Micropores in Al-Cu alloys

September 4, 2011

Curvature of micropores in Al–Cu alloys: An X-ray tomography study

Felberbaum and Rappaz

Micropores formed in Al–Cu alloys cast under controlled conditions have been analyzed using high-resolution X-ray tomography. The influence of inoculation conditions, copper content, cooling rate and initial hydrogen content on the morphology of pores has been investigated. Based on the three-dimensional reconstructed shape of the pores, the distribution of curvature was estimated. It is shown that the mean curvature of pores in either non-inoculated or inoculated Al–4.5 wt.%Cu alloys can be as large as 0.35 μm−1 near the end of solidification and can be fairly well approximated by a set of interconnected cylinders growing in between the primary phase dendrites. The so-called “pinching” effect, i.e. the restriction of the pore curvature by the solid network, is a function of the volume fraction of the primary phase and of the secondary dendrite arm spacing. If the fraction of porosity is highly dependent on the initial hydrogen content, the curvature itself is only weakly influenced by this parameter. Based on these results, it is concluded that curvature plays a major role in porosity models and that the analytical pinching model developed by Couturier et al. [1] offers a fairly good and simple approximation of this contribution.

Simulating creep of snow based on microstructure and the anisotropic deformation of ice

T Theile et al

It is generally agreed that the creep of low-density snow is accompanied by drastic microstructural changes, which are a major source of macroscopic strain hardening. There is, however, no agreement about the dominating mechanism which mediates structural mobility at the microscale. A widely used model of creeping snow allows for intercrystalline deformations at the grain boundaries but neglects intracrystalline deformations in the grains. Here we show that the opposite scenario, which solely uses intra-crystalline deformations, while neglecting grain boundary sliding, is in better agreement with experiments. To this end we have conducted in situ, microtomography measurements of snow microstructure during creep experiments. 3-D tomography images are used to simplify the full microstructure to a 3-D beam-network. This reduces the number of degrees of freedom drastically, which enables us to carry out creep simulations by finite-element methods. We use Glen’s law for secondary creep of ice as the material model and account for the anisotropic creep behaviour of single crystals by assigning individual network strands a random orientation of the c-axis. The results suggest a separation of time scales between creep stress relaxations and slow microstructural changes make the key contribution to snow hardening. Although open-cell foam models clearly fail in predicting the observed viscosity–density relations, they are interestingly suggested as a potential limiting behaviour in our experiments.

Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

Equilibrium morphology

March 30, 2011

After Ni, it is WC now.

The equilibrium morphology of WC particles – A combined ab initio and experimental study

Y Zhong et al

We report an ab initio density functional theory study, complemented by parallel experimental work, of the equilibrium shape of WC particles. The equilibrium shape is simulated under the condition of little or no liquid-phase sintering. The effects of the carbon-rich and carbon-deficient conditions and the adsorption of Co and Ni atoms on the surface of WC particles are investigated. The equilibrium shape of WC particles is found to be a truncated triangular prism under both carbon-rich and carbon-deficient conditions. The adsorption of Co and Ni on the WC surface can promote the formation of either truncated triangular prisms or near-hexagonal prisms, depending on their specific combination with the carbon chemical potential. Under all the conditions investigated, the equilibrium shapes of WC crystals can be described as “bulky” rather than “plate-like”. The findings in this study are consistent with the experimental observations.

[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.

[1] Dislocation–grain boundary interaction in left angle bracket1 1 1right-pointing angle bracket textured thin metal films

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.

[4] Application of classical nucleation theory to phase selection and composition of nucleated nanocrystals during crystallization of Co-rich (Co,Fe)-based amorphous precursors

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.

[5] Transmission electron microscopy study of the microstructure and crystallographic orientation relationships in V/Ag multilayers

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.

[7] Role of discrete intragranular slip on lattice rotations in polycrystalline Ni: Experimental and micromechanical studies

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.

[10] Constraint-dependent twin variant distribution in Ni2MnGa single crystal, polycrystals and thin film: An EBSD study

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.

[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.

Diffusivities of an Al–Fe–Ni melt and their effects on the microstructure during solidification

Lijun Zhang et al

A systematical investigation of the diffusivities in an Al–Fe–Ni melt was presented. Based on the experimental and theoretical data about diffusivities, the temperature- and composition-dependent atomic mobilities were evaluated for the elements in Al–Ni, Al–Fe, Fe–Ni and Al–Fe–Ni melts via an effective approach. Most of the reported diffusivities can be reproduced well by the obtained atomic mobilities. In particular, for the first time the ternary diffusivity of the liquid in a ternary system is described in conjunction with the established atomic mobilities. The effect of the atomic mobilities in a liquid on microstructure and microsegregation during solidification was demonstrated with one Al–Ni binary alloy. The simulation results indicate that accurate databases of mobilities in the liquid phase are much needed for the quantitative simulation of microstructural evolution during solidification by using various approaches, including DICTRA and the phase-field method.