Keating Method (First-Order, s=s(T))

Keating has proposed a method to determine E, for the first-order, when s is supposed to be temperature dependent [1].

The equation giving the TL intensity, when the frequency factor is temperature dependent, is the following:

(1)

Putting n _o s _o= I _o and making the logarithm of Eq.(1), one gets

(2)

Differentiation of this equation with respect to T, and setting the derivative at the maximum equal to zero, yields

from which

(3)

Remembering that the integral in Eq.(1) can be evaluated by an asymptotic series, in this case we have

(4)

with

Thus, Eq.(2) becomes

(5)

Inserting in Eq.(5) the expression (3), we get

(6)

Using now the temperature T ₁ and T ₂ when I=I _M/2, the following parameters are defined:

(7)

Hence, the following expressions, with T ₁ and T ₂ respectively, can be obtained

(8a)

(8b)

with

(9a)

(9b)

Since ? 1 for E/kT>10 the expressions ( ?+2) kT ₁/ E and ( ?+2) kT ₂/ E have been taken equal to ?=( ?+2 )kT _M /E.

Equations (8a, b) can be resolved numerically for ? ₁ and ? ₂ for values of a =0, 2 and E/kT _M between 10 and 35. Analysis of the data shows that E can be found by the following linear equation

(10)

with

?= ? ₁+