• PDF / 487,434 Bytes
• 9 Pages / 593.972 x 792 pts Page_size
• 96 Downloads / 227 Views

DOWNLOAD

REPORT

---

ON

IT is generally accepted that the discovery of the Kirkendall effect constitutes an inviolable evidence for the operation of the vacancy mechanism as the predominant mode of substitutional diffusion in crystalline solids.[1] The vacancy mechanism involves the interchange of atomic sites in a crystal lattice between an atom and a vacancy, e.g., Figure 1. Historically, Huntington and Seitz[2] and Huntington[3] calculated the activation energies for self-diffusion in pure copper via (1) direct exchange of atomic sites between two neighboring atoms, (2) migration of atoms from one interstitial site to another, and (3) the vacancy mechanism. Among these, the vacancy mechanism was energetically most favored. However, Zener[4] later argued that energy involved in atomic exchange between two nearest neighboring atoms in the absence of a vacancy could be significantly lowered if the rotational movement in an atomic ring consisting of 3, 4, or more atoms is considered as an alternative to the direct exchange between two atoms that can be thought of as ring diffusion involving only two atoms. Zener[4] showed that the energy for exchange of atomic sites decreases with the increase in the number of atoms associated with ring diffusion. The difficulty was that the precision of calculation was not sufficient to choose between the vacancy mechanism and multiatom ring diffusion process. The discovery of the Kirkendall effect changed this scenario completely.[5–7] Phenomenologically, as discussed subsequently, the process of ring diffusion is incompatible with the Kirkendall effect.[1] Hence, the observation of the Kirkendall effect helped to establish the vacancy mechanism as the predominant mechanism G.P. TIWARI, Professor, is with the Ramrao Adik Institute of Technology, Vidyanagari, Nerul, Navi Mumbai 400709, India. Contact e-mail: [email protected] R.S. MEHROTRA, Consultant, is with the Rohini CHS, Sector 9A, Vashi, Navi Mumbai 400703, India. Manuscript submitted September 22, 2011. Article published online May 9, 2012 3654—VOLUME 43A, OCTOBER 2012

for self-diffusion as well as substitutional solute diffusion in metallic systems. The object of the current study is to discuss the incidence of the Kirkendall effect in B2 intermetallic compounds and its implication for the mechanism of self-diffusion in these systems.

II.

DIFFUSION IN SOLIDS: BASIC CONSIDERATIONS

The edifice of modern theory of diffusion in crystalline solids[8,9] rests on following two axioms: (a) Einstein-Smoluchowski relation based on random walk: Einstein-Smoluchowski expression for diffusion coefficient D is

2 X ½1 D¼ 2s

 where X2 is the mean square displacement averaged over the ensemble of diffusing particles and s represents the time period of diffusion. This equation is based on random walk, implying no correlation between two successive jumps of the diffusing particle. In general, Eq. [1] forms the basis of all the expressions for diffusion coefficients in solids. (b) Substitutional diffusion in crystalline solids is mediated through vacancies. Equation [1] is a