Volume 2, No. 1,1987 Journal o f the Faculties of 
Engineering of Uludağ University 
SINGLE PEAK DIFFERENTIAL THERMOLUMINESCENCE 
METHOD FOR CALCULATION OF THE TRAP ENERGIES 
Ata SELÇUK* 
ABSTRACT 
The energy level o f the traps of natural calcium fluorite sample is calculated 
using a single thermoluminescence glow curue peak by new non-isothermal kinetic 
da 1 ı 
method. The p};ot of Ln ( dT ı _ a ) versus ----;y- yields a straight line with a 
alope of - -k- , where E is the trap energy k, is the Boltzman constant, "a" is 
the fraction of the total occupied trap number. The frequency factor S can be cal· 
culated from y intercept which is equal to Ln (Sxb) where b is the constant heating 
rat e. 
The trap energy value of the main glow curue peak of the natural calcium 
fluorite is calculated as O. 64 e V by using single pea k differential thermoluminescen-
ce method . 
ÖZET 
Tabii kalsiyum floriiriin tuzak enerjilerini tayin için yeni bir değişen sıcaklık 
meto du .. L da 1 ) b V u. ygulanmıştır. Bu metod  a gore n (dT --- agıntısını 1/T nin fonksi· ı - a 
yonu o larak gösteren grafik bir doğru denklemi vermekte ue bu doğrunun eğiminin 
(- ~) değerine eşit olması özelliğinden E tuzak enerjisi tayin edilebilmektedir. 
k 
Kalsiyum {loriiriin ana piki için E= O. 64 e V değeri bulunmuştur. 
DEFINATION OF THE METHOD 
Since the method applied should be used for a single peak of the thermolumi-
nescence glow curve (monoenergetic traps) is named as "Single Peak Differential 
Metbod" 1 • 
As known from Randall-Wilkins2 thermoluminescence model ligbt intencity 
was given for isotbermal experiments as 
* Yrd. Doç. Dr.; U. V. Mühendislik Fakültesi Balıkesir - TURKEY. 
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d n 
1= -C - - ı 
dt 
where n is the number of the occupied traps at time t and C is the proportionality 
constant. Integration of this equation, if n0 is the initial number of occupied traps 
at time zero 
/ [dt=- / c dn 2 
O n0 
The left side of the equation 2 is the area under the glow curve in the time 
interval of (o - t). So 
Aı = C(no- n)=Cno-Cn=A-A 2 3 
is obtained by abbriviating A as the whole area under the glow curve peak and A2 
as the area completing the A1 to the A value as shown in Figure-1. Asa result the 
area under the glow curve peak is proportional to the occupied trap number at that 
moment. From the equation 3 
A2 = Cn can be drived. Differentiating the equation 
dA2 dn 
--=C is obtained 4 
dt dt 
d n 
Si nce - --= pn 
dt 5 
was given by Randall-Wilkins model if n was the occupied trap number, p was the 
probability. Combination of the equation 3, 4 and 5 yields 
dA2 
- dt= Aı P 6 
As seen from Figure-1 
Figure - l 
- 148 -
A == A ı -ı A2 is ı:iven . A ı and A2 variables and A is coııstant so differentiation of 
this equation yields 
dAı dAı 
- -- =-- 7 
dt dt 
For the lineer hcating rates this equation can be modified (by using ~ = b 
. ) dt 
cquatıon as 
8 
Aı 
dividin~ by A and defining A = a 
b dAı 
A dT= (ı-a)p is obtained 9 
Aı 
Sin ce "a" was defined as a = --;;:-- differential of the equation can be ob-
tained as 
da ı dAı 
--=----
dT A dT 
dA 
The value of __ı  can be derived and place in to equation 8 
dT 
da ı p 
can be obtained ı o 
dT (ı-a) b 
Probability p was given by Randall-Wilkins as 
p = S exp (- ___g_) 
kT 
where k is the Blotzman constant, S is the Frequency factor E is the trap energy, 
T is the absolute temperature of the sample. Having natural logarithm of the 
equation ıo 
da ı E 
Ln ( dT (ı _ a)) = - ~ + Ln S- Ln b is obtained ll 
da ı ı 
The plot of Ln (~ (ı_ a)) versus T yields a straight line having a 
slope of (E/k) and y intercept which is equal to (Ln S- Ln b). 
APPLICA TION OF THE METHOD 
The data obtained from the main peak of the glow curve of the natural cal-
cium fluorite phosphore (numbered ı8 blue) which is shown in Figure-2 is tabula-
ted in Table-ı which contains the heights measured from the curve and the areas 
(Aı) calculated by Library program ı o of TI-58 or 59 calculator. "a" values can be 
calculated dividing parti al areas A ı by the who le area u nder the glow curve peak. 
-149 -
ı . 
t- ---- - --t -·- - -
l 
ı ' 
• o • o 
47l k 523 K 62.l ~o K.o  
Figure - 2 
Table : 1 
{a-T) Data Obtained From The MainPeakof The Glow Curve Of 
The Natural CALCIUM FLUORITE (No: 18, Blue) 
0 
b = 2.3 6 C /see 
0 
T 0 = 459.95 K
0 
T m = 546.91 K
0 d a ı 
TK a ( I (f) 105 Arc a l (mm ) Ln ( - x--) 
d T ( l -a) 
459 .95 0.0 0000 21 7 .41 00000.00 ooo.s 
474.45 0.02247 210 .77 ~43.96 23 
488.94 0 .06341 204 .5 2 688.4 4 1 
496.19 0 .0951 3 201.54 1032.8 5 4 
503.43 0 .1 35 28 198.6 4 1468.6 6 6 -4.984 
517.93 0.24207 193. ::18 2628 94 - 4.466 
5 25.17 0.3 095 2 19 0.41 3 3G0. ?.5 108 4.245 
533.42 0.38514 18 7 .82 4 1 81.2 117 - ·· 4 .029 
539.67 0.46495 185. 29 5047.58 1 2 2 3 .859 
546 .91 0.54734 182.85 594 2 1 24 -- 3 .681 
554.16 0 .6 2914 18 0 .45 68 30.1 1 21 3.5 10 
561.4 1 ::1.707 09 178 .12 7 676. 3 110 - · 3.344 
568 .65 0.7 7654 175 .85 8430.3 98 
5 75 .9 0 .837 25 ı 73.64 9089 .4 83 
583 .14 0 .88733 17 1.48 9632.2 6 7 
590 .39 0 .9 267 4 169.38 10060.95 51 
6 19.38 1.00000 16 1.45 108 56.28 10.5 
- 150 -
a i 
ı. o --------- t_ ·- - __ ___ _1 ._____ t-
o_,.ı  _;:::::::=-ı 
, t ' ı 
o. r' . i • 1 
\ . -ı 
o .ı . 
.- !1 .' • ı : 1 1 :' ' ı 
---1-- . ' 
o.~4t , . ·: . i ı / 
:: ' ;Yi . .. ı. ; ı ı · · 
ı 
0 .1 / ' 1 
o 45-0 - ---- ,0' 0 ıı  ı 
ı 
Figure- 3 
The plot of "a" versus T is shownin Figure-3. a = F(T) function should be defined 
to calculate the da/dT values for the different temperature values. In this work it is 
thought to fit this curve to a polinominal in the third order in the interval of "a" 
value as shown bel o w. 
a = A + BT + CT1 + DT3 12 
Substituting the values of T 1 , T 1 , T 3, T 4 and corresponding values of a 1 , a1 , 
a3, a4 into this function, the lineer equation of 
a 1 = A + BT 1 + CTT +DT~ 
a2 = A + BT 1 + CT
2  1 + DT1 
3 
 13 
83 = A + BT3 + CTi +DT~ 
84 = A + BT4  + CT~ + DT! 
is obtained. 
From this equation the coefficients of 'A~ B, C, D, can be defined in an inter-
val of (a 1 - a4 ). So the.function of a ~(T) and so the ~!;!rivative function da/dT can 
be obtained. 
RESULTS 
In the interval of 0.13528 ~ a ~ 0.38514 the a F(T) function is 
a = 80.67 - 438.48 x 10- 3 T + 776.89x 10- 6 T1 -:444.30 x 10- 9 T3 
and derivative function is 
da 
--= 438.48 x 10- 3 + 1552.78 x 10-6 T- 1332.90 x 10-9 T1 
dT 
In the interval of 0.38514 ~ 8 ~ 0.70709 the function a F(T) is 
a = 217.4 7 -1216.40 x 10-3 T- 2251.66 X 10-6 T1 - 1376.40 x 10- 9 T3 
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and derivative function is 
~ = 1216.40 x ıo-3 + 4503.32 x 1o- 6 T + 4129.20 x ıo -9 T2 
dT 
da ı ı 
The values of Lti (- - x --) versus -T yields a straight line as seen in 
dT ı - a 
Figure-4. The ~lo pe of this line is calculated as - 7 436.68 and then, si nce this value 
0 
is equal to- k (k 8.61 x ıo-s eV /K mol.) 
E= 0.64 eV is found in the interval of 0.24 EO;; a EO;; 0.71. 
4~~ ·rı!e.J> 
J' 
2 ı "' '~ 
! ~ 
' 
10~ 1 ~  -
:1 __:  ~ -~: ~- --- -- -- --
, ı ,. ıcf'ft_ ! sL- -------------
ıeo 1'- ı,. 
Figure- 4 
DISCUSSION. 
This method is applied to natural calcium fluorite phosphore together with 
other two method. One of themis Garlick-Gibson3 method which yields 0.64 eV 
trap energy value. This value fits the result obtained by that method. The second 
method is "Single Peak Integration Method"4 which isaiso introduced together with 
the methodusedin that work. 0.54 eV trap energy value is obtained by that second 
method. 
Although the application of that method takes a long time but it is most beliv· 
able since substantial part of the peak is used. 
REFERENCES 
1. SELÇUK, A.: Ph. D. Thesis, U. O. Mühendislik Fakültesi, Balıkesir-Turkey, p. 39· 
45. 
2. RANDALL, J.T. and M.H.F. WILKINS: Proc. of Royal Society A-184 (1945). 
3. GARLICK, G.F.J. and A.F. GIBSON: Proc. Phys. Soc. 60 (ı948) 574. 
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