Temperature Gradient in a TL Sample

In case high heating rates are used during readout, a temperature difference between the bottom and the top of a sample can be observed and the glow peak becomes broader [1,2].

In case a temperature gradient across a TL sample is ignored, the TL intensity is given by

(1)

On the other hand, assuming a constant temperature gradient across a TLD sample, the emission can be written as

(2)

where

T ₂=temperature of the sample

n( T ₂+ ?)=density of trapped charge carriers at temperature T ₂+ ? at a given position within the sample.

Assuming a linear time dependence of temperature at each position in the sample and neglecting the energy dissipation to the surroundings, we can write, for each position in the sample:

(3)

where and ? ? are, respectively, the effective starting temperature and the effective heating rate in the sample, and ? ?t ?= ?.

Indicating with dn the difference of n between two positions, corresponding to a difference in temperature of dT at a certain time, we can write

(4)

so that, the quantity n( T ₂+ ?) can be approximated by

(5)

Using last Eq.(5), Eq.(2) becomes

which can be approximated as

(6)

and again, solving the integral:

(7)

The last exponential on the right of Eq.(7) can be developed into powers of around :

and then Eq.(7) becomes