Cláudio Geraldo Schön

Ab-initio calculations of the formation energies of BCC-based superlattices in the FeAl system

Abstract First-principles calculations of the total energies of A2 iron and aluminum, B2 (FeAl), B32 (FeAl) and D0 3 (Fe 3 Al and FeAl 3 ) compounds were performed in the frame of density functional theory (DFT) using the Full Potential - Linear Augmented Plane Wave method (FP-LAPW). These results have been used to obtain formation energies of the respective ground states. The calculated formation energies of the D0 3 (Fe 3 Al) and B2 (FeAl) compounds show excellent agreement with available calorimetric data on standard enthalpies of formation of FeAl alloys up to 50 at.% aluminum. As the FeAl system has a controversial magnetic behavior when described by ab-initio methods in the DFT, this agreement is remarkable.

Order-disorder transformations and diffusion in ternary bcc alloys: The role of second-order boundaries

Isopotential curves of the thermodynamic forces for ternary diffusion have been calculated as a function of the composition for the bcc Fe-Cr-Al system at T = 1073 K and T = 1273 K, using the cluster variation method in the irregular tetrahedron approximation with interaction parameters fitted to experimental thermochemical data. At both temperatures, the system presents extended second-order lines for the B2/A2 equilibrium. The results show that the isopotential lines present a discontinuous change of slope coinciding with the position of the second-order line in the phase diagram. This justifies experimental observations published in the literature of anomalies in the concentration plots of diffusion couples corresponding to the position of the corresponding second-order boundary. The results of the calculation suggest that the magnitude of the discontinuity should decrease with temperature.

Prototype calculations of B2 miscibility gaps in ternary b.c.c. systems with strong ordering tendencies

Prototype calculations in ternary ordering systems based on the b.c.c. lattice have been carried out with the Cluster Variation Method (CVM) in the irregular tetrahedron approximation including tetrahedron interactions. The systems under investigations were characterized by strong ordering tendencies (i.e. with large, negative first neighbour interactions in all binary sub-systems) which resulted in the opening of a miscibility gap inside the B2 single-phase field. This miscibility gap is shown to be produced by frustration of the B2 cluster by a calculation using a hypothetical system with identical first neighbour interactions in the three binary sub-systems. This phase diagram presents as a key feature a central three-phase miscibility gap, which transforms into an ordinary two-phase miscibility gap involving two B2 phases after the symmetry of the interactions is broken. The results are discussed in connection with the experimental Fe–Ti–Rh phase diagram. # 2003 Elsevier Ltd. All rights reserved.

CVM study of FCC and BCC Ising magnets with generalised spin number

Abstract Calculations using the cluster variation method (CVM) in the tetrahedron approximation have been applied to multicomponent FCC and BCC Ising systems with spin number up to s =7/2. The magnetic specific heat capacity ( C H ) of ferro- and antiferromagnetic FCC and BCC systems has been calculated in the first neighbour approximation and compared with data obtained with other methods. A concavity in the C H curve at T ≈ T C /2 develops with increasing spin number.

Comparison between Monte Carlo and Cluster Variation method calculations in the BCC Fe–Al system including tetrahedron interactions

Abstract The BCC Fe–Al system has been modeled with the Monte Carlo (MC) method in the grand-canonical ensemble calculation using the Ising model. The present calculation was performed in isothermal conditions with a computer crystal with 483 atoms at 1000 K. The interaction parameters for this calculation were taken from a previous Cluster Variation Method (CVM), which included tetrahedron interactions. The comparison of the integral thermodynamic properties (internal energy and equilibrium alloy composition) obtained in both calculations shows good agreement. Small deviations are observed only in the neighborhood of the second-order B2/A2 critical composition.

Experimental study and Cluster Variation modelling of the A2/B2 equilibria at the titanium-rich side of the Ti–Fe system

Abstract The experimental data concerning the A2 (β-Ti)/B2 (TiFe) equilibrium have been reviewed and four new tie-lines at T = 1343 K, 1173 K, 1073 K and 973 K were determined. These new experimental data confirm the assessed phase boundary A2/B2 at the A2 side, except for temperatures near the eutectic. No data were available of the solubility range of the intermetallic B2 phase. The present data of the phase boundary at the B2 side give a lower solubility than previously assumed. The set of experimental data and additional new information on the Fe–Rh–Ti phase diagram lead to new pair and tetrahedron interaction energies by Cluster Variation Method calculations in the tetrahedron cluster approximation.

Hot rolling mill roll microstructure interpretation: A computational thermodynamics study

The microstructure of the interface of a high chromium cast iron/ductile cast iron composite hot rolling mill roll has been interpreted with the help of Fe-Cr-Si-C laboratory alloys and thermodynamic calculations of their solidification paths. It has been shown that the mill roll presents two limiting microstructures: the ductile cast iron core and the white cast iron shell. While the core is heavily contaminated with chromium, originating from the partial dissolution of the shell during core pouring, the shell shows a typical high chromium white cast iron micro-structure, since it remains solid during processing. The high chromium contents in the core originate a typical “mottled” cast iron microstructure, combining nodular graphite and ledeburite. The region between the two limiting microstructures is called interface. As the distance from the core toward the shell increases in the interface, the content of chromium increases but that of silicon decreases. The resulting microstructural gradient shows ledeburitic M3C, hexagonal-section M3C, duplex M3C/M7C3 carbides, and M7C3 carbide, which could be well correlated with the calculated solidification paths of the laboratory samples.

CVM study of BCC Ising ferromagnets with antiferromagnetic second neighbour interactions: implications to the magnetism of the heavy rare earths

Abstract Calculations using the cluster variation method (CVM) in the tetrahedron approximation have been applied to BCC Ising systems with spin number up to s =15/2. Ferromagnetic first neighbour interactions ( J (1) J (2) >0) of variable strength α =− J (2) / J (1) have been analysed. For small α values the system is completely ferromagnetic, showing a second order transition from the ferromagnetic to the paramagnetic state. The Curie temperature T C depends on the value of α . For a critical value α C a multicritical point appears at T C in the α × T phase diagram. For α values higher than α C , two transitions occur: at low temperatures, a first order transition from the ferromagnetic ground state to the antiferromagnetic state, followed by a second order transition from the antiferromagnetic to the paramagnetic state. The specific heat capacities calculated for these model systems present a remarkable resemblance to experimental data for HCP Tb ( s =6) and Dy ( s =15/2). These results suggest that the complex magnetic structures observed in these metals should be interpreted as an effect of the high spin number statistics.

Uniaxial near plane strain tensile tests applied to the determination of the FLC0 formabillity parameter

b An alternative procedure for the determination of the FLC 0 value, the limit strain value corresponding to the plane strain mode of the Forming Limit Curves (FLC), a critical parameter in the sheet formability analysis, is suggested and compared with conventional Nakazima simulation tests. The procedure was tested using two different materials: interstitial-free quality steel (IF) and a spheroidized SAE 1050 steel. The intrinsic tensile test, in a near plane strain state, was performed using a small number of samples, with dimensions suggested by the literature. The results were checked against Nakazima test results using the same materials. The plane strain test was reliable in determining consistent FLC 0 values and should be preferred since it is not affected by the geometric aspects and by friction, which do affect the Nakazima test. The reliability of the FLC 0 values obtained by near plane strain was also corroborated through comparison with literature data.

The spin s = 7/2 FCC ferromagnet: comparison between cluster variation method and Monte Carlo calculations

Abstract Internal energy, reduced magnetisation, point probabilities and specific heat capacity have been calculated for the hexagonal close packed (HCP) Ising ferromagnet with spin 7/2 using the Monte Carlo (MC) method in the isotropic nearest neighbour approximation for a 48×48×48 computer crystal. The results are compared with previously published calculations obtained for the face-centred cubic (FCC) structure from the cluster variation method (CVM) in the tetrahedron approximation. Internal energy, reduced magnetisation and point probabilities obtained from MC and CVM are almost identical in a large range of temperatures both above and below the Curie temperature (TC). A slight difference appears only in the critical region close to TC. The specific heat capacity has been calculated at temperatures above TC. In this paramagnetic region the MC calculations yield considerably higher values than the CVM, leading to a better agreement with experimental data for Gadolinium than previously obtained with the CVM.