[1] Migration of grain boundaries in free-standing nanocrystalline thin films

Dynkin and Gutkin

Theoretical models are suggested which describe stress-coupled migration of grain boundaries in free-standing nanocrystalline films under external loading. The critical stresses for the start of migration and the transition from stable to unstable migration are calculated and analyzed in dependence on the grain size, grain boundary misorientation angle, film thickness, distance from the closest free surface, and migration direction. It is shown that the least stable are low-angle grain boundaries of larger length which emerge on surfaces of thinnest films.

[2] Insight into the phase transformations between Ice Ih and Ice II from electron backscatter diffraction data

D J Prior et al

Electron backscatter diffraction data from polycrystalline water ice, cycled three times through the 1h to II phase transformation, show that an area equivalent to the original grain-size (∼450μm) now comprises equant 10μm grains with a non-random crystallographic preferred orientation (CPO). Pole figures show small-circle ring and fence patterns characteristic of CPO development controlled by an orientation relationship during phase transformation. Misorientation analysis shows that one of two orientation relationships can explain the data: 1h/II, {10-10}1h/{0001}II or 1h/II, {10-10}1h/{0001}II .

[3] Comment on ”Simulation of damage evolution in composites: A phase-field model”

Emmerich and Pilipenko

Here we reassess the results of [S.B. Biner, S.Y. Hu Acta Matt. 57(2009) 2088-2097] on phase-field simulations of damage evolution in composite materials. In particular we discuss the validity of the results presented therein in the framework of linear elasticity theory.

Update: Reply to “comment on simulation of damage evolution In composites: a phase-field model by H. Emmerich and D. Pilipenko ”

Biner and Yu

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[1] Dynamic effects in the lamellar–rod eutectic transition

S Liu et al

Critical experiments in the Al–Cu system are carried out to establish the conditions for the stability of rod and lamellar eutectics. It is shown that the instability of a lamella initiates locally through the formation of a sinusoidal perturbation, and the fastest growing wavelength of perturbation, which corresponds to the rod spacing, is related to the local lamella spacing. The instabilities in adjacent lamellae are observed to be out of phase to give rise to a hexagonal arrangement of rods at the transition. The specific relationship found between the unstable lamella spacing and the resulting rod spacing at the transition is then taken into account to develop a general model of the rod–lamellar transition which also includes the relative undercooling and the presence of a spacing distribution. A microstructure map is presented which defines the regimes of rod, lamellar and mixed structures, which is shown to be in good agreement with the experimental results.

[2] On the effect of superimposed external stresses on the nucleation and growth of Ni4Ti3 particles: A parametric phase field study

W Guo et al

Abstract

The effect of a superimposed stress on the coarsening of interacting Ni4Ti3 particles is studied using the multi-phase field method. It is found that the thickness/diameter ratio of a Ni4Ti3 particle in a (1 1 1)B2 plane increases with an increasing [1 1 1]B2 stress component. The particle shape can change from a disk to a sphere with increasing applied stress. It is also found that diffusional and mechanical interactions between two Ni4Ti3 particles can promote the nucleation of new particles. This provides an explanation for the autocatalytic nature of nucleation reported previously. Compressive stresses along [1 1 1]B2 increase the volume fraction and growth velocity of the Ni4Ti3 particles of the (1 1 1)B2 plane. Misoriented particles disappear during particle growth. The simulation results are discussed in the light of previous experimental results.

Research highlights

► Nucleation and growth of Ni4Ti3 precipitates in NiTi shape memory alloys is studied by multi-phase field simulations. ► A model of for thermodynamically consistent treatment of stoichiometric phases is proposed and applied in the present study. ► External compressive stress is predicted to change the morphology of the precipitates and to favor variants whose axis is parallel to the direction of stress. ► Autocatalytic nucleation of a chain of precipitates is explained by the trade of between solutal and strain related deviation for thermodynamic equilibrium.

[3] Thermodynamics of formation of tetragonal and rhombohedral heterophase polydomains in epitaxial ferroelectric thin films

Y Ouyang et al

Abstract

In this work, the thermodynamics of formation of tetragonal and rhombohedral heterophase polydomains in ferroelectric films is explained by the theory of elastic domains. The energetics of the heterophase polydomain microstructure are analyzed. The three major energy terms determining the crystalline orientation of the interdomain interface, i.e. interdomain elastic energy, interdomain electrostatic energy and domain interface energy, are investigated and compared. The crystalline orientation of the elastically best fitting plane between the two phases is analytically solved under an isotropic approximation of elasticity. It is found that a {1 1 2} type of domain interface minimizes interdomain elastic energies. Using available material parameters, it is found that the {1 1 2} domain interface prevails in Pb(Zr, Ti)O3, Pb(Mg1/3 Nb2/3)O3–PbTiO3 and BiFeO3 heterophase polydomains under zero applied electric field, as elastic energy is the dominant factor of interdomain interactions in all three systems. On the other hand, an increasing interdomain electrostatic energy under a poling field may induce a different domain interface, which is beneficial to extrinsic electromechanical responses.

Research highlights

► Tetragonal and rhombohedral phases coexist in ferroelectric films as elastic domains. ► Elastic energy is the dominant factor in determining the as-grown microstructure. ► A left angle bracket1 1 2right-pointing angle bracket domain interface prevails in the as-grown heterophase polydomain film. ► An increasing electrostatic energy under field may induce a different microstructure. ► Evolution of the microstructure under field enhances electromechanical responses.

Phase-field simulation of magnetoelastic couplings in ferromagnetic shape memory alloys

L J Li et al

Ferromagnetic shape memory alloys (FSMAs) possess coupled ferroelastic and ferromagnetic orderings simultaneously, making it possible to manipulate ferroelastic twins of FSMAs via a magnetic field or magnetic domains via mechanical loading. In this paper, we develop a phase-field model to simulate the formation and evolution of magnetoelastic domains in FSMAs under combined mechanical and magnetic loadings, taking into account both variant rearrangement and magnetization rotation. It is found that the large magnetic field induced strain in FSMAs results from a variant rearrangement process, yet such variant rearrangement can be blocked by a relatively large compressive stress, substantially reducing the magnetic field induced strain. Furthermore, either pseudoelastic or quasiplastic behavior is exhibited in FSMAs subjected to varying compressive stress, depending on the strength of the constant magnetic field applied. These results agree well with experiments, and can be used to guide the design and optimization of FSMAs.

Shearing of γ′ precipitates by a<1 1 2> dislocation ribbons in Ni-base superalloys: A phase field approach

V.A. Vorontsov et al

The phase field model of dislocations has been used to study the propagation of dislocation ribbons with an overall Burgers vector of a through a simulated Ni-base superalloy. The driving force for dislocation dissociation reactions and formation of planar faults is incorporated into the free energy functional using periodic functions specially fitted to ab initio γ-surface data. The model shows that the mechanism of cutting of the γ′ precipitates by these ribbons exhibits significant dependence on stress magnitude, orientation and precipitate shape. In the case of mixed screw–edge ribbons a change of shearing mode is observed, from stacking fault shear to anti-phase boundary shear, when the applied stress approaches the yield of the material. This transition is absent in pure edge ribbons.

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 InxAl1−xN layers have compositions around lateral lattice-matching to GaN (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 InxAl1−xN layer on GaN, homogeneous on a nanoscopic scale.

[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.

[1] A new ultrahigh-strength stainless steel strengthened by various coexisting nanoprecipitates

W Xu et al

A general computational alloy design approach based on thermodynamic and physical metallurgical principles and coupled with a genetic optimization scheme is presented. The model is applied to develop a new ultrahigh-strength maraging stainless steel. The alloy composition and heat treatment parameters are integrally optimized so as to achieve microstructures of fully lath martensite matrix strengthened by multiple precipitates of MC carbides, Cu particles and Ni3Ti intermetallics. The combined mechanical properties, corrosion resistance and identification of actual strengthening precipitates in the experimental prototype produced on the basic of the model predictions provide a strong justification for the alloy design approach.

[2] An investigation of the effect of structural order on magnetostriction and magnetic behavior of Fe–Ga alloy thin films

A Javed et al

This paper reports results from a comprehensive study of Fe–Ga films fabricated over a wide range of growth conditions. Polycrystalline Fe100−xGax films (14 less-than-or-equals, slant x less-than-or-equals, slant 32) were deposited (using three different combinations of growth parameters) on Si(1 0 0) using a co-sputtering and evaporation technique. The growth parameters (sputter power, Ga evaporation rate and chamber pressure) were used primarily to control the Fe:Ga ratio in the films. X-ray diffraction showed that all films had left angle bracket1 1 0right-pointing angle bracket crystallographic texture normal to the film plane. The lattice parameter increased with % Ga up to x = 22 and was independent of growth parameters. Conversion electron Mössbauer spectroscopy studies showed a predominance of the disordered A2 phase in all films. It appears that the use of vacuum deposition with appropriate parameters can effectively suppress the D03 ordered phase. Systematic studies of the effective magnetostriction constant as a function of composition support this conclusion. It was found that films of high effective saturation magnetostriction constant and low stress could be fabricated using low Ar pressure, irrespective of sputter power or evaporation rate, giving properties useful for application in microelectromechanical systems.

[3] Coarsening of a multimodal nickel-base superalloy

K Coakley et al

The coarsening of γ′-Ni3Al precipitates in the nickel superalloy Ni115 has been examined and compared to the results of a numerical model based on LSW coarsening theory. Ni115 has a γ′ fraction of around 60%, and at the coarsening temperatures of interest the γ′ distribution is bimodal, with two populations not, vert, similar5 nm and not, vert, similar90 nm in radius. It is found that during the initial transient (around 2000 h at 800 °C), the fine γ′ dissolve, leading to a rapid increase in the mean radius followed by a plateau. At long times, the expected steady-state unimodal t1/3 coarsening is observed. The model reproduces these features in form and approximately in magnitude, a first for LSW model-experiment comparisons in nickel superalloys.

[4] Growth morphologies in peritectic solidification of Fe–C: A phase-field study

A Choudhury et al

We use a thermodynamically consistent multi-phase, multi-component phase-field model, where the evolution equations for the different fields are derived from an entropy functional, for simulating peritectic growth structures in two and three dimensions. Different solidification morphologies are obtained in the computations and the characteristic properties of the growth forms are discussed. The phase-field method allows for a prediction of the surface energies in the three-phase system δ-ferrite, γ-austenite and liquid based on comparison between experimentally observed and simulated structures. Additionally an investigation of possible nucleation sites in evolving domains is presented and its dependence on the solid–solid surface energy is examined.

[5] Topological characteristics of plane sections of polycrystals

G S Rohrer and H M Miller

Homology metrics have been used to assess the connectivity of grain boundary networks in plane sections of polycrystals. The analysis is based on orientation maps, and four characteristic microstructure types were examined: SrTiO3 microstructures with normal and bimodal grain size distributions and two Ni microstructures with different concentrations of Σ3 grain boundaries. The inverse connectivity, defined as the ratio of the number of independent pieces of the network to the number of closed loops, is proposed as a metric for the extent to which certain types of grain boundaries are connected. The variation in inverse connectivity with disorientation threshold, below which boundaries are excluded from the network, produces distinct signatures for the different microstructures.

[6] Controlling Ag whisker growth by using very-thin metallic films

H Tohmyoh et al

The selective growth of Ag nano-whiskers on polycrystalline films has been realized by introducing an additional artificial layer onto the films. Ag nano-whiskers with diameters of about 200 nm and lengths of around 3 μm have been successfully generated from Ag films covered with a 1 nm-thick SiO2 layer. On the other hand, the formation of Ag whiskers/hillocks on the top surface of the film could be suppressed by using thick SiO2 layers or ductile Au layers.

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.

[2] Analysis by high-resolution electron microscopy of elastic strain in thick InAs layers embedded in Ga0.47In0.53As buffers on InP(0 0 1) substrate

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.

[3] The influence of solid-liquid interfacial energy anisotropy on equilibrium shapes, nucleation, triple lines and growth morphologies

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.