Diffusion, Solute Segregations and Interfacial Energies in Some Material: An Overview

We have shown a connection among the three important properties of interfaces, namely, the free energy, diffusion and solute segregation through the conjecture that the interface free energy is the difference between those responsible for diffusion in the lattice and the interface itself. The interface energy is known to decrease upon solute additions. We discuss the methodology and the thermodynamical analysis of the diffusion parameters which enable extraction of the interfacial energies and illustrate them by results obtained in a wide variety of materials. Investigations carried out in pure polycrystalline metals have yielded grain boundary energies comparable to those directly measured. Furthermore, we discuss the role of solute segregation at grain boundaries in alloys in altering diffusion. From the perturbations caused, the solute segregation parameters—the enthalpy and the entropy of binding—have been extracted and levels of solute concentrations estimated. It is shown that similar analyses when applied to complex materials, e.g. the Pb–Sn eutectic alloy, several intermetallic compounds, and oxide systems, also result in acceptable values of interface energies and segregation factors. Finally, some ad-hoc guidelines are provided to alter diffusion in interfaces through solute additions in order to achieve some end use engineering objectives.     

Theory of grain boundary motion during high-temperature DIGM

A theory of diffusion induced grain boundary migration (DIGM) is presented for high temperatures where volume diffusion of solute atoms out of the grain boundary is important. It is shown that due to the presence of a gradient term in the expression for the free energy of solid solution, even a relatively small discontinuity in the solute distribution across the gain boundary provides enough driving force for grain boundary migration. From the expression obtained for the grain boundary velocity the coefficient for the Ni diffusion across the grain boundaries in a Cu(Ni) polycrystal has been estimated.     

Fast ionic transport in Ag<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>TiS<Subscript>2</Subscript>

The enthalpy of the subsystem of silver ions in the intercalation compounds Ag _x TiS₂ has been calculated from the electrochemically measured thermodynamic functions of the silver subsystem. The ionic conductivity and the coupled chemical diffusion coefficients for silver in the intercalation compound have been measured. The activation energy for diffusion of silver ions is determined and the obtained value is interpreted from analyzing the concentration dependence of the enthalpy of the ionic subsystem. The conclusion has been drawn that the high diffusion mobility is associated with the competition between the covalent and elastic interactions, which decreases the activation energy for diffusion of ions.     

Computer simulation of solute segregation to a Σ = 5 tilt boundary in Au,Cu and Ni

A Lattice Energy Function that combines a Mie type interatomic potential and a free electron gas volume dependence has been applied to the study of grain boundary energy and structure of a Σ = 5 tilt boundary in Au, Cu and Ni and of solute segregation to the same. Interatomic potentials and volume dependencies of the solvent and solute were adjusted to fit the relative partial molar enthalpy and volume at infinite dilution order to construct a AB type potential and volume dependence. This AB interaction is then applied to calculate the binding energies of solute to various grain boundary sites and the resulting change in grain boundary energy. A relationship between the binding energy and change in grain boundary is derived. The relative values of the grain boundary energy are in agreement with experimental values of the average grain boundary energies. The relative binding energies of the tested solvent-solute systems are in agreemnet with expectations that certain systems should have larger binding energies than others. The behavior of solute binding energies and local relaxations are in agreement with other studies of grain boundary segregation which use different Lattice Energy Functions and relaxation algorithms. The change in grain boundary energy is shown to be directly proportional to the binding energy.     

A thermodynamic model for the compensation law and its physical significance for polymers

This paper describes how the compensation law can be explained by a linear relation between the activation entropy and enthalpy of a given process in a polymer. These two variables are related by the thermal expansion coefficient and a constant approximately equal to the Rao acoustical parameter. A relation between the activation free energy and some thermodynamic parameters is presented. The activated volumes for the α and β relaxations of polyethylene are shown to vary with temperature and cry-stallinity. The activated volume has also been calculated for some other polymers and is of the order of 1 to 6 molar volumes at 295 K.     

Mechanism of solid-state eutectoid transformation in an aluminium-zinc alloy

The growth rate of pearlite during isothermal transformation of an aluminium-zinc eutectoid has been determined experimentally. Different theoretical models, assuming either volume or boundary diffusion of zinc to be a rate controlling mechanism for the eutectoid transformation, have been applied. With volume diffusion models, the calculated growth rates were lower than the experimental growth rates by a factor of three orders of magnitude. Reasonable agreement between the calculated and experimental growth rates has been obtained on applying the boundary diffusion models. The activation energy for boundary diffusion of zinc in the aluminium-zinc alloy was estimated to be ≅11.6 kcals/mole.     

Analysis of the mobility of migrating austenite–ferrite interfaces

Dilatometric studies assisted by high-temperature laser scanning confocal microscopy provide a comprehensive experimental picture with regard to cyclic austenite-to-ferrite transformations in Fe–C alloys. The validity range for the sharp interface and effective mobility approach is identified by comparing modelling results with calculations based on experiments. The interface velocity for the austenite-to-ferrite transformation in pure iron is exclusively controlled by the intrinsic interface mobility conforming to the upper boundary of mobilities. The austenite-to-ferrite transformation in Fe–C alloys under conventional cooling and heating conditions is primarily controlled by carbon diffusion in austenite. The lower boundary of the temperature-dependent interface mobility has been established for an Fe–C alloy over a wide range of temperatures during cycling transformation. Austenite-to-ferrite transformations in Fe–C–X alloys are characterized by still lower effective mobilities depending on both temperature and composition, because substitutional elements X give rise to a solute drag effect. An estimate for the effective mobility valid for the austenite-to-ferrite transformation in lean Fe–C–Mn alloys is provided.     

Microstructure changes and steady state creep characteristics in Pb-Sn alloys during transformation

The steady state creep of Pb-10 wt.% Sn and Pb-61·9 wt.% Sn alloys have been investigated under different constant stresses near the transformation temperature. The temperature dependence of steady creep rate has shown two different transition points; at 423 K for Pb-10 wt.% Sn alloy and at 403 K for Pb-61·9 wt.% Sn (the eutectic composition). The strain rate sensitivity parameter (m) has been found to increase by raising the working temperature and to reach 0·45 and 0·85 for the first and second alloy, respectively. The activation energies of steady state creep of Pb-10 wt. % Sn have been found to be 46·2 kJ/mole and 88·2 kJ/mole in the low and high temperature regions (below and above 423 K) referring to dislocation and self diffusion mechanisms. While activation energies of steady creep in Pb-61·9 wt.% Sn have been found to be 42 kJ/mole and 63 kJ/mole in the low and high temperature region (below and above 403 K), characterizing grain boundary diffusion in Sn and Pb respectively. X-ray analysis and microscopic investigations of the test alloys have confirmed the above mentioned mechanisms.     

Oxygen diffusion in SrZrO3

Oxygen diffusion coefficients in SrZrO₃ polycrystals were determined using the isotopic exchange method with ¹⁸O as oxygen tracer. Diffusion treatments were performed at different temperatures between 1173 K and 1473 K. Oxygen diffusion profiles were established by secondary ion mass spectroscopy (SIMS). Classical diffusion equations were used to fit experimental results and to determine bulk diffusion (D_vol) and surface exchange (k) coefficients of oxygen in SrZrO₃ polycrystalline materials. From these values, bulk diffusion and grain boundary diffusion coefficients as well as oxygen surface exchange coefficients were determined. The activation energy of oxygen diffusion in the bulk is 2.1 eV, while for the diffusion in the grain boundary, 1.8 eV was found. The surface exchange reaction has an activation enthalpy of 1.2 eV.     

Theoretical study of quantum dots distribution function and the process of nucleation during Ostwald ripening in InAsSbP system

Experimental results on distribution of quantum dots versus sizes in InAsSbP system at different growth times are analyzed theoretically. It is shown that depending on growth time the process of nucleation and ripening of QDs is controlled either by transition kinetics in the grain-matrix boundary (Wagner distribution) or by the volume diffusion (Lifshitz-Slyozov distribution). Comparing theoretically calculated results with experimental data, numerical value of the reaction rate on the grain surface and the volume diffusion coefficient at nucleation temperature T = 550°C were estimated.     

Grain Boundary Migration in Fe-3wt.%Si Alloys

The studies of three different laboratories on grain boundary migration in Fe-3wt.%Si alloys are presented. In all cases bicrystal techniques employing capillarity as driving force were used. [100] tilt boundaries were studied in the temperature range from 1223 K to 1373 K, and [110] tilt boundaries in the range from 1220 K to 1625 K. Proportionality between grain boundary velocity and driving force was confirmed. All data fulfil a linear relation between activation enthalpies and logarithms of the pre-exponential factors, corresponding to a compensation temperature of 1386 K where all boundaries theoretically should possess the same mobility. A considerably lower activation enthalpy was found in one case for an asymmetrical grain boundary compared to the symmetrical boundary of the same misorientation. High values of activation enthalpy of migration were found for special [100] boundaries compared to general ones although an opposite tendency was also observed for [100] boundaries.     

Study of interdiffusion of Ni/Fe layers by Auger Sputter profiling

Bulk and grain boundary diffusion of Fe into Ni films has been studied under UHV in the temperature range of ?150 to 500°C using AES and sputter profiling methods. The concentration profiles at the interface are corrected for the various broadening and damage effects inherent in ion bombardment. Grain boundary diffusion coefficients are derived on the basis of the Whipple model. The measured activation energies are 46 $\text{kcal}\text{mole}$ for bulk diffusion and 34 $\text{kcal}\text{mole}$ for grain boundary diffusion. An additional migration phenomenon not previously resolved is observed for very thin films annealed at relatively low temperatures (150–250°C). A possible mechanism involved in this initial “interface healing” is discussed.     

Water molecules migration at oil–paper interface under the coupling fields of electric and temperature: a molecular dynamics study

Moisture is an important factor affecting the insulation properties of transformers. Due to the limitations of macroscopic experimental methods, the diffusion of water at oil–paper interface cannot be accurately measured. Therefore, molecular dynamics method was used in this work to establish oil–paper layer model of 10⁵ atoms. Through jointly analysing the aggregation degree, diffusion coefficient, free volume as well as radial distribution function of water molecules, the diffusion mechanism of water molecules at oil–paper interface was studied. The results show that when the initial water content in paper was high, water molecules would accumulate at oil–paper interface to form the local high-water region during heating. The polarisation of the electric field strengthened the hydrogen bonding interaction between water molecules and increased the probability of occurrence of the high-water region. Meanwhile, electric field reduced the free volume and diffusion coefficient of water molecules and rendered its diffusion coefficient anisotropic. What’s more, when the electric field was combined with the temperature field, the electric field played a leading role in the diffusion of water molecules while the temperature field was less affected. Diffusion coefficients of water molecules at different temperatures from molecular dynamics simulations were well consistent with experimental results, which verified the rationality of the model.     

Grain Boundary Kinetics in Oxide Ceramics with the Cubic Fluorite Crystal Structure and its Derivatives

Kinetics of grain boundaries in oxides with the cubic fluorite structure and its derivatives has been investigated using fine grain ceramics that are fully dense. Grain growth measurements in these materials have provided information on grain boundary diffusivity over a diffusion distance of the order of the initial grain size. With the addition of solute cations, grain boundary mobility can be varied over many orders of magnitude, often with very different activation energies. This is caused by the variation of defect population and the defect-solute association. Definitive evidence for solute drag has also been observed in some cases, but solute drag can not be confirmed as a general mechanism in solid solutions. Lastly, while grain boundary at low temperature may continue to serve as a fast diffusion path, it may not be able to migrate because of additional pinning mechanisms such as those exerted by grain boundary nodal points or lines. This means that sintering without grain growth is possible, opening up an avenue for obtaining ultrafine ceramics by pressureless sintering.     

The investigation of electrochemical properties and ionic motion of functionalized copolymer electrolytes based on polysiloxane

The effect of EO side chain functionalization on the transport and electrochemical properties of polysiloxane electrolytes has been examined in this report. First, a study of the electrochemical stability of the electrolytes by linear sweep voltammetry shows that the polymer electrolytes have a negligible effect on the electrolyte stability windows. In addition, the parameters of cation mobility in polysiloxane electrolytes, such as ionic transference numbers and diffusion coefficients, were increased by increasing the lengths of the EO side chain. However, cation mobility in polymer structures is quite different compared to liquid-based systems and is probably suppressed, resulting in their polymer structure. Therefore, Positron Annihilation Lifetime Spectroscopy (PALS) was used to study the relationship between orthopositronium (o-Ps) lifetime, free volume radius, free volume of micro voids and EO side chain affection at different temperatures. Finally, a battery application with LiCoO₂ and LiFePO₄/polymer electrolyte/lithium metal electrode was monitored for its potential use in the future.     

Effect of hydrostatic pressure on self-diffusion in metal nanoparticles

The thermodynamics approach has been developed to describe the self-diffusion in nano-sized solids. It has been established that identical homologous temperatures of metal nanoparticles with their fixed characteristic size give the identical coefficients of diffusion under different pressures. The dependence of the activation enthalpy of diffusion on pressure and on the characteristic size of nanoparticles is first obtained.     

Effect of hydrostatic pressure on self-diffusion in metal nanoparticles

The thermodynamics approach has been developed to describe the self-diffusion in nano-sized solids. It has been established that identical homologous temperatures of metal nanoparticles with their fixed characteristic size give the identical coefficients of diffusion under different pressures. The dependence of the activation enthalpy of diffusion on pressure and on the characteristic size of nanoparticles is first obtained.     

Effect of iodine sorption on the free volume of polycarbonate

 The effect of iodine sorption on the free volume of polycarbonate is investigated by Positron Annihilation Lifetime method. The observed results are interpreted in terms of the Charge Transfer Complex formation and precipitation of iodine at the initial and final stages of sorption, respectively. At higher levels of sorption, changes in the second lifetime and its intensity seem to suggest a conformational transformation, probably due to the net change in the amorphous-crystalline boundary regions of the polymer matrix. The free volume cavities have been predominantly occupied by I^- ₃ species and the diffusion process obeys Fick’s law. An exponential type correlation has been observed between fractional free volume and the diffusion coefficient. Received: 13 June 1996/Accepted: 20 September 1996     

Radiation transport and internal reflection in a two region, turbid sphere

We construct an integral equation for the flux intensity in a scattering and absorbing two-region turbid spherical medium using the integro-differential form of the radiative transfer equation. The sphere is uniformly irradiated by an external source of arbitrary angular distribution and contains a distributed volume source. Anisotropic scattering is accounted for by the transport approximation. The Fresnel boundary conditions, which incorporate reflection and refraction, are used at the outer surface and at the interface between the two regions. In this respect, some new interfacial boundary conditions are introduced. For the special case of a non-scattering medium, we obtain exact solutions for specular reflection. Some numerical examples are given which show qualitative agreement with some recent work of other authors. Of particular interest are the emergent angular distribution and the albedo of the surface as a function of the refractive index and the radii of the two regions. We also draw attention to the fact that the boundary conditions at the interface differ according to the relative values of the refractive indices in the two regions. The interfacial boundary conditions for use in diffusion theory are derived and compared with those of Aronson [Boundary conditions for diffusion of light. J opt Soc Am 1995;12:2532]. In appendix B, we show how diffusion theory may be used to include scattering into the problem in a simple way.     

New theory of undercooling during rapid solidification: application to pulsed laser heated silicon

A new theory of undercooling has been developed based on the Fickian form of heat flux expressed in terms of a gradient in enthalpy density. It is shown that heat diffusion is more fundamental than Fourier’s law of heat conduction. During the solid–liquid phase change, diffusion requires continuity of the enthalpy density across the phase-change boundary, which has two important consequences. First, the calculated melt-depth during rapid heating is reduced, and second, during cooling the rate of loss of heat is independent of both the rate of release of latent heat and the temperature of the interphase layer. The cause of undercooling is diffusive heat loss without recrystallisation, which simply causes the temperature of the liquid to drop. Both the nature of melting and classical nucleation have been examined and shown to support diffusion over conduction. In particular, it is established that the literature supports a model of melting in which phase fluctuations at the melting point occur, and that these phase fluctuations must inevitably lead to thermal transport at uniform temperature. Hitherto unrecognized inconsistencies in classical nucleation theory also support the diffusive framework. The model is applied to pulsed laser melting and amorphisation of (111) silicon. PACS  64.70.Dv; 66.30.Xj; 68.18.Jk