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The validity of peak resolution process for obtaining the trap parameters of an isolated thermoluminescence glow peak
Illlm ELSEVIER
Physica B 228 (1996) 342 344
The validity of peak resolution process for obtaining the trap parameters of an isolated thermoluminescence glow peak M.S. Rasheedy Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
Received 3 March 1996; revised 20 June 1996 Abstract A method is suggested for checking the isolation and singularity of a thermoluminescence (TL) glow peak. This method depends on obtaining the order of kinetics (b) at several portions of the glow peak. The glow peak is considered fairly isolated if all values of b given by the independent methods at several portions of the peak are identical with each other. The method was checked for a numerically computed first-order glow peak, Keywords: Thermoluminescence; Glow curves; Kinetics order
1. Introduction Thermoluminescence (TL) is the thermally stimulated light emitted from an insulator or semiconductor when it is heated after previous absorption of energy from radiation. The resulting curve of TL intensity versus temperature, or time, is called a glow curve and contains one or more glow peaks. In the case of real TL glow curves, the occurrence of a single and fairly isolated peak is rare. As a result, several methods of peak separation have been devised to obtain a single and isolated peak. These methods are described in details elsewhere [-1]. However, according to McKeever [1], peak separation techniques are extremely difficult when the peaks are characterized by non-first-order kinetics, where a shift in the peak position is expected as the traps are partially emptied. Also, with closely overlapping peaks, there is always the danger that the proceeding peaks will not have been completely removed. For these reasons, we now discuss a procedure to check the complete isolation and singularity of the glow peak. This procedure depends on obtaining
the order of kinetics (b) at several portions of the peak. The peak is considered fairly isolated peak if all values of b given by the independent methods at several portions of the peak are identical with each other.
2. The theoretical basis of the present work Many researchers, see for example [2], found it useful to describe the TL curve by using the following empirical equation: I -
dn - nbS'exp( - E / k T ) , dt
(1)
where b is the order of kinetics, E(eV) the activation energy and S' (cm3
dn dt-N
nb b 1Sexp(-E/kT),
(2)
where S(s-1) is the frequency factor and N(cm 3) is the concentration of traps. Recently, an expression has been suggested for obtaining b [4]. This expression is based on earlier
0921-4526/96/$15.00 © 1996 ElsevierScienceB.V. All rights reserved PII S092 1-4526(96)00487-5
M.S. Rasheedy / Physica B 228 (1996) 342-344
343
w h e r e , A m is
the area under the glow curve between Tm and Tf. Let I1 = (Im/2) and 12 = (Ira/2) be the half-maximum intensities, which occur at temperatures T1 and T2, respectively. Also, let 13 = (Ira/4) and 14 = (Im/4) be the quarter-maximum intensities, which occur at temperatures T3 and T4, respectively, as shown in Fig. 1. Then, similar to Eq. (3) the following expressions are obtained:
Irn
2 11 = Im/2
-
-
(A1) N b- bi S exp( - E/kT1 ),
(4)
-
-
(A2) N b- b1 Sexp( - E/kT2),
(5)
-
-
(A3)b N b I Sexp( - E/kT3),
(6)
14 = Im/4 -- N (A4)b b- 1 Sexp( - E/kT4),
(7)
4
12 = Im/2
r35
Tm r2r4 13 = Im/4
Fig. 1. An isolated TL glow peak. The parameters I3, 11, Ira, 12, 14, T3, T1, Tm, T2 and T4 are as defined in the text.
works of Moharil [5-7], assuming that the glow curve consists of a single glow peak, corresponding to traps of only one kind. At the end of the glow curve all the traps are emptied. The concentration of populated traps at temperature Ti during the TL run is proportional to the area Ai which is equal to
and A 4 indicate the areas under the peak from the temperatures T 1 to Tf, T 2 to Tf, T 3 t o Tf, and T4 to Tv, respectively, where, as shown in Fig. 1, T 3 < T1 < Tm < T2 < T4. By using Eqs. (3)-(5) the following expression has been obtained [4]: w h e r e A1, A2, A3
T m [ T 1 -- T2] ln(2)
b_ T, IT m -
T23 In J A m ~ A , ] -
T2 [Tm - - T 1 ] In JAm~A2]"
(8)
Now, by using Eqs. (3), (5) and (7), one can obtain T2 [Tm - - T4] In (2) - T4 [Tm -- T2] In(4)
b_
T: IT m -
T 4 ] in J A m / A 2 ] -
T 4 [Tm - T 2 ] In J A m / A 4 ] "
(9)
Also, by using Eqs. (3), (6) and (7) one obtains b=
ln(4) T3 [Tm -- T4] In [Am/A3] -- T4 [Tin - T3] In JAm~A4]" T mIT 3 -
the area under the glow curve between the Ti and Tr, where Tf(K) is the temperature at which the TL intensity falls to zero after reaching a maximum value. Consider the maximum intensity of the glow peak, lm, Eq. (2) thus becomes (Am)b1 S exp( - E/kTm), Im - Nb_
(3)
T4]
(10)
Now, we have three expressions for (b), which are described in Eqs. (8)-(10). As shown in Fig. 1, these expressions of b covering different portions of the peak. However, more expressions of (b) may be obtained by selecting different values of lm/(Im/X), where x = 2, 3,4 . . . . etc. Therefore, these expressions can give enough indication on the singularity of the peak if all values of b are identical with each other.
M.S. Rasheedy / Physica B 228 (1996) 342-344
344
3. Numerical application of the present method The above-mentioned method will be applied here for an isolated first-order peak generated with E = 0 . 9 e V , S = 3 x 1 0 1 3 s -1 and a heating rate R = 2.0Ks -1 shown in Fig. 2. The areas A3, A1, Am, A2, A4 (in arbitrary units) and the temperatures T3, Ta, Tin, T2, T4 are evaluated as shown in Table 1. Then, Eqs. (8)-(10) are numerically solved for these peak parameters to evaluate the value of b. The results of these calculations are presented
90 80 70 60
z lad
50
z~
4o
~_
30 20
0
~r
~
280
I
t
500
320
340
TEMPERATURE
I 360
( K )
Fig. 2. A numerically generated first-order peak with E = 0.9eV, S = 3 x l 0 1 3 s - l a n d R = 2 . 0 K s 1. Table 1. The areas and temperatures of the glow peak appearing in Fig. 2. The order of kinetics (b) of samples (101), (102) and (103) are estimated according to Eqs. (8)-(10), respectively. Other parameters involved are described in the text (101) A 3 (a.u.) A1 (a.u.) A~, (a.u.) A2 (a.u.) A4 (a.u.) T3 (K) T1 (K) Tm (K) Tz (K) T4 (K) b
(102)
(103)
in Table 1; samples (101), (102) and (103) where b is obtained according to Eqs. (8)-(10), respectively. From Table 1, no difference was observed between the values of b in case of samples (101), (102) and (103), which shows the validity and the accuracy of the present method in checking the isolation of the glow peaks using different portions of the glow peak.
4. Conclusion A method is described for checking the isolation of a TL glow curve. The procedure depends on determining the order of kinetics (b) of the glow peak at different portions of the glow peak. Therefore, several expressions are derived which give the value of b in terms of its temperatures and areas at different portions of the increasing and decreasing part of the glow peak. In these expressions, the values of b can be obtained by using the temperatures T3, T 1 , Tm, T2 and T4 at the intensities 13 = Im/4, 11 = Im/2 of the increasing part of the peak, Im of the maximum intensity of the peak and 12 = Ira~2, 14 = Im/4 of the descending part of the peak, respectively, and the peak areas A3, A~, Am, A2 and A 4 estimated from T3, Tx, Tin, T2 and T4 to the final temperature of the glow peak, respectively, where T3 < T1 < Tm< Tz < T4. Also, more expressions for b may be obtained by selecting different values of (Im/X), where x = 2, 3, 4 .... etc. All of these expressions can give enough indication on the singularity of the peak if all values of b are identical with each other. The applicability of the present method is demonstrated by taking a numerically computed first-order TL glow peak.
73262.0 64995.0 31197.4 6032.02
31197.4 6032.02 2219.12
31197.4 -2219.12 299.671
306.825 320.260 329.888 1.00097
-320.260 329.888 333.127 1.00099
320.260 333.127 1.00109
References [1] S.W.S. McKeever, Thermoluminescence of Solids (Cambridge University Press, Cambridge, 1985). [2] R. Chen, J. Electrochem. Soc. 116 (1969) 1254. [3] M.S. Rasheedy, J. Phys.: Condens. Matter 5 (1993) 633. [4] M.S. Rasheedy, J. Phys.: Condens. Matter 8 (1996) 1291. [5] S.V. Moharil, Phys. Status Solidi A 66 (1981) 767. [6] S.V. Moharil, Phys. Status Solidi A 68 (1981) 413. [7] S.V. Moharil, Phys. Status Solidi A 73 (1982) 509.
Physica B 228 (1996) 342 344
The validity of peak resolution process for obtaining the trap parameters of an isolated thermoluminescence glow peak M.S. Rasheedy Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
Received 3 March 1996; revised 20 June 1996 Abstract A method is suggested for checking the isolation and singularity of a thermoluminescence (TL) glow peak. This method depends on obtaining the order of kinetics (b) at several portions of the glow peak. The glow peak is considered fairly isolated if all values of b given by the independent methods at several portions of the peak are identical with each other. The method was checked for a numerically computed first-order glow peak, Keywords: Thermoluminescence; Glow curves; Kinetics order
1. Introduction Thermoluminescence (TL) is the thermally stimulated light emitted from an insulator or semiconductor when it is heated after previous absorption of energy from radiation. The resulting curve of TL intensity versus temperature, or time, is called a glow curve and contains one or more glow peaks. In the case of real TL glow curves, the occurrence of a single and fairly isolated peak is rare. As a result, several methods of peak separation have been devised to obtain a single and isolated peak. These methods are described in details elsewhere [-1]. However, according to McKeever [1], peak separation techniques are extremely difficult when the peaks are characterized by non-first-order kinetics, where a shift in the peak position is expected as the traps are partially emptied. Also, with closely overlapping peaks, there is always the danger that the proceeding peaks will not have been completely removed. For these reasons, we now discuss a procedure to check the complete isolation and singularity of the glow peak. This procedure depends on obtaining
the order of kinetics (b) at several portions of the peak. The peak is considered fairly isolated peak if all values of b given by the independent methods at several portions of the peak are identical with each other.
2. The theoretical basis of the present work Many researchers, see for example [2], found it useful to describe the TL curve by using the following empirical equation: I -
dn - nbS'exp( - E / k T ) , dt
(1)
where b is the order of kinetics, E(eV) the activation energy and S' (cm3
dn dt-N
nb b 1Sexp(-E/kT),
(2)
where S(s-1) is the frequency factor and N(cm 3) is the concentration of traps. Recently, an expression has been suggested for obtaining b [4]. This expression is based on earlier
0921-4526/96/$15.00 © 1996 ElsevierScienceB.V. All rights reserved PII S092 1-4526(96)00487-5
M.S. Rasheedy / Physica B 228 (1996) 342-344
343
w h e r e , A m is
the area under the glow curve between Tm and Tf. Let I1 = (Im/2) and 12 = (Ira/2) be the half-maximum intensities, which occur at temperatures T1 and T2, respectively. Also, let 13 = (Ira/4) and 14 = (Im/4) be the quarter-maximum intensities, which occur at temperatures T3 and T4, respectively, as shown in Fig. 1. Then, similar to Eq. (3) the following expressions are obtained:
Irn
2 11 = Im/2
-
-
(A1) N b- bi S exp( - E/kT1 ),
(4)
-
-
(A2) N b- b1 Sexp( - E/kT2),
(5)
-
-
(A3)b N b I Sexp( - E/kT3),
(6)
14 = Im/4 -- N (A4)b b- 1 Sexp( - E/kT4),
(7)
4
12 = Im/2
r35
Tm r2r4 13 = Im/4
Fig. 1. An isolated TL glow peak. The parameters I3, 11, Ira, 12, 14, T3, T1, Tm, T2 and T4 are as defined in the text.
works of Moharil [5-7], assuming that the glow curve consists of a single glow peak, corresponding to traps of only one kind. At the end of the glow curve all the traps are emptied. The concentration of populated traps at temperature Ti during the TL run is proportional to the area Ai which is equal to
and A 4 indicate the areas under the peak from the temperatures T 1 to Tf, T 2 to Tf, T 3 t o Tf, and T4 to Tv, respectively, where, as shown in Fig. 1, T 3 < T1 < Tm < T2 < T4. By using Eqs. (3)-(5) the following expression has been obtained [4]: w h e r e A1, A2, A3
T m [ T 1 -- T2] ln(2)
b_ T, IT m -
T23 In J A m ~ A , ] -
T2 [Tm - - T 1 ] In JAm~A2]"
(8)
Now, by using Eqs. (3), (5) and (7), one can obtain T2 [Tm - - T4] In (2) - T4 [Tm -- T2] In(4)
b_
T: IT m -
T 4 ] in J A m / A 2 ] -
T 4 [Tm - T 2 ] In J A m / A 4 ] "
(9)
Also, by using Eqs. (3), (6) and (7) one obtains b=
ln(4) T3 [Tm -- T4] In [Am/A3] -- T4 [Tin - T3] In JAm~A4]" T mIT 3 -
the area under the glow curve between the Ti and Tr, where Tf(K) is the temperature at which the TL intensity falls to zero after reaching a maximum value. Consider the maximum intensity of the glow peak, lm, Eq. (2) thus becomes (Am)b1 S exp( - E/kTm), Im - Nb_
(3)
T4]
(10)
Now, we have three expressions for (b), which are described in Eqs. (8)-(10). As shown in Fig. 1, these expressions of b covering different portions of the peak. However, more expressions of (b) may be obtained by selecting different values of lm/(Im/X), where x = 2, 3,4 . . . . etc. Therefore, these expressions can give enough indication on the singularity of the peak if all values of b are identical with each other.
M.S. Rasheedy / Physica B 228 (1996) 342-344
344
3. Numerical application of the present method The above-mentioned method will be applied here for an isolated first-order peak generated with E = 0 . 9 e V , S = 3 x 1 0 1 3 s -1 and a heating rate R = 2.0Ks -1 shown in Fig. 2. The areas A3, A1, Am, A2, A4 (in arbitrary units) and the temperatures T3, Ta, Tin, T2, T4 are evaluated as shown in Table 1. Then, Eqs. (8)-(10) are numerically solved for these peak parameters to evaluate the value of b. The results of these calculations are presented
90 80 70 60
z lad
50
z~
4o
~_
30 20
0
~r
~
280
I
t
500
320
340
TEMPERATURE
I 360
( K )
Fig. 2. A numerically generated first-order peak with E = 0.9eV, S = 3 x l 0 1 3 s - l a n d R = 2 . 0 K s 1. Table 1. The areas and temperatures of the glow peak appearing in Fig. 2. The order of kinetics (b) of samples (101), (102) and (103) are estimated according to Eqs. (8)-(10), respectively. Other parameters involved are described in the text (101) A 3 (a.u.) A1 (a.u.) A~, (a.u.) A2 (a.u.) A4 (a.u.) T3 (K) T1 (K) Tm (K) Tz (K) T4 (K) b
(102)
(103)
in Table 1; samples (101), (102) and (103) where b is obtained according to Eqs. (8)-(10), respectively. From Table 1, no difference was observed between the values of b in case of samples (101), (102) and (103), which shows the validity and the accuracy of the present method in checking the isolation of the glow peaks using different portions of the glow peak.
4. Conclusion A method is described for checking the isolation of a TL glow curve. The procedure depends on determining the order of kinetics (b) of the glow peak at different portions of the glow peak. Therefore, several expressions are derived which give the value of b in terms of its temperatures and areas at different portions of the increasing and decreasing part of the glow peak. In these expressions, the values of b can be obtained by using the temperatures T3, T 1 , Tm, T2 and T4 at the intensities 13 = Im/4, 11 = Im/2 of the increasing part of the peak, Im of the maximum intensity of the peak and 12 = Ira~2, 14 = Im/4 of the descending part of the peak, respectively, and the peak areas A3, A~, Am, A2 and A 4 estimated from T3, Tx, Tin, T2 and T4 to the final temperature of the glow peak, respectively, where T3 < T1 < Tm< Tz < T4. Also, more expressions for b may be obtained by selecting different values of (Im/X), where x = 2, 3, 4 .... etc. All of these expressions can give enough indication on the singularity of the peak if all values of b are identical with each other. The applicability of the present method is demonstrated by taking a numerically computed first-order TL glow peak.
73262.0 64995.0 31197.4 6032.02
31197.4 6032.02 2219.12
31197.4 -2219.12 299.671
306.825 320.260 329.888 1.00097
-320.260 329.888 333.127 1.00099
320.260 333.127 1.00109
References [1] S.W.S. McKeever, Thermoluminescence of Solids (Cambridge University Press, Cambridge, 1985). [2] R. Chen, J. Electrochem. Soc. 116 (1969) 1254. [3] M.S. Rasheedy, J. Phys.: Condens. Matter 5 (1993) 633. [4] M.S. Rasheedy, J. Phys.: Condens. Matter 8 (1996) 1291. [5] S.V. Moharil, Phys. Status Solidi A 66 (1981) 767. [6] S.V. Moharil, Phys. Status Solidi A 68 (1981) 413. [7] S.V. Moharil, Phys. Status Solidi A 73 (1982) 509.