## Plasticity, shape memory and strain accommodation

### December 30, 2010

B Eidel

Pyramidal microindentation into the (0 0 1) surface of an face-centered cubic (fcc) single crystal made of a Ni-base superalloy is analyzed in experiment and crystal plasticity finite-element simulations. The resultant material pile-up at the surface reflects the material’s symmetry and turns out to be insensitive to different loading scenarios as induced by (i) different azimuthal orientations of the pyramidal indenter, (ii) different indenter shapes (sphere or pyramid) and (iii) the elastic anisotropy. Experiments and simulations are in agreement and suggest that pile-up deformation patterns merely depend on the geometry of discrete slip systems but are invariant to different anisotropic stress distributions as induced by (i)–(iii). The local adaption of pile-up to the pyramidal indenter leads to convex or concave indent shapes corresponding to the indenter orientation. We contrast the present findings for curved indent shapes of fcc single crystals to similar, well-known observations for quasi-isotropic polycrystals. Although phenomenologically similar in kind, the driving mechanisms are different: for the single crystal it is the discrete and anisotropic nature of plastic glide in certain slip systems; for isotropic polycrystals it is the rate of strain-hardening caused by the cumulative response of dislocations.

Phase transformation in free-standing SMA nanowires

F R Phillips et al

The primary focus of this work is on determining if the phase transformation of shape memory alloy (SMA) nanowires exhibits a critical size below which the phase transformation is inhibited. The SMA nanowires are fabricated through the use of the mechanical pressure injection method. The mechanical pressure injection method is a template-assisted nanowire fabrication method in which an anodized aluminum oxide (AAO) template is impregnated with liquid metal. The fabrication of SMA nanowires with different diameters is accomplished through the fabrication of AAO templates of varying diameters. The phase transformation behavior of the fabricated SMA nanowires is characterized using transmission electron microscopy. By analysis of the fabricated SMA nanowires, it is found that the phase transformation of SMA nanowires is not affected for nanowires ranging in diameter from 650 to 10 nm.

The role of strain accommodation during the variant selection of primary twins in magnesium

J J Jonas et al

Samples of magnesium alloys AM30 and AZ31 were deformed in tension at room temperature and a strain rate of 0.1 s−1 to strains of 0.08 and 0.15. Of the numerous contraction twins that formed, the orientations of 977 were determined by electron backscatter diffraction techniques. The orientations of their host grains were also measured, so that the Schmid factors (SFs) applicable to each of the six contraction twins that could potentially form in each grain could also be calculated. About half of the observed twins were of the “high SF” (0.3–0.5) type, while nearly half had “low” SFs (0.15–0.30). Furthermore, 5% of the observed twins had associated Schmid factors of only 0.03–0.15, i.e. these were of the “very low SF” type. Of particular interest is the observation that many potential “high Schmid factor” twins did not form. The presence of the low and very low SF twins and the absence of many potential high SF twins are explained in terms of the accommodation strains that are or would be required to permit their formation. These were calculated by rotating the twinning shear displacement gradient tensor into the crystallographic reference frame of the neighboring grain. It is shown that the very high plastic anisotropy of Mg grains permits the “easy” accommodations to take place but conversely prevents accommodation of the potential twinning shears when these are “difficult” (when these involve high critical resolved shear stresses). The twins that appear require little or no “difficult” accommodation.

## Some recent papers from Acta

### June 19, 2010

D V Bachurin et al

The interaction of lattice dislocations with symmetrical and asymmetrical tilt grain boundaries in left angle bracket1 1 1right-pointing angle bracket textured thin nickel films was investigated using atomistic simulation methods. It was found that the misorientation angle of the grain boundary, the sign of the Burgers vector of the incoming dislocation and the exact site where the dislocation meets the grain boundary are all important parameters determining the ability of the dislocation to penetrate the boundary. Inclination angle, however, does not make an important difference on the transmission scenario of full dislocations. Only limited partial dislocation nucleation was observed for the investigated high-angle grain boundary. The peculiarities of nucleation of embryonic dislocations and their emission from tilt grain boundaries are discussed.

[2] Comparing calculated and measured grain boundary energies in nickel

G S Rohrer et al

Recent experimental and computational studies have produced two large grain boundary energy data sets for Ni. Using these results, we perform the first large-scale comparison between measured and computed grain boundary energies. While the overall correlation between experimental and computed energies is minimal, there is excellent agreement for the data in which we have the most confidence, particularly the experimentally prevalent Σ3 and Σ9 boundary types. Other CSL boundaries are infrequently observed in the experimental system and show little correlation with computed boundary energies. Because they do not depend on observation frequency, computed grain boundary energies are more reliable than the experimental energies for low population boundary types. Conversely, experiments can characterize high population boundaries that are not included in the computational study. Together the experimental and computational data provide a comprehensive catalog of grain boundary energies in Ni that can be used with confidence by microstructural scientists.

[3] Thermodynamic model of hydride formation and dissolution in spherical particles

Y Mishin and W J Boettinger

A model of hydride formation and dissolution has been proposed for a single spherical particle and for a collection of such particles with a given size distribution. The phase transformation strain gives rise to an elastic barrier to the transformation, which scales with the volume of the particle and produces a hysteresis effect known experimentally. Experimentally observed finite slopes of hydrogen pressure vs. chemical composition plots (instead of expected plateaus) are explained by the model for both the hydrogenization and dehydrogenization processes. These finite slopes and the amount of the pressure hysteresis depend on elastic properties of the hydride and metal phases, the transformation strain, and on the particle-size distribution in the powder.

P R Ohodnicki Jr. et al

Classical steady-state nucleation theory is applied to Co-rich Fe,Co-based alloys to provide a rationale for experimental observations during the nanocrystallization of Co-rich (Co,Fe)89Zr7B4 and (Co,Fe)88Zr7B4Cu1 amorphous precursors. The amorphous precursor free energy is estimated using density functional theory. This simple theory suggests: (i) strain or interface energy effects could explain a tendency for a body-centered cubic (bcc) phase to form during crystallization. Dissolved glass formers (Zr,B) in crystalline phases may also contribute; (ii) similar face-centered cubic (fcc) and hexagonal close-packed (hcp) free energies could explain the presence of some hcp phase after crystallization even though fcc is stable at the crystallization temperature; (iii) nanocrystal compositions vary monotonically with the Co:Fe ratio of the amorphous precursor even when multiple phases are nucleating because nucleation is not dictated by the common tangency condition governing bulk phase equilibria; and (iv) Fe-enrichment of the bcc phase can be attributed to a relatively small free energy difference between the amorphous and bcc phases for high Co-containing alloys.

Q Wei and A Misra

Microstructures and orientation relationships in sputter-deposited, polycrystalline V/Ag multilayers with different individual thicknesses ranging from 1 to 50 nm were investigated. It was found that the wavy morphology of layers resulting from competitive kinetic limitations of deposited atoms gives rise to a variety of orientation relationships between two adjacent layers. At the top or bottom of curved layers Kurdjumov–Sachs and Nishiyama–Wasserman orientations were dominant, while on the slopes of the wavy interfaces close-packed face-centered cubic and body-centered cubic planes joined each other. As a consequence, Bain, Pitsch and many intermediate orientation relationships were generated. In most cases intermediate orientations with 1–3° deviations from the parallel planes or directions in standard orientations were observed. The tilted interfaces, followed by the introduction of disconnections to relieve misfit stress, had a tendency to form an invariant habit plane in which the strain was completely relieved. A model describing disconnections and invariant planes can explain the observed deviations and orientation of the habit plane. Calculations of the evolution of the surface morphology on the basis of the kinetic behavior of deposits were performed to facilitate interpretation of the formation of the wavy structure.

[6] A model for interphase precipitation based on finite interface solute drag theory

R Okamoto and J Agren

A model for interphase precipitation with the ledge mechanism, based on a eutectoid reaction, has been developed and combined with the finite interface solute drag model and a numerical solution of the diffusion equations inside the migrating phase interface. In the model, niobium flows in two directions, i.e. perpendicular to the direction of the ledge migration by eutectoid-like reaction and simultaneously parallel to the direction of the ledge migration inside the ledge interface. The difference between ledge transformation and typical phase transformation is compared using this model and the effects of row spacing, temperature and segregation energy are discussed. The calculation results using the model are compared with experimental results and the critical driving force for interphase precipitation is evaluated. The estimations of the niobium carbide precipitation using this model are in good agreement with experimental results.

C Perrin et al

In this paper, a new micromechanical approach accounting for the discreteness of intragranular slip is used to derive the local misorientations in the case of plastically deformed polycrystalline nickel in uniaxial tension. This intragranular microstructure is characterized in particular single slip grains by atomic force microscopy measurements in the early stage of plastic deformation. The micromechanical modelling accounts for the individual grain size, the spatial distances between active slip bands and the magnitude of slip in bands. The slip bands are modelled using discrete distributions of circular super glide dislocation loops constrained at grain boundaries for a spherical grain boundary embedded in an infinite matrix. In contrast with classic mean field approaches based on Eshelby’s plastic inclusion concept, the present model is able to capture different intragranular behaviours between near grain boundary regions and grain interiors. These theoretical results are quantitatively confirmed by local electron backscatter diffraction measurements regarding intragranular misorientation mapping with respect to a reference point in the centre of the grain.

[8] Quantitative three-dimensional characterization of pearlite spheroidization

Y-T Wang et al

We investigated the pearlite spheroidization of a 0.8 mass% C–Fe steel under 700 °C static annealing conditions using a combination of computer-aided three-dimensional (3-D) tomography and electron back-scattered diffraction. The holes present in naturally grown cementite lamellae cause shape instability and induce shape evolution of the lamellar structure during spheroidization. 3-D visualization demonstrated that the intrinsic holes play an important role in the initiation and development of pearlite spheroidization. The hole coalescence and expansion causes the break-up up of large cementite lamellae into several long narrow ribbons. Furthermore, the growth mechanism of inter-hole coalescence is related to the ratio of half the inter-hole distance on a cementite lamella to the thickness of that lamella. The driving force for hole growth is either the difference in surface energy or the curvature between the hole edges and the adjacent flat surface of the lamella. The morphologies of cementite ribbons depend on the hole expansion position on cementite lamella, and can change their shape to cylinders or small spheres by Rayleigh’s perturbation process after prolonged spheroidization.

[9] Interphase precipitation in niobium-microalloyed steels

R Okamoto et al

The interphase precipitation in niobium steel has been investigated. In the present work, the austenite/ferrite transformation speed should be fast due to hot deformations, and interphase precipitation can be observed after 10 s isothermal holding in the temperature range 923–1023 K. The dominant interphase precipitation is planar and is not oriented on the {1 1 0}α plane suggested by the ledge mechanism but on other planes.

N Scheerbaum et al

The capability of showing large magnetically induced strains (MFIS) up to not, vert, similar10% has attracted considerable research interest to magnetic shape memory (MSM) alloys. The prototype MSM alloy is the ternary Ni2MnGa. In this work, a comprehensive study of the local unit cell orientation distribution on single crystalline, polycrystalline and epitaxial thin film of martensitic Ni2MnGa is conducted by electron backscattering diffraction (EBSD). By EBSD, the constraint-dependent twin variant distribution, the corresponding stresses and the three-dimensional orientation of twin planes will be investigated. In polycrystals, the differentiation between twin and grain boundaries as well as proof of twin boundary motion is shown. From the knowledge of the local unit cell orientation at surfaces, it is possible to explain the magnetic domain configuration imaged by magnetic force microscopy.

[11] Domain models for ferromagnetic shape-memory materials

A T Onisan et al

A domain model for the twin variant and magnetic domain distribution in bulk systems of ferromagnetic shape-memory materials has been developed. The approach combines crystal elasticity, compatibility of a twinned microstructure with a tetragonal lattice structure, and micromagnetic domain theory. The model is applied to calculate phase diagrams under external magnetic fields and stresses for Ni–Mn–Ga as a magnetic system with easy-axis anisotropy and for Fe–Pd with easy-plane 4-fold anisotropies.

## 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.

## Void migration, electron microscopic analysis of strain measurement and anisotropy in interfacial energy

### March 5, 2010

Few papers of interest from Acta and Scripta:

[1] Phase-field simulation of void migration in a temperature gradient

S Y Hu and C H Henegar Jr

A phase-field model simulating vacancy diffusion in a solid with a strong vacancy mobility inhomogeneity is presented. The model is used to study void migration via bulk and surface diffusion in a temperature gradient. The simulations demonstrate that voids migrate up the temperature gradient, and the migration velocity varies inversely with the void size, in agreement with theory. It is also shown that the current model has the capability to investigate the effects of surface diffusion, temperature gradient and vacancy concentration on the void migration velocity. An interesting potential application of the model is to study the kinetics of void migration and the formation of a central hole in nuclear fuels.

C Gatel et al

Elastic strain has been investigated by transmission electron microscopy in nanometric InAs layers grown on Ga0.47In0.53As/InP(0 0 1) by molecular beam epitaxy using a residual Sb flux. Deposits of 10 and 15 monolayers of InAs (3 and 4.5 nm) remain elastically stressed with a two-dimensional growth mode. The out-of-plane strain in the layers is analyzed by cross-sectional high-resolution electron microscopy. A distortion of the substrate below and on top of the InAs layers is detected and is attributed to a significant surface relaxation effect due to thinning. Surface relaxation is modeled by three-dimensional finite element modeling. An additional relaxation effect is obtained when the sample is not infinite along the direction perpendicular to the thinning. This effect enhances the buffer distortion of the buffers below and on top of the strained layers. Taking into account thin foil effects, the experimental out-of-plane strain is in excellent agreement with the theoretical value calculated for a pure InAs layer (i.e. 0.035), demonstrating the high level of strain and stress in the layers.

M Rappaz et al

The anisotropy of the solid-liquid interfacial energy plays a key role during the formation of as-solidified microstructures. Using the ξ-vector formalism of Cahn and Hoffman, this contribution presents the effect that anisotropy has on the equilibrium shapes of crystals and on surface tension equilibrium at triple lines. Consequences on heterogeneous nucleation of anisotropic crystals and on dendritic growth morphologies are detailed with specific examples related to Al-Zn and Zn-Al alloys.

## Misfit dislocation arrays of interfaces

### January 8, 2010

Use of the Frank–Bilby equation for calculating misfit dislocation arrays in interfaces

J B Yang et al

The Frank–Bilby equation has been utilized to develop a general approach in which a simple criterion is proposed to classify interfaces with discrete misfit dislocation arrays into four types so that these misfit dislocation arrays can be conveniently characterized with uniform formulae. The relation connecting misfit dislocation configurations with the matrices in the Frank–Bilby equation, the special interfaces consistent with the Δg-parallelism and the continuity of misfit dislocations at intersection edges of interfaces are discussed.

## Few interesting reads

### August 5, 2009

From the latest PNAS:

[1] The elastic modulus, percolation, and disaggregation of strongly interacting, intersecting antiplane cracks

P M Davis and L Knopoff

We study the modulus of a medium containing a varying density of nonintersecting and intersecting antiplane cracks. The modulus of nonintersecting, strongly interacting, 2D antiplane cracks obeys a mean-field theory for which the mean field on a crack inserted in a random ensemble is the applied stress. The result of a self-consistent calculation in the nonintersecting case predicts zero modulus at finite packing, which is physically impossible. Differential self-consistent theories avoid the zero modulus problem, but give results that are more compliant than those of both mean-field theory and computer simulations. For problems in which antiplane cracks are allowed to intersect and form crack clusters or larger effective cracks, percolation at finite packing is expected when the shear modulus vanishes. At low packing factor, the modulus follows the dilute, mean-field curve, but with increased packing, mutual interactions cause the modulus to be less than the mean-field result and to vanish at the percolation threshold. The “nodes-links-blobs” model predicts a power-law approach to the percolation threshold at a critical packing factor of p c = 4.426. We conclude that a power-law variation of modulus with packing, with exponent 1.3 drawn tangentially to the mean-field nonintersecting relation and passing through the percolation threshold, can be expected to be a good approximation. The approximation is shown to be consistent with simulations of intersecting rectangular cracks at all packing densities through to the percolation value for this geometry, p c = 0.4072.

From the latest issue of Phil. Mag.:

The effect of a high magnetic field on the morphology of the MnBi primary phase during the directional solidification has been investigated experimentally and the results show that an application of a high magnetic field has enhanced the faceted growth and the coarsening of the MnBi primary phase. This may be attributed to the effect of a high magnetic field on the diffusion of the solute Mn and the growth anisotropy of the MnBi crystal.

[2] A new counter-example to Kelvin’s conjecture on minimal surfaces

R Gabbrielli

A new counter-example to Kelvin’s conjecture on minimal surfaces has been found. The conjecture stated that the minimal surface area partition of space into cells of equal volume was a tiling by truncated octahedra with slightly curved faces (K). Weaire and Phelan found a counter-example whose periodic unit includes two different tiles, a dodecahedron and a polyhedron with 14 faces (WP). Successively, Sullivan showed the existence of an infinite number of partitions by polyhedra having only pentagonal and hexagonal faces that included WP, the so-called tetrahedrally close packed structures (TCP). A part of this domain contains structures with lower surface area than K. Here, we present a new partition with lower surface area than K, the first periodic foam containing in the same structure quadrilateral, pentagonal and hexagonal faces, in ratios that are very close to those experimentally found in real foams by Matzke. This and other new partitions have been generated via topological modifications of the Voronoi diagram of spatially periodic sets of points obtained as local maxima of the stationary solution of the 3D Swift-Hohenberg partial differential equation in a triply periodic boundary, with pseudorandom initial conditions. The motivation for this work is to show the efficacy of the adopted method in producing new counter-examples to Kelvin’s conjecture, and ultimately its potential in discovering a periodic partition with lower surface area than the Weaire-Phelan foam. The method seems tailored for the problem examined, especially when compared to methods that imply the minimization of a potential between points, where a criterion for neighboring points needs to be defined. The existence of partitions having a lower surface area than K and an average number of faces greater than the maximum value allowed by the TCP domain of 13.5 suggests the presence of other partitions in this range.

[3] The cross-slip energy unresolved

G Schoeck

Recent progress in dislocation dynamics modeling of work hardening has reawakened the interest in cross-slip, which can lead to dynamic recovery in fcc crystals. It is pointed out that neither continuum theory nor atomic modeling at present are able to reliably derive the reaction path and the activation energy of cross-slip. Classical continuum theory with the concept of Volterra dislocations fails, because during the nucleation process the effective Burgers vectors of the partials are not conserved and the specific atomic misfit energy changes. Atomistic modeling fails, because the ad hoc potentials used at present are unable to reliably predict the energies for atomic displacements far from equilibrium. It is, however, possible to derive the stress conditions necessary in order that cross-slip can spread. An important contribution to the driving force results from the ‘Escaig stress’ acting on the edge components of the partials forming a dissociated screw dislocation and changing their separation. Contrary to the widely held assumption, the driving force is however independent of whether the dislocation in the cross-slip plane will be expanded or compressed.

Some recent papers from scripta:

[1] Kinetics and size effect of grain rotations in nanocrystals with rounded triple junctions

F Yang and W Yang

A kinetic model is developed to quantify the rate of grain rotations driven by either grain boundary energy or stress. The critical roles of triple junctions and grain shape are emphasized. The size effects for the rotation rate are analyzed. As the grain size decreases, the model predicts shifts in the dominating driving forces and dissipation mechanisms.

[2] Direct non-destructive observation of bulk nucleation in 30% deformed aluminum

S S West et al

A 30% deformed aluminum sample was mapped non-destructively using Three-Dimensional X-ray Diffraction (3DXRD) before and after annealing to nucleation of recrystallization. Nuclei appeared in the bulk of the sample. Their positions and volumes were determined, and the crystallographic orientations were compared with the orientations of the deformed grains. It was found that nuclei with new orientations can form and their orientations have been related to the dislocation structure in the deformed grains.

[3] Dynamic abnormal grain growth: A new method to produce single crystals

J Ciulik and E M Taleff

Dynamic abnormal grain growth (DAGG) is a newly discovered phenomenon which can be used to produce large single crystals from polycrystalline material in the solid state at temperatures above approximately half the melting temperature. The unique aspect of DAGG, compared to previously understood abnormal grain growth phenomena, is the requirement of plastic straining for initiation and propagation of abnormal grain growth. Our findings demonstrate that DAGG can be used to produce large single crystals of molybdenum in the solid state.

[4] Evaluation of the liquid-solid interfacial energy from crystallization kinetic data

J Torrens-Serra et al

The kinetic data obtained from the analysis of experimental measurements of nanocrystallization in Fe65Nb10B25 metallic glass are used to successfully estimate the molten alloy viscosity, Fe23B6 crystallization driving force and solid-liquid interface energy in the framework of the classical theory of nucleation and growth. We use a Vogel-Fulcher-Tamman law for the viscosity and linear temperature dependence for the crystallization driving force and interfacial energy. A negative temperature coefficient for the crystal-melt interfacial energy is obtained. Both the thermal stability and the glass forming ability of this alloy are discussed.

[5] Experimental study of the miscibility gap and calculation of the spinodal curves of the Au–Pt system

X N Xu et al

The miscibility gap (MG) of the Au–Pt binary system in the temperature range 600–1050 °C has been experimentally determined by the diffusion couple technique. The results show that the determined MG deviates from the currently accepted one, which shifts to the Au-rich side of the Au–Pt system. Based on the present experimental data, the Au–Pt system has been thermodynamically reassessed, with the result that the critical point of the miscibility gap is not, vert, similar1200 °C at 56 at.% Pt, in contrast to the currently accepted 1260 °C at 61 at.% Pt. The chemical and coherent spinodals of the Au–Pt system have been thus calculated.

[6] Estimation of dislocation density in bainitic microstructures using high-resolution dilatometry

C Garcio-Mateo et al

It is possible by means of high-resolution dilatometry, together with a model based on isotropic dilatation and atomic volumes, to estimate the dislocation density introduced in the microstructure as a consequence of the isothermal decomposition of austenite into bainitic ferrite. The relatively high dislocation density associated with this microstructure is attributed to the fact that the shape deformation accompanying this displacive transformation is accommodated by plastic relaxation.

[7] Magnetic phase transition and magneto-optical properties in epitaxial FeRh0.95Pt0.05 (0 0 1) single-crystal thin film

W Lu et al

This paper reports an investigation of the structure, magnetic phase transition and magneto-optical properties of FeRh0.95Pt0.05 thin film. A first-order magnetic phase transition occurs at a temperature around 180 °C, accompanied by a lattice expansion in the c-axis. The effect of substitution on the phase transition in ordered FeRh-based alloy systems is discussed. The nucleation and growth mechanism of the phase transition is quite similar to that of the crystallization of solids. In addition, the Kerr rotation spectrum was also studied.

May be this can be a case study for the course?

M J Santofimia et al

The quenching and partitioning (Q&P) process is a new heat treatment for the creation of advanced high-strength steels. This treatment consists of an initial partial or full austenitization, followed by a quench to form a controlled amount of martensite and an annealing step to partition carbon atoms from the martensite to the austenite. In this work, the microstructural evolution during annealing of martensite–austenite grain assemblies has been analyzed by means of a modeling approach that considers the influence of martensite–austenite interface migration on the kinetics of carbon partitioning. Carbide precipitation is precluded in the model, and three different assumptions about interface mobility are considered, ranging from a completely immobile interface to the relatively high mobility of an incoherent ferrite–austenite interface. Simulations indicate that different interface mobilities lead to profound differences in the evolution of microstructure that is predicted during annealing.

[1] Transformation kinetics for nucleus clusters

E Villa and P R Rios

A rigorous mathematical approach based on stochastic geometry concepts is presented to extend previous Johnson–Mehl, Avrami, Kolmogorov treatment of transformation kinetics to situations in which nuclei are not homogeneously located in space but are located in clusters. An exact analytical solution is presented here for the first time assuming that nucleation sites follow a Matérn cluster process. The influence of Matérn cluster process parameters on subsequent growth kinetics and the microstructural path are illustrated by means of numerical examples. Moreover, using the superposition principle, exact analytical solutions are also obtained when nucleation takes place by a combination of a Matérn cluster process and an inhomogeneous Poisson point process. The new solutions presented here significantly increase the number of exactly solvable cases available to formal kinetics.

[2] Anisotropic sintering stress for sintering of particles arranged in orthotropic symmetry

F Wakai and Y Shinoda

Many sintering bodies shrink in an anisotropic manner when the particle packing is not isotropic. The thermodynamic driving force for the anisotropic shrinkage, i.e. the sintering stress tensor, is determined numerically for an open pore structure with orthotropic symmetry in three dimensions. The sintering stress tensor is calculated rigorously by the energy method, the force balance method and the volume averaging method. The deviatoric component of sintering stress is approximately proportional to the logarithm of the aspect ratio of the orthorhombic volume element, and acts so as to deform the elongated particles to be more isotropic in most cases.

[3] Phase field study of precipitate growth: Effect of misfit strain and interface curvature (Note: self-promotion!)

R Mukherjee et al

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

[4] Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

D L Olmsted et al

The energies of a set of 388 distinct grain boundaries have been calculated based on embedded-atom method interatomic potentials for Ni and Al. The boundaries considered are a complete catalog of the coincident site lattice boundaries constructible in a computational cell of a prescribed size. Correlations of the boundary energy with other boundary properties (disorientation angle, *Σ* value, excess boundary volume and proximity of boundary normals to 1 1 1) are examined. None of the usual geometric properties associated with grain boundary energy are useful predictors for this data set. The data set is incorporated as supplementary material to facilitate the search for more complex correlations. The energies of corresponding boundaries in Ni and Al are found to differ by approximately a scaling factor related to the Voigt average shear modulus or C_{44}. Crystallographically close boundaries have similar energies; hence a table of grain boundary energies could be used for interpolation.

[5] Thermodynamics of grain boundary premelting in alloys. I. Phase-field modeling

Y Mishin et al

The rich nature of the premelting transition of grain boundaries in solid solutions is analyzed. Part I of this paper uses a multi-phase field model, whereas Part II employs atomistic Monte Carlo simulations. To enable comparison, Cu-rich Cu–Ag solid solutions are chosen for study. In the phase-field model, a system composed of two grains and a liquid phase is treated with three phase field parameters and with a realistic bulk thermodynamic description of Cu–Ag alloys obtained with the CALPHAD approach. Several different computation methods are employed, both rigorous and approximate, to examine the premelting behavior and relate it to the so-called “disjoining potential” between the solid–liquid interfaces in the grain boundary region. Depending on the grain boundary energy, temperature and grain composition chosen, several different classes of premelting transitions have been detected. As the grain concentration approaches the solidus line, one class shows a premelted layer whose thickness diverges continuously to infinity (complete wetting). Another class shows a discontinuity of the premelted layer thickness, exhibiting a first-order thin-to-thick transition prior to continuous thickening to infinity at the solidus line. In other cases, a metastable grain boundary state can exist above the solidus line, indicating the possibility of superheating/supersatuation of the grains together with the grain boundary. The possibility of such transitions has been predicted previously for generic thermodynamics by many authors. The results of the current investigation are compared with the atomistic calculations for the Cu–Ag system in Part II of this work.

[1] On the frequency of occurrence of tilt and twist grain boundaries

A. Morawiec

Homophase grain boundaries are frequently classified into twist, tilt and mixed-type boundaries. With small deviations from pure twist and tilt allowed, there are finite probabilities of occurrence of these particular boundary types in a set of random boundaries. These probabilities are determined for the case of cubic crystal symmetry. If the limit on the deviations is 3°, then 3.9% of random boundaries have near-twist character, and as many as 84.0% of random boundaries are near-tilt boundaries.

[2] A study of low-strain and medium-strain grain boundary engineering

V Randle and M Coleman

Grain boundary engineering (GBE) processing schedules, involving low-strain (5% deformation) iterative treatments, have been carried out on copper. Misorientation and grain boundary plane statistics have been derived, plus tensile and hardness measurements. The Σ3 length fraction and Σ9/Σ3 number ratio decreased during the first two processing iterations, whereas maximum GBE misorientation statistics were achieved after three processing iterations. Analysis of mechanical properties data revealed an accumulation of strain energy throughout the first three processing iterations, sufficient to provide enough driving force for extensive Σ3n interactions. The density of Σ3 boundaries had a larger effect on the rate of hardening than did the density of grain boundaries. This finding indicates the effectiveness of Σ3 interfaces as barriers to plastic flow, which plays an important role in the early stages of GBE processing. Data from samples that had undergone the low-strain iterations were also compared to medium-strain (25% deformation) processing iterations.

[3] Phase-field model study of the crystal morphological evolution of hcp metals

R S Qin and H K D H Bhadeshia

An expression for anisotropic interfacial energy of hexagonal close-packed metals has been formulated which is able to reproduce published data obtained using the modified embedded-atom method, covering the variation in interface energy as a function of orientation for a number of metals. The coefficients associated with the expression can be determined fully by measured or calculated interfacial energies of just three independent crystal planes. Three-dimensional phase-field model simulations using this representation of interfacial energy have been found to yield convincing crystal morphologies. The apparent rate of crystal growth as a function of orientation in the phase-field simulation agrees with predictions made by surface energy theory.

[4] Metallographic evidence of carbon diffusion in the growth of bainite

A Borgenstam, M Hillert and J Agren

There are two paradigms regarding the formation of bainite. One is based on the first stage being rapid, diffusionless growth of acicular ferrite and the subsequent formation of carbide occurring by precipitation from the supersaturated ferrite. An assumption that the first stage occurs as a series of subsequent rapid steps resulting in sub-units plays an important role as an explanation of the not so rapid growth observed macroscopically. The other paradigm is based on the first stage being the formation of acicular ferrite under carbon diffusion and on the subsequent growth of carbide and ferrite side by side. Metallographic observations are presented that support the second paradigm. It is difficult to see how they can be accounted for by the first paradigm, in particular the observation of the shapes of sub-units.

[5] Temperature and structure dependency of solid–liquid interfacial energy

K Mondal et al

A new model has been proposed for the prediction of solid–liquid interfacial energy for pure elements. It is assumed that the interface between crystalline solid embryo and bulk liquid consists of a monolayer of atoms having a similar atomic packing factor as that of the crystalline solids. It has been observed that the solid–liquid interfacial energy is a strong function of temperature and structure of the solid and planar density of the interface. The solid–liquid interfacial energy has a lower value close to melting temperature and it reaches a maximum at some intermediate temperature. This model tries to correlate the classical nucleation phenomena and structure model of interfaces.