at large twin spacings, cross-slip and dissociation of the Lomer dislocations create dislocation locks that restrict and block dislocation motion and thus enhance strength, at twin spacings below the critical size, cross-slip does not occur, steps on the twin boundaries form and deformation is much more planar. These twin steps can migrate and serve as dislocation nucleation sites, thus softening the material. Based on these mechanistic observations, a simple, analytical model for the critical twin spacing is proposed and the predicted critical twin spacing is shown to be in excellent agreement both with respect to the atomistic simulations and experimental observations. In addition, atomistic reaction pathway calculations show that the activation volume of this dislocation crossing twin boundary process is consistent with experimental values. This suggests that the dislocation mechanism transition reported here for the first time can be a source of the observed transition in nanotwinned copper strength.

[1] Effect of microelasticity on grain growth: Texture evolution and abnormal grain growth

D-U Kim et al

A phase field grain growth model including elastic anisotropy and inhomogeneity was developed to demonstrate the effect of microelasticity on the grain growth. The mechanical response against an external load was found to control grain growth and texture evolution. In contrast to previous macroelastic descriptions, these results showed that elastically soft grains with higher strain energy density can grow at the expense of the elastically hard grains to reduce the total strain energy.

► We develop a phase field grain growth model combined with a micro-elasticity effect. ► The micro-elasticity turns out to play a key role in controlling grain growth and texture evolution. ► Strong localization of strain energy density and inhomogeneous distribution even inside grains are observed. ► An external load can cause abnormal grain growth in the system with high elastic anisotropy. ► Elastically soft grains with higher strain energy density grow at the expense of the elastically hard grains to reduce the total strain energy.

[2] Interface-facilitated deformation twinning in copper within submicron Ag–Cu multilayered composites

J Wang et al

Rolling of Ag–Cu layered eutectic composites with bilayer thicknesses in the submicron regime (not, vert, similar200–400 nm) activated deformation twinning in Cu. Using atomistic simulations and dislocation theory, we propose that the Ag–Cu interface facilitated deformation twinning in Cu by permitting the transmission of twinning partials from Ag to Cu. In this way, twins in Ag can provide an ample supply of twinning partials to Cu to support and sustain twin growth in Cu during deformation. Interface-driven twinning as revealed by this study suggests the exciting possibility of altering the roles of dislocation slip and twinning through the design of heterophase interface structure and properties.

► Deformation twins in Cu are observed within submicron Ag–Cu multilayers. ► We propose that the Ag–Cu interface facilitated deformation twinning in Cu. ► We demonstrate the proposal using atomistic simulation and dislocation theory. ► Interface-driven twinning suggests the possibility of altering the roles of slip and twinning through the hetero-phase interface design.

[3] Twinning system selection in a metastable β-titanium alloy by Schmid factor analysis

E Bertrand et al

Electron backscattering diffraction and Schmid factor analysis were used to study the twinning variant selection in a Ti–25Ta–24Nb (mass%) metastable β-titanium alloy. The two twinning systems {1 1 2}left angle bracket1 1 1right-pointing angle bracket and {3 3 2}left angle bracket1 1 3right-pointing angle bracket were observed. For each system the Schmid factor was shown to be a relevant parameter to determine the activated variant. Moreover, selection between the two twinning systems depends on the crystallographic orientation of the grain with respect to the tensile direction.

► A metastable beta Ti-25Ta-24Nb alloy was synthesized by cold crucible semi-leviation melting. ► Electron backscattering diffraction was used to characterize the deformation mechanisms. 2 twinning systems have been identified. ► The Schmid factor was used to determine the activated variant.

[4] The effects of grain size on the phase transformation properties of annealed (Ti/Ni/W) shape memory alloy multilayers

P J S Buenconjeso et al

(Ti/Ni/W)n multilayer films were annealed to form a two-phase (B2-TiNi and β-W) system. Grain sizes extracted from X-ray diffraction profiles of annealed films revealed that B2-TiNi decreases with increasing W, due to the immiscible W layers obstructing its grain growth. With decreasing B2-TiNi grain size the Rs (B2–R) transformation temperature is not affected but the Ms (R–B19′) transformation temperature decreases significantly. Thus the addition of W to Ti–Ni is effective to induce the B2–R single-step transformation due to grain size effects.
Research highlights

► Annealed Ti/Ni/W multilayer films forms two-phase B2-TiNi and β-W system. ► Grain size of B2-TiNi decreases with increasing W amount. ► Grain size effects explains the separation of Ms and Rs temperatures. ► W alloying is effective to induce B2–R transformation.

[1] Dissipated energy measurements as a marker of microstructural evolution: 316L and DP600

Connesson et al

The thermomechanical characteristics and, more specifically, the dissipative behavior of two steels (a DP600 and a 316L stainless steel) have been studied using infrared measurement methods. All dissipated energy measurements have been performed during traction–traction uniaxial tests in the elastic domain. It has been shown that the dissipated energy of these materials is dependent on the material plastic strain and could be used as a non-destructive criterion to monitor the material evolution during loading sequences. Different kinds of loading sequences have been tested, including uniaxial tensile tests, alternative traction–traction loadings and recovery periods to underline specific characteristics of the materials.

[2] Diffusive model of pore shrinkage in final-stage sintering under hydrostatic pressure

Kim et al

A grain-boundary-diffusion model is developed to understand the densification behavior of pores in the final stage of sintering under compressive hydrostatic pressure. From analysis of the diffusive model, the bulk viscosity, densification rate and shrinkage rate of pores are predicted for a dense matrix polycrystal containing spherical pores, and compared with the existing experimental results and models. A transition in the sintering mechanism is predicted from the different pore-size dependence of the shrinkage rate between the diffusive and the viscous flow models. The transition effect is experimentally confirmed by the appearance of a downward inflection in the size distribution of pores during sintering. The upward inflection observed experimentally in the cavity-size distribution after superplastic deformation is also explained by the transition of the mechanism.

[3] Phase-field analysis of a ternary two-phase diffusion couple with multiple analytical solutions

Heulens et al

Under certain conditions, there are multiple analytical solutions for the interface velocity in ternary two-phase diffusion couples. We have tackled this degeneracy problem by employing an isothermal phase-field model for diffusion couples that allows comparison with the analytical solutions. We find that, besides the three analytically predicted single-interface diffusion paths, a triple-interface diffusion path can also form. Furthermore, analysis of the phase-field simulation results shows that the Gibbs energies of both the bulk phases and the interfaces must be considered to determine uniquely the evolution of a diffusion couple, in case whether a single or multiple interfaces form.

[4] Atomistic study of the buckling of gold nanowires

Olsson and Park

In this work, we present results from atomistic simulations of gold nanowires under axial compression, with a focus on examining the effects of both axial and surface orientation effects on the buckling behavior. This was accomplished by using molecular statics simulations while considering three different crystallographic systems: left angle bracket1 0 0right-pointing angle bracket/{1 0 0}, left angle bracket1 0 0right-pointing angle bracket/{1 1 0} and left angle bracket1 1 0right-pointing angle bracket/{1 1 0}{1 0 0}, with aspect ratios spanning from 20 to 50 and cross-sectional dimensions ranging from 2.45 to 5.91 nm. The simulations indicate that there is a deviation from the inverse square length dependence of critical forces predicted from traditional linear elastic Bernoulli–Euler and Timoshenko beam theories, where the nature of the deviation from the perfect inverse square length behavior differs for different crystallographic systems. This variation is found to be strongly correlated to either stiffening or increased compliance of the tangential stiffness due to the influence of nonlinear elasticity, which leads to normalized critical forces that decrease with decreasing aspect ratio for the left angle bracket1 0 0right-pointing angle bracket/{1 0 0} and left angle bracket1 0 0right-pointing angle bracket/{1 1 0} systems, but increase with decreasing aspect ratio for the left angle bracket1 1 0right-pointing angle bracket/{1 1 0}{1 0 0} system. In contrast, it was found that the critical strains are all lower than their bulk counterparts, and that the critical strains decrease with decreasing cross-sectional dimensions; the lower strains may be an effect emanating from the presence of the surfaces, which are all more elastically compliant than the bulk and thus give rise to a more compliant flexural rigidity.

[5] Analysis by synchrotron X-ray radiography of convection effects on the dynamic evolution of the solid–liquid interface and on solute distribution during the initial transient of solidification

Bogno et al

In situ monitoring of the initial transient of directional solidification was carried out by means of synchrotron X-ray radiography. Experiments with Al–4 wt.% Cu alloy samples were performed on beamline ID19 of the European Synchrotron Radiation Facility (ESRF) in a dedicated Bridgman-type furnace. X-ray radiography enabled a detailed analysis of the evolution over time of the solid–liquid interface macroscopic shape in interaction with convection in the melt. Lateral solute segregation induced by fluid flow resulted in a significant deformation of the solid–liquid interface. The time-dependent velocity of the solidification front was determined at different abscissa values along the curved interface during the solidification process, from the growth phase with a smooth interface to the onset of morphological instability. Further, using a novel quantitative image analysis technique we were able to measure longitudinal solute profiles in the melt during the initial transient. Solutal length was then deduced as well as concentration in the melt, both at the interface and far away from it. The influence of convection on growth velocity and the characteristic parameters of the solute boundary layer are discussed, and a comparison with the Warren and Langer model is also presented.

[1] Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: Experiments and molecular dynamics simulations

M A Lodes et al

In this work, the indentation size effect and pop-in behavior are studied for indentations in undeformed and locally pre-deformed CaF2 single crystals, using both nanoindentation experiments and molecular dynamics simulations. To study the influence of dislocation density on the indentation behavior, small-scale indentations are carried out inside the plastic zone of larger indentations. This experiment is mimicked in the simulations by indenting a small sphere into the center of the residual impression of a larger sphere. The undeformed material shows the well-known pop-in behavior followed by the indentation size effect. Pre-deforming the material leads to a reduction in the indentation size effect both for experiments and simulations, which is in accordance with the Nix–Gao theory. Furthermore, the pop-in load is reduced in the experiments, whereas a smooth transition from elastic to plastic deformation is found in the simulations. There, plasticity is initiated by the movement of pre-existing dislocation loops in the vicinity of the plastic zone. The simulations thus give a detailed insight into the deformation mechanism during indentation and highlight the importance of the dislocation microstructure for the indentation size effect and dislocation nucleation.

[2] Evolution equations and size distributions in nanocrystalline grain growth

Streitenberger and Zoellner

Size effects observed in nanocrystalline grain growth are modelled by attributing a specific energy and finite mobility to each structural feature of a polyhedral grain. By considering grain growth as a dissipative process that is driven by the reduction in the Gibbs free interface, edge and vertex energy, a general grain evolution equation is derived that can be divided into nine types of possible growth kinetics. The corresponding self-similar grain size distributions are derived and compared with results from modified Monte Carlo Potts model simulations taking into account size effects in triple and quadruple junction limited grain growth.

[3] Surface eigen-displacement and surface Poisson’s ratios of solids

Zhang et al

Theoretical analysis and molecular dynamics simulations were conducted to study systematically surface eigen-displacement and surface Poisson’s ratios of solids, which play essential roles in surface energy, surface strain and surface stress. Face-centered cubic (0 0 1) Au thin films were taken as typical examples to illustrate the physical picture. The surface eigen-displacement is a critical surface strain at the equilibrium state after normal relaxation and thus an intrinsic surface property. Surface Poisson’s ratios are also intrinsic surface properties. Combining surface eigen-displacement and surface Poisson’s ratios with surface eigen-stress and surface tangential elastic constants lays foundations of surface elasticity of solids.

► Surface eigen-displacement is a critical surface strain at the equilibrium state after normal relaxation. ► Surface Poisson’s ratio is the surface excess of Poisson’s ratio. ► Surface eigen-displacement and Surface Poisson’s ratio are surface intrinsic properties.

[4] Thermodynamic assessment of the stabilization effect in deformed shape memory alloy martensite

Kato et al

When a martensitic shape memory alloy is deformed, the reverse transformation occurs at higher temperature than that of undeformed martensite. This is a typical case of the stabilization effect of martensite that is commonly observed in shape memory alloys. Regarding previous results measured by electric resistance and/or dilatometoric methods in NiTi and CuAlNi shape memory alloys, this study has performed calorimetric measurement in these alloys in order to re-examine the stabilization effect in terms of thermodynamics. Experimental evidence for appreciable changes in the reverse transformation temperature due to variant change of the martensite is presented. The elastic energy stored in the deformed martensite and the irreversible energy dissipated during the reverse transformation are estimated from the transformation temperatures, the stress–strain curves of the martensite and the latent heat of transformation. The temperatures of the reverse martensitic transformation have been related to these energies in explicit form.

[5] Quantitative analysis of layering and in-plane structural ordering at an alumina–aluminum solid–liquid interface

Kauffmann et al

Real-time observations of Al–Al2O3 dynamic liquid–solid interfaces on the atomic scale indicate the presence of structural ordering in the liquid at the solid–liquid interface. The main problem with direct high resolution transmission electron microscopy (HRTEM) interpretation is that the imaging conditions and aberrations in the imaging system have a significant influence on the contrast in the image, and may lead to inaccurate conclusions about the structure examined. New quantitative results based on using a single image iterative wave function reconstruction are presented. This technique requires only a single experimental image, and allows extraction of reliable and aberration-free structural information from experimental HRTEM micrographs. This numerical phase retrieval method was successful in analysis of the experimental data and allowed, for the first time, direct extraction of quantitative information regarding the degree of ordering (parallel and perpendicular to the interface) at liquid–solid interfaces. The degree of ordering at the Al2O3–Al interface at 750 °C was quantified and both layering and in-plane ordering were found. The layering in the liquid extends to about four to five layers (about 1 nm from the edge of the crystal). The in-plane ordering, which was observed only in the first three layers of the liquid, decays faster than the layering. In addition, the interlayer spacings measured in the liquid indicate that the liquid atoms at the interface are influenced by the structure of the crystal, while further away the ordering of the liquid atoms gradually disappears, until they adopt the characteristics of the bulk liquid.

► In-situ HRTEM of Al–Al2O3 liquid–solid interfaces show ordering in the liquid at the interface. ► Quantitative results using a single image iterative wave function reconstruction are presented. ► Both layering and in-plane ordering exist at the interface at 750 °C. ► Layering extends to 4–5 liquid layers. In-plane ordering exists in the first 3 layers of the liquid.

[6] Phase field theory of proper displacive phase transformations: Structural anisotropy and directional flexibility, a vector model, and the transformation kinetics

Rao and Khachaturyan

A phase field theory of proper displacive transformations is developed to address the microstructure evolution and its response to applied fields in decomposing and martensitic systems. The theory is based on the explicit equation for the non-equilibrium free energy function of the transformation strain obtained by a consistent separation of the total strain into transformation and elastic strains. The transformation strain is considered to be a relaxing long-range order parameter evolving in accordance with the system energetics rather than as a fixed material constant used in the conventional Eshelby theory of coherent inclusions. The elastic strain is defined as a coherency strain recovering the crystal lattice compatibility. The obtained free energy function of the transformation strain leads to the concepts of structural anisotropy and directional flexibility of low symmetry phases. The formulated vector model of displacive transformation makes apparent a similarity between proper displacive transformation and ferromagnetic/ferroelectric transformation and, in particular, a similarity between the structural anisotropy and magnetic/polar anisotropy of ferromagnetic/ferroelectric materials. It even predicts the feasibility of a glass-like structural state with unlimited directional flexibility of the transformation strain that is conceptually similar to a ferromagnetic glass. The thermodynamics of the equilibrium be

A few papers from scripta

October 7, 2009

[1] Do bainitic and Widmanstätten ferrite grow with different mechanisms?

M Hillert et al

Caballero et al. recently presented new evidence for different growth mechanisms of Widmanstätten and bainitic ferrite. The argument was based on Zener’s hypothesis of diffusionless growth of bainitic ferrite. It is now demonstrated that Bhadeshia’s model, based on Zener’s hypothesis, predicts that some of the new measurements, claimed to fall above Bs and to be due to Widmanstätten ferrite, actually fall within the predicted temperature range of bainite, indicating that they cannot be used as new support for Bhadeshia’s model.

[2] Nucleation of nanosize particles following the spinodal decomposition in the pseudo-ternary Ge0.6Sn0.1Pb0.3Te compound

B Dado et al

Demixing following a spinodal decomposition, takes place in Sn-lean compounds in the pseudo-ternary (Ge, Sn, Pb)Te system, giving rise to both Pb- and Ge-rich telluride areas. After quenching from the high-temperature single cubic phase in the course of an aging treatment at 663 K, a Ge0.6Sn0.1Pb0.3Te sample undergoes several microstructural stages. The last stage consists of nucleation and growth of nanosize particles which maintain their dimensional stability for relatively extended periods of time.

[3] Twin boundary nucleation and motion in Ni–Mn–Ga magnetic shape memory material with a low twinning stress

E Aaltio et al

The twin boundary motion in the Ni–Mn–Ga single crystal 10M martensite magnetic shape memory material was studied by mechanical twinning stress and magnetic measurements at ambient temperature. The compressive stress required to trigger the movement of the twin boundaries was higher in the sample with the single variant state than in that with the multivariant state. Magnetometer measurements confirmed that the energy needed to move the twin boundaries in a high-quality single crystal 10M Ni–Mn–Ga is lower than that for the nucleation of a twin boundary.

Some papers from Acta

August 27, 2009

[1] An attempt to correct the quasichemical model

M Hillert et al

[2] Continuum simulations of the formation of Kirkendall-effect-induced hollow cylinders in a binary substitutional alloy

H-C Yu et al

[3] Spatial correlation in grain misorientation distribution

B Beausir et al

[4] Effect of second-phase particle morphology on grain growth kinetics

K Chang et al

[5] Stress-driven migration of symmetrical left angle bracket1 0 0right-pointing angle bracket tilt grain boundaries in Al bicrystals

T Gorkaya et al

[6] Low-angle grain boundary migration in the presence of extrinsic dislocations

A T Lim et al

[7] Thin film epitaxy and structure property correlations for non-polar ZnO films

P Pant et al