Lushchik [1] also proposed a method based on the glow-peak shape for both first- and second-order kinetics. Introducing the parameter ?= T ₂ ?T _M , a glow-peak can be approximated to a triangle as shown in Fig. 8.

Fig. 8: Approximation of a glow-peak in a triangle.

In this case, with a good approximation, one has

(1)

where n _M is the carrier concentration at the maximum.

For the first-order kinetics, the equation

at the maximum point becomes

(2)

Using the condition at the maximum

Eq.(2) gets

(3)

The substitution of expression (1) in (3) allows to obtain the Lushchik s expression for the activation energy for the first-order process:

(4)

The Lushchik formula for a second-order kinetics is obtained using the solution for n, valid for a second order kinetics, replacing n with n _M :

(5)

Using now the expression for the intensity at the maximum, I _M , and doing the ratio between I _M and n _M , one has

(6)

The insertion of the maximum condition for the second order in Eq.(6) yields

(7)

Using again Eq.(1) and rearranging, the expression of Lushchik for the second order is obtained:

(8)

Chen [2] modified the two previous equations for a better accuracy in the E value by multiplying by 0.978 Eq.(4) and by 0.853 Eq.(8), i.e

The frequency factor for the first-order process is obtained by...