[Show abstract][Hide abstract] ABSTRACT: A model lattice ab initio parameterised 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. Thermodynamic and
magnetic properties of the alloys are explored using configuration and magnetic
Monte Carlo simulations in a temperature range extending well over 1000 K.
Physical Chemistry Chemical Physics 04/2014; · 3.83 Impact Factor
[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.
[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: 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: 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.
Journal of Applied Physics 03/2011; 109(7):07E123-07E123-3. · 2.21 Impact Factor
[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.
Journal of Nuclear Materials 01/2011; 417(1):1086-1089. · 2.02 Impact Factor
[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). · 3.66 Impact Factor
[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.
Computational Materials Science - COMPUT MATER SCI. 01/2010; 49(4).
[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.
Journal of Nuclear Materials 03/2009; · 2.02 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.
Journal of Nuclear Materials 01/2009; · 2.02 Impact Factor
[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.
Journal of Nuclear Materials 01/2009; · 2.02 Impact Factor
[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.
Journal of Nuclear Materials 01/2009; · 2.02 Impact Factor
[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.
Computational Materials Science - COMPUT MATER SCI. 01/2008; 44(1):1-8.
[Show abstract][Hide abstract] ABSTRACT: To understand the behaviour of irradiated defects and kinetic pathways of micro-structural evolution in Fe–Cr alloys, we use a combination of density functional theory with statistical approaches involving cluster expansions and Monte Carlo simulations. A lowest negative mixing enthalpy is found at 6.25% Cr that is consistent with our DFT prediction of an ordered Fe15Cr structure. At 50% Cr, it is found that the predicted enthalpy of formation is 4 times smaller than that calculated by the CPA approach. Thermodynamic and precipitation properties are then discussed in term of segregation between the Fe15Cr and α′-Cr phases and of vacancy-mediated kMC simulation. To cite this article: D. Nguyen-Manh et al., C. R. Physique 9 (2008).
[Show abstract][Hide abstract] ABSTRACT: To understand the behaviour of point defects generated in irradiated FeCr ferritic/martensitic steels and to identify the
kinetic pathways of micro-structural evolution of binary model Fe–Cr alloys, we use a combination of density functional theory
(DFT) with statistical approaches involving cluster expansion and Monte Carlo 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 over the entire range of Fe–Cr alloy compositions. In the limit of low Cr concentration,
DFT calculations predict that an intermetallic compound Fe15Cr has the lowest negative heat of formation. At higher Cr concentrations,
simulations performed using a 4×4×4 super-cell show that magnetism is responsible for the nano-segregation of the ferromagnetic
Fe15Cr and anti-ferromagnetic (α′-Cr) phases giving rise to the formation of clusters characterised by a very low positive heat of formation. We perform a
systematic investigation of formation energies of point defects and their energies of interaction with Cr atoms. Further investigation
of interaction of interstitial and vacancy defects with impurities (V, Nb, Ta, Mo, W, Al, Si, P, S) also shows a complex picture
of interplay between magnetism and short-range ordering that affects the interaction between defects and impurities in the
presence of chromium in Fe-rich alloys.
[Show abstract][Hide abstract] ABSTRACT: Iron-chromium alloys are characterised by a complex phase diagram, the small negative heat of formation at low Cr concentrations
in bcc α-structure of Fe and by the inversion of short-range order parameter. We present Monte Carlo simulations of Fe-Cr alloy based
on cluster expansion (CE) approximation for the enthalpy of the system. The set of cluster expansion coefficients is validated
versus the DFT results on small clusters in bcc structure. The enthalpy of mixing is negative at small Cr concentrations up
to high temperatures. Also, at small concentrations chromium atoms are well separated from each other. Clustering of Cr atoms
begins at concentrations of about 10% at 800K and 20% at 1400K. Short-range order parameters were calculated and it was
confirmed that negative values of the first and second parameters at low Cr concentrations change sign at about 10.5% Cr,
in agreement with experiment. We demonstrate that complex ordering reactions in Fe-Cr and its properties may be described
by 12 concentration-independent expansion coefficients.
[Show abstract][Hide abstract] ABSTRACT: Iron-chromium alloys are characterized by a complex phase diagram, by the small negative enthalpy of mixing at low Cr concentrations in the bcc α-phase of Fe, and by the inversion of the short-range order parameter. We present Monte Carlo simulations of the binary Fe-Cr alloy based on the cluster expansion approximation for the enthalpy of the system. The set of cluster expansion coefficients is validated against density functional calculations of energies of small clusters of chromium in bcc structure. We show that in the limit of small Cr concentration the enthalpy of mixing remains negative up to fairly high temperatures, and individual Cr atoms remain well separated from each other. Clustering of Cr atoms begins at concentrations exceeding approximately 10% at 800 K and 20% at 1400 K, with Cr-Fe interfaces being parallel to the  planes. Calculations show that the first and the second short-range order parameters change sign at approximately 10.5% Cr, in agreement with experimental observations. Semi-grand-canonical ensemble simulations used together with experimental data on vibrational entropy of mixing give an estimate for the temperature of the top of the α-α′ miscibility gap. We find that the complex ordering reactions occurring in Fe-Cr, as well as the thermodynamic properties of the alloy, can be reasonably well described using a few concentration-independent cluster expansion coefficients.
Physical Review B 01/2007; 75(1). · 3.66 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss how two techniques, based on (1) lattice dynamics (lattice statics) simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of solid solutions and highly disordered systems. The lattice dynamics calculations involve a full free-energy structural optimisation of each of a number of configurations, followed by thermodynamic averaging. The Monte Carlo simulations include the explicit interchange of cations and use the semi-grand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parameterisation. We discuss the application of the Monte Carlo technique to the study of surfaces. A range of examples, including binary oxides, spinels, carbonates and surface segregation, is used to illustrate the methods.