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Thermal expansion measurements for estimating vacancy concentration in X-ray irradiated KCl single crystals
Solid State Communications, Vol. 34, PP. 655—657. Pergamon Press Ltd. 1980. Printed in Great Britain. THERMAL EXPANSION MEASUREMENTS FOR ESTIMATING VACANCY CONCENTRATION IN X-RAY IRRADIATED KC1 SINGLE CRYSTALS A.K. Gupta and K.V. Rao Physics Department, Indian Institute of Technology, Kharagpur, India (Received 11 February 1979 by MF. Collins) A sensitive capacitance technique is used for measuring changes in length (i~l)of KC1 single crystals with temperature in the region 30—300°C. These measurements have been taken on KC1 in (i) as-cleaved (ii) X-ray irradiated (iii) quenched and X-ray irradiated conditions (X-ray irradiation was always done at room temperature (~30°C).The linear coefficient of thermal (a)temperature of the as-cleaved sample is 40.8crystal x 10-6shows °C1.two Variationexpansion of L~lwith in X-ray irradiated regions: (a) 30—180 C where a is 48.1 x 10-6 C1, (b) 180—300 C where a is 40.4 x 10-6 °C’.Similar behaviour is exhibited b~quenched and later X-ray irradiated KC1 the first region is up to 140 C, beyond which the second region takes over. From these data, concentration of vacancies in X-ray irradiated KC1 at room temperature is calculated to be 3.4 x iO’~ cm3 which is in fairly good agreement with the value obtained from F-band absorption measurements on the sample. An attempt has been made to understand these results.
A CONSIDERABLE AMOUNT of data has been collected in the past on the linear coefficient of thermal expansion (a) of the materials using different methods for measurement of a [1—31. The effect of X-ray irradiation near room temperature on lattice expansion of KBr crystals was studied by Fuchs and Wiegand [4] and also by Balzer et al. [5]. The influence of X-ray and 7-rays on thermal expansion of KC1—KBr system was reported by Ivankina and co-workers [6]. White [7] (following Bijl and Pullan’s ideas [8]) measured the change in capacity of a condenser produced by a change in the length of a specimen. Using this technique, Sakaguchi and Suita [9] have measured at room temperature the change in length of KCI crystal during X-ray irradiation; they have also estimated the vacancy concentration in it. The changes in density of KCI due to vacancies produced by X-ray irradiation have been measured using the flotation method [10]. We have reported [11] details of an experimental set-up (using capacitance technique) for measurement of minute changes in length of a solid sample (of length about 1 cm). The sensitivity of this apparatus was subsequently stepped up and now it can measure change in length to an accuracy of 106cm in a 1 cm long sample. Using this apparatus and measuring the changes in length, we have shown [12] that X-ray irradiation of NaC1 crystal increases its a-value considerably in the temperature region 30—170°C.It is the aim of this communication to present data in the temperature range 30—300°C 655
taken with this apparatus on the changes in length of a KC1 single crystal before the after X-ray irradiation. Similar measurements have also been reported on a quenched and X-ray irradiated KC1; quenching of the crystal was carried out after heating it to a temperature of 700°C.X-ray irradiation was always carried out at room temperature (~30°C).From these data, we have attempted to estimate the concentration of vacancies at room temperature (~ 30°C)in these crystals after X-ray irradiation. The KC1 single crystals used in the present work are mostly laboratory grown; a few crystals obtained from Harshaw Chemical Company, U.S.A. were also studied yielding similar data. The sample dimensions are approximately 1.51 x 0.30 x 0.12cm3. Irradiation was carried out with 35 KV, 15 mA X-rays for 4 hr; two hours on either side along the thickness. The changes in length with temperature in KC1 crystal before and after X-ray irradiation are shown in Fig. I ; this figure also presents similar data on a quenched and X-ray irradiated KC1. The linear coefficient of thermal expansion (a) for KC1 is calculated to be 40.8 x 10-6 °C1which is in good agreement with literature value [13]. a of X-ray irradiated KC1 is 48.1 x 10-6 °C1in the temperature region 30—180°C but has a value of 40.4 x 106 °c’ in the region 180—300°C. The data are summarised in Table 1. The increase in length at room temperature in the
656
VACANCY CONCENTRATION IN X-RAY IRRADIATED KC1
Vol. 34, No. 8
Table 1. Summary ofdata on KCI single crystal Vacancy concentration from thermal expansion measurement x 10’7cm3 at room temperature (30°C)
Vacancy concentration from optical absorption measurement x l0’7cm3 at room temperature (30°C)
Sample condition
a-value x 10—6 °C’
(1)
As-cleaved
40.8
(2)
As-cleaved and X-ray irradiated 30—180°C 180—300°C
48.1 40.4
3.4
2.2
Quenched and X-ray irradiated 30—140°C 140—300°C
49.9 40.5
4.5
2.8
(3)
180
I~J~
11/
%‘/ ,~“,/ /7/ 1/ /
160
E140 -
=
Putting the value of~pin the equation N n=~p— M
~l20
100
f~/
-~
/
80
17/
60
—
p7/
40
/1/ ~/
20
40
80
120
1~
200
2~o
280
320
TEMPERATURE °c
Fig. 1. Variation of increase in length (&) with temperature on KC1 single crystal in (a) as-cleaved (b) X-ray irradiated (c) quenched and latter X-ray irradiated condition, X-ray irradiated KC1 over the as-cleaved condition was obtained by extrapolating the graph (this quantity was calculated by numerical methods) and the volume of the X-ray irradiated crystal was calculated. The increase in volume (tv) over the original volume (V) of the crystal brings out the change in density (b.p) of the crystal because of vacancies in the sample after X-ray irradiation, According to Eastermann eta!. [10], the relation connecting these quantities is given by
(where Nis Avogadro s number and M the molecular weight of KC1), n, the number of pairs of ions per cm3 which migrate to the surface, is calculated to be 3.4 x 10’T cm3. But such migration leaves the crystal with an equivalent number of vacancies; as such, this number is also the number of vacancies present in the crystal. Using a Beckman DU spectrophotometer the optical absorption of this KCI crystal in the F-band region has been measured; the F-centre concentration which is equivalent to vacancy concentration in the sample has been calculated using Smakula’s equation. This comes out to be 2.2 x 1017cm’3 which is in fair agreement with the value obtained from thermal expansion measure measurements. It is interesting to note that the change in length as a function of temperature for X-ray irradiated KCI exhibits two stages; in the temperature range 30—180°C, the a-value is larger compared to the value in the as-cleaved condition whereas at higher temperature range, the a value is practically the same as in the as-cleaved condition. The X-ray irradiated crystal can be considered to be in a more disordered state due to the larger concentration of vacancies present in it. Under such conditions, it is apparently possible that the ions of the crystal can be moved through larger distances by temperature changes in comparison to the as-cleaved sample, thus leading to larger changes in length and
Vol. 34, No. 8
VACANCY CONCENTRATION IN X-RAY IRRADIATED KC1
657
hence larger a-value in the temperature range 30—180°C. tion of temperature in alkali halide and similar crystals Our results regarding the decrease in the a-value in under different conditions yields information regarding the temperature range 180—300°Ccompared to its value the defect processes taking place in them. in the range 30—180°Csuggest that clustering of vacancies seems to take place in this temperature region. REFERENCE From the above mentioned considerations, it seems 1. R.J. Curruccinni & J.J. Gniewek, Thermal reasonable to expect that a quenched and X-ray Expansion of Technical Solids at Low Ternperairradiated KC1 crystal containing a larger vacancy tures (National Bureau of Standards, Washington (defect) concentration exhibits a larger a-value (cornD.C., U.S.A.), Monograph 29 (1961). 2. S.G. Starling & A.J. Woodall, Physics. Longmans, pared with the as-cleaved as well as the X-ray irradiated London (1963). crystal), also it is likely that the clustering of vacancies 3. K. Andres, Cryogenics 2,93 (1961). takes place at a lower temperature compared with the 4. W. Fuch & D.A. Wiegand, J. Ploys. Chem. Solids KC1 which has been irradiated but not quenched. Our GB 36, 17(1975). data on quenched and X-ray irradiated KC1 (Fig. 1) 5. R. Baizer, H. Peisl & W. Waiderlich, Phys. Status support this conclusion. Solidi 31, K29 (1969). 6. Izv. M.S.Vuz. Ivankina, A.V. Vyatkina F.A. Sergurova, It may be mentioned here that these measurements Fiz. (USSR) 10, 104 & (1973); Phys. were taken on several laboratory grown and cornAbstract 65 10/1974. mercially available KC1 single crystals and the data are 7. G.K. White, Cryogenics 1, 151(1961). found to be reproducible. There was no observable 8. D. Bijl & H. Pullan,Physica 21, 285 (1955). effect of changing the time (up to 3 hr) between the 9. K. Sakaguchi & T. Suita, Tech. Report ofOsaka 177 & (1952). time of X-ray irradiation and measurements on thermal 10. University,2,No.43, 1. Eastermann W.J. Leivo 0. Stem,Phys. Rev. expansion. Repeating the process of X-ray irradiation 75, 627 (1949). and heating to 300°Cseveral times is found to have 11. K.V. Rao & J. Maity, md. J. Pure Appi. Phys. influence on these data. Further work is in progress and 15, 437 (1977). it is planned to communicate these results in due course 12. A.K. Gupta, K.V. Rao & A. Subramanyam, of time Phys. D: App!. (in print). 13. J. W.A. Weye, OfficePhys. of Naval Res. Tech. Repts. In summary, it may be concluded that the present No. 54, 65 and 66. Pennsylvania State University, work points Out that a study of length changes as a funcU.S.A. (1955).
A CONSIDERABLE AMOUNT of data has been collected in the past on the linear coefficient of thermal expansion (a) of the materials using different methods for measurement of a [1—31. The effect of X-ray irradiation near room temperature on lattice expansion of KBr crystals was studied by Fuchs and Wiegand [4] and also by Balzer et al. [5]. The influence of X-ray and 7-rays on thermal expansion of KC1—KBr system was reported by Ivankina and co-workers [6]. White [7] (following Bijl and Pullan’s ideas [8]) measured the change in capacity of a condenser produced by a change in the length of a specimen. Using this technique, Sakaguchi and Suita [9] have measured at room temperature the change in length of KCI crystal during X-ray irradiation; they have also estimated the vacancy concentration in it. The changes in density of KCI due to vacancies produced by X-ray irradiation have been measured using the flotation method [10]. We have reported [11] details of an experimental set-up (using capacitance technique) for measurement of minute changes in length of a solid sample (of length about 1 cm). The sensitivity of this apparatus was subsequently stepped up and now it can measure change in length to an accuracy of 106cm in a 1 cm long sample. Using this apparatus and measuring the changes in length, we have shown [12] that X-ray irradiation of NaC1 crystal increases its a-value considerably in the temperature region 30—170°C.It is the aim of this communication to present data in the temperature range 30—300°C 655
taken with this apparatus on the changes in length of a KC1 single crystal before the after X-ray irradiation. Similar measurements have also been reported on a quenched and X-ray irradiated KC1; quenching of the crystal was carried out after heating it to a temperature of 700°C.X-ray irradiation was always carried out at room temperature (~30°C).From these data, we have attempted to estimate the concentration of vacancies at room temperature (~ 30°C)in these crystals after X-ray irradiation. The KC1 single crystals used in the present work are mostly laboratory grown; a few crystals obtained from Harshaw Chemical Company, U.S.A. were also studied yielding similar data. The sample dimensions are approximately 1.51 x 0.30 x 0.12cm3. Irradiation was carried out with 35 KV, 15 mA X-rays for 4 hr; two hours on either side along the thickness. The changes in length with temperature in KC1 crystal before and after X-ray irradiation are shown in Fig. I ; this figure also presents similar data on a quenched and X-ray irradiated KC1. The linear coefficient of thermal expansion (a) for KC1 is calculated to be 40.8 x 10-6 °C1which is in good agreement with literature value [13]. a of X-ray irradiated KC1 is 48.1 x 10-6 °C1in the temperature region 30—180°C but has a value of 40.4 x 106 °c’ in the region 180—300°C. The data are summarised in Table 1. The increase in length at room temperature in the
656
VACANCY CONCENTRATION IN X-RAY IRRADIATED KC1
Vol. 34, No. 8
Table 1. Summary ofdata on KCI single crystal Vacancy concentration from thermal expansion measurement x 10’7cm3 at room temperature (30°C)
Vacancy concentration from optical absorption measurement x l0’7cm3 at room temperature (30°C)
Sample condition
a-value x 10—6 °C’
(1)
As-cleaved
40.8
(2)
As-cleaved and X-ray irradiated 30—180°C 180—300°C
48.1 40.4
3.4
2.2
Quenched and X-ray irradiated 30—140°C 140—300°C
49.9 40.5
4.5
2.8
(3)
180
I~J~
11/
%‘/ ,~“,/ /7/ 1/ /
160
E140 -
=
Putting the value of~pin the equation N n=~p— M
~l20
100
f~/
-~
/
80
17/
60
—
p7/
40
/1/ ~/
20
40
80
120
1~
200
2~o
280
320
TEMPERATURE °c
Fig. 1. Variation of increase in length (&) with temperature on KC1 single crystal in (a) as-cleaved (b) X-ray irradiated (c) quenched and latter X-ray irradiated condition, X-ray irradiated KC1 over the as-cleaved condition was obtained by extrapolating the graph (this quantity was calculated by numerical methods) and the volume of the X-ray irradiated crystal was calculated. The increase in volume (tv) over the original volume (V) of the crystal brings out the change in density (b.p) of the crystal because of vacancies in the sample after X-ray irradiation, According to Eastermann eta!. [10], the relation connecting these quantities is given by
(where Nis Avogadro s number and M the molecular weight of KC1), n, the number of pairs of ions per cm3 which migrate to the surface, is calculated to be 3.4 x 10’T cm3. But such migration leaves the crystal with an equivalent number of vacancies; as such, this number is also the number of vacancies present in the crystal. Using a Beckman DU spectrophotometer the optical absorption of this KCI crystal in the F-band region has been measured; the F-centre concentration which is equivalent to vacancy concentration in the sample has been calculated using Smakula’s equation. This comes out to be 2.2 x 1017cm’3 which is in fair agreement with the value obtained from thermal expansion measure measurements. It is interesting to note that the change in length as a function of temperature for X-ray irradiated KCI exhibits two stages; in the temperature range 30—180°C, the a-value is larger compared to the value in the as-cleaved condition whereas at higher temperature range, the a value is practically the same as in the as-cleaved condition. The X-ray irradiated crystal can be considered to be in a more disordered state due to the larger concentration of vacancies present in it. Under such conditions, it is apparently possible that the ions of the crystal can be moved through larger distances by temperature changes in comparison to the as-cleaved sample, thus leading to larger changes in length and
Vol. 34, No. 8
VACANCY CONCENTRATION IN X-RAY IRRADIATED KC1
657
hence larger a-value in the temperature range 30—180°C. tion of temperature in alkali halide and similar crystals Our results regarding the decrease in the a-value in under different conditions yields information regarding the temperature range 180—300°Ccompared to its value the defect processes taking place in them. in the range 30—180°Csuggest that clustering of vacancies seems to take place in this temperature region. REFERENCE From the above mentioned considerations, it seems 1. R.J. Curruccinni & J.J. Gniewek, Thermal reasonable to expect that a quenched and X-ray Expansion of Technical Solids at Low Ternperairradiated KC1 crystal containing a larger vacancy tures (National Bureau of Standards, Washington (defect) concentration exhibits a larger a-value (cornD.C., U.S.A.), Monograph 29 (1961). 2. S.G. Starling & A.J. Woodall, Physics. Longmans, pared with the as-cleaved as well as the X-ray irradiated London (1963). crystal), also it is likely that the clustering of vacancies 3. K. Andres, Cryogenics 2,93 (1961). takes place at a lower temperature compared with the 4. W. Fuch & D.A. Wiegand, J. Ploys. Chem. Solids KC1 which has been irradiated but not quenched. Our GB 36, 17(1975). data on quenched and X-ray irradiated KC1 (Fig. 1) 5. R. Baizer, H. Peisl & W. Waiderlich, Phys. Status support this conclusion. Solidi 31, K29 (1969). 6. Izv. M.S.Vuz. Ivankina, A.V. Vyatkina F.A. Sergurova, It may be mentioned here that these measurements Fiz. (USSR) 10, 104 & (1973); Phys. were taken on several laboratory grown and cornAbstract 65 10/1974. mercially available KC1 single crystals and the data are 7. G.K. White, Cryogenics 1, 151(1961). found to be reproducible. There was no observable 8. D. Bijl & H. Pullan,Physica 21, 285 (1955). effect of changing the time (up to 3 hr) between the 9. K. Sakaguchi & T. Suita, Tech. Report ofOsaka 177 & (1952). time of X-ray irradiation and measurements on thermal 10. University,2,No.43, 1. Eastermann W.J. Leivo 0. Stem,Phys. Rev. expansion. Repeating the process of X-ray irradiation 75, 627 (1949). and heating to 300°Cseveral times is found to have 11. K.V. Rao & J. Maity, md. J. Pure Appi. Phys. influence on these data. Further work is in progress and 15, 437 (1977). it is planned to communicate these results in due course 12. A.K. Gupta, K.V. Rao & A. Subramanyam, of time Phys. D: App!. (in print). 13. J. W.A. Weye, OfficePhys. of Naval Res. Tech. Repts. In summary, it may be concluded that the present No. 54, 65 and 66. Pennsylvania State University, work points Out that a study of length changes as a funcU.S.A. (1955).