Papers by Author: Graeme E. Murch

Abstract: Molybdenum disilicide (MoSi₂) is an interesting material for high-temperature applications. It has a high melting temperature, good thermal and electrical conductivity and an excellent oxidation resistance. For many years the primary use of MoSi₂ has been in heating elements, which can be used for temperatures up to 1800°C. Since the 1990s the potential of MoSi₂ as a high-temperature structural material has been recognized as well. Its brittleness at lower temperatures and a poor creep resistance above 1200°C have hindered its use as in load-bearing parts. These disadvantages may be offset at least partly by using it together with a second material in a composite or an alloy. Projected applications of MoSi₂-based materials include, e.g. stationary hot section components in gas turbine engines and glow plugs in diesel engines. For future research and development directions of MoSi₂-based composites diffusion is a crucial property because creep is closely connected with diffusion. This paper is devoted to the basic diffusion and defect properties of MoSi₂. Data of Si and Mo as well as Ge diffusion from the Münster laboratory for both principal directions are briefly summarized. For all three kinds of atoms diffusion perpendicular to the tetragonal axis is faster than parallel to it. The diffusivities of Mo in both directions are many orders of magnitude slower than those of Si and Ge. The huge asymmetry between Mo and Si (or Ge) diffusion suggests that atomic motion of each constituent is restricted to its own sublattice. Positron annihilation studies on MoSi₂ from the Stuttgart laboratory are reviewed as well. They show that formation of thermal vacancies occurs primarily on the Si sublattice but cannot exclude vacancy formation on the Mo sublattice at higher temperatures. Correlation factors for Si and Mo diffusion via sublattice vacancies in the respective sublattices of MoSi₂ have been calculated recently mainly by Monte Carlo simulation techniques and are also briefly described. Diffusion, in particular self-diffusion, is discussed in connection with literature data on high-temperature creep, which is diffusion-controlled. Grain-size effects of creep have been reported and can be attributed to Nabarro-Herring and Coble creep. Power-law creep is attributed to diffusion-controlled dislocation creep. Some details are, however, not completely understood, presumably due to a lack of theoretical concepts for creep in uniaxial, stochiometric compounds and due to missing information on grain-boundary diffusion.

Abstract: The location of the transition points for the three main Harrison’s kinetics regimes (Type-A, B and C) for the measurement of grain boundary diffusivities from tracer concentration depth profiles (self-diffusion) has been extensively studied in (Divinski et al. Zeit. Metallk, 2002, Belova and Murch, Phil. Mag, 2001, 2009; Defect and Diffusion Forum, 2006, 2008, 2009) by making use of the phenomenological Lattice Monte Carlo numerical method. Those locations are mainly dependent on the dimensionality of the problem. For the case of impurity grain boundary diffusion, the segregation effect is very important. In the present study, the influence of segregation on the transition points is investigated for the parallel slab model (2-dimensional) of the grain boundary diffusion problem by making use of the tracer-type solution to the equivalent diffusion problem. It is shown that the Type-B regime is most likely not realized for the cases of fine-grain material with a strong segregation effect present.

Abstract: This work addresses the numerical analysis of anisotropic composite structures for thermal energy storage and temperature stabilization. The basic idea of heat sink composites is the combination of metallic matrices for fast energy transfer with phase change materials for thermal energy storage. Anisotropic matrices, such as lotus-type structures, allow for increased control of the thermal energy flow, without the necessity of additional thermal insulation. As an example, thermal energy can be directed towards a surface cooled by convection and excess energy is stored in the phase-change material. Computed tomography data of copper lotus-type material is used for the generation of the numerical calculation models. Due to its particular meso-structure, this material is characterised by strongly anisotropic properties. The void space of this cellular metal is filled with the phase-change material paraffin in order to enhance the energy storage capacity. A recently extended Lattice Monte Carlo method is used to evaluate the anisotropic thermal properties of these promising materials.

Abstract: The Lattice Monte Carlo (LMC) method recently developed by the authors is an unusually powerful and flexible method in which a given phenomenological thermal or mass transport problem is mapped onto a fine-grained lattice which is then analyzed with discrete random walk methods. We provide an overview of the LMC method. For mass diffusion we highlight the addressing of diffusion with reversible reaction. For thermal transport we highlight a calculation of the effective thermal conductivity of sintered hollow sphere structures making use of CT scans of actual material as well as the determination of temperature profiles in phase-change composites.

Abstract: Recently, the transition point between the Harrison Type-A and Type-B kinetics regimes as well as the emerging intermediate AB transition regime have been analysed in detail by making use of Lattice Monte Carlo (LMC) simulations of tracer depth concentration profiles as a function of diffusion time and distance between grain boundaries e.g. [1-3]. In the present study, we analyse Harrison Type-B to Type-C kinetics regimes in the transient grain boundary diffusion problem using the parallel slabs model and LMC numerical simulation. The transition point where the Harrison Type-B kinetics regime last occurs (transition point between the Harrison Type-B kinetics and the Type-BC kinetics) is estimated at  (= 0.5δ(Dlt)-1/2) = 0.1. The Harrison Type-C grain boundary diffusion kinetics regime is also analysed using LMC simulated concentration depth profiles. The transition point where the Harrison Type-C kinetics regime first occurs (transition point between the Type-BC kinetics and the Harrison Type-C kinetics) is estimated at  = 5.0. Therefore an intermediate Type-BC regime can be expected to occur between 0.1 <  < 5.0. Preliminary results for the cubic grain model show that the interval for the intermediate Type-BC regime is somewhat narrower for this model and occurs at 0.5 <  < 5.0.

Abstract: First discovered by the late Dr John Manning, the vacancy-wind effect is a subtle phenomenon that occurs when two or more atomic species compete for vacancies in a net vacancy flux. The vacancy-wind effect is incorporated in (for example) the vacancy-wind or Manning factor that appears in the Darken-Manning Equation relating the interdiffusivity, the tracer diffusivities and the thermodynamic factor. The mechanism of the vacancy-wind phenomenon has long been very poorly understood. Recently, a moving reference frame Monte Carlo method was used to illustrate graphically how the vacancy-wind effect operates in both ionic conductivity in an ionic solid with a dilute solute and chemical interdiffusion in concentrated alloys and ionic compounds. That strategy is extended in this paper to show graphically how the vacancy-wind effect operates in interdiffusion in a stoichiometric intermetallic taking the B2 structure. A simple 4-frequency vacancy diffusion model is used. In previous work, it was shown that depending on composition and temperature, this model can exhibit the six-jump-cycle mechanism. It is shown that in the limit of perfect order that there is no vacancy-wind effect associated with this mechanism when both types of cycle operate equally (zero net vacancy flux). The non-unity value of the vacancy-wind factor found for this mechanism under zero vacancy flux conditions is purely a consequence of a particular geometric mix of tracer and collective atom displacements. The concept that a non-zero off-diagonal phenomenological coefficient provides the vacancy-wind effect is verified.

Abstract: Heat sinks enable the storage of energy that would otherwise be lost, thus ensuring significant energy-savings and fewer greenhouse gas emissions. Heat sinks also play the major role in the efficient temperature control of devices such as batteries. In principle, any material can act as a heat sink – traditionally, copper is used for many applications. However, copper is relatively expensive, has a high density and only a limited energy storage capacity. In contrast, a phase-change material (PCM) allows in effect an additional storage of energy through its phase change thus greatly increasing the achievable energy density. The aim of this work is the numerical analysis of the transient heat transfer in composite heat sinks containing phase-change materials. For the first time, a recently formulated Lattice Monte Carlo Method is applied to determine temperature distributions and the amount of energy transferred versus time in phase change materials.

Abstract: Recently, there has been a great deal of interest in the properties of hollow nanoparticles for use in advanced technologies. The diffusion phenomenon known as the Kirkendall effect features in one of the important experimental methods of synthesis of hollow binary nanoparticles. Diffusion naturally features prominently in shrinkage mechanisms of hollow nanoparticles. In this paper, we summarize the progress made so far in understanding the formation and shrinkage by diffusion processes of hollow nanoparticles and their apparent stability.

Abstract: Results of kinetic Monte Carlo simulation of the formation of a hollow nanosphere by interdiffusion from a core-shell binary system are presented for the first time. The faster diffusing species is located in the core whilst the slower diffusing species form the shell. With its self-generated vacancy composition all stages of the hollow sphere formation process are observed in our model: interdiffusion, the supersaturation of the core of the nanosphere by vacancies, precipitation of pores and eventual void formation. Results of this simulation confirm the experimental conclusions that interdiffusion accompanied by the Kirkendall effect and Kirkendall porosity is one of the mechanisms responsible for the formation of hollow nano-objects.

Abstract: In this paper, a hollow random binary alloy nanosphere and initially homogeneous is considered under the approximation that the radial dependence of the vacancy formation free energy can be neglected. On the basis of a theoretical description and kinetic Monte Carlo simulations it is shown that the steady-state condition for the atomic components is not achievable during its shrinkage at any composition when the ratio of the tracer diffusion coefficients is not greater than two orders of magnitude. In the theoretical description, the dependence of the collapse time of the hollow random binary alloy nanosphere on the atomic fraction of the faster diffusing species at can be estimated by using the geometric mean of the ratios of the atomic fluxes at self-diffusion and steady-state. At the ratio of the atomic fluxes approaches the self-diffusion ratio as increases.