Publications (62)155.13 Total impact

Article: Magnetic Cluster Expansion model for random and ordered magnetic facecentered cubic FeNiCr alloys
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ABSTRACT: A Magnetic Cluster Expansion (MCE) model for ternary facecentered cubic FeNiCr 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 FeNi 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 FeCr coupling, similar to that found in bcc FeCr 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: Lowenergy magnetic states and finitetemperature properties of Cr nanoclusters in bulk bcc Fe and Fe nanoclusters in bulk Cr are investigated using density functional theory (DFT) and the HeisenbergLandau 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 FeCr coupling dominates over ferromagnetic FeFe interactions. MCE predictions broadly agree with DFT data on the lowenergy magnetic structures, and extend the DFT analysis to larger systems. Nonvanishing cluster magnetization caused by the dominance of FeCr over CrCr 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. CrCr magnetic moment correlations are retained at high temperatures due to the coupling of interfacial Cr atoms with the Fe environment. Variation of magnetization of FeCr alloys as a function of temperature and Cr clusters size predicted by MCE is assessed against the available experimental data.  [Show abstract] [Hide abstract]
ABSTRACT: The phase stability of fcc and bcc magnetic binary FeCr, FeNi, and CrNi alloys, and ternary FeCrNi 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 FeCrNi 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 FeCrNi alloys the crossvalidation 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 Cu2NiZnlike crystal structure is predicted to be the global ground state of ternary FeCrNi alloys, with the lowest chemical ordering temperature of 650 K. DFTbased MonteCarlo (MC) simulations are applied to the investigation of orderdisorder transitions in FeCrNi 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 WarrenCowley shortrange 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 FeCrNi 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 FeCrNi matrix.  [Show abstract] [Hide abstract]
ABSTRACT: The phase stability of fcc and bcc magnetic binary FeCr, FeNi, CrNi alloys and ternary FeCrNi 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 FeCrNi alloys, associated with nonlinear 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 crossvalidation 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 Cu2NiZnlike structure is predicted as the global ground state with the lowest chemical ordering temperature of 650K. DFTbased Monte Carlo (MC) simulations are used for assessing finite temperature fccbcc phase stability and orderdisorder transitions in FeCrNi 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 WarrenCowley shortrange 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 FeCrNi 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 antiferromagnetic coupling between (Fe,Ni) and Cr atoms in the ternary FeCrNi matrix.  [Show abstract] [Hide abstract]
ABSTRACT: A model lattice ab initio parameterized HeisenbergLandau magnetic cluster expansion Hamiltonian spanning a broad range of alloy compositions and a large variety of chemical and magnetic configurations has been developed for facecentered cubic FeNi 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 facecentered cubicbodycentered 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 facecentered cubic phase of FeNi 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 ferriticmartensitic, ferritic, and austenitic steels. In this work, disordered magnetic configurations of pure iron and FeCr alloys are investigated using Density Functional Theory (DFT) formalism, in the form of constrained noncollinear 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 FeCr alloy, a penalty contribution to the usual spinpolarized DFT total energy has been calculated by constraining the magnitude and direction of magnetic moments. An extensive database of noncollinear magnetic moment and force components for various atomic configurations has been generated and used for interpolating the spatiallydependent magnetic interaction parameters, for applications in largescale spinlattice dynamics and magnetic MonteCarlo simulations.  [Show abstract] [Hide abstract]
ABSTRACT: We develop a Magnetic Cluster Expansion (MCE) model for binary bcc and fcc FeCr alloys, as well as for fcc FeNi 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 MCEbased Monte Carlo study describes the magnetic properties of these alloys, for example the composition and microstructure dependence of the Curie temperature, the noncollinearity of magnetic structures found in bcc FeCr alloys, phase transitions between bcc and fcc in FeCr, and the enthalpy of mixing of FeNi alloys. The results of simulations are in excellent agreement with experimental observations.  [Show abstract] [Hide abstract]
ABSTRACT: Generic materialsrelated 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 firstprinciplesbased atomistic models for radiation defects and phase stability of bodycentred cubic FeCrbased ferriticmartensitic and ferritic steels and tungsten alloys, which are presently under consideration as candidate structural materials for the first wall and diverter applications. Densityfunctional calculations predict that lowCr iron alloys are stabilized by intraatomic 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 nonmagnetic bodycentred cubic metals, for example vanadium or tungsten. Ab initiobased magnetic cluster expansionbased MonteCarlo simulations showed unusual noncollinear magnetic configurations forming at interfaces and around Cr precipitates in FeCr alloys. In WTa and WV alloys, ab initio calculations helped to identify several low temperature ordered intermetallic phases that are not included in the existing phase diagrams based on hightemperature 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 FeCr alloys with chromium content up to about 20 at.%. The magnetic cluster expansion method is applied to model the magnetic properties of random FeCr alloys, and in particular the Curie transition temperature, as a function of alloy composition. We find that at low (36 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 thermomagnetic measurements performed on model FeCr 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 FeCr 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 lowtemperature 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 lowtemperature 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. 
Article: Modelling phase separation in Fe–Cr system using different atomistic kinetic Monte Carlo techniques
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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 twoband 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 crosscheck 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 FeCr alloys treated as a function of Cr content, the spatial distribution of Cr atoms, and temperature. Random FeCr 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 temperaturedependent magnetic specific heat. Simulations show that in random FeCr alloys and in alloys containing Cr clusters, the interplay between antiferromagnetic interactions characterizing FeCr and CrCr atom pairs gives rise to unusual patterns of finite temperature magnetic ordering.  [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. Finitetemperature 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. 
Article: Cluster expansion models for Fe–Cr alloys, the prototype materials for a fusion power plant
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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 initiobased magneticclusterexpansion treatment developed for body and facecentered cubic phases of iron and ironchromium alloys is applied to modeling the αγ and γδ phase transitions in these materials. The Curie, Néel, and the structural phasetransition 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 FeCr alloys for a realistic interval of temperatures and Cr concentrations.  [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 tightbinding Stoner model combined with the charge neutrality condition. We investigate the environmental dependence of magnetic moment distributions for various selfinterstitial 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 (Fe6.25% 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 fusionrelevant conditions. The programme presently gives emphasis to modelling a single class of materials, which are ferriticmartensitic EUROFERtype 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 twoband model and the concentrationdependent model, which are independently developed extensions of the embeddedatom 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, lowenergy states and vibrational entropy on the phase diagram is examined for the different cohesive models.  [Show abstract] [Hide abstract]
ABSTRACT: A multiscale 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 lowenergy configurations required for the subsequent DFT study of intrinsic defects (vacancies, interstitials) and impuritydefect 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 downspin density of states value at the Fermi energy, showing Cr atom with a strong local magnetic moment aligned in one antiferromagnetic direction with the Fe atoms. Furthermore, it is shown that magnetism is responsible for anomalous nanosegregation of the α′Cr phase into various clustered configurations that are confirmed by a large scale kinetic Monte Carlo simulations. The impurityinterstitial 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 tightbinding 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.
Publication Stats
846  Citations  
155.13  Total Impact Points  
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Institutions

20112012

Culham Centre for Fusion Energy
AbingdononThames, England, United Kingdom


20032006

Novosibirsk Institute of Organic Chemistry
NovoNikolaevsk, Novosibirsk, Russia


20012006

University of Bristol
 School of Chemistry
Bristol, England, United Kingdom


19982002

The University of Sheffield
 Department of Physics and Astronomy
Sheffield, ENG, United Kingdom
