Diffusional Phase Transformations Research Articles

Influence of solute segregation and drag on properties of migrating interfaces

Recent models on solute segregation and drag search for steady-state solutions of the diffusion equation in the region of a migrating interface and adjacent semi-infinite grains. Such solutions are limited to model massive transformations, for which the chemical composition of the parent grains and that of the product grains are the same. Simulation of diffusive transformations in transient systems with grains of different chemical composition is a hot issue. In the present model the steady-state solution of the diffusion equation is investigated only in the interface. The coupling with the diffusion equation in the adjacent grains is ensured by proper boundary conditions. For simulation of transient diffusive phase transformations it is very convenient if the interface can be treated as a sharp interface with a known effective mobility and prescribed boundary conditions at the interface. In this paper it is shown that solute segregation and drag can be taken into consideration by the effective mobility of a sharp interface and by proper boundary conditions at the sharp interface. The effective interface mobility reflects Gibbs energy dissipation due to rearrangement of solvent atoms and to trans-interface diffusion and drag of solute atoms in the migrating interface. Trans-interface diffusion and drag of solute atoms are also reflected by the jump of the chemical potential of the solute across the interface, which represents a boundary condition for coupling with the diffusion equation in the adjacent grains. Finally, it is shown that the incorporation of the effects of trans-interface diffusion and drag of solute atoms does not make the simulation more complicated provided that some necessary calculations are performed in preprocessing.

Phase field model for phase transformations of multi-phase and multi-component alloys

We propose a numerical model for computer simulation of macroscopic processes of diffusive phase transformations of alloys. It is an extension of a phase field model and can treat multi-phase and multi-component alloys. This gives a general framework for computer aided studies of many phenomena—complicated microstructure formations in alloys and intermetallic compound generation, for example. We also present some numerical results which reproduce qualitative aspects of typical phase transformations observed in real alloys.

Diffusional phase transformations in steel - theory and application to continuous casting

In addition to the thermal stresses the bending and straightening operations in a curved type slab caster cause mechanical strains and stresses in the temperature region between 700°C and 1200°C. Many investigations have shown a breakdown of the hot ductility behaviour of several steel grades due to the austenite / ferrite transformation and due to the precipitation of non-metallic inclusions in the temperature range mentioned above. The arrangement of the two phases - austenite and ferrite - as well as the arrangement of non-metallic inclusions in the austenite matrix play an important role. The formation of ferrite is observed as thin ferritic films along the austenite grain boundaries. The movement of the interphase boundary has been modeled. The coupled processes, carbon diffusion and interface migration, have been taken into account. This procedure allows an estimation of the ferrite film thickness. In the second part of the paper, a two-dimensional micromechanical study is performed assuming a small amount of ferrite. The stress strain distribution has been analyzed in this composite.

On an elastically induced splitting instability

We show that a morphological instability driven by deviatoric applied stresses can generate elastically induced particle splitting during diffusional phase transformations. The splitting instability occurs when the elastic fields are above some critical value. For subcritical elastic fields, one observes a small perturbation of the particle shape consistent with splitting, but this perturbation is stabilized by surface tension. Both the onset of the splitting instability and the nonlinear evolution of the particle towards splitting depend on the precise form of the applied stress, the elastic constants of the precipitate and matrix, and the initial shape of the precipitate. We also investigate whether non-dilatational misfit strains can generate splitting instabilities in the absence of an applied stress.

Variant selection in heterogeneous nucleation on defects in diffusional phase transformation and precipitation

In heterogeneous nucleation on lattice defects in the matrix during diffusional phase transformation and precipitation reactions, the variant of product phase with the specific orientation relationship is strongly selected by the nature of the defects. For dislocations, effective accommodation of the transformation strain by the strain field of dislocations occurs, leading to the variant selection in which the direction of the maximum misfit is nearly parallel to the Burgers vector of the dislocations. For high-angle grain boundaries and subgrain boundaries, precipitates tend to select the variant with a low-energy interface (often the parallel close packed planes) inclined at the smallest angle to the grain boundary plane. On the other hand, precipitates that nucleate on the incoherent inclusions embedded in the matrix do not hold any specific orientation relationship with respect to the matrix. It is important to produce many variants locally for the effective refinement of microstructures that improves the mechanical properties of steel and titanium alloys.

Energy-filtered electron microscopy study on phase transformation of alloys

Recent progress of electron microscopy on phase transformations of alloys, especially energy-filtered electron microscopy, was reviewed mainly on the basis of the recent works by the authors. In the energy-filtered electron diffraction patterns of both Cu 72.5Pd 27.5 and Ti 50Ni 48Fe 2 alloys, weak diffuse scattering which resulted from the diffusional and displacive phase transformations, respectively, was clearly observed by virtue of the background subtraction. In a short-range ordered state of a Cu 72.5Pd 27.5 alloy, through the careful evaluation of the dynamical diffraction effect on the diffuse scattering, short-range order parameters were evaluated quantitatively. On the other hand, in the premartensitic state of a Ti 50Ni 48Fe 2 alloy, the morphology and growth process of microdomains less than 5 nm with a single transverse type of atomic displacement were clarified by energy-filtered electron diffraction and in situ dark-field electron microscopy. Furthermore, through in situ electron energy-loss spectroscopy on L 2,3 core edges of a Ti 50Ni 48Fe 2 alloy, the change in the electronic structure due to the martensitic transformation was analyzed. Thus, it is clearly demonstrated that advanced electron microscopy utilizing electron energy-loss spectroscopy is effective to make clear the change in both crystal and electronic structures associated with phase transformations in alloys.

Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials

We present a brief review of the application of boundary integral methods in two dimensions to multicomponent fluid flows and multiphase problems in materials science. We focus on the recent development and outcomes of methods which accurately and efficiently include surface tension. In fluid flows, we examine the effects of surface tension on the Kelvin–Helmholtz and Rayleigh–Taylor instabilities in inviscid fluids, the generation of capillary waves on the free surface, and problems in Hele-Shaw flows involving pattern formation through the Saffman–Taylor instability, pattern selection, and singularity formation. In materials science, we discuss microstructure evolution in diffusional phase transformations, and the effects of the competition between surface and elastic energies on microstructure morphology. A common link between these different physical phenomena is the utility of an analysis of the appropriate equations of motion at small spatial scales to develop accurate and efficient time-stepping methods.

Coupled thermodynamic/kinetic analysis of diffusional transformations during laser hardening and laser welding

Several important industrial material processes, such as welding and surface treatments with high energy beams, incorporate rapid thermal cycles characterized by high heating/cooling rates and short dwell times. Computational simulation of the evolution of microstructure under these extreme conditions has received rather limited attention. With the advent of modern computational tools regarding alloy thermodynamics and kinetics, it is possible to simulate the progress of diffusional phase transformations and thus to predict microstructural development. In the present work, moving boundary diffusion problems have been simulated for two cases. In the first case the rapid austenitization during laser transformation hardening of a hypoeutectoid steel was examined. The effects of heating rate, maximum temperature, dwell time and initial microstructure fineness were analyzed. In the second case the aging, dissolution and coarsening of strengthening precipitates in the heat affected zone of laser welds in Al–Mg–Si alloys was examined. The simulation provided the variation of the volume fraction and average size of the strengthening phase during the weld thermal cycle. In both cases the calculations were performed by applying the coupled thermodynamics and kinetics approach, incorporated in the DICTRA program. This kind of simulation provides useful information for the design of the above processes.

Aspects of interphase boundary structure in diffusional phase transformations

Distinctions among fully coherent, partly coherent and incoherent interphase boundaries are presented. Introduction of a single linear misfit compensating defect is concluded to represent the most useful definition of the transition between fully and partly coherent interfaces. The limit between partly and fully incoherent interphase boundaries is taken operationally as the absence of detectable misfit accommodating defects (i.e., localization) at the interface by high-resolution transmission electron microscopy. An answer to the question of whether or not a precipitate crystal can be fully or partly coherent at one or more boundary orientations and incoherent at others is developed.

Propagation and ignition of fast gasless detonation waves of phase or chemical transformation in condensed matter

Fast self sustained waves of chemical or phase transformations, observed in several contexts in condensed matter effectively result in “gasless detonation". The phenomenon is modelled by coupling the reaction diffusion equation, describing chemical or phase transformations, and the wave equation, describing elastic perturbations. The coupling considered in this work involves (i) a dependence of the sound velocity on the chemical (phase) field, and (ii) the destruction of the initial chemical equilibrium when the strain exceeds a critical value (strain induced phase transition). Both the case of an initially unstable state (first order kinetics) and metastable state (second order kinetics) are considered. An exhaustive analytic and numerical study of travelling waves reveals the existence of supersonic modes of transformations. The practically important problem of ignition of fast waves by mechanical perturbation is investigated. With the present model, the critical strain necessary to ignite gasless detonation by local perturbations is determined.

Interfacial dislocation mechanism for diffusional phase transformations exhibiting martensitic crystallography: formation of TiAl + Ti 3Al lamellae

The displacive–diffusive transformation, which gives rise to lamellar γ-TiAl+ α 2-Ti 3Al microstructures, has been analysed theoretically. Using the formulation due to Hirth and Pond, the shear produced and extent of diffusional flux associated with interfacial defect motion can be quantified in terms of the Burgers vectors, step heights of the defects and the chemical compositions of the adjacent crystals. Moreover, this formulation also enables the effects of chemical composition, misfit at the interface and ordering to be investigated systematically. It is shown that for the defects observed on such interfaces in recent high-resolution transmission electron microscopy studies, their motion would lead to the conservation of sites and, correspondingly, to equal and opposite fluxes of Ti and Al atoms. Consequently, although this transformation is diffusional, it exhibits crystallographic features consistent with martensitic processes.

Kinetics of hydrogen induced diffusion phase transformation in intermetallic compound TbFe 2

The effect of temperature on the rate of isothermal diffusion phase transformation in the intermetallic compound TbFe 2 in hydrogen atmosphere has been investigated by means of magnetic and powder X-ray diffractometry methods. It was shown, that in the temperature range of 450–580°C the rate of decomposition was increased with increasing temperature. The final products of decomposition were TbH 2 and α-Fe.

Kinetics of the hydrogen-induced diffusive phase transformation in Nd–Fe–B industrial alloy

The kinetics of the hydrogen-induced diffusive phase transformation in industrial alloy Nd–Fe–B has been investigated. The isothermal kinetic curves were received for temperatures from 750 to 620°C at the hydrogen pressure 0.1 MPa. An isothermal kinetics diagram was obtained. This diagram is similar to the ones of the transformations in steels during heating. It is shown that the investigated phase transformation is a diffusion-controlled one with the mechanism of nucleation and growth.

A phenomenological treatment of diffusion in Al–Fe and Al–Ni alloys having B2-b.c.c. ordered structure

A model for diffusion in ordered phases with B2-b.c.c. structure is presented and generalized to multicomponent alloys. The model makes use of thermodynamic data to evaluate the thermodynamic factor as well as the degree of ordering at a given temperature. The activation energy for diffusion is expressed as a function of the degree of order. The model is suitable for implementation in software for simulation of diffusional phase transformations. The available experimental data for the Al–Ni and Al–Fe systems is discussed. Some inconsistencies in the data for the Al–Fe system are pointed out. A CALPHAD-like assessment procedure is applied successfully to a selected set of experimental information showing that the model is capable of representing this information in the Al–Fe and Al–Ni systems. The practical use of the model is demonstrated by the computer simulation of a diffusion experiment. It is shown that the results of the simulation agree well with the experimental observations.

Computer simulations of diffusional phase transformations: Monte Carlo algorithm and application to precipitation of ordered phases

A Monte Carlo (MC) simulation technique which is well suited for studying diffusional phase transformations is presented. This technique accounts for atom transport through vacancy migration, and allows a physically meaningful definition of time. This MC technique is used for studying the precipitation of an L1 2 ordered phase from a supersaturated, disordered f.c.c. matrix. Three alloys have been studied of compositions x B=0.125, 0.15 and 0.175, with equilibrium volume fraction of the L1 2 phase of 0.23, 0.47 and 0.71, respectively. The results show that, during early stages of the transformation, both phase separation (i.e. formation of regions of different compositions) and ordering (i.e. creation of atomic order in the solute-rich regions) proceed simultaneously in all the three alloys. In particular, there is no evidence for homogeneous ordering prior to phase separation even in the most concentrated alloy with x B=0.175. Thus, the results are in direct contradiction to those obtained in recent simulations by Chen and Khachaturyan, and underscore the limitations of the Bragg–Williams approximation used by them. The late stage behaviour of all the three alloys obey classical laws of coarsening: (i) the microstructures are self similar, and (ii) the cube of the characteristic microstructural length scale increases linearly with time. Thus, the range of validity of the classical laws appears to extend to large precipitate volume fractions.

Phase transformations during cooling in α+ β titanium alloys

A simplified methodology for investigating the effects of cooling rate from elevated temperature on phase transformations observed in α+ β titanium alloys is described. It involves adaptation and refinement of a circumferentially insulated and instrumented Jominy end quench bar, time–temperature profiles obtained during cooling at locations along the bar length providing a complete thermal history. The ability of this procedure to examine the phase transformation for α+ β titanium alloys has been demonstrated in Ti–6Al–4V where varying cooling rates from 525 to 1.5°C s −1 are shown to result in a series of martensitic, massive and diffusional phase transformations. Cooling rates above 410°C s −1 result in a fully martensitic microstructure, a massive transformation being observed between 410 and 20°C s −1, this transformation being gradually replaced by diffusion controlled Widmanstätten α formation with decreasing cooling rate.

Analytical electron microscopy of discontinuous solid state reactions

The discontinuous solid state reactions represent a group of diffusional solid state phase transformations during which the solute redistribution accompanying the formation of a new phase occurs on a nanometer scale just at the moving reaction front. Such solute changes can be sufficiently revealed by means of analytical electron microscopy (AEM). A number of systematic investigations made using AEM during the last decade in discontinuous precipitation, dissolution, and coarsening are reviewed and critically analysed. Measurements of the solute concentration profiles in the direction parallel to the reaction front are strongly emphasised, as they allow verification of theoretical models of discontinuous reactions and consideration of discontinuous reactions as local phenomena in the form of a number of events occurring in individual cells. Such an attempt removes the divergence between the tracer diffusivity values obtained by the sectioning technique and the chemical diffusivity data obtained from the discontinuous precipitation and dissolution reactions. A discussion is also presented on how the results obtained via AEM can be used for an optimisation of the theory of discontinuous solid state reactions. The implementation of alternative electron optic techniques for the determination of the solute redistribution accompanying the discontinuous reactions is demonstrated.

Computer simulation of atomic ordering and compositional clustering in the pseudobinary Ni 3Al–Ni 3V system

The kinetics of diffusional phase transformations in the pseudobinary Ni 3Al–Ni 3V system were studied using a computer simulation technique based on microscope diffusion equations. Our focus is on the initial stages of atomic ordering and compositional clustering process during the phase transformation of an initially homogeneous disordered f.c.c. ternary alloy (Ni 75Al 25− x V x ) into a two-phase mixture of L1 2 (Ni 3Al) and DO 22 (Ni 3V) ordered phases. A thermodynamic model is proposed to describe the phase equilibria in this pseudobinary system. Our computer simulations demonstrated that at small vanadium content, the L1 2 ordered domains appear first, followed by the nucleation of DO 22 ordered domains at the antiphase domain boundaries of L1 2, whereas at large vanadium content, precipitation of DO 22 precedes L1 2 domain formation. The simulation results are discussed employing the thermodynamic stability analysis. The ordering and clustering kinetics predicted from our computer simulation are consistent with recent experimental observations.

Mechanisms for the development of tent-shaped and invariant-plane-strain-type surface reliefs for plates formed during diffusional phase transformations

Tent-shaped and invariant-plane-strain type surface reliefs are considered for f.c.c.→ h.c.p., f.c.c.→b.c.c. and b.c.c.→ h.c.p. diffusional phase transformations that produce plate-shaped products. Mechanisms of growth by means of mobile structural ledges with disconnection character are described. Different mechanisms are proposed to account for the two types of surface relief in cases where the transformation product is a single crystal. The predicted relief shapes and relief angles are in good agreement with experimental observations.

Atomic Structure, Composition, Mechanisms and Dynamics of Transformation Interfaces in Diffusional Phase Transformations

This overview describes progress that has been made in understanding the atomic structure, composition, mechanisms and dynamics of transformation interfaces in diffusional transformations involving plate-shaped transformation products in the past eight years. Some of the important developments in the area of structure include recognition that diffusional phase transformations obey many of the same crystallographic principles developed for martensite, widespread application of high-resolution transmission electron microscopy (HRTEM) and atomistic modelling to understand interphase boundary structure and energetics, and determination of the atomic structure and energetics of high-index ledged interfaces. In the area of composition, recent development of thermal field-emission and energy-filtering HRTEM allows compositional profiling at precipitate interfaces with subnanometer spatial resolution. In addition, the position sensitive atom-probe (PoSAP), which can determine both the mass and position of individual atoms, makes it possible to map elemental distributions in some materials with atomic resolution. These techniques are expected to provide an abundance of data on composition at transformation interfaces approaching the atomic level in the near future. In terms of the dynamics of transformation interfaces, application of in situ hot-stage HRTEM to precipitate growth and dissolution has provided information on the atomic mechanisms and kinetics of ledge motion and interaction, the mechanisms and kinetics of kink nucleation, and mechanisms of faceting/roughening of precipitate plates at the atomic level. Also, kinetic models for ledge growth which are able to treat multiple-ledge interactions and time-dependent growth have been developed and are available for comparison with experimental data. In addition to discussion of these and other major developments, effort is made to emphasize current strengths and limitations in each area and indicate possible directions for future research.