[Show abstract][Hide abstract] ABSTRACT: A Magnetic Cluster Expansion (MCE) model for ternary face-centered cubic
Fe-Ni-Cr alloys has been developed using DFT data spanning binary and ternary
alloy configurations. Using this MCE model Hamiltonian, we perform Monte Carlo
simulations and explore magnetic structures of alloys over the entire range of
alloy compositions, considering both random and ordered alloy structures. In
random alloys, the removal of magnetic collinearity constraint reduces the
total magnetic moment but does not affect the predicted range of compositions
where the alloys adopt low temperature ferromagnetic configurations. During
alloying of ordered fcc Fe-Ni compounds with Cr, chromium atoms tend to replace
nickel rather than iron atoms. Replacement of Ni by Cr in alloys with high iron
content increases the Curie temperature of the alloys. This can be explained by
strong antiferromagnetic Fe-Cr coupling, similar to that found in bcc Fe-Cr
solutions, where the Curie temperature increase, predicted by simulations as a
function of Cr concentration, is confirmed by experimental observations.
[Show abstract][Hide abstract] ABSTRACT: Low-energy magnetic states and finite-temperature properties of Cr nanoclusters in bulk bcc Fe and Fe nanoclusters in bulk Cr are investigated using density functional theory (DFT) and the Heisenberg-Landau Hamiltonian based magnetic cluster expansion (MCE). We show, by means of noncollinear magnetic DFT calculations, that magnetic frustration caused by competing ferromagnetic and antiferromagnetic interactions either strongly reduces local magnetic moments while keeping collinearity or generates noncollinear magnetic structures. Small Cr clusters generally exhibit collinear ground states. Noncollinear magnetic configurations form in the vicinity of small Fe clusters if antiferromagnetic Fe-Cr coupling dominates over ferromagnetic Fe-Fe interactions. MCE predictions broadly agree with DFT data on the low-energy magnetic structures, and extend the DFT analysis to larger systems. Nonvanishing cluster magnetization caused by the dominance of Fe-Cr over Cr-Cr antiferromagnetic coupling is found in Cr nanoclusters using both DFT and MCE. Temperature dependence of magnetic properties of Cr clusters is strongly influenced by the surrounding iron atoms. A Cr nanocluster remains magnetic until fairly high temperatures, close to the Curie temperature of pure Fe in the large cluster size limit. Cr-Cr magnetic moment correlations are retained at high temperatures due to the coupling of interfacial Cr atoms with the Fe environment. Variation of magnetization of Fe-Cr alloys as a function of temperature and Cr clusters size predicted by MCE is assessed against the available experimental data.
Physical Review B 03/2015; 91(9). DOI:10.1103/PhysRevB.91.094430 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni, and Cr-Ni alloys, and ternary Fe-Cr-Ni alloys is investigated using a combination of density functional theory (DFT), cluster expansion (CE), and magnetic cluster expansion (MCE) approaches. Energies, magnetic moments, and volumes of more than 500 alloy structures have been evaluated using DFT, and the predicted most stable configurations are compared with experimental observations. Deviations from the Vegard law in fcc Fe-Cr-Ni alloys, resulting from the nonlinear variation of atomic magnetic moments as functions of alloy composition, are observed. The accuracy of the CE model is assessed against the DFT data, where for ternary Fe-Cr-Ni alloys the cross-validation error is found to be less than 12 meV/atom. A set of cluster interaction parameters is defined for each alloy, where it is used for predicting new ordered alloy structures. The fcc Fe2CrNi phase with Cu2NiZn-like crystal structure is predicted to be the global ground state of ternary Fe-Cr-Ni alloys, with the lowest chemical ordering temperature of 650 K. DFT-based MonteCarlo (MC) simulations are applied to the investigation of order-disorder transitions in Fe-Cr-Ni alloys. The enthalpies of formation of ternary alloys predicted by MC simulations at 1600 K, combined with magnetic correction derived from MCE, are in excellent agreement with experimental values measured at 1565 K. The relative stability of fcc and bcc phases is assessed by comparing the free energies of alloy formation. The evaluation of the free energies involved the application of a dedicated algorithm for computing the configurational entropies of the alloys. Chemical order is analyzed, as a function of temperature and composition, in terms of the Warren-Cowley short-range order (SRO) parameters and effective chemical pairwise interactions. In addition to compositions close to binary intermetallic phases CrNi2, FeNi, FeNi3, and FeNi8, pronounced chemical order is found in fcc alloys near the center of the ternary alloy composition triangle. The calculated SRO parameters compare favorably with experimental data on binary and ternary alloys. Finite temperature magnetic properties of fcc Fe-Cr-Ni alloys are investigated using an MCE Hamiltonian parameterized using a DFT database of energies and magnetic moments computed for a large number of alloy configurations. MCE simulations show that the ordered ternary Fe2CrNi alloy phase remains magnetic up to 850–900 K due to the strong antiferromagnetic coupling between (Fe,Ni) and Cr atoms in the ternary Fe-Cr-Ni matrix.
Physical Review B 01/2015; 91(2):024108. DOI:10.1103/PhysRevB.91.024108 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni, Cr-Ni alloys
and ternary Fe-Cr-Ni alloys is investigated using a combination of density
functional theory (DFT), Cluster Expansion (CE) and Magnetic Cluster Expansion
(MCE). Energies, magnetic moments, and volumes of more than 500 alloy
structures are evaluated using DFT, and the most stable magnetic configurations
are compared with experimental data. Deviations from the Vegard law in fcc
Fe-Cr-Ni alloys, associated with non-linear variation of atomic magnetic
moments as functions of alloy composition, are observed. Accuracy of the CE
model is assessed against the DFT data, where for ternary alloys the
cross-validation error is smaller than 12 meV/atom. A set of cluster
interaction parameters is defined for each alloy, where it is used for
predicting new ordered alloy structures. Fcc Fe2CrNi phase with Cu2NiZn-like
structure is predicted as the global ground state with the lowest chemical
ordering temperature of 650K. DFT-based Monte Carlo (MC) simulations are used
for assessing finite temperature fcc-bcc phase stability and order-disorder
transitions in Fe-Cr-Ni alloys. Enthalpies of formation of ternary alloys
calculated from MC simulations at 1600K combined with magnetic correction
derived from MCE are in excellent agreement with experimental values measured
at 1565K. Chemical order is analysed, as a function of temperature and
composition, in terms of the Warren-Cowley short-range order (SRO) parameters
and effective chemical pairwise interactions. In addition to compositions close
to the known binary intermetallic phases like CrNi2, FeNi, FeNi3 and FeNi8,
pronounced chemical order is found in fcc alloys near the centre of the ternary
alloy composition triangle. The SRO parameter characterizing pairs of Fe and Ni
atoms decreases as a function of Cr concentration. The calculated SRO
parameters are compared to the available experimental data on binary and
ternary alloys, and good agreement is found. Finite temperature magnetic
properties of fcc Fe-Cr-Ni alloys are investigated using an MCE Hamiltonian
constructed using a DFT database of energies and magnetic moments. MCE
simulations show that ordered ternary Fe2CrNi alloy phase remains magnetic up
to fairly high temperatures due to anti-ferromagnetic coupling between (Fe,Ni)
and Cr atoms in the ternary Fe-Cr-Ni matrix.
[Show abstract][Hide abstract] ABSTRACT: A model lattice ab initio parameterized Heisenberg-Landau magnetic cluster expansion Hamiltonian spanning a broad range of alloy compositions and a large variety of chemical and magnetic configurations has been developed for face-centered cubic Fe-Ni alloys. The thermodynamic and magnetic properties of the alloys are explored using configuration and magnetic Monte Carlo simulations over a temperature range extending well over 1000 K. The predicted face-centered cubic-body-centered cubic coexistence curve, the phase stability of ordered Fe3Ni, FeNi, and FeNi3 intermetallic compounds, and the predicted temperatures of magnetic transitions simulated as functions of alloy composition agree well with experimental observations. Simulations show that magnetic interactions stabilize the face-centered cubic phase of Fe-Ni alloys. Both the model Hamiltonian simulations and ab initio data exhibit a particularly large number of magnetic configurations in a relatively narrow range of alloy compositions corresponding to the occurrence of the Invar effect.
[Show abstract][Hide abstract] ABSTRACT: The development of quantitative models for radiation damage effects in iron,
iron alloys and steels, particularly for the high temperature properties of the
alloys, requires understanding of magnetic interactions, which control the
phase stability of ferritic-martensitic, ferritic, and austenitic steels. In
this work, disordered magnetic configurations of pure iron and Fe-Cr alloys are
investigated using Density Functional Theory (DFT) formalism, in the form of
constrained non-collinear magnetic calculations, with the objective of creating
a database of atomic magnetic moments and forces acting between the atoms. From
a given disordered atomic configuration of either pure Fe or Fe-Cr alloy, a
penalty contribution to the usual spin-polarized DFT total energy has been
calculated by constraining the magnitude and direction of magnetic moments. An
extensive database of non-collinear magnetic moment and force components for
various atomic configurations has been generated and used for interpolating the
spatially-dependent magnetic interaction parameters, for applications in
large-scale spin-lattice dynamics and magnetic Monte-Carlo simulations.
Annals of Nuclear Energy 09/2013; 77. DOI:10.1051/snamc/201401302 · 0.96 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We develop a Magnetic Cluster Expansion (MCE) model for binary bcc and fcc
Fe-Cr alloys, as well as for fcc Fe-Ni alloys, and apply it to the
investigation of magnetic properties of these alloys over a broad interval of
concentrations, and over a broad interval of temperatures extending well over
1000 K. We show how an MCE-based Monte Carlo study describes the magnetic
properties of these alloys, for example the composition and microstructure
dependence of the Curie temperature, the non-collinearity of magnetic
structures found in bcc Fe-Cr alloys, phase transitions between bcc and fcc in
Fe-Cr, and the enthalpy of mixing of Fe-Ni alloys. The results of simulations
are in excellent agreement with experimental observations.
[Show abstract][Hide abstract] ABSTRACT: Generic materials-related problems foreseen in connection with the operation of a fusion power plant present a major challenge for the development of magnetically confined fusion as a commercial power generation option. In this review, we focus on the predictive capabilities of first-principles-based atomistic models for radiation defects and phase stability of body-centred cubic Fe-Cr-based ferritic-martensitic and ferritic steels and tungsten alloys, which are presently under consideration as candidate structural materials for the first wall and diverter applications. Density-functional calculations predict that low-Cr iron alloys are stabilized by intra-atomic exchange, giving rise to magnetism and changes in interatomic chemical bonding. Magnetic effects are also responsible for the fact that the atomic structure of radiation defects in iron and steels is different from the structure of defects formed under irradiation in non-magnetic body-centred cubic metals, for example vanadium or tungsten. Ab initio-based magnetic cluster expansion-based Monte-Carlo simulations showed unusual non-collinear magnetic configurations forming at interfaces and around Cr precipitates in FeCr alloys. In W-Ta and W-V alloys, ab initio calculations helped to identify several low temperature ordered inter-metallic phases that are not included in the existing phase diagrams based on high-temperature experimental data. Ab initio calculations have also made it possible to predict atomic structures of point defects formed in these alloys under irradiation.
[Show abstract][Hide abstract] ABSTRACT: We present a combined experimental and computational study of high temperature magnetic properties of Fe-Cr alloys with chromium content up to about 20 at.%. The magnetic cluster expansion method is applied to model the magnetic properties of random Fe-Cr alloys, and in particular the Curie transition temperature, as a function of alloy composition. We find that at low (3-6 at.%) Cr content the Curie temperature increases with the increase of Cr concentration. It is maximum at approximately 6 at.% Cr and then decreases for higher Cr content. The same feature is found in thermo-magnetic measurements performed on model Fe-Cr alloys, where a 5 at.% Cr alloy has a higher Curie temperature than pure Fe. The Curie temperatures of 10 and 15 at.% Cr alloys are found to be lower than the Curie temperature of pure Fe.
[Show abstract][Hide abstract] ABSTRACT: Noncollinear configurations of local magnetic moments at Fe/Cr interfaces in Fe-Cr alloys are explored using a combination of density functional theory (DFT) and magnetic cluster expansion (MCE) simulations. We show that magnetic frustration at Fe/Cr interfaces can be partially resolved through the formation of noncollinear magnetic structures, which occur not only at stepped but also at smooth interfaces, for example at the (110) interface where magnetic noncollinearity predicted by simulations is observed experimentally. Both DFT and MCE simulations predict that the magnetically frustrated (110) interface has the highest formation energy in the low-temperature limit. Using MCE and kinetic Monte Carlo simulations, we investigate the effect of temperature on magnetic order at interfaces and on interface energies. We find that while the low-temperature noncollinear bulk magnetic configurations of Cr remain stable up to the Néel temperature, the chromium atomic layers close to the interfaces retain their magnetic order well above this temperature. We also show that above the Curie temperature the (110) interface is the lowest energy interface, in agreement with DFT simulations of interfaces separating ferromagnetic Fe and nonmagnetic Cr.
[Show abstract][Hide abstract] ABSTRACT: Atomistic kinetic Monte Carlo (AKMC) simulations were performed to study α–α′ phase separation in Fe–Cr alloys. Two different energy models and two approaches to estimate the local vacancy migration barriers were used. The energy models considered are a two-band model Fe–Cr potential and a cluster expansion, both fitted to ab initio data. The classical Kang–Weinberg decomposition, based on the total energy change of the system, and an Artificial Neural Network (ANN), employed as a regression tool were used to predict the local vacancy migration barriers ‘on the fly’. The results are compared with experimental thermal annealing data and differences between the applied AKMC approaches are discussed. The ability of the ANN regression method to accurately predict migration barriers not present in the training list is also addressed by performing cross-check calculations using the nudged elastic band method.
[Show abstract][Hide abstract] ABSTRACT: Magnetic Cluster Expansion method is applied to the investigation of magnetic properties of Fe-Cr alloys treated as a function of Cr content, the spatial distribution of Cr atoms, and temperature. Random Fe-Cr alloys and Cr clusters formed in concentrated alloys are analyzed. We find significant differences between the types of magnetic order characterizing those systems, which are reflected in the characteristic variation of the temperature-dependent magnetic specific heat. Simulations show that in random Fe-Cr alloys and in alloys containing Cr clusters, the interplay between antiferromagnetic interactions characterizing Fe-Cr and Cr-Cr atom pairs gives rise to unusual patterns of finite temperature magnetic ordering.
Solid State Phenomena 06/2011; 172-174:1002-1007. DOI:10.4028/www.scientific.net/SSP.172-174.1002
[Show abstract][Hide abstract] ABSTRACT: Magnetic cluster expansion model is developed for bcc Fe–Cr alloys, and applied to the investigation of magnetic properties of these alloys over a broad interval of concentrations ranging from pure Fe to pure Cr, and over a broad interval of temperatures extending well over 1000 K. Finite-temperature configurations simulated using the magnetic cluster expansion Hamiltonian describe various magnetically ordered ferromagnetic and antiferromagnetic phases, partially magnetically ordered phases, and transitions between them and paramagnetic phases. We investigate the dependence of the Curie and Néel transition temperatures on the composition of the alloy. Analysis of the magnetic specific heat treated as a function of Cr concentration shows that in the low Cr concentration limit the Curie temperature increases as a function of Cr content. We find that for alloys containing high level of Cr the Curie temperature depends sensitively on the degree of Cr precipitation, varying by as much as 150 K between random alloy configurations and configurations containing Cr precipitates.
[Show abstract][Hide abstract] ABSTRACT: We compare two approaches to modelling the phase stability of iron and Fe–Cr binary alloys: Cluster expansion and magnetic cluster expansion. The first, based on a cluster expansion Hamiltonian, describes the effects of configurational disorder in an alloy on its thermodynamic properties. Cluster expansion can be used for studying alloys by both equilibrium and kinetic Monte Carlo methods. The second, recently proposed, “magnetic” cluster expansion (MCE) method extends cluster expansion treatment to magnetic degrees of freedom by including magnetic moments of individual atoms as variables. MCE has a unique capability for modelling the properties of a magnetic alloy in a broad range of compositions ranging from pure ferromagnetic Fe to antiferromagnetic Cr. We describe applications of both methods to modelling various properties of candidate fusion materials.
[Show abstract][Hide abstract] ABSTRACT: An ab initio-based magnetic-cluster-expansion treatment developed for body- and face-centered cubic phases of iron and iron-chromium alloys is applied to modeling the α-γ and γ-δ phase transitions in these materials. The Curie, Néel, and the structural phase-transition temperatures predicted by the model are in good agreement with experimental observations, indicating that it is the thermal excitation of magnetic and phonon degrees of freedom that stabilizes the fcc γ phase. The model also describes the occurrence of the γ loop in the phase diagram of Fe-Cr alloys for a realistic interval of temperatures and Cr concentrations.
Physical Review B 05/2010; 81(18). DOI:10.1103/PhysRevB.81.184202 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An integrated ab initio and statistical Monte Carlo investigation has been recently carried out to model the thermodynamic and kinetic properties of Fe–Cr alloys. We found that the conventional Fe–Cr phase diagram is not adequate at low temperature region where the magnetic contribution to the free energy plays an important role in the prediction of an ordered Fe15Cr phase and its negative enthalpy of formation. The origin of the anomalous thermodynamic and magnetic properties of Fe–Cr alloys can be understood using a tight-binding Stoner model combined with the charge neutrality condition. We investigate the environmental dependence of magnetic moment distributions for various self-interstitial atom dumbbells configurations using spin density maps found using density functional theory calculations. The mixed dumbbell Fe–Cr and Fe–Mn binding energies are found to be positive due to magnetic interactions. Finally, we discuss the relationship between the migration energy of vacancy in Fe–Cr alloys and magnetism at the saddle point configuration.
[Show abstract][Hide abstract] ABSTRACT: We present a new method for simulating magnetic alloys characterized by configurational disorder, the magnetic cluster expansion. Each atom in an alloy is assigned a discrete variable denoting the atomic species, and the (continuous) magnetic moment. The parameters of the model are determined by matching energies and magnetic moments of atoms found in trial simulations to DFT calculations. Monte Carlo simulations are then performed to investigate magnetic properties of pure iron, and magnetic and structural properties of FeCr alloys. We found that the Curie temperature of the ordered FeCr alloy with small concentration of Cr (Fe15Cr) increases in comparison with pure Fe and the random mixture of Cr in iron (Fe-6.25% Cr). The method is also applied to the investigation of the correlation functions for the directions of magnetic moments at elevated temperatures.
[Show abstract][Hide abstract] ABSTRACT: The EU fusion materials modelling programme was initiated in 2002 with the objective of developing a comprehensive set of computer modelling techniques and approaches, aimed at rationalising the extensive available experimental information on properties of irradiated fusion materials, developing capabilities for predicting the behaviour of materials under conditions not yet accessible to experimental tests, assessing results of tests involving high dose rates, and extrapolating these results to the fusion-relevant conditions. The programme presently gives emphasis to modelling a single class of materials, which are ferritic-martensitic EUROFER-type steels, and focuses on the investigation of key physical phenomena and interpretation of experimental observations. The objective of the programme is the development of computational capabilities for predicting changes in mechanical properties, hardening and embrittlement, as well as changes in the microstructure and phase stability of EUROFER and FeCr model alloys occurring under fusion reactor relevant irradiation conditions.
[Show abstract][Hide abstract] ABSTRACT: In this work the capability of existing cohesive models to predict the thermodynamic properties of Fe–Cr alloys are critically evaluated and compared. The two-band model and the concentration-dependent model, which are independently developed extensions of the embedded-atom method, are demonstrated to be equivalent and equally capable of reproducing the thermodynamic properties of Fe–Cr alloys. The existing potentials fitted with these formalisms are discussed and compared with an existing cluster expansion model. The phase diagram corresponding to these models is evaluated using different but complementary methods. The influence of mixing enthalpy, low-energy states and vibrational entropy on the phase diagram is examined for the different cohesive models.
[Show abstract][Hide abstract] ABSTRACT: A multi-scale modeling approach is presented to investigate the phase stability and clustering in Fe–Cr alloys by combining density functional theory (DFT) calculations with statistical approaches involving cluster expansion (CE) and Monte Carlo (MC) simulations. This makes it possible to generate, in a systematic way, the low-energy configurations required for the subsequent DFT study of intrinsic defects (vacancies, interstitials) and impurity-defect interactions in the entire range of Fe–Cr alloy compositions under irradiation. The lowest mixing enthalpy configuration generated by MC simulation is found at Cr concentration of 6.25% that is consistent with the ab initio prediction of an intermetallic compound Fe15Cr characterized by the negative heat of formation. The ordering structureFe15Cris stabilized by lowest down-spin density of states value at the Fermi energy, showing Cr atom with a strong local magnetic moment aligned in one anti-ferromagnetic direction with the Fe atoms. Furthermore, it is shown that magnetism is responsible for anomalous nano-segregation of the α′-Cr phase into various clustered configurations that are confirmed by a large scale kinetic Monte Carlo simulations. The impurity-interstitial defect interaction is investigated and we found that the binding energies of mixed dumbbell Fe–Cr in Fe15Cr alloy are positive at variance with predictions made by elastic theory. Using the Stoner model within a tight-binding mean field approximation we are able to explain the origin of anomalous enthalpy of mixing as well as the complex correlation between magnetic moment distribution and phase stability in the Fe–Cr system.