Joakim Odqvist

The phase-field approach and solute drag modeling of the transition to massive γ → α transformation in binary Fe-C alloys

The transition between diffusion controlled and massive transformation gamma --> alpha in Fe-C alloys is investigated by means of phase-field simulations and thermodynamic functions assessed by the ...

Phase Equilibria and Thermodynamic Properties in the Fe-Cr System

Phase equilibria and thermodynamic properties in the Fe-Cr system have been reviewed comprehensively based on experimental information and available computer simulations in different scales. The evaluated phase equilibria show significant differences from the currently accepted thermodynamic description by CALPHAD (calculation of phase diagram) approach. The thermodynamic properties of the Fe-Cr system, such as heat capacity, enthalpy, and activity, have been evaluated in reported experiments. The experiments on phase separation in the Fe-Cr system have also been critically reviewed with a focus on spinodal decomposition. The reported data are concentrated in the temperature range from 673 to 823 K. In addition, there is a transition region between spinodal decomposition and nucleation regimes within the composition limit from 24 to 36.3 at.% Cr and the temperature range between 700 and 830 K. In view of the importance of magnetism in the Fe-Cr system, some inadequacies of the currently used thermodynamic description are pointed out in addition to some problems with the current magnetic model. Remaining issues on the thermodynamics of the Fe-Cr system have been elaborated for future refinement of the thermodynamic description of the Fe-Cr system. According to the present review, the melting temperature of Cr is recommended to be about 2136 K, which is 44 K lower than the value adopted in the research community on thermodynamics, such as the Scientific Group Thermodata Europe.

Effect of alloying elements on the γ to α transformation in steel. I

Abstract A newly constructed computer program was used to simulate partitionless growth of α in γ of Fe-Ni-C alloys, taking into account so-called solute drag by evaluating the dissipation of Gibbs energy due to diffusion inside the interface and in the nickel spike being pushed in front of it. It could be shown how the conditions at the α/γ interface vary with the velocity. A continuous change from paraequilibrium to quasi-paraconditions could be illustrated in the phase diagram. By combination with an approximate analytical growth equation, it was possible to derive the thickness of α as function of time. The growth velocity was assumed to start at very high values but decreased due to the pile-up of carbon. For alloy compositions outside the limit for quasi-paraconditions and just inside it the growth was predicted to stop suddenly when critical conditions are approached during the reaction. For alloy compositions further inside the limit, there was no such stop, except by the action of impingement of diffusion fields for carbon. Somewhere between the lines for paraequilibrium and quasi-paraconditions there is a rather rapid drop of the final thickness of α. In order to explain experimental information on this drop one must accept an appreciable tendency of segregation of nickel to the α/γ interface.

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.

Quantitative evaluation of spinodal decomposition in Fe-Cr by atom probe tomography and radial distribution function analysis.

Nanostructure evolution during low temperature aging of three binary Fe-Cr alloys has been investigated by atom probe tomography. A new method based on radial distribution function (RDF) analysis to quantify the composition wavelength and amplitude of spinodal decomposition is proposed. Wavelengths estimated from RDF have a power-law type evolution and are in reasonable agreement with wavelengths estimated using other more conventional methods. The main advantages of the proposed method are the following: (1) Selecting a box size to generate the frequency diagram, which is known to generate bias in the evaluation of amplitude, is avoided. (2) The determination of amplitude is systematic and utilizes the wavelength evaluated first to subsequently evaluate the amplitude. (3) The RDF is capable of representing very subtle decomposition, which is not possible using frequency diagrams, and thus a proposed theoretical treatment of the experimental RDF creates the possibility to determine amplitude at very early stages of spinodal decomposition.

Comparison between solute drag and dissipation of Gibbs energy by diffusion

The solute drag and the dissipation of Gibbs energy in a partitionless phase transformation are compared numerically. They agree if the solute drag is compared with the driving force over the interface and the solute spike in front of the interface. The dissipation can be evaluated over this whole region or over the interface alone.

Observations of copper clustering in a 25Cr-7Ni super duplex stainless steel during low-temperature aging under load

Atom-probe tomography was used to investigate phase separation and copper (Cu) clustering in the ferrite phase of a 25Cr-7Ni super duplex stainless steel. The steel was subjected to a tensile load during aging at 325°C for 5800 h. The degree of phase separation into α (Fe-rich) and α′ (Cr-rich) was small, but still, it was the highest in the steel subjected to the highest load. Cu was found to cluster, and the number density of clusters increased with increasing load. In the material subjected to the highest load, Cu was enriched in regions that were neither Fe-rich nor Cr-rich. These regions also had the highest number density of Cu clusters.

Investigation of Spinodal Decomposition in Fe-Cr Alloys: CALPHAD Modeling and Phase Field Simulation

This work is dedicated to simulate the spinodal decomposition of Fe-Cr bcc (body centered cubic) alloys using the phase field method coupled with CALPHAD modeling. Thermodynamic descriptions have been revised after a comprehensive review of information on the Fe-Cr system. The present work demonstrates that it is impossible to reconcile the ab initio enthalpy of mixing at the ground state with the experimental one at 1529 K using the state-of-the-art CALPHAD models. While the phase field simulation results show typical microstructure of spinodal decomposition, large differences have been found on kinetics among experimental results and simulations using different thermodynamic inputs. It was found that magnetism plays a key role on the description of Gibbs energy and mobility which are the inputs to phase field simulation. This work calls for an accurate determination of the atomic mobility data at low temperatures.

Structural Characterization of Phase Separation in Fe-Cr: A Current Comparison of Experimental Methods

Self-assembly due to phase separation within a miscibility gap is important in numerous material systems and applications. A system of particular interest is the binary alloy system Fe-Cr, since it is both a suitable model material and the base system for the stainless steel alloy category, suffering from low-temperature embrittlement due to phase separation. Structural characterization of the minute nano-scale concentration fluctuations during early phase separation has for a long time been considered a major challenge within material characterization. However, recent developments present new opportunities in this field. Here, we present an overview of the current capabilities and limitations of different techniques. A set of Fe-Cr alloys were investigated using small-angle neutron scattering (SANS), atom probe tomography, and analytical transmission electron microscopy. The complementarity of the characterization techniques is clear, and combinatorial studies can provide complete quantitative structure information during phase separation in Fe-Cr alloys. Furthermore, we argue that SANS provides a unique in-situ access to the nanostructure, and that direct comparisons between SANS and phase-field modeling, solving the non-linear Cahn Hilliard equation with proper physical input, should be pursued.

Phase-Field Modeling of Sigma-Phase Precipitation in 25Cr7Ni4Mo Duplex Stainless Steel

Phase-field modeling is used to simulate the formation of sigma phase in a model alloy mimicking a commercial super duplex stainless steel (SDSS) alloy, in order to study precipitation and growth of sigma phase under linear continuous cooling. The so-called Warren–Boettinger–McFadden (WBM) model is used to build the basis of the multiphase and multicomponent phase-field model. The thermodynamic inconsistency at the multiple junctions associated with the multiphase formulation of the WBM model is resolved by means of a numerical Cut-off algorithm. To make realistic simulations, all the kinetic and the thermodynamic quantities are derived from the CALPHAD databases at each numerical time step, using Thermo-Calc and TQ-Interface. The credibility of the phase-field model is verified by comparing the results from the phase-field simulations with the corresponding DICTRA simulations and also with the empirical data. 2D phase-field simulations are performed for three different cooling rates in two different initial microstructures. A simple model for the nucleation of sigma phase is also implemented in the first case. Simulation results show that the precipitation of sigma phase is characterized by the accumulation of Cr and Mo at the austenite-ferrite and the ferrite-ferrite boundaries. Moreover, it is observed that a slow cooling rate promotes the growth of sigma phase, while a higher cooling rate restricts it, eventually preserving the duplex structure in the SDSS alloy. Results from the phase-field simulations are also compared quantitatively with the experiments, performed on a commercial 2507 SDSS alloy. It is found that overall, the predicted morphological features of the transformation and the composition profiles show good conformity with the empirical data.