Diffusion atomic movement

Further support for this approach is provided by modern computer studies of molecular dynamics, which show that much smaller translations than the average inter-nuclear distance play an important role in liquid state atom movement. These observations have conhrmed Swalin s approach to liquid state diffusion as being very similar to the calculation of the Brownian motion of suspended particles in a liquid. The classical analysis for this phenomenon was based on the assumption that the resistance to movement of suspended particles in a liquid could be calculated by using the viscosity as the frictional force in the Stokes equation... 

It should be realized that unlike the study of equilibrium thermodynamics for which a model is often mapped onto Ising system, elementary mechanism of atomic motion plays a deterministic role in the kinetic study. In an actual alloy system, diffusion of an atomic species is mainly driven by vacancy mechanism. The incorporation of the vacancy mechanism into PPM formalism, however, is not readily achieved, since the abundant freedom of microscopic path of atomic movement demands intractable number of variational parameters. The present study is, therefore, limited to a simple spin kinetics, known as Glauber dynamics [14] for which flipping events at fixed lattice points drive the phase transition. Hence, the present study for a spin system is regarded as a precursor to an alloy kinetics. The limitation of the model is critically examined and pointed out in the subsequent sections. 

Many metals and metallic alloys show martensitic transformations at temperatures below the melting point. Martensitic transformations are structural phase changes of first order which belong to the broader class of diffusion js solid-state phase transformations. These are structural transformations of the crystal lattice, which do not involve long-range atomic movements. A recent review of the properties and the classification of diffusionless transformations has been given by Delayed... 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

J. Philibert, Atom Movements Diffusion and Mass Transport, translated by S. J. Rothman, Les Editions de Physique, F-91944 Les Ulis, 1991. 

Einstein to describe Brownian motion.5 The model can be used to derive the diffusion equations and to relate the diffusion coefficient to atomic movements. 

Normal diffusion rates and the time elapsed during atomic movements are usually such that reaction would be very fast if there were no intermediate free energy barrier. But in most cases rates are not that fast. We conclude that normally there is a free energy barrier. That is. 

In both gas and cation diffusion, the movement of atoms through solid glasses is often described in terms of the permeability. Pm, which is directly proportional to the... 

J. Bardeen and C. Herring. Diffusion in alloys and the Kirkendall effect. In J.H. Hol-lomon, editor, Atom Movements, pages 87-111. American Society for Metals, Cleveland, OH, 1951. 

At t0, chemical reactions start to proceed simultaneously at both interfaces of the AB layer with initial phases. As a result of those, a row (a plane) of A vacancies and a row (a plane) of B vacancies occur in the AB layer. Between t and h, these move across the AB layer in opposite directions towards its interfaces and then are filled with appropriate atoms from A and B phases. Arrows of different length show the sequence of movement of diffusing atoms. At t2, the system returns to a new initial state, and all the processes are repeated. 

The movement of atoms within a crystal lattice occurs through a diffusion process, which is easiest when atomic vibrations are present at high temperatures. That is, atoms must move from their lattice positions in order to let the diffusing atoms pass. As one would also expect, smaller atoms diffuse more readily than larger ones. If the interstitial atom is identical to the lattice atoms, the occupancy is referred to as selfinterstitial. Empirically, the likelihood of an atom occupying interstitial sites of the... 

Philibert, J. (1991) Atom Movement, Diffusion and Mass Transport in Solids,... 

Atom Movements by Jean Philibert, Les Editions de Physique, Les Ulis Cedex A Prance, 1991. My personal favorite on the subject of diffusion. This book is filled with both descriptive and quantitative accounts of point defects and their motion. 

In this model, the interface is assumed to be rough on the atomic scale, and a sizable fraction of the interface sites are available for growth to take place. Under these circumstances, the rate of growth is solely determined by the rate of atoms jumping across the interface (that is, the assumption is the process is controlled by the surface reaction rate and not diffusion). Using an analysis that is almost identical to the one carried out in Sec. 7.2.3, where the net rate of atom movement down a chemical potential gradient was shown to be [Eq. (7.26)]... 

The freezing of a liquid into a glass requires atomic movement, which occurs by the concentration the free volume into ephemeral voids of the size This process can be regarded as a diffusion of the void away from the interface into the interior, where it becomes trapped as the freezing is completed. Thus within the originally liquid clusters there forms one void of volume somewhat greater than for each = v /ty atoms. 

In the foregoing discussion, every possible atom jump is allowed. This may not be true in real crystals. For example, in the case of vacancy diffusion, no movement is possible if the vacancy population is zero. Equation (7.8) for the number of successful jumps ignores this, and should contain a term pj, that expresses the probability that the jump is possible from a structural point of view ... 

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