THE DUSHMAN AND LANGMUIR RELATION. In 1922 Dushman and Langmuir1 proposed a relation for dif- fusion in metallic systems. They derived the relation.
Chapter 2
Empirical and Semi-Empirical Diffusion Relations Many empirical relations between the diffusion parameters Q and Do and other physical properties of materials have been proposed during the past 30 to 40 years. In general the relations are of two types: (a) those derived without any consideration of diffusion mechanism, and (b) those derived on the basis of some assumed mechanism. The purpose here is to present the more important relations and to discuss their usefulness in estimating the diffusion parameters Do and Q for systems for which experimental data are not yet available. 1.
THE DUSHMAN AND LANGMUIR RELATION In 1922 Dushman and Langmuir 1 proposed a relation for dif-
fusion in metallic systems. They derived the relation D == Qa 2 exp (-Q/RT) Nh where a is the lattice constant, N is Avogadro's number, and h is 1S. Dushman and 1. Langmuir, Phys.. Rev •• 20:113 (1922).
where a is measured in A (1 x 10-s cm) and Q is measured in kcal/mole. The values of Do vary over the fairly narrow limits of 0.2 to 0.9 cm2/sec for the various elements. However, the equation is useful since it permits values of Do and Q to be calculated from one experimental measurement of the diffusion coefficient at one temperature. If we assume a typical value of Do of 0.5 cm2/ sec, this is essentially the same as calculating Q from Q =-RTln2D
(2.2)
where Q is the activation energy in cal/mole, R is the gas constant (1.98 cal/mole • deg) , T is the temperature in degrees Kelvin, and D is the diffusion coefficient in cm2/ sec. Equations (2.1) and (2.2) are in good agreement with selfdiffusion data in pure metals (except for the "anomalous" b.c.c. metals) and for much of the impurity and alloy data. 2.
SIMPLE EMPIRICAL CORRELATIONS
BETWEEN THE SELF-DIFFUSION
.
AC TIVA TION E NERG Y AND VARIOUS PHYSICAL PROPERTIES OF METALS A number of empirical correlations have been suggested between the self-diffusion activation energy Q and various physical properties of materials such as melting point, heats of fusion and vaporization, and elastic moduli since all of these and atomic diffusion in solids depend on the binding forces between atoms. In such correlations the self -diffusion activation energy Q is related to the physical property P by a relation of the form
Q =AP
or
Q =B/P
(2.3)
where A and B are proportionality constants. Some of these correlations are very useful in predicting values of the self -diffusion activation energy with a fair degree of accuracy. However, care must be taken in attempting to give the correlation any type of fundamental interpretation.
