J. PRAKASH: Pliotjo-Induced Polarization and Photo-Induced Depolarization

phys. stat. sol. (a) 64, 681 (1979)

Subject classification: 10.2; 14.4; 20.1 ; 22.5.2

681

Physikalisches Ins t i tu t der Unicersitut Miinster')

Photo-Induced Polarization and Photo-Induced Depolarization of S"--Anion Vacancy Dipoles in Potassium Iodide BY J. YRAKASH~)

The effect of irradiation in the presence/absence of a n electric field is studied in S2--doped K I single crystals using ITC technique. It is observed that the irradiation in the 368 nm absorption band in the presence of a n electric field creates a situation in which more dipoles are aligned along the electric field direction, whereas snch a n irradiation in the absence of an electric field destroys the preferred orientation of the frozen-in dipoles. These phenomena are named photo-induced polarization (PIP) and photo-induced depolarization (PID), respectively. PIP is studied as a function of the electricfield strength. It is observed tha t PIP measurements below a limiting value of the electric field result in a decrease of the ITC peak whereas above they yield an increase of the ITC peak. PID is st'udied as a function of the irradiation temperature and ir- radiation time. It is observed that P I D does not take place below 130 K. The results are quali- tatively explained following a bistable model.

Der EinfluB von Bestrahlung in Anwesenheit/Abwesenheit eines elektrischen Feldes wird in Si2- dotierten KJ-Einkristallen niit der ITC-Technik untersueht. Es wird beobachtet, daD eine Ein- strahlung in die 368 nm-Absorptionsbande bei Anwesenheit cines elektrischen Feldes eine Situation hervorruft, bei der mehr Dipole langs des elektrischen Feldes ausgerichtet werden, wahrend eine derartige Bestrahlung bei Abwesenheit eines elektrisehen Feldes die Vorzugsorientierung der eingefrorenen Dipole zerstort. Diese Erscheinungen werden photoinduzierte Polarisation (PIP) bzw. photoinduzierte Depolarisation (PID) genannt. PIP wird in Abhangigkeit von der elek- trischen Feldstarke untersucht. Es wird beobachtet, daD PIP-Messungen unterhalb eines Grenz- wertes des elektrischen Feldes eine Abnahme des ITC-Maximums ergeben, wahrend sie oberhnlb dieses Feldcs zu einem Anstieg des ITC-Maximums fuhren. P I D wird in Abhhngigkeit von der Bestrahlangstemperatur und der Bestrahlnngszeit untersucht. Es wird beobachtet, daB PJD unterhalb 130 I< nicht stattfindet. Die Ergebnisse werdcn qualitativ mit einem bistabilen Modell erklart .

1. Introduction The dielectric relaxation observed in alkali halide crystals doped with divalent inipu- rity ions is due to impurity-vacancy (IV) dipoles. With respect to the divalent impurity ion, the IV dipole lies along one of the twelve equivalent orientations (110). The orien- tation of these dipoles is influenced by the temperature and the frequency of the applied electric field giving rise to dielectric dispersion and absorption. The method of ionic thermocurrent (ITC) [l] is widely used for determining the dielectric behaviour of IV dipoles. It has recently been reported by us [ 2 to 41 that the irradiation in the 368 nrn absorption band in the presence of an electric field in the KI :S2- system creates a situa- tion in which more dipoles are aligned along the electric field direction, whereas such an irradiation in the absence of an electric field destroys the preferred orientation of the frozen-in dipoles. These phenomena are named as photo-induced polarization (PIP) and photo-induced depolarization (PID), respectively. PIP and PID have re-

l) SchloDplatz 5 , D-4400 Munster, BRD. 2, DAAD post doctoral research fellow. Present address: Department of Physics, University of

Gorakhpur, Gorakhpur-273001, India.

682 J. PRAKASR

cently been reported also for the Suzuki phase by Benci et al. [5] in Pb2+-doped KCl. The present paper reports the measurements on S2--doped potassium iodide single crystals which form a part of our systematic study of the phenomena of PIP and PID. PIT) has been studied as a function of the irradiation temperature and irradiation time. It has been observed that PID does not take place below 130 K. PIP has been studied as a function of the electric field strength. A limiting value of the electric field, E,, is obtained below which the peak of the ITC spectrum decreases instead of increasing even during the PIP procedure.

2. Experimental Techniques Single crystals of K I doped with S2- are prepared by an almost similar procedure as described in an earlier paper [6]. For ionic therniocurrent measurements (for details see [3]) the crystal is polarized by applying a polarizing voltage U p a t the polarization temperature T, for about 4 min, and with the electric field still on it is rapidly cooled down to LNT when the electric field is switched off. This experimental procedure for ITC measurement is mentioned in the present paper as: The crystal is polarized a t T , by applying a polarizing voltage U p in the polarization temperature range T , to LNT. The results reported here have been found to be repeatable for various single crystals of varying concentration.

3. Results and Discussions The ITC spectrum in sulphur-doped potassium iodide single crystals due to fi2-- anion vacancy dipoles is shown by curve 1 of Fig. 1, where the depolarization current ( I ) has been plotted as a function of temperature (T). For recording the ITC spectrum the crystal is polarized a t 210 K by applying a polarizing voltage of 1500V in the polarization temperature range 210 K to LNT. It is apparent from the figure that the maximum current of the ITC spectrum lies a t 204 K (TmJ for a heating rate of 0.05 K/s. The other relevant dielectric relaxation parameters are reported elsewhere [3].

The S2--anion vacancy dipole in KI has three characteristic absorption bands at 232,278, and 368 nm [7]. Irradiation in the 232 and 278 nm absorption bands a t 240 K results into a photochemical reaction [8]. No photocheniical reaction is observed when the crystal is irradiated a t LET in the 232 and 278 nm absorption bands. Also, irradia- tion in the 368 nm absorption band from room temperature down to LNT has no effect a t all.

However, irradiation in the 368 nni absorption band in the presence of an electric field (U,,, = U p ) creates a situation in which more dipoles are aligned along the elec- tric field direction [3]. The effect of irradiation in the presence of an electric field (V,,,) is shown by curves 2, 3, and 4 of Fig. 1 [3]. It is apparent from Fig. 1 that the peak of the ITC spectrum increases. The difference in the area of ITC curves 2, 3, and 4 with respect to 1 gives the number of I V dipoles which have undergone further orientation. This phenomenon of increase in the ITC peak is called photo-induced polarization

f 6 Fig. 1. Photo-inducedpolarization of the S2--anion vacancy dipole in sulphur-doped potassium iodide'single crystals. T, = 210 K, 3

b4 U p = 1500 V, polarization temperature range 210 K to LNT, + irradiation wavelength 368 nm, U,,, = Up = 1500 V, and

2 irradiation time 210 s. (1 ) Normal ITC spectrum, (2) irradiated a t 107. (3) 185, (4) 179 K. For the normal ITC spectrum the crystal is not irradiated 0

140 160 180 200 220 T i K j -

- -

Photo-Induced Polarization of S2--Anion Vacancy Dipoles in Potassium Iodide 683

(PIP). PIP has been studied as a function of irradiation temperature, irradiation time, and electric field strength and the results are reported in our earlier paper [3]. It is speculated that the further polarization during PIP procedure takes place through the electronic excited state where the activation energy for the orientation of IV dipoles (E&) is sufficiently small in comparison to that required in the electronic ground state (E,). It has been shown by Fischer [9] that Ei < E, is not a sufficient condition for orientation in the electronic excited state. The phenomenon of PIP does take place only when EH is sufficiently less than E,. If this is a mechanism responsible for the phenomenon of PIP, it should also happen that the polarized dipoles disorient when being irradiated in the absence of an electric field in the 368 nni absorption band. The effect of irradiation in the absence of an electric field ( Uirr = 0 V) is shown by curve 2 of Fig. 2 [3]. It is apparent that the peak of the ITC spectrum decreases in comparison to curve 1 (normal ITC spectrum) of Fig. 2. The difference in the area of ITC curve 1 and 2 of Fig. 2 gives the concentration of IV dipoles which have undergone depolariza- tion. This phenomenon of decrease in the ITC peak is named photo-induced depolariza- tion (PID). PIP and PID have also been recently observed for the Suzuki phase (hete- rogeneous phase occlusions of I V dipoles) by Benci et al. [5] in Pb2+-doped KCl. It should be mentioned, however, that according to them the maximum current of the ITC spectrum corresponding to an isolated I V dipole occurs a t 222 K, whereas that corresponding to the Suzuki phase a t 278 K. It is the ITC spectruni at 278 K corre- sponding to the Suzuki phase which shows the phenomena of PIP and PID. They have argued that PIP and PI Din the Suzuki phase are taking place via an electrically excited state. I n another report on Pb2+-doped KCI, Capelletti et al. [lo] have emphasized that the disorientation of IV dipoles via the electronic excited state is the mechanism responsible for PID. I n the present paper we report some more measurements on S2--doped potassium iodide single crystals which will help in building up a suitable model for understanding the mechanism responsible for PIP and PID.

I n the case of Fig. 2, the crystal is polarized a t 210 K by applying a polarizing voltage of 1500 V in the polarization temperature range 210 to 179 K (for details see [3]). For curve 2 the crystal after polarization is soon irradiated for 5 min a t 179 I< in the absence of an electric field (U,,, = 0 V) in the 368 nm absorption band. The decrease in the peak of the ITC spectrum comes out to be 23%. Just to insure that this depolarization is solely due to PID and does not have any contribution from the self-depolarization, the crystal after polarization is left as such a t 179 K for 5 min. The depolarization current recorded showed a decrease in the ITC peak by 11 yo when com- pared with curve 1 of Fig. 2. Thus, the effective contribution due to PID a t 179 K is only 12% whereas polarized dipoles depolarize due to thermal agitation a t 179 K by 11 yo. For the time being let us not stick to the magnitudes just mentioned, but infer simply that there are temperatures a t which the phenomena of PID and self-depolar- ization take place simultaneously. Although. it is not advisable to study the time de- pendence at 179 K because of the presence of simultaneous phenomena of self-depolar- ization and PID. Even then, just for the sake of inforniation the data of Fig. 3 are

Fig. 2. Photo-induced depolarization of the S2--anion vacancy dipole in sulphur-doped potassium iodide single crystals. T, = 210 K, Up = 1500 V, Ui,, = 0 V, irradiation tempera- ture 179 K, irradiation wavelength 368 nm, and irradiation time 5 min. (1) Normal ITC spectrum when polarized in the temperature range 210 t o 179 K; (2) ITC spectrum when polar- ized in the temperature range 210 to 179 K and soon irradiated

$40 160 180 200 220 at 179 K for 5 min in the absence of an electric field in the 368 nm absorption band T i K ) -

684 J. PRAKASH

Fig. 3. The dependence of photo-induced depolar- ization of the S2--anion vacancy dipole on irradiation time ( t ) in the KI: S2- system recorded at the irradi- ation temperature of 179 K where the phenomena of PID and self-depolarization take place simultaneously. T, = 210 K, Up = 1500 V, polarization temperature range 210 t o 179 K, irradiation temperature 179 K, Uirr = 0 V, and irradiation wavelength 368 nm

collected. The crystal is polarized a t 210 K by applying a polarizing voltage of 1500 V in the polarization temperature range 210 to 179K. Soon after switching off the electric field a t 179 K, the crystal is irradiated a t 179 K in the absence of an electric field (U,, , = 0 V) in the 368 niii absorption band for varying irradiation time ( t ) . It is obvious from Fig. 3 that the peak of the ITC spectrum initially decreases linearly as expected and then tends towards a constant value exponentially. The exponential decrease of the ITC peak is due to the simultaneous presence of self-depolarization along with PID. Since self-depolarization and PID are simultaneously present, it is planned to study the irradiation temperature dependence at first and then to study the time dependence of the phenomenon of PID. It will he worth mentioning that the self-depolarization due to thermal disturbances will take place through the electronic ground state, whereas PID takes place through the electronic excited state.

In order to study the dependence of PID on the irradiation temperature, the crystal is polarized a t 210 K by applying a polarizing voltage of 1500 V in the polarization temperature range 210 K to the irradiation temperature. At the irradiation temperature (!PIT,) the electric field is switched off and the crystal is soon irradiated in the absence of an electric field (U,,, = 0 V) in the 368 nm absorption band for 210 s. ,Just after the irradiation the crystal is rapidly cooled down to LNT. The results of such experiments corresponding to different temperatures of irradiation are shown in Fig. 4. It is apparent from the figure that from LNT up to 130 K the phenomenon of PID does not take place. The ITC peak starts decreasing slowly with increasing irradiation tempera- ture above 130 K and then rapidly above 170 K. The rapid decrease of the 1°C peak above 170 K is partly due to the self-depolarization of the polarized dipoles. Self- depolarization below 170 K is experimentally found to be absent. It is obvious that below 130 I< the IV dipoles are unable to cross the potential energy barrier in the elec- tronic excited state through which the phenomenon of PID takes place.

Let us try to explain the irradiation temperature dependence of PID following the bistable model of IV dipoles where there are two orientations in the electronic ground state [ l l ] and similarly only two orientations in the electronic excited state. The cor- responding potential energy barrier heights in the electronic ground state and in the electronic excited state are E, and Eh, respectively. During the PID procedure, we irradiate in a state where polarized dipoles are frozen in and thereby statistically the

- 0 Fig. 4. The dependence of photo-induced depolarization of the S2--anion vacancy dipole on irradiation temperature k 2 -10 (Tirr) in the KI:S2- system. !Zip = 210 K, Up = 1500 V, polarization temperature range 210K to Tirr, Uirr = OV, 8

b t $ -20 'Ob 60 100 140 180 220 irradiation wavelength 368 nm, and irradiation time 210 s

Trr fKI -

Phot.0-Induced Polarizat,ion of S2--Anion Vacancy Dipoles in Potassium Iodide 685

number of dipoles in the frozen-in condition in one of the potential wells corresponding to the preferred orientation (say, well No. 1) will he larger than the number of dipoles in the other potential well which corresponds to the unpreferred orientation (say, well S o . 2). This difference in the number of dipoles in the two potential wells is responsible for the frozen-in polarization. Also, in the electronic excited state the number of dipoles in potential well No. 1 will be larger than that present in the potential well No. 2 since dipoles from potential well No. 1 as well as from potential well No. 2 of the elec- tronic ground state are excited siniultaneonsly. The potential energy barrier height will not be modified during PID (since the electric field is absent) and hence the jump probabilites per second in going from one of the potential wells to the other, i.e. from No. 1 to 2 (P1J or No. 2 to 1 (Pz1), will be the same. So, statistically more dipoles will jump from potential well NO. 1 to 2 through the electronic excited state resulting into the decrease of the polarization during PID. Since E , < E,, there niust still be a suf- ficiently high probability for depolarization via electronic excited state below 170 K. The relaxation time (z’) of the dipole centres in the electronic excited state depends on temperature in accordance with z‘ = zb exp (EiIlcT) where zb is the pre-exponential factor, whereas the lifetinie Z, (= s) of the dipole centres in the electronic excited state is temperature independent. I n the cases when z’ < z, (i.e. above 130 K), the dipole centres in the electronic excited state are able to attain the thermal equilibrium corresponding to the crystal temperature. As soon as z’ 2 z, (i.e. below 130 K), the thermal equilibrium in the electronic excited state cannot be obtained any niore. The dipole centres then return to the electronic ground state befoi e they could cross the potential energy barrier in the electronic excited state. This leads to the disappearance of the phenomenon of PID below 130 K.

We have seen that during PID above 170 K, self-depolarization also contributes and hence the effective temperature range in which further properties of PID can be in- vestigated is 130 to 170 K (see Fig. 4). We choose a temperature of 162 K for study- ing the depencence of PID on irradiation time. I n this case, the crystal is polarized a t 210 K by applying a polarizing voltage of 1500 V in the polarization temperature range 210 to 162 K. At 162 K, the electric field is switched off and the crystal is soon irradiated at 162 K for varying irradiation time ( t ) in the absence of an electric field (U,,, = 0 V) in the 368 nm absorption band. It is apparent from Fig. 5 that the peak of the ITC spectruni initially decreases linearly with irradiation time and finally tends towards a constant value. We notice from the figure that the polarized dipoles depolar- ize to an extent of 8%. If there is a single mechanlsrn responsible for the phenomenon of PID, all the dipole centres should behave alike. One should expect, then, a decrease of 100% after long enough irradiation following an exponential law. When only 8% of the polarization can be bleached one has to suspect that a t least two different groups of dipole centres are involved. This value of 8% obtained a t 162 K could depend on the temperature of irradiation. This aspect has not yet been checked. J t will be justified to mention here, however, that in the present investigations the whole area of the crys- tal specimen is exposed to irradiation.

Fig. 5 . The dependence of photo-induced depolarization of the SZ--anion vacancy dipole on irradiation time ( t ) in the KI: S2- system. Tp = 210 I<, 77, = 1500 V, polar- ization temperature range 210 to 162 K, irradiation tem- perature 162 K, Uirr = 0 V, and irradiation wavelength

- Q - - f (mini -

686 J. PRAKASH

Fig. 6. Polarizationof theP-anion vacancy dipole in sulphur-doped potassium iodide single crystals a t different polarizing temperatu- res ( Tp). Polarized a t T,, Up = 1500 V, and polarization temper- ature range T, to LNT E;y3v;l -4 -, 2

0 140 180 220

1

5 iKI-

To visualize the niechanism of orientation in the electronic ground state, the polar- ization of I V dipoles a t varying polarization temperatures has been recorded. The results of such experiments are presented in Fig. 6. I n this case the crystal is polarized a t varying polarization temperature T, by applying a polarizing voltage of 1500 V in the polarization temperature range T, to LNT. It is apparent from the figure that when the crystal is polarized in the vicinity of T,,, (204 K) such that T, 2 T,,,, the peak of the ITC spectrum (Ip.& is unaffected and the crystal is polarized to the same extent. The polarization starts decreasing rapidly below 204 K. At about 170 I< and a t other lower temperatures the crystal ceases to be polarized by the application of the electric field. We h a w already observed that above 170 K self-depolarization also contributes to PID, whereas below 170 K self-depolarization is absent which obviously takes place through the electronic ground state. Thus, the inference that the crystal cannot be polarized at = 170 K and a t other lower temperatures by the application of the electric field, is in accordance with the results of PID measurements.

To record the dependence of PIP on the electric field strength a routine experiment was carried out which is reported in our earlier paper [3]. It has been observed that the peak of the ITC spectrum (Ipeak) recorded when the crystal was not irradiated varies linearly with the applied polarizing voltage (Up). Also, when the crystal was irradiated a t 179 K in the presence of an electric field (U,,, = Up) in the 368 nm absorption band, Ipe.,k varies linearly with Up. Although, there is a linear dependence of Ipeak on Up in the latter case, we had some doubt that a t lower polarizing voltage the linear depend- ence does not hold. This deviation could not be emphasized with certainty as a t lower voltages the accuracy was too poor to draw a definite conclusion. To decide whether the straight line dependence deviates a t lower polarizing voltage during PIP, the fol- lowing experiments are performed.

Based on the findings of PID (see Fig. 4 and 5), a temperature of 162 K was chosen for the purpose of irradiation. The crystal is polarized a t 210 K by applying a polarizing voltage of 1500 V for =: 4 min, and with the electric field still on the crystal is cooled down to the irradiation temperature of 162 K. At 162 K the electric field is decreased to different irradiation voltages (say 500 V) and the crystal is irradiated in the presence of this irradiation voltage (500 V) in the 368 nm absorption band for 210 s. Soon after the irradiation the crystal is rapidly cooled down to LNT, where the electric field is switched off and the depolarization current is recorded. The results of such experiments are presented in Fig. 7. It should be worth mentioning that a t 162 K the contribution of the self-depolarization is practically zero and hence just after the irradiation, in- creasing the irradiation voltage up to the polarizing voltage of 1500 V or leaving it a t its values has no effect a t all on the ITC spectrum. Ipeak in Fig. 7 corresponds to the peak of the ITC spectrum when the crystal is polarized a t 210 K and is irradiated a t 162 I<, whereas 10 peak in Fig. 7 corresponds to the peak of the ITC spectrum when the crystal is polarized a t 210 K and is not irradiated. I n Fig. 7 the ratio has

Photo-Induced Polarization of S2--Anion Vacancy Dipoles in Potassium Iodide 687

Fig. I . Photo-inducedpolarization of theS2--anionvacancydipole in sulphur-doped potassium iodide single crystals as a function of irradiation voltage (Uirr) in the presence of which the crystal is irradiated a t 162 K in the 368 nm absorption band for 210 s. T, = 210 K, Up = 1500 V, irradiation temperature 162 K. voltage a t the irradiation temperature Uir,, and polarization 10

temperature range 210 K to LNT. Ipeak corresponds to the peak 0dG 4oo 71200 ,600 of the ITC spectrum when the crystal is irradiated. IOpeak cor-

responds to the peak of the ITC spectrum when the crystal is not irradiated

*::p! - 3

u,, (vI - been plotted against the irradiation voltage (U,,,) kept a t the irradiation temperature of 162 K, in the presence of which the crystal has been irradiated a t 162 K i n the 368 nni absorption band for 210 s. During PIP the peak of the ITC spectrum increases and hence the ratio of ( I / I o ) p e a k should be larger than unity. The positive deviation from unity gives the magnitude of extra polarization which occurs during the PIP procedure. It is apparent from the figure that the value of (I/Io)peak is larger than unity when the voltage during irradiation (Ulrr) is kept above 100 V. At U,,, = 100 V, the ratio of ( I / / o ) p & happens to be unity, which effectively speaks that there is no change in the ITC spectrum. At U,,, = 100 V, the phenomenon of PIP is absent. Further, when U,,, is kept equal to 50 V, we notice a decrease in the peak of the ITC spectrum resulting into a value below unity for ( I / Io)peal , . Obviously, when the crystal is irradiated in the presence of an electric field with U,,, = 50 V a t 162 K, the peak of the ITC spectrum decreases instead of increasing. And hence, the phenomenon of PIP in the case U,,, = 50 V seems to be a PID phenomenon. Thus, there exists a limiting value of the electric field strength (100 V / d , where d is the thickness of the crystal specimen). If U,,,/d is larger than the limiting value of the electric field strength (E,,), the pheno- menon of PIP will take place. In the cases Ui,,/d < Eo the phenomenon of PIP will behave as a P ID Phenomenon. Further, when U,,,/d = E, there will be no change in the ITC spectrum.

The behaviour of PIP asPID in the cases when U,,,/d < Eo can be conceived following the bistable model of I V dipoles. When an electric field is applied, the potential wells are modified and the jump probabilities Plz and P,, now differ, resulting into the net polarization according to the relation

where AE, = Er is the change in the activation energy for the orientation of IV dipole (or in the potential energy barrier height E,) in the presence of the electric field E and r the cation- anion separation. For irradiation voltages higher than E,d, the jump prob- abilities will differ to such an extent to give an extra polarization via an electric excited state. However, for irradiation voltages lower than E,,d the potential wells No. 1 and 2 will not be modified considerably leading to a very small difference in the jump probabilities Plz and P,, or practically the jump probabilities remain unaffected. Ob- viously enough, since the jump probabilities P,, and P,, are almost the same, the ex- perimental conditions during the phenomenon of PIP will look like a condition prevail- ing during PID. I n the case when U,,,/d = E,,, the jump probabilities are such that they overcome the contributions of each other leading to no change in the ITC spectrum or (I/Io)peak equal tounity. Thus the resultsofPIPandPIDin theKI: S2-systenipresent- ed here can be qualitatively explained following the bistable model of IV dipoles. It is plausible to presume that the limiting value of the electric field (E,) depends partly on the local internal field. Further nreasurements on this system and various other

688 J. PRAKASH: Photo-Induced Polarization and Photo-Induced Depolarization

systenis, e.g. ICI: Se2-, KBr: S2-, KBr : Se2- etc. are carried out such that the proper understanding of the mechanisms responsible for the phenomena of PIP and PID can be conceived.

Acknowledgements

The author is grateful to Prof. Dr. F. Fischer, University of Mimeter (FRG) for valuable suggestions and for providing the necessary facilities for measurements in his Iaboratory. He is also thankful to Dr. J. Honer zu Siderdissen for his cooperation in setting bhc cryostat. Thanks are also due to Mr. R. Arends for his help during crystal growing.

References [l] C. BIJCCI, R. FIESCHI, and G. GUIUI, Phys. Rev. 148, 816 (1966). [2] J. PRAK.4SH and F. F~SCHER, J. Physique 37, C7-167 (1976). [3] 6. F’RAKASH and F. FISCHER, phys. stat. sol. (a) 39, 499 (1977). [4] J. PRAKASH, Indian J. pure appl. Phys. 16, 995 (1978). IS] S. BENCI, R. CAPELLETTI, R. E’ERMI, and M. &fA4NFREDI, J. Physique 37, C7-138 (1976). [6] F. FISCHER and H. G R ~ N D I G , Z. Phys. 184, 299 (1965). [7] P. HESNL, phys. stat. sol. (a) 46, 147 (1978). [XI J. PRAKASH, Japan. J. appl. Phys. 17 , 1067 (1978). [9] F. FISCHER, private communication.

[lo] B. CAPELLETTI, R. FIESWII, and E. OKUNO, Internat. Conf. Color Centers in Ionic Crystals,

[111 A. S. NOWICK, Point Defects in Solids, Chap. 3, Ed. J. H. CRaWFORD, ,JR. and I,. M. SLIFHIN, Sendai (Japan) 1974 (p. G138).

Plenum Press, New York 1972 (p. 166).

(IleeeiePd dpril 5, 1979)