Short Notes K179

phys. stat. sol. (a) 130, K179 (1992)

Subject classification: 78.60; 71.55; S10

Chemical Department of the E.-M.-Arndt-University Greifswald I )

On the Analysis of Complex Thermoluminescence Glow Curves

BY W. LANGE and G. HERZOG

The normal way of displaying thermoluminescence data is to plot the luminescence intensity I as a function of temperature T - known as glow curve. The glow curve is got by the thermal release of electrons at uniform heating rate w after being irradiated at a low temperature.

Several expressions exist for the determination of the activation energy E A and the frequency factors in the literature /l/. The methods can be roughly divided into two groups:

1. Methods making use of heating rate variation, for instance by Hoogenstraaten /2/ . A plot of In ( w / T i ) versus 1/T, should yield a straight line with a slope E,/k.

2. Methods making use of geometrical approximations, for instance by Chen /3/:

k T : EA = C , __ - bX(2kT,)

X

The parameters c,, b,, and x are constants which depend on the reaction order, k is the Boltzmann constant and T, the temperature of the glow maximum.

We need for the calculation of E, and s the following parameters from the experimental glow curve: The heating rate w, the temperature of the glow maximum T,, and the temperatures TI and T2 at the lower and higher temperature sides of the glow curve where the luminescence intensity equals half its maximum value.

In the case of a thermoluminescence glow curve which exhibits overlapping glow maxima the usual methods cannot be successfully used to determine the trapping parameters unless the different glow peaks are well separated.

In the present case the glow curve of the hexagonal aluminate Ba,,,Eu,,,Mg,Al,,O,, is characterized by one significant glow maximum at the high temperature side and by a strongly marked shoulder at the low temperature side.

By the way the phosphor sample was irradiated at room temperature by means of 254 nm UV light, after that a constant heating rate of about 0.5 K s-' was maintained.

The glow maximum T, was observed at 532 K, the temperature T2 at the high temperature side and at half intensity at 584 K, whereas we cannot find the temperature TI at the low temperature side from the experiment because of the overlapping. For that reason it was neccessary to separate the measured glow curve on experimental and numerical ways.

The first step consisted in the experimental isolation of the glow peaks from the complex glow curve.

I ) Soldtmannstr. 16, 0-2200 Greifswald, FRG.

12*

K180 physica status solidi (a) 130

Possibly the most popular of these separation procedures is the so-called “thermal cleaning” technique described by Nicholas and Woods /4/ and modified by McKeever 151.

In this method the irradiated phosphor is heated to a temperature step by step just beyond the maximum of the first peak in the glow curve, thereby substantially emptying the traps responsible for this peak.

Then the sample is rapidly cooled and reheated to a temperature just beyond the maximum of the next peak and so on throughout the whole glow curve. Thus by removing in stages the lower temperature peak, an essentially “clean” initial rise part of the next peak in the series is obtained. With closely overlapping peaks, however, there is always the danger that the preceding peak will not have been completely removed.

In Fig. 1 and 2 we can see that the experimental separation was successfully carried out. The cleaning temperature up to about 430K seems to be exact enough inside the experimental possibilities.

By means of the thermal cleaning technique we get two separated glow curves, the experimental “rest” curve with a glow maximum T, at 534 K and a “synthetic” glow curve with a glow maximum at 432 K by subtraction from the whole glow curve the cleaning “rest ” curve.

The second step of the isolating consisted in a numerical calculation of the glow curve by means of the experimentally determined parameters E , and s. This curve fitting should demonstrate the correspondence of experiment and calculation.

For the numerical calculation of first-order kinetics we have used the following expressions

(2) /6,7/:

I l ,o = sco exp [(-x) - /2q(x)]

and in the case of second-order kinetics

= sc,[l + i q ( ~ ) ] - ~ exp (-x), (3)

where x = E,/kT and ,i = E,s/wk . The parameter co is the concentration of trapped electrons at depth E,. O n the basis of

a polynomial approximation the term q ( x ) was calculated as follows:

AIx + A2 q ( x ) = ~ (4)

where A , = 0.995924, A , = 1.430913, b , = 3.330651, b, = 1.681 534.

On the basis of the Hoogenstraaten relations /2/ and assuming first-order or second-order kinetics, respectively, for the thermoluminescence process a curve fitting does not exactly achieve a close overlapping of both curves. The calculated glow curves agree with the maximum temperatures of the glow peaks, but they show a too narrow or too broad profile, respectively (Fig. 1).

It is obvious that the reaction kinetics is characterized by a fractional order and cannot be clearly categorized on the extreme model of first or second order.

O n the basis of the Chen relations /3/ and assuming first-order kinetics a curve fitting does not achieve any correspondence of the experimental and calculated glow curves for both glow peaks. The glow maxima temperatures scatter in a wide range. By comparison, on the assumption of second-order kinetics the curve fitting shows approximately a coincidence (Fig. 2).

Short Notes K181

Fig. 1. The curve fitting of the glow peak A (T, = 432 K, E , = 0.38 eV, s = 2.4 x lo2 s-’) and glow peak B (T, = 532K, E , = 0.6eV, s = 4.3 x lo3 s-’) for a second-order kinetics (Hoogenstraaten): (1) experi- mental glow curve, (2) “rest ” glow curve after the “thermal cleaning”, (3) “synthetic” glow curve by subtrac- tion of the experimental minus the “rest” curve, (4) calculated glow cur- ves for the glow peaks A and B

Fig. 2. The curve fitting of the glow peak A (T, .= 432 K, E , = 0.55 eV, s = 3.4 x lo4 s - l ) and glow peak B (T, = 532 K, E , = 0.81 eV, s = 5.6 x lo5 s- ’) for a second-order kinetics (Chen): (1) experimental glow curve, (2) “rest” glow curve after the “thermal cleaning”, (3) “synthetic” glow curve by subtraction of the experimental minus the “rest” curve, (4) calculated glow curves for the glow peaks A and B

K182 physica status solidi (a) 130

That means we should interpret the thermoluminescence process of the Bao,sEu,.lMg,Al,,O,, phosphor as a process of fractional-order kinetics in which the recombination between the conductivity band or the excited states, respectively, and the ground state of the activator centre is rate-determining.

In this case the processes of recombination and retrapping should show a rather comparable probability.

Further investigations should check up the influence of retrapping on the calculation of the glow curves and clear up the differences between the experimental and calculated glow curves.

References

/1/ P. KNITS and H. J. L. HAGEBEUK, J. Lum. Is, 1 (1977). /2/ W. HOOGENSTRAATEN, Philips Res. Rep. 13, 515 (1958). /3/ R. CHEN, J. appl. Phys. 9, 570 (1969). /4/ K. H. NICHOLAS and J. WOODS, Brit. J. appl. Phys. 15, 783 (1964). /5/ S. W. S. MCKEEVER, phys. stat. sol. (a) @, 331 (1980). /6/ H. L. OCZKOWSKI, phys. stat. sol. (a) @, 199 (1981). /7/ H. L. OCZKOWSKI, phys. stat. sol. (a) 3, 65 (1982).

(Received February 17, 1992)