Arrhenius-Plot

Many thermally excited reactions are described by
y =  y0 exp – Ea
kT
With Ea = activation energy (or enthalpy) of the process, and kT with its usual meaning.
This equation governs not only the equilibrium concentration of point defects, but also, for example, the emission of electrons from a hot wire or the growth of bacterial cultures.
An Arrhenius plot of this equation is simply a plot of log y (or ln y) over 1/T (or 1/kT). This produces a straight line:
ln y  =  ln y0  –   Ea
kB
·  1
T
The (extrapolated) cut with the ln y-axis gives directly the value of the pre-exponential factor y0, and the slope of the straight line gives the activation energy.
An Arrhenius plot is extremely useful if data are determined experimentally. It shows at a glance if the scatter of the data points is small or large, if we have an Arrhenius relation at all (i.e. a straight line), and if we have enough data points to get unambigous values for the activation energy and the pre-exponential factor.

In the following Java module, you can play a bit with the representations of the exponential law.
Shown is the function
cV = c0 · exp   –   HF
kB
in a direct plot and in an Arrhenius plot. You can change the values of the parameters and see what happens.

2.1.1 Simple Vacancies and Interstitials

2.2.1 Extrinsic Point Defects and Agglomerates

3.2.2 Self-Diffusion

Table of JAVA-Applets "Defects in Crystals"

© H. Föll (Defects - Script)