Atom jumping isotope effect

In Section 3.1.1, self-diffusion was analyzed by studying the diffusion of radioactive tracer atoms, which were isotopes of the inert host atoms, thereby eliminating any chemical differences. Possible effects of a small difference between the masses of the two species were not considered. However, this difference has been found to have a small effect, which is known as the isotope effect. Differences in atomic masses result in differences of atomic vibrational frequencies, and as a result, the heavier isotope generally diffuses more slowly than the lighter. This effect can—if migration is approximated as a single-particle process—be predicted from the mass differences and Eq. 7.14. If mi and m2 are the atomic masses of two isotopes of the same component, Eqs. 7.13 and 7.52 predict the jump-rate ratio,... 

The diffusion coefficient /), was introduced in eqs. (5-4) and (5-13). From eq.(5-ll) it can be seen that is a measure of the mobility or of the jump frequency of the particles of type L Ever since sufficient quantities of stable or radioactive isotopes for most elements have become available, the so-called tracer method of measuring diffusion coefficients has been widely used. In this method, small quantities of isotope are permitted to diffuse into the system under investigation, and isotopic effects are neglected. In completely homogeneous material, the mean square displacement xf of the tracer atoms is experimentally determined. The following formula then applies [13] ... 

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