Decomposition kinetics of Fe-Cr solid solutions during thermal aging

Modeling of nanostructure evolution in solids requires comprehensive data on the properties of defects such as the vacancy and foreign atoms. Since most processes occur at elevated temperatures not only the energetics of defects in the ground state but also their temperaturedependent free energies must be known. The first-principles calculation of contributions of phonon and electron excitations to free formation, binding, and migration energies of defects is illustrated in the case of bcc-Fe. First of all, the ground state properties of the vacancy, the foreign atoms Cu, Y, Ti, Cr, Mn, Ni, V, Mo, Si, Al, Co, O, and the O-vacancy pair are determined under constant volume (CV) as well as zero pressure (ZP) conditions, and relations between the results of both kinds of calculations are discussed. Second, the phonon contribution to defect free energies is calculated within the harmonic approximation using the equilibrium atomic positions determined in the ground state under CV and ZP conditions. In most cases the ZPbased free formation energy decreases monotonously with temperature, whereas for CV-based data both an increase and a decrease were found. The application of a quasi-harmonic correction to the ZP-based data does not modify this picture significantly. However, the corrected data are valid under zero-pressure conditions at higher temperatures than in the framework of the purely harmonic approach. The difference between CV-and ZP-based data D. Murali, M. Posselt, M. Schiwarth: First-principles calculation of defect free energies… MS#BD12759 2 is mainly due to the volume change of the supercell since the relative arrangement of atoms in the environment of the defects is nearly identical in the two cases. A simple transformation similar to the quasi-harmonic approach is found between the CV-and ZP-based frequencies.Therefore, it is not necessary to calculate these quantities and the corresponding defect free energies separately. In contrast to ground state energetics the CV-and ZP-based defect free energies do not become equal with increasing supercell size. Third, it was found that the contribution of electron excitations to the defect free energy can lead to an additional deviation of the total free energy from the ground state value or can compensate the deviation caused by the phonon contribution. Finally, self-diffusion via the vacancy mechanism is investigated. The ratio of the respective CV-and ZP-based results for the vacancy diffusivity is nearly equal to the reciprocal of that for the equilibrium concentration. This behavior leads to almost identical CV-and ZP-based values for the self-diffusion coefficient. Obviously, this agreement is accidental. The consideration of the temperature dependence of the magnetization yields self-diffusion data in very good agreement with experiments.

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“…Within the harmonic approximation the vibrational free energy vib ( ) F T of a system of N atoms is given by 3 3 vib…”

Section: A Computational Proceduresmentioning

confidence: 99%

First-principles calculation of defect free energies: General aspects illustrated in the case of bcc Fe

2015

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“…Much work has been devoted to the development of models able to predict spinodal decomposition via, e.g., phase-field modeling solving the Cahn-Hilliard equation [9,10] or via kinetic Monte Carlo simulations [11,12]. In most of these modeling studies, the initial structure is assumed to be random.…”

Section: Introductionmentioning

confidence: 99%

Effect of solution treatment on spinodal decomposition during aging of an Fe-46.5 at.% Cr alloy

et al. 2016

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Spinodal decomposition is a key phase transition in advanced materials and a significant effort is paid to the quantitative modeling of the phenomenon. The initial materials condition is often assumed to be random during modeling, but this may be an oversimplification. In this work, the effect of solution treatment above the miscibility gap, on spinodal decomposition during subsequent aging, has been investigated for an Fe-46.5 at.% Cr alloy. By atom probe tomography (APT), it is found that different extents of quenched-in Cr clustering exist after solution treatments at different temperatures. The clustering is pronounced at 800°C but decreases significantly with increasing temperature to 900°C. Thermodynamic Monte Carlo simulations show that there is a difference in atomic short range order between the different solution treatment temperatures. By APT, it is, furthermore, found that the kinetics of spinodal decomposition at 500°C, i.e., within the miscibility gap, is enhanced in the initial alloy condition, where Cr was less randomly distributed. These observations are supported by kinetic Monte Carlo simulations, predicting a similar but less pronounced qualitative effect on spinodal decomposition kinetics. Other possible reasons for the enhanced kinetics could be related to clustering of interstitial elements and/ or sigma phase, but neither was found in the experiments. Nonetheless, the observations in this work suggest that it is necessary to implement a modeling strategy, where the initial structure is properly accounted for when simulating spinodal decomposition.

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“…In rigid lattice MC simulations [12,20,[34][35][36][37] using Ising-type interaction the Hamiltonian must be made temperature dependent. Semiempirical potentials have been used in both Metropolis MC (MMC) [38][39][40] and kinetic MC (KMC) [9,[41][42][43][44][45][46][47] studies.…”

Section: B Large-scale Monte Carlo Simulationsmentioning

confidence: 99%

Segregation, precipitation, andα−α′phase separation in Fe-Cr alloys

et al. 2015

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Iron-chromium alloys, the base components of various stainless steel grades, have numerous technologically and scientifically interesting properties. However, these features are not yet sufficiently understood to allow their full exploitation in technological applications. In this work, we investigate segregation, precipitation, and phase separation in Fe-Cr systems analyzing the physical mechanisms behind the observed phenomena. To get a comprehensive picture of Fe-Cr alloys as a function of composition, temperature, and time the present investigation combines Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods have to be used. Using the exact muffin-tin orbitals method with the coherent potential approximation (CPA-EMTO) the effective chemical potential as a function of Cr content (0-15 at. % Cr) is calculated for a surface, second atomic layer, and bulk. At ∼10 at. % Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr-containing surfaces are expected when the Cr content exceeds ∼10 at. %. The second atomic layer forms about a 0.3 eV barrier for the migration of Cr atoms between the bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. However, for Cr concentration regions less than 10 at. %, the ab initio (CPA-EMTO) result of the important role of the second atomic layer to the surface is not reproducible from the large-scale Monte Carlo molecular dynamics (MCMD) simulation. On the other hand, for the nominal concentration of Cr larger than 10 at. % the MCMD simulations show the precipitation of Cr into isolated pockets in bulk Fe-Cr and the existence of the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer systems. For high Cr concentration alloys the performed spectroscopic measurements support the MCMD simulations. Hard x-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in the Fe/Cr double layer and Fe 0.95 Cr 0.05 and Fe 0.85 Cr 0.15 alloys. Initial oxidation of Fe-Cr was investigated experimentally at 10 −8 Torr pressure of the spectrometers showing intense Cr 2 O 3 signal. Cr segregation and the formation of Cr-rich precipitates were traced by analyzing the experimental atomic concentrations and chemical shifts with respect to annealing time, Cr content, and kinetic energy of the exited electron.

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Decomposition kinetics of Fe-Cr solid solutions during thermal aging

Cited by 78 publications

References 59 publications

First-principles calculation of defect free energies: General aspects illustrated in the case of bcc Fe

First-principles calculation of defect free energies: General aspects illustrated in the case of bcc Fe

Effect of solution treatment on spinodal decomposition during aging of an Fe-46.5 at.% Cr alloy

Segregation, precipitation, andα−α′phase separation in Fe-Cr alloys

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