Studies of concentration and temperature dependences of precipitation kinetics in iron-copper alloys using kinetic Monte Carlo and stochastic statistical simulations

The previously developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using an improved version of the previously suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependences of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM usually describes the precipitation kinetics in good agreement with the KMCM, and using the SSM in conjunction with the KMCM allows extending the KMC simulations to the longer evolution times. The results of simulations seem to agree with available experimental data for Fe-Cu alloys within statistical errors of simulations and the scatter of experimental results. Comparison of simulation results with experiments for some multicomponent Fe-Cu-based alloys allows making certain conclusions about the influence of alloying elements in these alloys on the precipitation kinetics at different stages of evolution.     

Kinetics of nanocrystallization in FeCoNbB(Cu) alloys

HITPERM alloys (FeCoMBCu; M=Nb, Zr, Hf...) have been recently developed and proposed as competitive soft magnetic materials for high-temperature applications. To our knowledge, this work contains the first results on nanocrystallization isothermal kinetics for these alloys. Analysis of nanocrystallization of the studied FeCoNbB(Cu) alloys in the frame of the Johnson–Mehl–Avrami theory shows a slowing-down of the kinetics and anomalously low values of the Avrami exponent, in a similar way to that reported for FeSiBNbCu (FINEMET)-type alloys. Compositional effects of Co substitution and Cu addition are considered. A more realistic kinetic model developed by Hermann et al. accounts for the experimental data. Received: 14 November 2001 / Accepted: 24 June 2002 / Published online: 4 December 2002 RID="*" ID="*"Corresponding author. Fax: +34-95/461-2097, E-mail: conde@us.es     

Stochastic description of phase separation near the spinodal curve in alloys

The earlier-developed statistical methods for nonequilibrium alloys are applied to stochastically describe phase separation near the spinodal curve. An important parameter of the theory is the size of local equilibrium regions, which is estimated using simulations for the different values of this parameter. The simulations based on this approach reveal significant changes in the type of evolution from nucleation to spinodal decomposition under variation of concentration and temperature across the spinodal curve. The scale of these changes seems to be mainly determined by the difference of the properly defined supersaturation parameters.     

Precipitate growth in concentrated binary alloys: a comparison between kinetic Monte Carlo simulations,cluster dynamics and the classical theory

The numerical modelling of concentrated alloy precipitation kinetics remains a challenge at all scales. At the microscopic scale, kinetic Monte Carlo (KMC) simulations can cope with nucleation and early growth whatever the solute concentration may be; it cannot, however, address coarsening. At the mesoscopic scale, the advantage of cluster dynamics (CD) is its ability to describe the whole kinetics of precipitation but lacks of reliability for nucleation in concentrated alloys. Finally, analytical models are preferred at the macroscopic scale for their simplicity, their flexibility and their ability to be incorporated within more general approaches, to predict mechanical properties, for instance. The present work aims at examining the ability of CD and classical analytical models to describe the growth of an isolated precipitate in a concentrated binary alloy, by comparison with KMC simulations taken as the reference.     

Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu,FeMn, FeNi,and FeCr

The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ? 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.     

On accuracy of different cluster models used in describing ordering phase transitions in fcc alloys

A general formulation of cluster methods applied to calculations of thermodynamic quantities of alloys in terms of renormalizing fields describing interaction between a cluster and its environment is given. We have shown that the well-known cluster variation method and the cluster field method, which was suggested earlier, are special cases of our approach. These methods have been used in calculations of phase diagrams of fcc alloys with L1₂ and L1₀ ordering transitions with several realistic interaction models. It turns out that, for all these models, the simple tetrahedron version of the cluster field method suggested in this paper describes the phase diagrams almost as accurately as more complicated cluster variation techniques. Possible applications of the tetrahedron version of the cluster field method to inhomogeneous states and kinetics of phase transitions in fcc alloys are discussed. Zh. éksp. Teor. Fiz. 115, 158–179 (January 1999)     

Production and decay of subcritical nuclei in a solid solution

The decay of “subcritical” nuclei in a solid solution has been revealed in the investigation of the CuCl phase nucleation kinetics in glass. As soon as “supercritical” nuclei with an average radius R = 1.1 nm are created at 500°C, a sharp temperature increase up to 650°C transforms most nuclei created in the first annealing stage into “subcritical” ones, and this results in the decay of 80% of the nuclei in 5 min, while the remaining 20% of the nuclei grow in size to 2.4 nm. Their growth provides a sixfold increase in the CuCl phase growth rate against that in conventional annealing at 650°C. The kinetic dependences of the nucleation parameters—the amount of the phase and the average radius and concentration of the particles—were determined by the intrinsic absorption spectra of the CuCl nanocrystals. The critical radius of the CuCl nanomelt at 650°C has been estimated as 1.3 nm and the evaporation heat of the CuCl phase molecules in glass, as 13 kJ/mol. It is shown that multistage annealing makes it possible not only to control the parameters of the particles of the new phase, but also to determine the critical parameters of the initial nucleation stage.     

Al-Zn-Mg-Cu合金时效过程的小角度x射线散射研究

通过同步辐射小角度x射线散射方法（SAXS），研究了三种Al_Zn_ Mg_Cu合金沉淀析出过程显微结构参数（析出相尺寸和体积分数），随时效温度和时效时间 的演化，同时分析了Zn含量对合金沉淀析出过程的影响.结果表明，三种合金（A，B，C） 在实验条件下析出相均属于纳米尺度，析出相的最大体积分数随Zn含量的增加而增加，最大体积分数分别为0.023—0.028，0.052—0.054和0.04.在一定时效温度下，体积分数随时效时间的变化规律，符合析出相的形核、核长大和粗化动力学过程.  关键词： 小角度x射线散射 Al_Zn_Mg_Cu合金 时效 析出相尺寸 析出相体积分数     

Impingement effect on the glass-crystal transformation kinetics by using DSC under non-isothermal regime. Application to the crystallization of the several semiconducting alloys of the Sb-As-Se and Ge-Sb-Se glassy systems

A procedure has been developed for analyzing the evolution with time of the actual volume fraction transformed, for calculating the kinetic parameters and for analyzing the glass-crystal transformation mechanisms in solid systems involving formation and growth of nuclei. By defining an extended volume of transformed material and assuming spatially random transformed regions, a general expression of the extended volume fraction has been obtained as a function of the temperature. Considering the mutual interference of regions growing from separate nuclei (impingement effect) and from the above-mentioned expression, the actual volume fraction transformed has been deduced. The kinetic parameters have been obtained, assuming that the reaction rate constant is a time function through its Arrhenian temperature dependence. The theoretical method developed has been applied to the crystallization kinetics of a set semiconducting alloys, prepared in our laboratory, corresponding to the Sb-As-Se and Ge-Sb-Se glassy systems. The obtained values for the kinetic parameters agree satisfactorily with the calculated results by the Austin-Rickett kinetic equation, under non-isothermal regime. This fact allows to check the validity of the theoretical model developed.     

Kinetics of formation of discrete nanostructures during vacuum condensation from a single-component vapor

The kinetics of cluster formation during the vacuum condensation of thin films from a single-component vapor is investigated by numerically solving the system of kinetic equations. The size distributions of clusters containing from a few atoms to several hundred atoms are obtained. The regions of dominant nucleation on active centers (point defects of the crystal substrate) and random nucleation are determined in the “condensation rate-temperature” coordinates. It is demonstrated that the regions corresponding to the pseudolayer and three-dimensional (rough) growth mechanisms can be separated in the condensation rate-temperature coordinates. The inference is made that the experimentally observed bimodal size distributions of islands can be associated with the difference between the growth rates of clusters at the stage preceding the coalescence.     

Space-time evolution induced by spinor fields with canonical and non-canonical kinetic terms

We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman–Robertson–Walker universe. The deceleration parameter is calculated by solving the equation of motion and the Friedman equation, simultaneously. It is shown that the spinor fields can accelerate and decelerate the universe expansion. To construct realistic models we discuss the contributions from the dynamical symmetry breaking.     

Statistical derivation of basic equations of diffusional kinetics in alloys with application to the description of diffusion of carbon in austenite

Basic equations of diffusional kinetics in alloys are statistically derived using the master equation approach. To describe diffusional transformations in substitution alloys, we derive the ??quasi-equilibrium?? kinetic equation that generalizes its earlier versions by taking possible ??interaction renormalization?? effects into account. For the interstitial alloys Me-X, we derive an explicit expression for the diffusivity D of an interstitial atom X. This expression notably differs from those used in previous phenomenological treatments. This microscopic expression for D is applied to describe the diffusion of carbon in austenite based on some simple models of carbon-carbon interaction. The results obtained enable us to make certain conclusions about the real form of these interactions and about the scale of the ??transition state entropy?? for diffusion of carbon in austenite.     

Nucleation kinetics in a CuCl solid solution in glass: Calculation and comparison with experiment

The kinetics of formation of CuCl nanoparticles in a glass has been studied. The experimental results obtained have been compared with the results of calculations. A method has been developed for calculating the nucleation kinetics, which decreases the time of calculations by a factor of several tens. This has been achieved using the joint kinetic equation for distributions of clusters over the number of particles and over the radius. The distributions over the number of particles and over the radius have been used for small and large clusters, respectively. The concentration of molecules near the surface of clusters has been determined from the asymptotic solution of the diffusion equation. For subcritical clusters, the concentration of molecules near the cluster surface has been taken to be equal to the average concentration in the solid solution. This method has been used to calculate the nucleation kinetics of CuCl nanoparticles in a glass. The results obtained from the calculation of the time dependences of the increase in the concentration and average radius of clusters agree well with experiment.     

Consideration of the growth mode in isochronal austenite-ferrite transformation of ultra-low-carbon Fe–C alloy

The three cooling rates of 10, 100, 200 K/min dilatometry experiments are used to investigate the kinetics of the isochronal austenite (γ) to ferrite (α) transformation of Fe–0.0036wt.%C alloy. “Normal transformation” and “abnormal transformation” have both been observed for transformations at different cooling rates. In accordance with the thermodynamic characteristics of the γ→α transformation investigated here and previous kinetic considerations, a JMAK-like approach for the kinetics of isochronal phase transformations was developed that incorporates three overlapping processes: site saturation nucleation, alternate growth modes (from interface-controlled to diffusion-controlled to interface-controlled growth), as well as impingement for random distribution nuclei. The JMAK-like approach has been employed to fit the experimental results, and the fitting results show that for the γ→α transformation of the Fe–C alloy at all applied cooling rates, the growth mode evolves in the corresponding order: from interface-controlled to diffusion-controlled growth; from interface-controlled to diffusion-controlled to interface-controlled growth; and interface-controlled growth.     

Recrystallization of the superplastic Zn-Cd alloy

The initial fine-grained structure of superplastic alloys is attained by rather complicated thermomechanical treatment. Various processes can take place during annealing of such materials due to the release of deformation energy stored in specimens in the course of their preparation. This paper deals with the measurements of the electrical resistivity annealing curves of the superplastic Zn-0·25 wt. % Cd alloy. The pronounced electrical resistivity drop due to the recrystallization was observed between 320 and 360 K. The value of kinetic exponentn from Avrami's equation was found to be 1<n<2;n increases with increasing temperature of annealing. The influence of superplastic deformation on the electrical resistivity annealing curves was investigated. Due to the softening during superplastic deformation the recrystallization becomes less pronounced and shifts to higher temperatures. The kinetic exponentn decreases to unity and its temperature dependence disappears. The attempt was made to explain these results on the ground of literature findings on the kinetics of recrystallization after preceding hot deformation.     

The relationship between kinetic and thermodynamic fragilities in metallic glass-forming liquids

The correlation between the temperature dependence of the kinetic and thermodynamic properties of a series of metallic glass-forming liquids is investigated using the concept of fragility. The results indicate a correlation between the kinetic fragility and thermodynamic fragility in these liquids. The correlation depends critically on the approach used to evaluate the thermodynamic fragility. Two distinct correlation lines are found for the metal–metalloid and for the all-metallic-constituents glass-forming liquids. For the same thermodynamic fragility the metal–metalloid liquids exhibit a distinctively larger kinetic fragility than the pure-metallic liquids. From the evaluation of the Gibbs free-energy difference between the undercooled liquid and the crystalline phase mixture, a correlation between the kinetic fragility and the driving force for nucleation is found, showing that for glass formation in metallic alloys the thermodynamic and kinetic contributions act together.     

Determination of pyrolysis temperature for charring materials

An energy and mass balanced method of determining the pyrolysis temperature is proposed. The concept is to find the pyrolysis temperature that consumes the same amount of energy to produce the same amount of mass when using the pyrolysis front model as when using finite rate kinetics models for the entire charring process. The resulting pyrolysis temperature has the form of pyrolysis rate weighted average temperature. Comparisons between finite rate kinetics and pyrolysis front models for various boundary conditions, geometries, heats of decomposition, kinetic parameters and assumptions used in the literature were made to assess the proposed method. Models using energy and mass balanced pyrolysis temperature show good agreement with finite rate models and the experiments. Extensive numerical studies on various factors influencing the charring material pyrolysis show that heat flux, sample size, heat of decomposition and kinetic parameters are the most important factors for determining an appropriate pyrolysis temperature. Thermal conductivity, specific heat and density have a lesser effect on the pyrolysis temperature. For practical application, a non-dimensional correlation is developed to determine the appropriate pyrolysis temperature without solving the problem by using finite rate models. With this correlation the energy and mass balanced pyrolysis temperature can be determined with a standard deviation of 7.6 K. These predictions are validated by comparison with measurements of wood cylinder pyrolysis. A good agreement suggests that simpler pyrolysis front models yield practically useful and accurate results given an appropriate pyrolysis temperature.     

Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study

We study the morphological evolution of strained heteroepitaxial films using kinetic Monte Carlo simulations in two dimensions. A novel Green's function approach, analogous to boundary integral methods, is used to calculate elastic energies efficiently. We observe island formation at low lattice misfit and high temperature that is consistent with the Asaro-Tiller-Grinfeld instability theory. At high misfit and low temperature, islands or pits form according to the nucleation theory of Tersoff and LeGoues.     

Charge transfer and martensitic nucleation

Summary The microscopic interpretation of phase stability in alloys undergoing thermoelastic martensitic transformation involves a difficult nucleation problem. The strong dependence of the critical temperature for the onset of martensite on composition requires the introduction of nonclassical defective nuclei, of dynamic nature, to obtain reasonable estimates of the energy barrier to nucleation. Experimental data on β-Au−Zn-based alloys are organized in the framework of the atomistic model of the valence electron localization degree. The resulting charge transfer scheme is strictly correlated to elementary surface segregation events driven by elemental surface energy differences within the studied alloys. The connection between martensitic nucleation and charge transfer segregation is discussed, focusing on the physical meaning of the various energy terms entering the model. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.