Transitions In Binary Alloys Research Articles

Phase-field simulation of radiation-induced phase transition in binary alloys

In this study, we simulate the radiation-induced phase transition in the binary alloy employing the modified Cahn–Hilliard (CH) equation that accounts for the process of radiation-enhanced diffusion, ballistic mixing, and compositional fluctuations. The influence of displacement rate on the dynamics of the average radius, number density, nucleation rate, and volume fraction of the second phase is discussed. Also, the mechanism of precipitate vanishing under irradiation condition is revealed.

Simulation of the first order phase transitions in binary alloys with variable mobility

The first order phase transitions in binary alloys were simulated basing on the Cahn–Hilliard equation for metastable states with mobility depending on the local composition. The simulation was carried out utilizing the semi-implicit Fourier spectral method for 3D fragment of a solid solution satisfying the regular solution approximation. We defined kinetics of the main characteristics of phase distribution: nucleation rate, average size, concentration of precipitates and autocorrelation function etc. Peculiarities of different stages of binary alloy decomposition (nucleation, diffusion growth and coarsening) were analyzed both for constant and variable mobility.

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

The paper presents the potential of an efficient front tracking method on a fixed control-volume grid in micro–macroscopic numerical modeling of both binary alloy solidification and a solid–liquid phase transition of single-component or doped optically functioning materials. In the former case, the method, basing on the assumption that an envelope of columnar dendrite tips moves locally according to a single crystal growth law, allows more precise identification of zones of different dendritic structures developing within the two-phase region, and thus more detailed analysis of some closing models. It is shown, by exploiting the commonly used benchmark problem that a porous medium model of the columnar mush must be carefully chosen since it strongly affects the predicted macro-segregation pattern. In the case of solidification of a single-component or doped semi-transparent material the combination of the front tracking method with the immersed boundary technique provides a new simulation method, which can handle different thermo-physical and optical properties of liquid and solid phases, processes of emission, absorption, reflection and refraction or transmission of thermal radiation at a diffusive or specular distinct solid–liquid interface detected by the front tracking technique. The method has been used in a detailed parametric analysis where the impact of different optical configurations of both phases and their various optical properties as well as variable transmissivity of solid–liquid interface on the phase change process development has been addressed.

Study of the effect of magnetic ordering on order–disorder transitions in binary alloys

We set up a mean-field approximation in a random Ising model characterized by two order parameters: the local sublattice magnetization and a mean-field occupation variable which act as an order parameter for the order–disorder transition. In the effective model Hamiltonian the two order-parameters are coupled. We solve the coupled equations arising from this to describe the total phase diagram. The exchange energies for FeCo alloys have then been accurately obtained from first-principles based on the technique of orbital peeling and a Monte Carlo analysis using a coupled Metropolis-Kawasaki updating has been carried out. Our results reasonably successfully agree with earlier experimental data.

The Surrounded Atom Theory of Order-disorder Phase Transition in Binary Alloys

In this paper, the surrounded atom model is developed to study the order-disorder phase transition in binary alloys. We calculate the configurational free energy of the alloys, derive the equation of equilibrium and determine the critical temperature of the phase transition.

Maximal attractor and inertial set for Eguchi–Oki–Matsumura equation

We consider the Eguchi–Oki–Matsumura equation describing phase transition in binary alloys. We show that the corresponding semigroup possesses a maximal attractor and prove the existence of an inertial set.

High temperature scaling of Ni–xSi–10 at.% Al alloys in 1atm of pure O2

The oxidation of Ni-xSi-10Al alloys (with x = 0, 2, 4 and 6 at.%), has been studied at 900 and 1000 C in 1 atm of pure O-2 to examine the effect of different silicon additions on the behavior of ternary Ni-Si-10Al alloys. The kinetic curves of Ni-10Al are approximately parabolic at both 900 and 1000 degrees C. Conversely, the kinetics of the ternary alloys at both temperatures correspond generally to a rate decrease faster than predicted by the parabolic rate law, except for the oxidation of Ni-6Si-10Al at 1000 degrees C, which exhibits a single nearly-parabolic stage. Oxidation of the binary alloy formed at both temperatures an internal oxidation zone beneath a layer of NiO. Oxidation of Ni-2Si-10Al at both temperatures and of the other two alloys at 900 degrees C formed initially a zone of internal oxidation of Al + Si. However, a layer of alumina forming at the front of internal oxidation after some time blocked the internal oxidation and produced a gradual conversion of the metal matrix of this region into NiO, with a simultaneous decrease of the oxidation rate. Conversely, the oxidation of Ni-4Si-10Al and Ni-6Si-10Al at 1000 degrees C did not produce an internal oxidation, but formed an alumina layer directly on the alloy surface after an initial stage when also Ni was oxidized. Therefore, silicon exerts the third-element effect by reducing the critical Al content needed for the transition from its internal to its external oxidation with respect to the corresponding Ni-Al alloy. This result is interpreted by means of an extension to ternary alloys of Wagner's criterion for the same transition in binary alloys based on the attainment of a critical volume fraction of internal oxide. (c) 2006 Elsevier Ltd. All rights reserved.

Grain Boundary Transitions in Binary Alloys

A thermodynamic diffuse interface analysis predicts that grain boundary transitions in solute absorption are coupled to localized structural order-disorder transitions. An example calculation of a planar grain boundary using a symmetric binary alloy shows that first-order boundary transitions can be predicted as a function of the crystallographic grain boundary misorientation and empirical gradient coefficients. The predictions are compared to published experimental observations.

Creation of ferromagnetic properties of V–Fe and Zr–Fe alloys by hydrogen absorption

The results of investigations of V1−y Fe y H x and Zr1−y Fe y H x alloys by 57Fe Mossbauer spectroscopy are presented and discussed in view of hydrogen ability to create ferromagnetic properties of the alloy. The results indicate two different possibilities of hydrogen influence on the hyperfine magnetic field. Hydrogen absorption causes the ferromagnetic behaviour of the alloys at significant lower iron concentration compared to the concentration of magnetic transition in binary alloys. The main reason for such behaviour is the anisotropic lattice expansion in hydrogenated V-Fe and Zr-Fe alloys as well as the decomposition of paramagnetic Zr-rich intermetallic compounds in the aftermath of the strong electron affinity of hydrogen for zirconium. These trends give rise to growth of magnetic clusters of Fe atoms so strong that they can participate in the overall magnetic properties of the system under investigation.

Effect of silicon additions on the oxidation of a Ni–6at.%Al alloy at 1273K

The oxidation of four Ni-xSi-6Al alloys (x = 0, 2,4 and 6 at.%) has been studied at 1273 K under 0.1 MPa O-2. Silicon exerts the third-element effect by reducing the critical Al content needed for the transition from its internal to its external oxidation with respect to Ni-Al alloys. This result is interpreted by extending to ternary alloys Wagner's criterion for the same transition in binary alloys. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Kinetic Monte Carlo simulations of the surface roughening of binary systems

Although the surface roughening transition in single component systems has been studied extensively, the surface roughening transition in binary alloys has not. We have conducted a kinetic Monte Carlo computer study to simulate alloy crystallization using the spin-one Ising Model with diffusion. The surface roughness, which is defined as the density of lateral unsatisfied bonds at the interface, has been determined for both the pure components and for alloys of various compositions. The surface roughness for a pure material depends on the change in bond energy associated with the transformation, divided by the melting point. The solid phase contains essentially one component, the surface roughness of the alloys was found to depend on the change in bond energy of the pure component, divided by the liquidus temperature of the alloy.

Order–disorder phase transition of the Co xFe 1− x system

The order–disorder phase transitions in binary alloys with magnetic interactions are studied. We introduced an electronic theory for magnetic binary alloys, which is an extension of the cluster-Bethe lattice method. In this approximation we incorporate electronic correlations, itinerant and localize nature of electrons 3d, and both long-range and short-range chemical correlations. The magnetism is described by means of a Hubbard Hamiltonian that in conjunction with Green's functions techniques is used to calculate local densities of electronic states. For it we take an atom in the real lattice and it is joined to a Bethe's lattice with the same coordination number. The diagram for order–disorder phase transition is obtained. It is achieved by coupling the electronic theory introduced here, to combinatorial theory developed by Kikuchi. The first is used for calculating the alloy internal energy so long as the second is used for obtain the configurational entropy. An application to order–disorder transition of Co x Fe 1− x is studied and good agreement with experiment is obtained.

Mean field rate equation for diffusion-controlled growth in binary alloys

A system of rate equations is developed for modeling the kinetics of diffusional phase transitions in binary alloys. By employing a mean field assumption and the quasi static approximation a novel expression for the growth law of the nuclei is obtained in terms of supersaturation and diffusion length of component in the parent phase. The mean field rate equations are integrated for the model case of a transformation ruled by simultaneous nucleation and the behaviour of both Avrami’s exponent and rate constant investigated as a function of the initial value of the supersaturation. The expression of the activation energy, as extracted by the Arrhenius plot of the rate constant, is determined and is shown to be a function of the activation energies for nucleation and diffusion, and of the initial value of the supersaturation. The limiting case of infinite diffusion length is also analysed and discussed.

Existence of solution for Eguchi–Oki–Matsumura equation describing phase separation and order–disorder transition in binary alloys

In this paper we consider the Eguchi–Oki–Matsumura equation which consists of the fourth- and second-order coupled equations of parabolic type. It is shown that this system admits the unique global solution.

Unified mean-field study of ferro- and antiferromagnetic behavior of the Ising model with external field

A simultaneous mean-field treatment, of both phenomena, ferro- and antiferromagnetism, in the framework of the Bragg–Williams theory, shows the importance of the interplay between the two corresponding order parameters in determining the features of the phase diagram. The problems of phase separation and order–disorder transition in binary alloys are also included in the solution. The different projections of the phase diagram are discussed.

Electronic structure changes associated with magnetic transitions in binary alloys: an exploratory seels study

The Curie temperature of a disordered alloy may differ from that of a partially ordered system. Alternatively, magnetism can influence chemical order and produce substantial changes in the phase diagram. These results have been established by a detailed investigation of the Col-xPtx system and the entire phase diagram, including magnetic and chemical effects, have been calculated and shown to be in good agreement with experimental data. In addition, ultrathin multilayers of Co/Pt show perpendicular anisotropy but the origin of this unique property is not well understood. Recently, we have shown that the d-electron density of states of a range of Cul-xPdx alloys, based on measurements of L3,2 transitions (“white lines” - WL) in electron energy-loss spectroscopy (EELS), is critically dependent on short-range order (SRO). In this paper we present results of the combined effect of magnetic and chemical order on the d -hole count, as measured by the normalized Co WL intensities, in four different Co/Pt alloys.

Phase-field model for isothermal phase transitions in binary alloys.

In this paper we present a phase-field model to describe isothermal phase transitions between ideal binary-alloy liquid and solid phases. Governing equations are developed for the temporal and spatial variation of the phase field, which identifies the local state or phase, and for the composition. An asymptotic analysis as the gradient energy coefficient of the phase field becomes small shows that our model recovers classical sharp-interface models of alloy solidification when the interfacial layers are thin, and we relate the parameters appearing in the phase-field model to material and growth parameters in real systems. We identify three stages of temporal evolution for the governing equations: the first corresponds to interfacial genesis, which occurs very rapidly; the second to interfacial motion controlled by diffusion and the local energy difference across the interface; the last takes place on a long time scale in which curvature effects are important, and corresponds to Ostwald ripening. We also present results of numerical calculations.

Surface and bulk order-disorder transitions

Interrelation of surface an bulk order-disorder transitions in binary alloys A x B 1− x is discussed within the framework of the Bragg-Williams approximation, using the fcc (100) and bcc (110) surfaces as an example. In an fcc alloy with a (100) surface, layers parallel to the surface undergo alternately second-order transitions. On the other hand, the bulk fee alloy reveals a first-order transition from the disordered phase to a mixture of the disordered and the AB 3- (or A 3B-) type ordered phases except for X = 0.5. The origin of the bulk first-order transition is discussed by taking into account order-disorder transitions in the surface region. For comparison, the bulk second-order transition in a bcc alloy is also discussed.

Surface and bulk order-disorder transitions

Interrelation of surface an bulk order-disorder transitions in binary alloys A X B 1− X is discussed within the framework of the Bragg-Williams approximation, using the fcc (100) and bcc (110) surfaces as an example. In an fcc alloy with a (100) surface, layers parallel to the surface undergo alternately second-order transitions. On the other hand, the bulk fcc alloy reveals a first-order transition from the disordered phase to a mixture of the disordered and the AB 3 − (or A 3B −) type ordered phases except for X = 0.5. The origin of the bulk first-order transition is discussed by taking into account order-disorder transitions in the surface region. For comparison, the bulk second-order transition in a bcc alloy is also discussed.

On the correctness of a model for phase transitions in binary alloys

The main result of this paper is a non-uniqueness theorem for the self-similar solutions of a model for phase transitions in binary alloys. The reason for this non-uniqueness is the discontinuity in the coefficients of heat conduction and diffusion at the inter-phase. Also the existence of a self-similar solution and the stability criterion are discussed.