A simulation study of the shape of β′ precipitates in Mg–Y and Mg–Gd alloys

The metastable β′ phase is a key strengthening precipitate phase in a range of Mg–RE (RE: rare-earth elements) based alloys. The morphology of the β′ precipitates changes from a faceted and nearly equiaxed shape in Mg–Y alloys to a truncated lenticular shape in Mg–Gd alloys. In this work, we study effects of interfacial energy and coherency elastic strain energy on the morphology of β′ precipitates in binary Mg–Y and Mg–Gd alloys using a combination of first-principles calculations and phase-field simulations. Without any free-fitting parameters and using the first-principles calculations, CALPHAD databases and experimental characterizations as model inputs (lattice parameters of the β′ phase, elastic constants and chemical free energy of Mg matrix and interfacial energies of the coherent β′/Mg matrix interfaces), the phase-field simulations predict equilibrium shapes of β′ precipitates of different sizes that agree well with experimental observations. Factors causing the difference in the equilibrium shape of β′-Mg₇Y and β′-Mg₇Gd precipitates are identified, and possible approaches to increase the aspect ratio of the β′ precipitates and thus to enhance the strength of Mg–RE alloys are discussed.     

Atomic-Scale Interfacial Structure in Rock Salt and Tetradymite Chalcogenide Thermoelectric Materials

Interfaces play important roles in the performance of nanostructured thermoelectric materials. However, our understanding of the atomic-scale structure of these interfaces is only beginning to emerge. In this overview article, we highlight and review several examples illustrating aspects of interfacial structure in the rock salt and tetradymite classes of chalcogenide materials. The chalcogenide compounds encompass some of the most successful and well-understood thermoelectric materials employed in actual application and are also relevant more broadly in diverse fields including phase-change memory materials, infrared radiation detection, and topological insulators. The examples we consider here focus in three areas: the influence of weak interlayer bonding on grain boundary structure in Bi₂Te₃, crystallographic alignment and interfacial coherency in rock salt and related cubic chalcogenides, and the structure of interfaces at tetradymite precipitates in a rock salt chalcogenide matrix. The complex interfaces in these systems can be understood and generalized by considering the similarities between the rock salt, tetradymite, and related structures and by analyzing of the relevant interfacial defects.     

低合金Cr-Mo-V钢中VC沉淀相的精细结构

采用透镜电子显微分析（ＴＥＭ）的高分辨透射电子显微分析（ＨＲＥＭ）技术研究了低合金Ｃｒ－Ｍｏ－Ｖ铜不同回火温度下ＶＣ深淀相质点和精细结构及其与基体和界面关系,结果表明：较低温度回火时,ＶＣ沉淀相系以｛１００｝ａ为惯习面的纳米尺度的薄片,与基体存在Ｂａｋｅｒ－Ｎｕｔｔｉｎｇ关系,随着回火温度升高,片状相聚集成碳化物团或者发生球化,与基化丧失共格或部分共格,。     

PRECIPITATION AND MICROSTRUCTURE OF Cr MODIFIED Al3Ti

1. IntroductionThe tetragonal D022 compound A13Ti has recently received attention as a possible structural material because of its low density, 3.4g/cm', and its good oxidation resistanced'2].However, D0zz-AlsTi has the disadvalltages, that it is a line compound and is extremelybrittle at room temperature, presumably due to the lack of slip systems associated withthe crystal symmetry[2]. It is known that partially replacing some of the aluminum atomsin AlsTi with Cr[31, Ni[4], or Ag['] etc…     

Effects of applied stress on coherent precipitates via a discrete atom method

Morphological evolution of coherent precipitates under an applied stress is analyzed by means of a discrete atom method, which is predicated upon Hookean atomic interactions and Monte Carlo diffusion, and mates no assumption of a specific shape. Precipitates having elastic constants different from those of the matrix phase art treated in dislocation-free, anisotropic elastic systems under a plane strain condition with a purely dilatational misfit. Under an applied tensile stress, soft particles with a positive misfit strain tend to become plates perpendicular to the applied stress axis, while hard particles elongate along the stress direction. If the elastic interaction between the applied stress and the coherency strain is strong enough, precipitates often split into smaller particles and then follow coarsening. Even in the absence of a coherency strain, particles are shown to undergo morphological evolution through Eshelby’s inhomogeneity effects. A particle shape depends on the following variables: the sign and magnitude of the coherency strain, the sense and magnitude of the applied stress, its stiffness relative to the matrix phase, and the magnitude of the interfacial energy.     

Wetting anisotropy and oxygen activity dependency for oxides by liquid transition metals studied through shape changes of liquid Cu inclusions within MgO

The equilibrium shape of liquid metal inclusions in oxides is used to study anisotropy and oxygen partial pressure dependency of the metal–oxide specific interfacial free energy. Liquid copper inclusions are formed within single crystalline magnesia by internal reduction of mixed oxide (Mg,Cu)O. Their equilibrium shape is studied by TEM for various oxygen chemical potential. Precipitates always adopt cubo-octahedral morphology, but relative facet size strongly depends on the oxygen chemical potential. The shape evolution with oxygen chemical potential reveals important and anisotropic Gibbs' adsorption of excess oxygen to the interfaces at high oxygen activities. Gibbs' adsorption to crystallographically different MgO–liquid Cu interfaces is discussed in terms of a point defect model recently developed by the author (Backhaus-Ricoult, M., Phil. Mag., 2001, in press), where oxygen activity-dependent formation of interfacial charge transfer clusters between liquid metal and excess oxygen or magnesium is considered, while the relevant site and charge conservation laws in the two-phase system are respected and matter exchange with the surrounding gas atmosphere is allowed. Present experimental results are interpreted in terms of this interfacial defect model and compared with interpretation by other wetting models from the literature.     

Changes in Cu–silica interfacial chemistry with oxygen chemical potential

Interfacial chemistry and equilibrium morphology of SiO₂ glass precipitates in a solid copper matrix are studied as a function of the oxygen chemical potential. Spherical SiO₂–glass precipitates are formed within copper by internal oxidation of (Cu,Si) single crystals at different oxygen activities. The metal–glass interfaces are rough at an atomic level. Atomic and electronic structures of the different interfaces are analyzed by high spatial resolution EELS. At high oxygen activity, two interfacial zones with specific electronic states are distinguished: on the metal-side of the interface, the correlated modifications in the O-1s and Cu-2p edges indicate O-2p–Cu-3d hybridization; on the glass-side of the interface, a modification of the Cu-2p edge is observed, which is interpreted in terms of a weak interaction of highly perturbed metallic copper with the constituents of the adjacent glass network. At intermediate oxygen activity, only the latter modification is observed at the interface.Oxygen adsorption and desorption to the silica–copper interface are modeled by a continuum approach; model results are compared to those obtained by experiments.     

Atomic scale investigation of Cr precipitation in copper

The early stage of chromium precipitation in copper was analyzed at the atomic scale by atom probe tomography (APT). Quantitative data about the precipitate size, three-dimensional shape, density, composition and volume fraction were obtained in a Cu–1Cr–0.1Zr (wt.%) commercial alloy aged at 713 K. Surprisingly, nanoscaled precipitates exhibit various shapes (spherical, plates and ellipsoid) and contain a large amount of Cu (up to 50%), in contradiction to the equilibrium Cu–Cr phase diagram. APT data also show that some impurities (Fe) may segregate along Cu/Cr interfaces. The concomitant evolution of the precipitate shape and composition as a function of the aging time is discussed. Special emphasis is given to the competition between interfacial and elastic energy, and to the role of Fe segregation.     

A comparison of the phenomenological theory of martensitic transformations with a model based on interfacial defects

Structural models of martensitic interfaces are those where the habit plane (HP) is comprised of coherent terraces reticulated by arrays of interfacial defects. Such interfaces are shown explicitly to exhibit no long-range displacements and to move in a glissile manner by lateral motion of disconnections along the interface. We quantify predictions of HP and orientation relationship (OR) between the parent and product crystals for such models in terms of a reference lattice in an approach called a topological model (TM). These crystallographic quantities for the TM are compared with those of the phenomenological theory of martensite crystallography (PTMC). For the case of transformations resembling α to β in Ti, but where lattice invariant deformation is suppressed, the two models agree when the interplanar spacings of the terraces in the two crystals are the same. However, although the OR’s according to the two approaches are very similar, the predicted HP’s differ systematically when the terrace plane spacings are varied. The differences arise because the PTMC interfaces are unrelaxed configurations that are invariant planes of the geometrical shape transformation, whereas TM interfaces are physically invariant planes as a transformation progresses.     

Effects of phase fraction on phase morphology and triple junction configuration in anisotropic systems

It has been demonstrated that Herring’s anisotropic triple-junction equilibrium conditions do not predict a unique triple-junction configuration for junctions involving at least one anisotropic interface. In this paper, we minimize the total interfacial energy of a model two-dimensional anisotropic system to predict the preferred triple-junction configuration(s). Both the relative values of the interfacial energies and the phase fractions affect the energetics. Maps of the energetically preferred configuration(s) spanning a wide range of phase fraction and relative interfacial energies are presented. Parallel trends and key differences between the behaviors of the model anisotropic system and a (similarly configured) isotropic system are detailed. Lastly, we show how the approach used to predict equilibrium configurations (based on assumed interfacial energies) can be reversed to obtain relative interfacial energies for experimental systems where equilibrium has been reached but only geometrical parameters can be measured.     

Microstructure dependence of strength of Ir-base refractory superalloys

Precipitation hardening was investigated in Ir–Nb and Ir–Zr alloys with a two-phase structure consisting of the fcc matrix and L1₂ coherent precipitate phases, similar to that in Ni-base superalloys. Cuboidal L1₂ precipitates and plate-like L1₂ precipitates were formed with coherent interfaces in the fcc matrix in the Ir–Nb and Ir–Zr alloys, respectively. Effects of precipitate shape and coherency strains on precipitation hardening are discussed in terms of lattice misfit. Plate-like precipitates forming a 3-dimensional maze structure in the Ir–Zr alloys were profitable to precipitation hardening in both factors, that is precipitate shape and coherency strains.     

A general method for calculating deviation from local equilibrium at phase interfaces

A general method to calculate the deviation from local equilibrium at phase interfaces in multicomponent systems is suggested. The deviation is caused by solute drag and finite interfacial mobility. In the limit of low transformation rates the new method degenerates to the well-known local equilibrium condition. The phase interface is divided into three zones, each with a finite thickness. In each zone a variation in thermodynamic properties and diffusional mobilities is assumed.     

Two- and three-dimensional equilibrium morphology of a misfitting particle and the Gibbs–Thomson effect

The equilibrium shapes of misfitting precipitates in elastically anisotropic systems are obtained in both two and three dimensions, and the corresponding Gibbs–Thomson equation is derived as a function of the characteristic ratio between elastic and interfacial energies, L′. The effect of elastic inhomogeneity is investigated systematically. For soft or moderately hard particles, the stable equilibrium shape bifurcates from a fourfold symmetric shape to a twofold symmetric one in 2D and from a cubic symmetric shape to a plate-like one in 3D. For a very hard particle, the shape bifurcation is not observed in 2D for the range of L′ investigated, but both plate-like and rod-like shapes are found in 3D. The computed Gibbs–Thomson equation is well approximated by a piecewise linear function of L′. Predictions are made for coarsening of many-particle systems based on an established mean-field theory. The results predict that the elastic stress has no effect on coarsening kinetics where most particles are highly symmetric (fourfold in 2D and cubic in 3D), and the exponent remains 1/3 but the rate constant increases if stress is sufficient to induce symmetry-breaking bifurcation on most particles.     

Atomic Mixing in Metals Under Shear Deformation

The fundamental processes of shear-induced chemical mixing in heterogeneous Cu-based alloy systems have been studied by molecular dynamics computer simulations. These simulations reveal that two very disparate mechanisms operate depending on whether or not the two phases are coherent. For the coherent systems, mixing occurs as dislocations transfer across phase boundaries. The mixing in these systems is “superdiffusive,” and for spherical precipitates, the rate of mixing increases quadratically with precipitate radius. In systems that have incoherent phases, the mixing occurs by a local shuffling of atoms at the interface, and for them, the mixing is diffusive, with the mixing rates of spherical precipitates scaling linearly with particle radius. The morphologies of the interfaces for the two situations are also different. Coherent precipitates form rough interfaces that are relatively sharp, whereas the interfaces of incoherent precipitates are smooth but diffuse. These simulations also show that for incoherent precipitates, shear-induced mixing can be very different at different crystallographic interfacial planes as well as for different strain directions.     

Interfacial defects of hard magnetic Pr2Fe14B phase from amorphous to nanostructures

The interfacial defects of hard magnetic Pr2Fe14B phase from amorphous to nanostructures have been investigated by positron lifetime spectroscopy. The nanostructure was produced by melt-spinning and nanocrystallization route. The two main components can be ascribed to vacancy-like defects in the intergranular layers or the interfaces, and microvoids or large free volumes with size compared to several missing atoms at the interactions of the atomic aggregates or the crystallites. The remarkable changes in the positron lifetimes from the amorphous structure to the nanocrystructure with varied sizes can be interpreted, indicating that the structural transformation and the grain growth induce the defect changes occurring at the interfaces with different shapes and sizes.     

Phase separation in Ni-rich Ni–Ti: the metastable states

The microstructure of Ni-11.3 at.% Ti single crystals was investigated after quenching from the solid solution at 1440 K and after ageing at 873 K for various periods of time by using transmission electron microscopy and X-ray scattering near fundamental reflections and superstructure reflections of the ordered precipitates. The two-stage decomposition sequence with the initial formation of metastable γ″ precipitates followed by metastable γ′ precipitates as found by small-angle neutron scattering is confirmed. The long-range order parameter of these precipitates is always close to the maximum value achievable at a given composition. The presence of the first metastable state (γ″) is related to a rearrangement of the precipitates on a macro-lattice in order to minimize the elastic energy due to coherency strains.     

FINE STRUCTURES OF BOTH INTERFACES AND INTERFACIAL REACTION PRODUCTS

The characteristic of interface depending on the atomic structure exerts an inportant,andsometime controlling,influence on performance of the interacial materials.The present paper reviews the main studies on fine structure of both the materials inter-faces and interfacial reaction products in semiconductor uperlattice,metal multilayer ceram-ics and composite materials by mean of selected area electron doffraction patterns and highresolution electron microscopy.The following features of interfaces are reviewed:the orientation relationships;the char-acteristic of steps,facets and ronghness of interfaces;atomic bonding across the interface;thedegree of coherency,the structure of misfit dislocations and elastic relaxations at the inter-faces:the presence of defects at the onterfaces:the structure of the interfacial reaction prod-ucts as well as the reaction kinetics and reaetion mechanism.     

Mechanisms related to different generations of γ′ precipitation during continuous cooling of a nickel base superalloy

This paper focuses on developing a mechanistic understanding of the process of multiple nucleation bursts leading to the formation of multiple generations (or populations) of γ′ precipitates with different size distributions, during the continuous cooling of a commercially used nickel base superalloy. This mechanistic understanding has been developed based on a number of critical experimental results: direct observation of the multiple nucleation bursts during in situ X-ray diffraction studies in the synchrotron, characterization of the size distributions associated with the different populations of γ′ precipitates by coupling multiple imaging techniques at the appropriate length scale and detailed compositional analysis of the γ′ precipitates as well as the γ matrix using atom probe tomography. These analyses reveal that while local compositional equilibrium appears to have been achieved near the γ′/γ interface for the first generation of precipitates, a non-equilibrium long range diffusion profile in the γ matrix is retained during the process of continuous cooling, which is largely responsible for the subsequent nucleation bursts at larger undercooling (or lower temperatures), leading to second and third generations of precipitates. Additionally, since these subsequent generations of precipitates are formed at larger undercoolings, they are typically finer in size scale, exhibit far-from equilibrium compositions and also have very diffuse γ′/γ interfaces, indicating a non-classical precipitation mechanism associated with their formation.     

Influence of misfit and interfacial binding energy on the shape of the oxide precipitates in metals: ; Interfaces between Mn3O4 precipitates and Pd studied with HRTEM

Transmission electron microcopy (TEM) revealed Mn₃O₄ precipitates with two types of dominant shape in Pd–3 at.% Mn that was internally oxidized in air at 1000°C. One type is octahedrally shaped and bounded by {111} planes of the Mn₃O₄. These observations were compared with earlier observations in the Ag/Mn₃O₄ system and the octahedrons show a relatively larger truncation by (002) in Pd than in Ag. Further, the second type of precipitate shape, comprising about 1/3 of all of the precipitates in Pd, was not observed in Ag. It corresponds to a plate-like structure, showing an orientation relationship where the tetragonal axes of Mn₃O₄ are parallel to the cube axes of Pd, with the c-axis of Mn₃O₄ as habit plane normal. High-resolution TEM observations revealed the presence of a square misfit dislocation network with line direction 〈110〉 and Burgers vector 1/2〈110〉 at these interfaces with (002)Mn₃O₄6{200}Pd. The general conclusions of the present analysis are: (1) the anisotropy in interface energy for oxide precipitates in a metal matrix is substantial due to the ionic nature of the oxide, giving well-defined shapes associated with the Wulff construction; (2) the influence of misfit energy on the precipitate shape as bounded by semi-coherent interfaces is important only if sufficient anisotropy in mismatch is present and if the matrix is sufficiently stiff; and (3) the stronger coupling strength due to electronic binding effects across the interface in Pd compared with Ag is responsible for formation of the dislocation network structures at larger misfit.