Here, a number of diffusion mechanisms from an atomistic viewpoint are dis­cussed. The simplest picture of diffusion can be visualized through diffusion of interstitial atoms through a lattice. In this mechanism, interstitial atoms move from one interstitial site to another. In the dilute interstitial solid solutions, the probability of finding an interstitial site is very high and close to unity. Note that Figure 2.45a shows a two-dimensional schematic illustration of a monatomic crys­tal with a very few number of impurity atoms that are of much smaller size than the interstitial sites themselves. So the impurity atom can squeeze past through the host lattice atoms to fall into another interstitial site. While it tries to go past the host atoms, repulsive forces would act on the impurity atom and so energy would be needed to surmount the barrier. That energy is supplied by the thermal energy of the interstitial atom. Figure 2.45b shows such an activated state. Following this state, the interstitial atom falls into a new interstitial position completing one jump (Figure 2.45c). If we calculate the energy of an atom as a function of position, we would see that energy is minimum when the impurity atom is at normal position (as shown in Figure 2.45a and b) and the maximum is at the midway between the two positions (i. e., at the activated state). The situation is shown in Figure 2.45d. The amount of this energy barrier is given by the difference between the energy at the activated state and that at the normal state, and is referred to as the activation energy for interstitial diffusion. The real event may consist of a series of such unit atomic jumps. Examples of such interstitial mechanism may comprise diffusion of C inside any allotropic form of iron (alpha iron, gamma iron, or delta iron) or hydrogen diffusion in zirconium, and so on.

Now, let us consider the atomic mechanism by which self-diffusion may occur. In self-diffusion, like atoms exchange lattice positions leaving the lattice identical before and after diffusion. One of the simplest modes of this is the direct exchange mechanism. In this mode, atom X can move to the site of lattice atom Y and at the same time, atom Y moves to the site of atom X (Figure 2.46). But such a direct exchange of atoms is not at all energetically favorable. This may seem implausible even in a very open structure as there are other mechanisms that can actually achieve the same result without expending that much energy. Ring mechanism is one such example. A four-ring mechanism is also depicted in Figure 2.46 (right). As is evident, a greater coordination between atoms is essential for this mechanism to have any consequence. Some evidences suggest that self-diffusion in chromium and sodium may occur by ring mechanism. However, most metals and other engi­neering materials are, in general, too close-packed for that mechanism to occur. That is to say that self-diffusion activation energy associated with direct exchange

and four-ring mechanisms will be always higher than what has commonly been observed such as through vacancy mechanism.

The predominant way by which the self-diffusion or self-substitutional atoms can diffuse is by changing its position with a neighboring vacant site. Figure 2.47a-c shows the different steps involved in substitutional atom diffusion. The same applies to self-diffusion, but for clarity ofthe process, it is shown in terms of substi­tutional atoms. Repetition of this process can result in the transfer of matter over

past two host lattice atoms to the neighboring interstitial site. (c) Configuration of the interstitial atom after diffusion. (d) Energyofan impurity atom as a function of position (E* is the activation barrier).

large atomic distances. This is known as the “vacancy mechanism of diffusion.” There is always an equilibrium number of vacant lattice sites (thermal vacancies) present at any particular temperature and their concentration increases with increasing temperature, as seen in Section 2.2 (Eq. (2.7)). Likewise, self-diffusion also takes place through this mechanism. It is also instructive to note that atom jump can occur into divacancies. However, larger vacancy agglomerates like triva­cancy and quadrivacancy are relatively immobile, and do not take part in general diffusion.

In the interstitialcy mechanism, an atom from a regular lattice site jumps into a neighboring interstitial site that is too small to accommodate it fully. As a result, it displaces another atom from a regular lattice site. Hence, both the atoms share a common site, although displaced from their original lattice sites.

2.3.4