Papers by Keyword: Correlation Factors

Abstract: In crystalline solids, during such processes as chemical interdiffusion in alloys, ionic conductivity and the annealing out of radiation damage there will inevitably be a net flux of vacancies. In most cases, when different species of atoms have different jump rates with vacancies within a net flux of vacancies, the phenomenon of the vacancy-wind effect will occur. This effect was first discovered in the 1960s by the late Dr John Manning. It is a subtle phenomenon that comes about because of the local redistribution of the equilibrium concentration of vacancies with respect to two or more species of drifting atoms in a driving force. The effect is captured in various ‘vacancy-wind factors’ (some of which are now sometimes called Manning factors) which formally arise from non-zero off-diagonal Onsager phenomenological transport coefficients and non-unity values of the tracer correlation factors. In this paper, the effect is reviewed and discussed.

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: Net fluxes of vacancies commonly occur during chemical interdiffusion in alloys, ionic conductivity and the annealing out of radiation damage. When atoms with different jump rates diffuse in a net flux of vacancies the phenomenon of the vacancy-wind effect will occur. This effect, first discovered by the late Dr John Manning, is a subtle phenomenon arising from a disturbed distribution of vacancies with respect to a given moving atom or species of atom. In this paper, the vacancy-wind effect is discussed and its visualization, performed for the first time by computer simulation, is demonstrated.

Abstract: The non-random interaction of vacancies with atoms during interdiffusion and ionic conductivity is referred to as the vacancy-wind effect. This effect, first discovered by the late Dr John Manning, is a subtle phenomenon arising from the non-random distribution of vacancies with respect to a given moving atom within a net flux of vacancies. Recently, a good deal of progress has been made in determining accurate expressions for vacancy-wind factors in binary and ternary alloys, and in mixed cation ionic systems. The present paper provides an overview of these recent findings and puts them into a broader and historical context.

Abstract: The six-jump-cycle (6JC) diffusion mechanism is used to analyze the behavior of vacancy-wind factors and collective correlation factors in partially ordered B2 intermetallic compounds at stoichiometric and near- stoichiometric compositions. Expressions for the vacancywind factors are obtained in the framework of the four-frequency model where the two sublattices exist a priori. The phenomenological coefficients on the two sublattices that remain hitherto independent in 6JC mechanism are connected through a microscopic detailed balance condition. The present results for collective correlation factors when compared with our earlier calculation based on taking the harmonic mean of the sublattice correlation factors show much better agreement with Monte Carlo simulation results. The collective correlation factors and tracer correlation factors are used to calculate the vacancy-wind factors. Our results for vacancy-wind factors agree qualitatively with the simulation data when the frequency ratio ( α ) of structural and antistructural atoms jumps decreases up to the order of unity.

Abstract: The six-jump-cycle (6JC) mechanism is used to derive expressions for collective correlation factors in a nonstoichiometric binary intermetallic compound AB. The 6JC is used as a fundamental unit for the cycle involving a perfectly ordered configuration and a two-jumpcycle (2JC) as a fundamental unit for the cycle involving existing antistructural atoms. The jump frequency for the 6JC is calculated in terms of a four-frequency-model using the mean first passage concept of Arita et al., while the jump frequency for the 2JC is taken to be the harmonic mean of the individual jump frequencies. The expressions for phenomenological transport coefficients are obtained through the linear response approximation using the kinetic equation approach. The results for collective correlation factors are compared with Monte Carlo simulation and are found to be in reasonably good agreement when the ratio of jump frequencies of regular site and antistructural atoms is of the order of 10-1.

Abstract: Tracer di f fusion by way of vacancies is invest igated in B2 intermetal l ics AB by means of a kinet ic equat ion approach. The model used is one wi th four inter sub-lat t ice frequencies where each sub-lat t ice is t reated as a random al loy. Coupl ing is achieved between the two types of cycles, i .e. , wi th the vacancy start ing on one sub- lat t ice and finishing on ei ther sub-lat t ice and wi th a vacancy start ing on the other sub-lat t ice and finishing on ei ther sub-lat t ice. An expression for the t racer cor relat ion factor is derived in terms of atom vacancy exchange frequencies and atomic concentrat ions. Resul ts from this expression are compared wi th Monte Car lo calculat ions and also resul ts f rom a previous Manning-type random al loy approach to the problem.

Abstract: Tracer diffusion in non-stoichiometric B2 intermetallic compounds having antistructural disorder is investigated using the six-jump-cycle (6JC) as a fundamental diffusion unit. For non-stoichiometric compositions, the antistructural atoms are assumed to be isolated and located at one of the six [110]-type and [100]-type sites (as only these sites are involved in the 6JC or 2JC). The jump frequencies for the 6JC involving a perfectly ordered configuration are calculated in terms of a four-frequency-model, using the meanfirst- passage concept of Arita et al. The jump frequency of an antistructural atom at [110] or [100]-type sites is taken to be the harmonic mean of frequencies of two successive nearestneighbour jumps of the same kind of atoms. The expressions for the tracer diffusion coefficients are derived for both atomic components at deviations from stoichiometry, assuming that the 6JC mechanism is valid. The results are compared with Monte Carlo simulations based on single vacancy jumps and found to be in fair agreement for compositions close to stoichiometry.