Atomic jumps

Physically, diffusion occurs because atoms, even in a solid, are able to move - to jump from one atomic site to another. Figure 18.4 shows a solid in which there is a concentration gradient of black atoms there are more to the left of the broken line than there are to the right. If atoms jump across the broken line at random, then there will be a net flux of black atoms to the right (simply because there are more on the left to jump), and, of course, a net flux of white atoms to the left. Pick s Law describes this. It is derived in the following way. 

But, meanwhile, some zinc atoms jump back. If the number of zinc atoms in layer B is Ug, the number of zinc atoms that can climb over the barrier from B to A per second is... 

Diffusion in the bulk of a crystal can occur by two mechanisms. The first is interstitial diffusion. Atoms in all crystals have spaces, or interstices, between them, and small atoms dissolved in the crystal can diffuse around by squeezing between atoms, jumping - when they have enough energy - from one interstice to another (Fig. 18.6). Carbon, a small atom, diffuses through steel in this way in fact C, O, N, B and H diffuse interstitially in most crystals. These small atoms diffuse very quickly. This is reflected in their exceptionally small values of Q/RTm, seen in the last column of Table 18.1. 

Polymers are a little more complicated. The drop in modulus (like the increase in creep rate) is caused by the increased ease with which molecules can slip past each other. In metals, which have a crystal structure, this reflects the increasing number of vacancies and the increased rate at which atoms jump into them. In polymers, which are amorphous, it reflects the increase in free volume which gives an increase in the rate of reptation. Then the shift factor is given, not by eqn. (23.11) but by... 

Some evolution types observed in our simulations are shown in Figs. 2-7. The simulations were performed for the same 2D alloy model as that used in Refs. , on a square lattice of 128x128 sites with periodic boundary conditions. The as-quenched distribution Ci(0) was characterized by its mean value c and small random fluctuations Sci = 0.01. The intersite atomic jumps were supposed to occur only between nearest neighbors and we used the reduced time variable t = <7,m-... 

Figure 5. Arrhenius-plot of three relaxation times involved in total ordering process. ( ) Xi, ( ) X2, atomic jump processes within domains (o) xj, change in domain size.

Atomic jump processes studied by order-order relaxation experiments, Acta Mater. 44 1573 (1996). 

Changes in the atomic correlations are enabled by atomic jumps between neighbouring lattice sites. In metals and their substitutional solutions point defects are responsible for these diffusion processes. Ordering kinetics can therefore yield information about properties of the point defects which are involved in the ordering process. 

Carlo-simulations for LI2 superlattice including saddle-point energies for atomic jumps in fact yielded two-process kinetics with the ratio of the two relaxation times being correlated with the difference between the activation barriers of the two sorts of atom. 

It should be emphasized here that usual tracer diffusion experiments in LI2 ordered alloys due to diffusion of majority atoms mainly over their own sublattice do not give any of the strongly desired information about ordering kinetics. The study of order-order relaxations in contrast, yields a selective information Just about those atomic Jump processes which are related to ordering phenomena. 

Electric current is conducted either by these excited electrons in the conduction band or by holes remaining in place of excited electrons in the original valence energy band. These holes have a positive effective charge. If an electron from a neighbouring atom jumps over into a free site (hole), then this process is equivalent to movement of the hole in the opposite direction. In the valence band, the electric current is thus conducted by these positive charge carriers. Semiconductors are divided into intrinsic semiconductors, where electrons are thermally excited to the conduction band, and semiconductors with intentionally introduced impurities, called doped semiconductors, where the traces of impurities account for most of the conductivity. 

The aim of many of the studies of diffusion is to relate the measured diffusion coefficient to a mechanism of diffusion. By this is meant a model of atomic jumps that accurately reproduces the diffusion coefficient and the measured concentration profile over a wide range of temperatures. This objective has been most pronounced... 

The high conductivity of (3-alumina is attributed to the correlated diffusion of pairs of ions in the conduction plane. The sodium excess is accommodated by the displacement of pairs of ions onto mO sites, and these can be considered to be associated defects consisting of pairs of Na+ ions on mO sites plus a V N l on a BR site (Fig. 6.12a and 6.12b). A series of atom jumps will then allow the defect to reorient and diffuse through the crystal (Fig. 6.12c and 6.12d). Calculations suggest that this diffusion mechanism has a low activation energy, which would lead to high Na+ ion conductivity. A similar, but not identical, mechanism can be described for (3"-alumina. 

Notice that, in this context, difiusion-less means no random-walk mixing of atoms or atom-by-atom jumping across the interface during the structural change the... 

A more interesting problem is that the Metropolis Monte Carlo studies used a different (physically simplified) kinetic rate law for atomic motion than the KMC work. That is, the rules governing the rate at which atoms jump from one configuration to the next were fundamentally different. This can have serious implications for such dynamic phenomena as step fluctuations, adatom mobility, etc. In this paper, we describe the physical differences between the rate laws used in the previous work, and then present results using just one of the simulation techniques, namely KMC, but comparing both kinds of rate laws. 

This rate law corresponds to an atom jumping out of a potential well by completely breaking i lateral bonds. The transition rate is independent of the energy of the final configuration, i.e, contains no information about the site to which the atom hops, see Figure 1(a). One sets... 

To be able to observe directly each atomic jump of the atomic... 

Fig. 4.7 (a) Atomically resolved (1 x l)Pt surface prepared by low temperature field evaporation. (b) and (c) show how atoms jump by pulsed-Iaser heating of the surface to —350 K for 5 ns. Atoms in a small [110] atomic row tend to jump together, or in a highly correlated way. 

Vq is the frequency of the small oscillation, and AG and AS are, respectively, the difference in Gibbs free energy and entropy of the adatom at the saddle point and the equilibrium adsorption site. Ed is the activation energy of surface diffusion, or the barrier height of the atomic jumps. 

Consider now a one-dimensional lattice of parameter /. The distance of each atomic jump depends on the rate of de-excitation once the adatom is excited and is translating along the lattice. This de-excitation process can be described by a characteristic life time r in the symmetric random walk, as in many other solid state excitation phenomena. The initial position of the adatom is taken to be the origin, denoted by an index 0. The adatom accomplishes a jump of distance il if it is de-excited within (i — i)l and (i + i)l, where / is the lattice parameter, or the nearest neighbor distance of the one-dimensional lattice, and i is an integer. The probability of reaching a distance il in one jump is given by... 

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