Irina V. Belova

Diffusion in nanocrystalline materials

Abstract The problem of calculating the effective diffusivity in nanocrystalline materials is addressed. Two simple two-dimensional grain patterns are constructed and several equations are derived from the Hart–Mortlock and Maxwell–Garnett equations. Monte Carlo computer simulation is used to test the validity of the various equations. It is shown that one of the derived equations provides an excellent description of the effective diffusivities up to a volume fraction of atoms in grain boundaries of 40%.

Tracer correlation factors in the random alloy

Abstract An extensive Monte Carlo study has been made of tracer correlation factors in simple cubic, bcc and fcc binary random alloys. Contrary to the findings of much of the earlier Monte Carlo work, where vacancy jump sequences were much too short, we found that generally Mannings diffusion kinetics formalism (Manning, J. R., 1968, Diffusion Kinetics for Atoms in Crystals; 1971, Phys. Rev. B, 4, 1111) provides only a fairly rough approximation for the tracer correlation factors except when the exchange frequency ratio is close to unity. It is found that the Holdsworth, P. C. and Elliott, R. J. (1986, Phil. Mag. A, 54, 601) kinetics formalism performs much better than Mannings over a wide range of exchange frequency ratios and, for the slow diffuser, is almost exact. The kinetics formalism of Moleko, L. K., Allnatt, A. R., and Allnatt, E. L., (1989, Phil. Mag. A, 59, 141) performs even better, with essentially exact agreement for the slow diffuser, and excellent agreement for the faster diffuser except for extreme values of the exchange frequency ratio.

Collective diffusion in the binary random alloy

Abstract In this study, extensive Monte Carlo simulation results are reported on the collective correlation factors (the correlated parts of the phenomenological coefficients) in the random binary alloy with the monovacancy mechanism operating at a very small vacancy concentration. It is found that results from the analytical formalism of Manning are in excellent agreement with the Monte Carlo results over a very wide range of the ratio of the atom-vacancy exchange frequencies. Surprisingly, it turns out that the expressions for the collective correlation factors derived in the self-consistent theory of Moleko et al. actually simplify to exactly the same expressions as those of Manning for the binary alloy (although in the case of ternary and higher multicomponent random alloys the Moleko et al. formalism provides a different solution from the collective correlation problem).

A theory of diffusion in the ordered alloy I. Tracer correlation effects

Abstract In this study, two and four frequency versions of a model of a long range ordered alloy where the sublattices exist a priori are proposed. This model is a natural extension to the ordered state of the well-known random alloy model. Mannings (1971) formalism for describing tracer correlation effects in the random alloy is adapted and extended to the present model. The model is applicable to any lattice which can be conceived as a combination of two sublattices with the same number of sites and where diffusion requires a vacancy jump from one sublattice to the other. Computer simulation results for the simple cubic lattice from a previous study (Belova, Ivory and Murch 1995) and new ones presented here are used to assess the new analysis. The general trends of the correlation factors across the complete frequency range are described very well. The detailed fit is generally better for the faster moving atomic component.

Diffusion in a model of an ordered alloy

Abstract In this paper a simple model of a stoichiometric ordered alloy is considered. Computer simulation is used to determine the behaviour of the tracer correlation factor and cosines of the angles between consecutive tracer jumps. The asymptotic behaviour of the average of the cosine of the angle between jumps for atoms starting from the ‘wrong’ lattice is derived analytically from consideration of vacancy jump sequences and verified by computer simulation. The efficiency of the six-jump cycle mechanism is also determined. It is clearly shown that this mechanism rapidly becomes dominant as the lattice becomes more ordered.

Reaction of a Ni-coated Al nanoparticle to form B2-NiAl: A molecular dynamics study

The kinetic reaction in a Ni-coated Al nanoparticle with equi-atomic fractions and diameter of approximately 4.5 nm is studied by means of molecular dynamics simulation, using a potential of the embedded atom type to model the interatomic interactions. First, the large driving force for the alloying of Ni and Al initiates solid state amorphization of the nanoparticle with the formation of Ni50Al50 amorphous alloy. Amorphization makes intermixing of the components much easier compared to the crystalline state. The average rate of penetration of Ni atoms can be estimated to be about two times higher than Al atoms, whilst the total rate of inter-penetration can be estimated to be of the order of 10−2 m/s. The heat of the intermixing with the formation of Ni50Al50 amorphous alloy can be estimated at approximately −0.34 eV/at. Next, the crystallization of the Ni50Al50 amorphous alloy into B2-NiAl ordered crystal structure is observed. The heat of the crystallization can be estimated as approximately −0.08 eV/at. Then, the B2-NiAl ordered nanoparticle melts at a temperature of approximately 1500 K. It is shown that, for the alloying reaction in the initial Ni-coated Al nanoparticle, the ignition temperature can be as low as approximately 200 K, while the adiabatic temperature for the reaction is below the melting temperature of the nanoparticle with the B2-NiAl ordered structure.

Shrinking kinetics by vacancy diffusion of a pure element hollow nanosphere

In this paper, shrinking via the vacancy mechanism of a hollow mono-atomic nanosphere is described. Using Gibbs–Thomson boundary conditions, an exact solution is obtained for the kinetic equation in quasi steady-state at the linear approximation. Collapse time as a function of the geometrical size of a hollow nanosphere is found. An extension to hollow binary alloy nanospheres is also made. Previous Monte Carlo simulations of this problem are discussed.

The effective diffusivity in polycrystalline material in the presence of interphase boundaries

The problem of calculating the long-time-limit effective diffusivity in stable two-phase polycrystalline material is addressed for the first time. We make use of a phenomenological model where the high-diffusivity interphase boundaries are treated as connected ‘coatings’ of the individual grains. The derivation of expressions for the effective diffusivity with segregation is along the lines of the analysis by Maxwell in 1904. Monte Carlo computer simulation using lattice-based random walks on a very fine-grained mesh is employed to test the validity of the expressions. It is shown that, for the specific cases analysed, the derived expressions for the effective diffusivity are in very good agreement with results from the simulations. Since the pattern of behaviour is not entirely clear at present, it is difficult to guide the choice for the best expression in a given case. The equivalent of the Hart equation for this problem is also derived. This equation is shown to be invariably in poor agreement with simulation results.

The transition from Harrison type-B to type-A kinetics in grain-boundary tracer diffusion

Abstract This paper is concerned with the lattice and grain boundary diffusivities that can be extracted from the tracer concentration depth profile resulting from diffusion of tracers from a thin film source in the presence of equally spaced parallel boundary slabs. We address this problem by mapping a grid over the phenomenologically conceived system and explore this grid with independent particles using Monte Carlo methods. It is shown that the transition from Harrison type-A kinetics (where the Hart equation provides the effective diffusivity) to Harrison type-B kinetics (where the lattice and grain boundary sections of the depth profile are delineated) occurs at a much smaller diffusion length than previously thought. In addition to the usual model where the mobility of tracers at the (surface) tracer source is matched to the immediate substrate, we also investigated a model which this mobility is made equal to the grain-boundary mobility. Similar behaviour was found.

Behaviour of the diffusion vacancy-wind factors in the concentrated random alloy

Abstract In this paper, the vacancy-wind factors which appear in the well known expressions relating the interdiffusion coefficient and intrinsic diffusion coefficients to the tracer diffusion coefficients are examined in the context of the random alloy model. It is shown by Monte Carlo simulation that the formalism of Moleko et al. provides a much better description of these factors than the well known and commonly used formalism of Manning. Even when the ratio of the tracer diffusion coefficients is relatively close to unity, it is preferable to use the Moleko et al. formalism. The latter formalism is re-expressed in this paper to be suitable for direct experimental use in determining vacancy-wind factors. The limiting behaviour of the ratios of the tracer diffusivities and intrinsic diffusivities is also discussed. In the latter case the ratio is given simply (and generally) by the ratio of the exchange frequencies.