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Ionic thermocurrents in impurity doped cesium bromide
Solid State Communications, Vol. 18, PP. 1247—1250, 1976.
Pergamon Press.
Printed in Great Britain
IONIC THERMOCURRENTS IN IMPURITY DOPED CESIUM BROMIDE S. Radhakrishna and S. Haridoss Department of Physics, Indian Institute of Technology, Madras-600 036, India (Received 8 September 1975 by MF. Collins) Ionic thermocurrents are observed in impurity doped cesium bromide crystals and from an analysis of the observed curves the activation energy of impurity—vacancy complex is calculated. This value (—‘ 0.50 eV in the case of calcium doped CsBr and -~ 0.59 eV in the case of lead doped CsBr) is compared with the activation energy values determined from other transport experiments. 1. INTRODUCTION
3. RESULTS AND DISCUSSION
THE TRANSPORT phenomena in pure and impurity doped cesium halides have been investigated previously13 and it has been shown that both cation and anion vacancies contribute to the conductivity of the crystal unless the crystal is heavily doped with an impurity in which case, the charge compensating vacancies dominate the conductivity. In the present work ionic thermocurrents (I.T.C.) are studied in impurity doped cesium bromide crystals with a view to getting similar information from a different technique. Although I.T.C. has been studied in several impurity doped potassium halide crystals4 and CaF 5 no work 2 type crystals, has been reported in cesium halides. The investigation is expected to prove useful because of the different structure and the very different transport properties reported on the basis of other experiments.
Figure 1 shows the I.T.C. spectrum obtained for a CsBr crystal containing 80 ppm of Ca2~and polarised at 250°Kfor 30 mm. and then warmed at a rate of 5°K/ mm. Different polarising voltages and temperatures were tried and the best result is shown here. Similarly Fig. 2 shows I.T.C. spectrum obtained for a CsBr crystal contaming 100 ppm of Pb2~and polarised at 270°Kfor 30 mm. and then warmed at a rate of 5°K/min.In both cases the polarising voltage is 250 V. The curves were analysed by different methods and the activation energy has been evaluated. In most cases the initial rise method has been used for evaluating the activation energy from experimentally observed results. While this method is quite satisfactory, our experience in analysing TL data has shown that the method can often give erroneous results especially when there are overlapping peaks. Thus we extend here the methods known for analysing TL data, in order to get more reliable parameters from I.T.C.
—
2. EXPERIMENTAL Single crystals of CsBr were grown from melt by Bridgman technique. In the case of calcium doping the impurity was added in the melt while in the case of lead doping the impurity was diffused into the crystal by heating the CsBr crystals and Pb metal in an evacuated sealed tube at 550°Cfor about lOOh. The presence of lead in the crystal was confirmed by correlated optical absorption measurements and the concentration of lead in the crystal is found to be 100 ppm. The amount of
spectra. 4 METHODS OF ANALYSIS The I.T.C. curve is represented by the equation ~j
=
exp
I
—
~ KT
—
—~--
I3ro
f
T
exp
T
/
I— —~--IdT’ \
(1)
KT’J
where J is the depolarisation current density, P
calcium in the crystal was found to be 80 ppm. The impurity content was analysed by polarographic analysis. The samples were mounted in a cryostat and were polarized at appropriate temperature and voltages for 30 mm. in each case. The samples were then heated from about l00°Kto RT at a rate of about 5°K/min.The currents were measured by using a Cary 401 vibrating reed electrometer.
0 the initial polarisation, r0 the time factor for the relaxation process, E the activation energy and g3 the heating rate. The parameters E and r0 are obtained by the following methods: 4.1. Initial rise method For the initial rise of temperature the second term in the exponent tends to zero so that effectively we have
1247
1248
IONIC THERMOCURRENTS IN CESIUM BROMIDE
Cs Br
Vol. 18, Nos. 9/10
Ca~ 2
~LA :7 210
230
220
240
250
260
4.2
4.3
4.5
4.4
4.6
remperatu~ (‘K)
Fig. I. l.T.C. spectrum of CsBr: Ca2’~together with the logarithmic plot of relaxation time T obtained from l.T.C. measurements according to equation (5) against the inverse of temperature.
CsBr: Pb
S.
2
/
10-
S.
S. S.
L)
/
2x/0
220
230
240
250
260
I
I
270
260
__L_____.____I___._~I_
40
4./
T.mp.f’utux* (K)
I
42 /Q3/
4~3
r
44
—~
Fig. 2. I.T.C. spectrum of CsBr: Pb2~together with the logarithmic plot of relaxation time T obtained from l.T.C. measurements according to equation (5) against the inverse of temperature. J
Po —exp[—-L/KT].
(2)
4.2. Full curve method
T 0
The Arrhenius equation for the activation process is
Therefore a plot of In J against lIT yields a straight line r = r0 exp E/KT. (3) with a slope E/K. This method, as we have stated Therefore in r = In T0 ~fE/KT. (4) earlier, is not so accurate but can serve as a good approxiination to start with. Hence a plot of in r against I IT yields F and T~.The —
Vol. 18, Nos. 9/10
IONIC THERMOCURRENTS IN CESIUM BROMIDE
1249
Table 1 Crystal
Impurity ion
F (eV)
Tm1450
0.53 0.50 0.53 0.52 0.51 0.52 0.53
2 3(a) 3(b) 3(c) 4
Ca2~
CsBr
Method analysis of
Tm1450
CsBr
quantity In T can be determined experimentally as follows: r(fl
=
=
JJ dT’/J(fl
(5)
where ~ J dT’ can be estimated by graphic integration T
of I.T.C. curve. Though this method is tedious it gives a good estimate of the parameters with the added advan. tage that this method of analysis is independent of ~3 the heating rate. 4.3. Chen’s Method The I.T.C. curve is also analysed by the method developed by Chen6 for TL glow curves. The method is based on Lushchik’s7 assumption for the area under the glow curve. Equations similar to those developed by Chen et al.6 are obtained for I.T.C. glow curves also, following the same arguments, and the parameters are determined taking: (a) half width of the curve, (b) low temperature side half peak, (c) high temperature side half peak. 4.4. Curve Fitting Method The procedure adopted is basically the one developed earlier89 but modified slightly, In equation (I) one can write A
=
B
=
—~.—.
0.25 x 1.15 x 0.58 x 0.40x 0.66 x 0.97 x
iU~
to~ i09 iO~ IO9 iO~
--
1.61 x 4.54 x 3.02 x 3.49 x 2.49 x 3.75 x
0.64
—
0.64
—
1010
iO~ iU~ l0~ l0~
method is used. Instead of using an approximation9 for B, it is calculated using the condition for the maximum:
T
j(fl
—
0.57 0.62 0.59 0.59 0.59 0.58 0.59
2 3(a) 3(b) 3(c) 4 Dielectric loss3 Conductivity2
Pb2~
(Sec)’
(6)
As a first approximation F value obtained by initial rise
~E/KT~, = To’ exp
(—
E./KTm).
(7)
For the integral in (1) an approximation suggested by Squire’°is used
j exp(—E/KT’) dT’ 7’
To
J
T
exp(—EIKT) dT’
0
Texp (—X)(X + 3.0396)/(X2 + 5.0364X + 4.1916) (8) whereX=E/KT. The value of A is adjusted so that the theoretical and experimental maxima coincide. The value of E is suitably altered in successive steps, in each step calculatingA and B, to attain a minimum variance. The results obtained using all the above methods in the case of CsBr : Ca2~are given in Table 1, and are found to agree well. The same is found to be true for the case of CsBr: Pb2~also. An attempt is also made to arrive at an empirical relation between E and Tm as the one used for TL glow curves. In the case of I.T.C. glow curves NaCI : M2~or KCl:M2~~ the empirical relation E = Tm/350 serves well to have a good “guess” for E which can be used as a first approximation close to the exact one. But as can be seen from the reported values for CsBr, the above relation gives a value quite far from the true value. A relation of the type F = Tm/450 serves better for cesium halides.
1250
IONIC THERMOCURRENTS IN CESIUM BROMIDE
The activation energy obtained for the case of impurity vacancy dipoles by dielectric loss compares with that observed from I.T.C. measurements. That the activation energy depends on the radius of the impurity has
Vol. 18, Nos. 9/10
been seen in the case of potassium halides doped with different impurities.” Although from our work such a definite conclusion cannot be drawn for cesium halides, the trend is certainly seen.
REFERENCES I.
PASHKOVSKI M.V., SPITKOVASKU IN, & TKACHUK AD., Soy. Phys. Solid State 12, 1036 (1970).
2. 3.
RADHAKRISHNA S. & PANDE K.P., Phys. Rev. B7, 424 (1973). RADHAKRISHNA S., PANDE K.P. & NARAYANAN R., J. Phvs. Soc. Japan 33, 1629 (1972).
4.
BRUN A., DANSAS P. & SIXOU P., Solid State Commun. 8,613 (1970).
5.
KIlTS EL., Jr. & CRAWFORD J.H., Jr., Phys. Rev. B9 (1974).
6.
CHEN R.,J. App!. Phys. 40, 570 (1969).
7.
LUSHCHIK C.B., Soy. Phys. JETP 3, 1306 (1956).
8.
COWELL T.A.T. & WOODS J., Brit. J. App!. Phys. 18, 1045 (1967).
9.
MOHAN N.S., & CHEN R.,J. Phvs. D,Appl. Phys. 3, 243 (1970).
10.
SQUIRE W.,J. Comp. Phys. 6,371(1970).
II.
BRUN A.&DANSAS P.,J.Phys. C7, 2593 (1974).
Pergamon Press.
Printed in Great Britain
IONIC THERMOCURRENTS IN IMPURITY DOPED CESIUM BROMIDE S. Radhakrishna and S. Haridoss Department of Physics, Indian Institute of Technology, Madras-600 036, India (Received 8 September 1975 by MF. Collins) Ionic thermocurrents are observed in impurity doped cesium bromide crystals and from an analysis of the observed curves the activation energy of impurity—vacancy complex is calculated. This value (—‘ 0.50 eV in the case of calcium doped CsBr and -~ 0.59 eV in the case of lead doped CsBr) is compared with the activation energy values determined from other transport experiments. 1. INTRODUCTION
3. RESULTS AND DISCUSSION
THE TRANSPORT phenomena in pure and impurity doped cesium halides have been investigated previously13 and it has been shown that both cation and anion vacancies contribute to the conductivity of the crystal unless the crystal is heavily doped with an impurity in which case, the charge compensating vacancies dominate the conductivity. In the present work ionic thermocurrents (I.T.C.) are studied in impurity doped cesium bromide crystals with a view to getting similar information from a different technique. Although I.T.C. has been studied in several impurity doped potassium halide crystals4 and CaF 5 no work 2 type crystals, has been reported in cesium halides. The investigation is expected to prove useful because of the different structure and the very different transport properties reported on the basis of other experiments.
Figure 1 shows the I.T.C. spectrum obtained for a CsBr crystal containing 80 ppm of Ca2~and polarised at 250°Kfor 30 mm. and then warmed at a rate of 5°K/ mm. Different polarising voltages and temperatures were tried and the best result is shown here. Similarly Fig. 2 shows I.T.C. spectrum obtained for a CsBr crystal contaming 100 ppm of Pb2~and polarised at 270°Kfor 30 mm. and then warmed at a rate of 5°K/min.In both cases the polarising voltage is 250 V. The curves were analysed by different methods and the activation energy has been evaluated. In most cases the initial rise method has been used for evaluating the activation energy from experimentally observed results. While this method is quite satisfactory, our experience in analysing TL data has shown that the method can often give erroneous results especially when there are overlapping peaks. Thus we extend here the methods known for analysing TL data, in order to get more reliable parameters from I.T.C.
—
2. EXPERIMENTAL Single crystals of CsBr were grown from melt by Bridgman technique. In the case of calcium doping the impurity was added in the melt while in the case of lead doping the impurity was diffused into the crystal by heating the CsBr crystals and Pb metal in an evacuated sealed tube at 550°Cfor about lOOh. The presence of lead in the crystal was confirmed by correlated optical absorption measurements and the concentration of lead in the crystal is found to be 100 ppm. The amount of
spectra. 4 METHODS OF ANALYSIS The I.T.C. curve is represented by the equation ~j
=
exp
I
—
~ KT
—
—~--
I3ro
f
T
exp
T
/
I— —~--IdT’ \
(1)
KT’J
where J is the depolarisation current density, P
calcium in the crystal was found to be 80 ppm. The impurity content was analysed by polarographic analysis. The samples were mounted in a cryostat and were polarized at appropriate temperature and voltages for 30 mm. in each case. The samples were then heated from about l00°Kto RT at a rate of about 5°K/min.The currents were measured by using a Cary 401 vibrating reed electrometer.
0 the initial polarisation, r0 the time factor for the relaxation process, E the activation energy and g3 the heating rate. The parameters E and r0 are obtained by the following methods: 4.1. Initial rise method For the initial rise of temperature the second term in the exponent tends to zero so that effectively we have
1247
1248
IONIC THERMOCURRENTS IN CESIUM BROMIDE
Cs Br
Vol. 18, Nos. 9/10
Ca~ 2
~LA :7 210
230
220
240
250
260
4.2
4.3
4.5
4.4
4.6
remperatu~ (‘K)
Fig. I. l.T.C. spectrum of CsBr: Ca2’~together with the logarithmic plot of relaxation time T obtained from l.T.C. measurements according to equation (5) against the inverse of temperature.
CsBr: Pb
S.
2
/
10-
S.
S. S.
L)
/
2x/0
220
230
240
250
260
I
I
270
260
__L_____.____I___._~I_
40
4./
T.mp.f’utux* (K)
I
42 /Q3/
4~3
r
44
—~
Fig. 2. I.T.C. spectrum of CsBr: Pb2~together with the logarithmic plot of relaxation time T obtained from l.T.C. measurements according to equation (5) against the inverse of temperature. J
Po —exp[—-L/KT].
(2)
4.2. Full curve method
T 0
The Arrhenius equation for the activation process is
Therefore a plot of In J against lIT yields a straight line r = r0 exp E/KT. (3) with a slope E/K. This method, as we have stated Therefore in r = In T0 ~fE/KT. (4) earlier, is not so accurate but can serve as a good approxiination to start with. Hence a plot of in r against I IT yields F and T~.The —
Vol. 18, Nos. 9/10
IONIC THERMOCURRENTS IN CESIUM BROMIDE
1249
Table 1 Crystal
Impurity ion
F (eV)
Tm1450
0.53 0.50 0.53 0.52 0.51 0.52 0.53
2 3(a) 3(b) 3(c) 4
Ca2~
CsBr
Method analysis of
Tm1450
CsBr
quantity In T can be determined experimentally as follows: r(fl
=
=
JJ dT’/J(fl
(5)
where ~ J dT’ can be estimated by graphic integration T
of I.T.C. curve. Though this method is tedious it gives a good estimate of the parameters with the added advan. tage that this method of analysis is independent of ~3 the heating rate. 4.3. Chen’s Method The I.T.C. curve is also analysed by the method developed by Chen6 for TL glow curves. The method is based on Lushchik’s7 assumption for the area under the glow curve. Equations similar to those developed by Chen et al.6 are obtained for I.T.C. glow curves also, following the same arguments, and the parameters are determined taking: (a) half width of the curve, (b) low temperature side half peak, (c) high temperature side half peak. 4.4. Curve Fitting Method The procedure adopted is basically the one developed earlier89 but modified slightly, In equation (I) one can write A
=
B
=
—~.—.
0.25 x 1.15 x 0.58 x 0.40x 0.66 x 0.97 x
iU~
to~ i09 iO~ IO9 iO~
--
1.61 x 4.54 x 3.02 x 3.49 x 2.49 x 3.75 x
0.64
—
0.64
—
1010
iO~ iU~ l0~ l0~
method is used. Instead of using an approximation9 for B, it is calculated using the condition for the maximum:
T
j(fl
—
0.57 0.62 0.59 0.59 0.59 0.58 0.59
2 3(a) 3(b) 3(c) 4 Dielectric loss3 Conductivity2
Pb2~
(Sec)’
(6)
As a first approximation F value obtained by initial rise
~E/KT~, = To’ exp
(—
E./KTm).
(7)
For the integral in (1) an approximation suggested by Squire’°is used
j exp(—E/KT’) dT’ 7’
To
J
T
exp(—EIKT) dT’
0
Texp (—X)(X + 3.0396)/(X2 + 5.0364X + 4.1916) (8) whereX=E/KT. The value of A is adjusted so that the theoretical and experimental maxima coincide. The value of E is suitably altered in successive steps, in each step calculatingA and B, to attain a minimum variance. The results obtained using all the above methods in the case of CsBr : Ca2~are given in Table 1, and are found to agree well. The same is found to be true for the case of CsBr: Pb2~also. An attempt is also made to arrive at an empirical relation between E and Tm as the one used for TL glow curves. In the case of I.T.C. glow curves NaCI : M2~or KCl:M2~~ the empirical relation E = Tm/350 serves well to have a good “guess” for E which can be used as a first approximation close to the exact one. But as can be seen from the reported values for CsBr, the above relation gives a value quite far from the true value. A relation of the type F = Tm/450 serves better for cesium halides.
1250
IONIC THERMOCURRENTS IN CESIUM BROMIDE
The activation energy obtained for the case of impurity vacancy dipoles by dielectric loss compares with that observed from I.T.C. measurements. That the activation energy depends on the radius of the impurity has
Vol. 18, Nos. 9/10
been seen in the case of potassium halides doped with different impurities.” Although from our work such a definite conclusion cannot be drawn for cesium halides, the trend is certainly seen.
REFERENCES I.
PASHKOVSKI M.V., SPITKOVASKU IN, & TKACHUK AD., Soy. Phys. Solid State 12, 1036 (1970).
2. 3.
RADHAKRISHNA S. & PANDE K.P., Phys. Rev. B7, 424 (1973). RADHAKRISHNA S., PANDE K.P. & NARAYANAN R., J. Phvs. Soc. Japan 33, 1629 (1972).
4.
BRUN A., DANSAS P. & SIXOU P., Solid State Commun. 8,613 (1970).
5.
KIlTS EL., Jr. & CRAWFORD J.H., Jr., Phys. Rev. B9 (1974).
6.
CHEN R.,J. App!. Phys. 40, 570 (1969).
7.
LUSHCHIK C.B., Soy. Phys. JETP 3, 1306 (1956).
8.
COWELL T.A.T. & WOODS J., Brit. J. App!. Phys. 18, 1045 (1967).
9.
MOHAN N.S., & CHEN R.,J. Phvs. D,Appl. Phys. 3, 243 (1970).
10.
SQUIRE W.,J. Comp. Phys. 6,371(1970).
II.
BRUN A.&DANSAS P.,J.Phys. C7, 2593 (1974).