3.2.4 Temperature Dependence of Diffusivity

Now, equation (3.9) can further be modified by replacing the jump frequency, Γ , which, by Boltzman statistics, is defined as

	(3.10)

where ν is the vibration frequency in s^-1, ΔG^* is the activation energy of migration in J and k is Boltzmann Constant (J/K).

Further, ΔG^* can be written as

	(3.11)

where ΔH^* is the enthalpy of migration and ΔS^* is the associated entropy change. Now, substitution of equation (3.10) in equation (3.11) leads to

	OR

or

where pre-exponential factor .

Equation (3.12) explains the thermally activated nature of diffusivity showing an exponential temperature dependence resulting in significant increase in the diffusivity upon increasing the temperature.