Theoretical relationship between collective and tracer diffusion coefficients has been derived and tested for different types of binary melts: (i) with an ordering tendency (case study on Ni-Al and Ni-Zr melts) and (ii) with a demixing tendency (case study on Cu-Ag melts). The obtained relationship explicitly demonstrates microscopic cross-correlation effects in the kinetics of collective diffusion. Our approach incorporates molecular dynamics calculations, modelling and statistical mechanical analysis based on fundamental concepts of the fluctuation-dissipation theorem, generalized Langevin equation and Mori-Zwanzig formalism. We also applied the developed theory to interpret recent available experimental data as well as our molecular dynamics data of diffusion kinetics in different types of binary melts: with chemical ordering and contrarily with demixing tendency.

An accurate database of diffusion properties of Ni-Zr melts is generated within the framework of the molecular-dynamics method in conjunction with a semi-empirical many-body interatomic potential. The reliability of the model description of Ni-Zr melts is confirmed via comparison of the simulation results with the existing experimental data on diffusion properties of Ni-Zr melts. A statistical mechanical formalism is employed to understand the behavior of the cross-correlation between the interdiffusion flux and the force caused by the difference in the average random accelerations of atoms of different species in the short time limit t -> 0. This theoretical description is exploited to analyze the simulation data on the diffusion properties of Ni-Zr melts. On this basis, it is found that in the composition range 0.25 less than or similar to c(NI) less than or similar to 0.5 both single-particle and collective diffusion dynamics slow down homogeneously upon undercooling of Ni-Zr melts. Furthermore, it is inferred that such homogeneous dynamical slowdown is related to the enhanced stability of undercooled melt against crystallization. As a consequence, Ni-Zr alloys within this composition range are identified as viable glass formers.

The interrelation between the kinetics of single-particle (tracer) and collective diffusion in a binary melt is investigated theoretically within the framework of the Mori–Zwanzig formalism of statistical mechanics. An analytical expression for the Onsager coefficient for mass transport and two self-diffusion coefficients of species in a binary melt is derived using analysis based on the generalized Langevin equation. The derived expression naturally accounts for manifestation of microscopic (dynamic) cross-correlation effects in the kinetics of collective diffusion. Hence, it presents an explicit extension of the well-known Darken equation which is currently often used for expressing collective interdiffusion in terms of the two self-diffusion coefficients. An application of our analysis for interpretation of recent experimental data on the interrelation between the kinetics of single-particle and collective diffusion in Al-rich Ni–Al melts is demonstrated.

The influence of composition on thermotransport (coupling between mass and heat transport) in Ni-Al melts is investigated by making use of equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism. To describe interatomic interactions in Ni-Al melt models, we employ the embedded-atom method potential developed in [G.P. Purja Pun, Y. Mishin, Phil. Mag., 2009, 89, 3245]. It is demonstrated that the employed interatomic potential gives good agreement with the recent experimental study [E. Sondermann, F. Kargl, A. Meyer, Presented at the 12th International Conference on Diffusion in Solids and Liquids (DSL-2016), 26-30 June 2016, Split, Croatia] regarding the direction of thermotransport in Al-rich liquid Ni-Al alloys. Moreover, the predicted values of the reduced heat of transport (the quantity which explicitly characterizes both the magnitude and direction of thermotransport) in Ni-Al melts, reveal fairly weak composition dependence while being practically independent of temperature at all. Accordingly, in the presence of a temperature gradient, our simulation results for the models of liquid Ni 25 Al 75 , Ni 50 Al 50 and Ni 75 Al 25 alloys predict consistently Ni and Al to migrate to the cold and hot ends, respectively. Meanwhile, the highest value, about eV, of the reduced heat of transport is observed for Ni 50 Al 50 alloy model and it slightly decreases towards Al-rich and Ni-rich compositions.

Abstract In this paper, we consider lattice-based diffusion kinetics for the direct exchange and ring mechanisms as possible proxy diffusion mechanisms for diffusion in liquid alloys. For these mechanisms, we assessed the Manning factor that arises from the Darken–Manning relation relating the interdiffusion coefficient and tracer diffusion coefficients and which can be obtained experimentally. The maximum values of the Manning factor for these two mechanisms occur when the exchange only takes place between the atoms of different type but not between the atoms of the same type. These values have strong composition dependence and reach a value of 2 (ignoring tracer correlation factors) for the direct exchange mechanism at equal compositions of the two components in binary alloys. But for the three atom ring mechanism, these values as a function of composition have a much more complicated form that sits below the direct exchange mechanism for compositions between 10 and 90%. When all exchanges (allowed by a mechanism) occur with approximately the same probability, then the Manning factor is about unity for all compositions.

We present an extensive and self-consistent database of diffusion and thermotransport properties of molecular-dynamics models of Ni-Al melts with an embedded-atom method potential. The database is generated over wide temperature and composition ranges. A careful comparison with available fragmentary experimental data is made to ensure reliability of the employed model description of Ni-Al melts. A comprehensive analysis of the presented data is carried out and the emerging trends are discussed in details. In particular, a phenomenological model for the composition dependence of the enthalpy of mixing is introduced. This model accurately describes our simulation data for Ni-Al melts as well as enables an ease access to the partial enthalpies of species essential for precise characterization of thermotransport. Furthermore, an intriguing similarity between the shapes of the composition dependence of the Manning factor (which characterizes the interrelation between the collective and single-particle diffusion) and the enthalpy of mixing in Ni-Al melts is brought to attention. Meanwhile, our results for the reduced heat of transport (which characterizes the pure heat conduction initiated by collective diffusion in isothermal conditions) allow us to predict that, in Ni-Al melts, Ni and Al tend to migrate, respectively, to the cold and hot ends in the presence of a temperature gradient. Overall, we highlight a great importance of the presented study for developing and testing of theoretical frameworks to enable sophisticated control of the heat and mass transport in binary melts.

In this study, mass transport properties of liquid Cu-Ag alloys are investigated over wide temperature and composition ranges. The calculations are performed within the framework of the Green-Kubo (GK) formalism by using equilibrium molecular dynamics (MD) simulations along with one of the most reliable embedded-atom method potentials for this system developed by [P. Williams et al.: Modell. Simul. Mater. Sci. Eng. vol. 14 (2006), p. 817]. The approach employed allows for evaluation of the components’ self-diffusion coefficients as well as the phenomenological coefficient for mass transport Lcc. The results obtained in this study can be used to predict the kinetics of solidification of real liquid Cu-Ag alloys.

Equilibrium molecular dynamics simulation in conjunction with the Green-Kubo formalism is employed to study the transport properties of a model Ni50Al50 melt with the embedded-atom method potential developed in [G.P. Purja Pun, Y. Mishin, Phil. Mag., 2009, 89, 3245]. The principal objective of the work is to quantitatively characterise and analyse thermotransport in the system, i.e. diffusion driven by a temperature gradient. In addition, direct phenomenological coefficients for mass and thermal transport are also evaluated and analysed in the process. Furthermore, the results obtained are compared with previously published data for a different model of Ni50Al50 melt with an alternative embedded-atom method potential for the alloy as well as with experiment where possible. It is found that both potentials are able to consistently predict both direct transport coefficients over a wide temperature range. However, these two potentials are found to be inconsistent in characterising the cross-coupled heat and mass transport, predicting even different directions (sign) of the heat of thermotransport. The origin of this difference is discussed in the paper in detail.

Using results of equilibrium molecular dynamics simulation in conjunction with the Green-Kubo formalism, we present a general treatment of thermal impedance of a crystal lattice with a monatomic unit cell. The treatment is based on an analytical expression for the heat current autocorrelation function which reveals, in a monatomic lattice, an energy gap between the origin of the phonon states and the beginning of the energy spectrum of the so-called acoustic short-range phonon modes. Although, we consider here the f.c.c. Al model as a case example, the analytical expression is shown to be consistent for different models of elemental f.c.c. crystals over a wide temperature range. Furthermore, we predict a frequency 'window' where the thermal waves can be generated in a monatomic lattice by an external periodic temperature perturbation.

The recently introduced analytical model for the heat current autocorrelation function of a crystal with a monatomic lattice [Evteev et al., Phil. Mag. 94 (2014) p. 731 and 94 (2014) p. 3992] is employed in conjunction with the Green-Kubo formalism to investigate in detail the results of an equilibrium molecular dynamics calculations of the temperature dependence of the lattice thermal conductivity and phonon dynamics in f.c.c. Ni. Only the contribution to the lattice thermal conductivity determined by the phonon-phonon scattering processes is considered, while the contribution due to phonon-electron scattering processes is intentionally ignored. Nonetheless, during comparison of our data with experiment an estimation of the second contribution is made. Furthermore, by comparing the results obtained for f.c.c. Ni model to those for other models of elemental crystals with the f.c.c. lattice, we give an estimation of the scaling relations of the lattice thermal conductivity with other lattice properties such as the coefficient of thermal expansion and the bulk modulus. Moreover, within the framework of linear response theory and the fluctuation-dissipation theorem, we extend our analysis in this paper into the frequency domain to predict the power spectra of equilibrium fluctuations associated with the phonon-mediated heat dissipation in a monatomic lattice. The practical importance of the analytical treatment lies in the fact that it has the potential to be used in the future to efficiently decode the generic information on the lattice thermal conductivity and phonon dynamics from a power spectrum of the acoustic excitations in a monatomic crystal measured by a spectroscopic technique in the frequency range of about 1-20 THz.

The self-or tracer diffusivity of one component in a binary alloy is often required when there is knowledge of the other component’s self-or tracer diffusivity and the interdiffusivity (and the thermodynamic factor). In the present paper, this problem is addressed for the random alloy model by applying three possible approximations having different levels of accuracy: Darken (low level of accuracy), Manning (medium level of accuracy) and Moleko, Allnatt and Allnatt (MAA) (high level of accuracy). There are unexpectedly large differences between the results of these approximations that sometimes are reflected in the high sensitivity of the vacancy-wind factor to the level of approximation. Generally, for the application of Manning and the MAA approximations, it is found that there is a difference in the number of self-diffusivity roots depending on whether the tracer diffusivity is available for the faster diffuser or for the slower diffuser and depending on how close the composition is to the forbidden (according to Manning’s description) region. Provided that the interdiffusion coefficient (divided by the thermodynamic factor) is greater than the available self-diffusion coefficient multiplied by its complementary composition, the application of the Darken approximation always results in one self-diffusivity root.

Phonon dynamics and phonon thermal conductivity of f.c.c. Cu are investigated in detail in the temperature range 200 1300 K within the framework of equilibrium molecular dynamics simulations making use of the Green-Kubo formalism and one of the most reliable embedded-atom method potentials. It is found that the temporal decay of the heat current autocorrelation function of the f.c.c. Cu model at low and intermediate temperatures demonstrates a more complex behaviour than the two-stage decay observed previously for the f.c.c. Ar model. After the first stage of decay, it demonstrates a peak in the temperature range 200 800 K. The intensity of the peak decreases as the temperature increases. At 900 K, it transforms to a shoulder which diminishes almost entirely at 1200 K. It is suggested that the peak may be activated by the influence of the Cauchy pressure in f.c.c. Cu on the phonon dynamics. A decomposition model of the heat current autocorrelation function of a monatomic f.c.c. lattice is introduced. This model can capture all contributions to the function discussed in the literature. It is found that the temperature dependence of the phonon thermal conductivity of the f.c.c. Cu model is in good agreement with previous calculations on the f.c.c. Ar model which follows an exponent close to-1.4, i.e. varies more rapidly than the T-1 law predicted by the theory. The calculated phonon thermal conductivity of the f.c.c. Cu is found to be about one order of magnitude higher than the f.c.c. Ar. This is explained by the inclusion of the electronic contribution to the bulk lattice properties during the fitting of the embedded-atom method potential functions to the experimental or ab initio data. It is demonstrated that the electronic contribution to the total thermal conductivity of f.c.c. Cu dominates over the whole studied temperature range. Nevertheless, the phonon contribution increases as the temperature decreases. The contribution can be estimated to be about 0.5 % at 1300 K and about 5 % at 200 K.

The phonon-mediated contribution to the thermal transport properties of liquid NiAl alloy is investigated in detail over a wide temperature range. The calculations are performed in the framework of equilibrium molecular dynamics making use of the Green–Kubo formalism and one of the most reliable embedded-atom method potentials for the intermetallic alloy. The phonon-mediated contribution to the thermal conductivity of the liquid alloy is calculated at equilibrium as well as for the steady state. The relative magnitude of the thermal conductivity decrease induced by the transition to the steady state is estimated to be less than 2% below 2000 K and less than 1% at 3000 and 4000 K. It is also found that the phonon-mediated contribution to the thermal conductivity of the liquid alloy can be accurately estimated (well within 1%) on the basis of an approximation which invokes the straightforwardly accessible microscopic expression for the total heat flux without demanding calculations of the partial enthalpies needed for the precise evolution of the reduced heat flux (pure heat conduction). On the basis of these calculations, the correspondence between the experimentally observed and modelled kinetics of solidification due to a difference in thermal conductivity is discussed.

The thermal resistance of a crystal lattice with a monatomic unit cell due to three-phonon scattering processes is investigated in detail theoretically. A general expression for the lattice thermal conductivity is derived from a combined analysis based on: (i) the Boltzmann equation and (ii) data on the heat current autocorrelation function obtained via molecular dynamics simulations in conjunction with the Green-Kubo formalism. It is argued that the phonon gas in a monatomic lattice conducts heat as if it consisted of two distinct parts (two 'thermal fluids'), so that the lattice thermal conductivity can be decomposed into contributions from these two parts. The origin of the behaviour of the phonon gas, which is explored in the present work, is due to an intrinsic interplay between Umklapp and normal three-phonon scattering processes. New insight into the nature of the lattice thermal conductivity is demonstrated and the results of the present work are in agreement with previous studies in this area.

In the present paper (1) the Hall method (HM) (specifically designed for determining the interdiffusion coefficient at the low and high composition limits of the corresponding interdiffusion composition profile) is further developed in order to be applied to the whole composition profile resulting in the Extended Hall method (EHM); (2) A comparative study of the HM, EHM, Boltzmann-Matano (BM) and Sauer and Freise (SF) methods is performed using composition profiles generated by computer simulation. The results clearly indicate that the HM/EHM technique is only applicable when the interdiffusion coefficient is constant (i.e. independent of composition) or almost constant at the low composition regions. In all other cases, the BM and SF methods give the best agreement with the input interdiffusion function even at the ends of the composition profiles.

The vibrational contribution to the thermal transport properties of liquid Cu is investigated in detail in the temperature range 1300-1800 K. The calculations are performed in the framework of equilibrium molecular dynamics making use of the Green-Kubo formalism and one of the most reliable embedded-atom method potentials for Cu. It is found that the temporal decay of the heat current autocorrelation function of the liquid Cu model can be described by a single exponential function, which is characterized in the studied temperature range by a constant value of the heat flux relaxation time of about 0.059 ps. The vibrational thermal conductivity of the liquid Cu model slightly decreases with temperature from about 1.1 W/(mK) at 1300 K to about 1 W/(mK) at 1800 K. Near the melting temperature it is about 30% lower than the vibrational thermal conductivity of the f.c.c Cu model. The calculated thermal diffusivity of the liquid Cu model is demonstrated to retain a constant value of about 2.7 x 10 (7) m(2)/s in the studied temperature range, which is about two orders of magnitude higher than the atomic diffusivity in the model at the melting temperature. The vibrational contribution to the total thermal conductivity of liquid Cu is found to slightly decrease with temperature, being estimated as about 0.7-0.5% in the temperature range of 1400-1800 K. Furthermore, the applicability of some simple theoretical treatments of vibrational thermal transport in liquid Cu is discussed. (C) 2014 Elsevier B.V. All rights reserved.

An analytical treatment of decomposition of the phonon thermal conductivity of a crystal with a monatomic unit cell is developed on the basis of a two-stage decay of the heat current autocorrelation function observed in molecular dynamics simulations. It is demonstrated that the contributions from the acoustic short- and long-range phonon modes to the total phonon thermal conductivity can be presented in the form of simple kinetic formulas, consisting of products of the heat capacity and the average relaxation time of the considered phonon modes as well as the square of the average phonon velocity. On the basis of molecular dynamics calculations of the heat current autocorrelation function, this treatment allows for a self-consistent numerical evaluation of the aforementioned variables. In addition, the presented analysis allows, within the Debye approximation, for the identification of the temperature range where classical molecular dynamics simulations can be employed for the prediction of phonon thermal transport properties. As a case example, Cu is considered.

Equilibrium atomic configurations and the kinetics of "order-order" and surface segregation processes in B2-ordering stoichiometric A-50 at.%B binary thin films are investigated by means of Semigrand Canonical Monte Carlo (SGCMC) and Kinetic Monte Carlo (KMC) simulations. The (100)-oriented films are modeled with an Ising-type Hamiltonian with previously evaluated pair-interaction energy parameters yielding the effect of "triple-defect disordering". The SGCMC simulations provide equilibrium vacancy concentration and atomic configuration in the films with B-atom termination of both free surfaces achieved at high temperatures by the generation of an antiphase boundary. Despite strong vacancy surface segregation, the thermodynamic activation energy for their formation inside the films is the same as in the bulk material. KMC simulations implemented with the SGCMC-determined equilibrium vacancy concentration reveal very slow relaxation of the films towards equilibrium configuration. The B-termination of the (100) free surfaces is produced by A-atom diffusion inwards into the films mediated by vacancies segregating on surfaces. (C) 2014 Elsevier Ltd. All rights reserved.

We analyse the formalism of transport in a binary system especially focussing on a detailed consideration of the heat of transport parameter characterizing diffusion driven by a temperature gradient. We introduce the reduced heat of transport parameter Qc*' which characterizes part of the interdiffusion flux that is proportional to the temperature gradient. In an isothermal system Qc*' represents the reduced heat flow (pure heat conduction) consequent upon unit interdiffusion flux. We demonstrate that Qc*' is independent of reference frame and is practically useful for direct comparison of simulation and experimental data from different sources obtained in different reference frames. Then, we use equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism to study the heat transport properties of a model of the liquid Ni 50 Al 50 alloy at three state points within the temperature range 1500 – 4000 K. Our results predict that in the liquid Ni 50 Al 50 alloy in the presence of a temperature gradient Ni tends to diffuse from the cold end to the hot end whilst Al tends to diffuse from the hot end to the cold end.

The formalism of thermotransport in a binary system is analysed. Focus is put on a detailed consideration of the heat of transport parameter characterizing diffusion driven by a temperature gradient. We introduce the reduced heat of transport parameter[GRAPHICS], which characterizes part of the interdiffusion flux that is proportional to the temperature gradient. In an isothermal system[GRAPHICS]represents the reduced heat flow (pure heat conduction) consequent upon unit interdiffusion flux. It is demonstrated that <inline-graphic xlink:href="tphm_a_965236_ilm0003.gif" is independent of reference frame and is useful in a practical way for direct comparison of simulation and experimental data from different sources obtained in different reference frames. In the case study of the liquid Ni50Al50 alloy, we use equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism to evaluate the heat transport properties of the model within the temperature range of 1500-4000 K. Our results predict that in the presence of a temperature gradient Ni tends to diffuse from the cold end to the hot end whilst Al tends to diffuse from the hot end to the cold end.