Diffusion mechanisms

There are several mechanisms by which diffusion of various elements in a solid material are thought to occur108. These mechanisms include the:

1) Interstitial diffusion mechanism; 2) Vacancy mechanism;

3) Place exchange mechanism; and 4) Ring type mechanism.

4.1.1 Interstitial diffusion

The interstitial mechanism of diffusion arises when an atom passes from its interstitial site to one of its nearest neighbour interstitial sites without any permanent displacement of the matrix atoms108. This is illustrated in Figure 4.1(a). The atom can move to either an interstitial site in the crystal lattice or to a lattice vacancy. Atom 1, which is dislocated, moves towards its nearest neighbours, atoms 2, 3, and 4, and occupies the interstitial site illustrated by the dotted circle. As the atom acquires sufficient energy, the atom may then jump to a neighbouring interstitial site, position 5108. For this to occur, atoms 3 and 4 must deviate from their equilibrium positions, and move in the direction indicated by the arrows. The required amplitude of vibration of these atoms is large, and must exceed half the diameter of the diffusing atom. This required distortion of atoms 3 and 4 constitutes the barrier to an interstitial atom changing sites. Examples of the interstitial mechanism include the diffusion of carbon, nitrogen, hydrogen and boron in iron.

(a) (b) (c)

Figure 4.1 Illustration of (a) the interstitial and vacancy diffusion mechanisms, (b) vacancy formation, leading to the vacancy mechanism of diffusion, and (c) the place exchange diffusion mechanism (from Ref. 108).

Diffusion via the interstitial mechanism may occur during the diffusion of atoms in interstitial solid solutions and phases. For close packed lattices where the small interstitial atom is surrounded by numerous solvent atoms, there is a high probability that the vibrations of the solvent atoms will have a large amplitude. Consequently, there is a high probability that the large interatomic spacings necessary for the movement of the interstitial atoms will be generated. However, this probability decreases sharply with increasing atomic diameters due to only those atomic vibrations with an amplitude to create a gap sufficient for the passage of the diffusing atom being significant. The activation energy of diffusion also increases with increasing atom size108.

This indicates that the same diffusion mechanism operates for carbon, nitrogen, hydrogen and boron where they form interstitial solid solutions, and their atoms diffuse along the interstices in the lattice. An increase in the solute atom diameter increases the distortions in the iron lattice produced when the diffusing atom jumps into the neighbouring empty interstitial sites. This greater deformation requires a larger activation energy, with the magnitude of the activation energy rising sharply as the diameter of the diffusing atoms approaches that of the solvent atoms.

4.1.2 Vacancy mechanism

Vacancy formation arises from the thermal motion of the atoms in the lattice. The vacancy mechanism of diffusion involves an atom on a site adjacent to a vacancy jumping into the vacancy110, Figure 4.1(b). Atom 1 in Figure 4.1(b) acquires sufficiently more energy than its neighbours, with the bonds between atoms 1 and 2 being broken, and atom 1 leaving the surface row of atoms to occupy position 1’108

. Thus, a vacancy appears at the site previously occupied by atom 1. Since the bond between atom 1 and 5 is unbroken, little energy is required for the vacancy to form as not all the bonds between atom 1 and its neighbours are broken. Vacancies also appear together with dislocated atoms, Figure 4.1(a). Consequently, the vacancy mechanism of diffusion is plausible, and has been established as the predominant mechanism in many metals and ionic compounds.

The energy required to move an iron atom into an adjacent vacancy is approximately equivalent to the energy required to move a carbon atom from one interstitial site to another in the same face centred cubic phase. However, iron diffuses much more slowly than carbon due to each carbon atom having several vacant nearest-neighbour sites, while the fraction of vacant iron sites is very small. Each iron atom must therefore wait an appreciable period before a vacancy becomes available. The possible cause of vacancy movement is as follows. In close packed metals and alloys, vacancies are surrounded by 8 or 12 atoms. Due to the random thermal vibrations, there is a high probability that any one of these atoms will acquire sufficient energy to leave its position in the lattice, and occupy a vacant site. Consequently, a vacancy will be on the former site of this atom, with the vacancy travelling in jumps through the crystal.

For iron at 1000°C, the period of time for which the vacancies occupies a specific site is very small, as they change places with lattice atoms 104 to 108 times a second108. If no concentration or stress gradients exist in the crystal, there is no preferred direction for vacancy movement. During a relatively long period of time, each vacancy changes place on average with the same amount of atoms in all directions in the crystal.

Real metals involve the formation and movement of a large number of vacancies in the lattice. In certain instances, vacancies may exhibit a preferred orientation in their motion, resulting in mass

concept of vacancy diffusion, where the formation and movement of vacancies is strongly dependent on the temperature110,111. An increased temperature raises the atomic mobility in metals and alloys, while the vacancy concentration also increases. Therefore, the heating of metals and alloys results in a simultaneous increase in the number of vacancies, and in their rate of position exchange with atoms, causing a sharp increase in the mobility of atoms.

4.1.3 Place exchange mechanism

The place exchange mechanism involves two atoms simultaneously leaving their equilibrium lattice positions, and exchanging places112, Figure 4.1(c). For the place exchange mechanism to be possible, atoms A and B must simultaneously acquire sufficient energy for the deformation of the crystal lattice, and for the considerable compression of the atoms. The energy required for the atoms to move from one site to another is called the activation energy of diffusion. However, this mechanism fails to explain the diffusion in metals with close packed atomic structures113.

4.1.4 Ring type mechanism

The ring type or annular mechanism is a further development of the place exchange mechanism. From energy considerations, it is more favourable for atoms to change positions within a group of atoms. Zener114 showed that the minimum energy is required for the rotation of a ring consisting of four atoms, Figure 4.2(a). The lattice deformations produced are small, due to the atom movement occurring upon the rotation of the whole group of atoms. Such a rotation eliminates the counter movement of closely located atoms. Figures 4.2(b) and (c) show rings of four atoms for face centred cubic and body centred cubic atoms respectively. Various researchers attribute diffusion in body centred cubic metals and alloys which have close packed atomic structures to the annular diffusion mechanism.