Atomic movement during diffusion

We can gain an estimate of the probability that an atom will successfully move by using Maxwell-Boltzmann statistics. The probability, p, that a single atom will move from one position of minimum energy to an adjacent position will be given by the equation  

The atoms in a crystal are vibrating continually with a frequency, v, which is usually taken to have a value of about lO Hz at room temperature. It is reasonable to suppose that the number of attempts at a jump, sometimes called the attempt frequency, will be equal to the frequency with which the atom is vibrating. The number of successful jumps that an atom will make per second, F, will be equal to the attempt frequency, v, multiplied by the probability of a successful move, that is. 

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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. 

Crack-tip growth mechanisms have been proposed that do not involve dislocation movement explicitly, but rather, in response to the stress field at the crack tip, interstitial atoms diffuse to the region of the stress field to reduce the stress substitutional atoms also will diffuse to the tip if the local stress is thereby reduced. Crack-tip growth would be increased if this local change in alloy composition enhances dissolution during slip displacement or alters the passive film such that it is more easily ruptured by dislocations emerging to the surface. That is, there is continuously produced at the crack tip a film that is more easily ruptured than the more stable passive film on the sides of the crack (Ref 158). 

During volume diffusion, an individual atom jumps from one stable position to another. If vacancies are present (Figure 7.9) atoms or ions can jump from a normal site into a neighbouring 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. This process is therefore firequently referred to as vacancy diffusion. In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus... 

This approach that links atom movement to pressure differences has the benefit of directly describing the diffusive deformation of dense polycrystalline materials caused by an applied stress (creep). Sintering rate equations for ceramics have been developed according to the assumption that behaviour caused by pressure differences during sintering is similar to diffusion creep behaviour. The rate of deformation caused by an applied stress is given by the general equation ... 

The mobility or diffusion of die atoms over the surface of die substrate, and over the film during its formation, will occur more rapidly as the temperature increases since epitaxy can be achieved, under condition of ctystallographic similarity between die film and the subsuate, when the substrate temperamre is increased. It was found experimentally that surface diffusion has a closer relationship to an activation-dependent process than to the movement of atoms in gases, and the temperamre dependence of the diffusion of gases. For surface diffusion the variation of the diffusion coefficient widr temperature is expressed by the Anhenius equation... 

The behavior of such a large system as a pore formed by a bacterial porine (E. coli OmpF) has been simulated in a lipid bilayer of palmitoyloleoylphosphatidylethanola-mine (POPE) [95]. Despite the use of united atoms, the final system of the trimeric porin embedded into 318 POPE molecules and solvated with water consisted of more than 65 000 atoms in total. During the 1 ns of the MD simulation the trimeric structure remained stable, with almost all flexibility in the loops and turns outside the 3-strands. The movement and orientation of the water molecules was investigated in detail. As found in case of the pore formed by the hexameric LS3 helix bundle [90], the diffusion of the water was decreased to about 10% of that of bulk water. Some ordering of the water molecules was evident from the average water dipole moments, which showed a strong dependence on the vertical position within the porine. 

As we have seen, the macroscopic treatment of diffusion using Pick s first and second laws makes no distinction about whether the diffusion process occurs in a solid, liquid, or gaseous medium. In general, these macroscopic laws apply fairly well to all three phases. The differences between solid-, liquid-, and gas-phase diffusion mostly show up in the magnitude of the diffusion coefficient Z),. This parameter quantifies the relative ease with which atoms or molecules can be transported via diffusion in a material. Because diffusion occurs by a series of discrete random movements, for example, as a species jumps from lattice site to lattice site in a solid, or veers from one collision event to another collision event in a liquid or gas, both the speed (y,) at which a species moves and the average distance traveled during each movement (A) are embedded in the diffusion coefficient. In a gas or liquid, this dependence is often expressed as... 

If the diffusivity (or the temperature) is raised even further, the speed of the dissolved atoms is so high that they simply accompany the dislocation during its movement. In this case, there is neither an apparent yield point nor serrated flow. 

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