- Email: [email protected]
D.C. electrical conductivity in LiNH4SO4
Solid State Communications, Vol. 34, pp. 899—903. Pergamon Press Ltd. 1980. Printed in Great Britain. D.C. ELECTRICAL CONDUCTIVITY IN LINH4SO4 U. Syamaprasad and C.P.G. Vallabhan Department of Physics, Cochin University, Cochin 682 022, India (Received 3 March 1980 by Y. Toyozawa) The d.c. electrical conductivity of pure, doped and quenched samples of LiNH4SO4 is measured between liquid nitrogen temperature and 290°C. A-type conductivity anomalies are observed at 10°Cand at 186.5°Calong the ferroelectric axis. The mechanisms of electrical conduction in the various phases and at the transition points are discussed. 1. INTRODUCTION AT ROOM TEMPERATURE lithium ammomum sulphate, LiNH4SO4, is known to have an orthorhombic symmetry with pseudohexagonal structure and it belongs to the spacegroup F21cn witha = 5.280, b = 9.140,c = 8.786 A andZ = 4 [1]. On cooling it exhibits ature first(point ordergroup phase2)in change a polarofmonoclinic thetovicinity 10°C[2]. strucIt has been reported by Toshiharu Mitsui et al. [3] that there exists another transition point for LiNH 4SO4 at 186.5°C and this substance is ferroelectric along the a-axis between the two transition points. The Raman [4] as well as the infrared spectrum [5] of this crystal has been studied in detail. No attempt has so far been made in studying the electrical conductivity of this material, In this communication we report the results of our study on the d.c. electrical conductivity of LiNH4SO4 along the three crystallographic axes from liquid nitrogen temperature to 290°C.The crystal samples were also doped with divalent cationic impurities and conductivity measurements were carried out with a view to establish the mechanism of electrical conduction.
and accuracy better than ±0.2°C. The heating of the chamber was done by direct current and it was carefully shielded from stray electrical disturbances. Tern. perature measurements were carried out by two copper— constantan thermocouples arranged just above and below the specimen. The rate of the temperature change 1 in the the other regions. A potential of was ~ hr~in vicinity of the transitiondifference points and 10°ChrV was applied across the crystal from dry 50—100 batteries and the resulting current was measured by a ‘..
vibrating condenser electrometer (Electronic Corporation of India Umited, Model EA8I 1) and the same was checked by means of a d.c. Microvoltmeter (Marconi, Model TF 2655). No appreciable polarization effects were observed for the above voltage ranges, the value of current remaining constant for several minutes after applying the field. Electrical leakage current through the mount was bypassed to earth by grounding the mount so that the meter reading gives only the current through the crystal. Each of the samples was first annealed at 120°C for 2 Hr in vacuum by keeping the same on the conductivity mount itself so as to avoid surface conduction.
2. EXPERIMENTAL Single crystals of LiNH4SO4 were grown over a period of a week by slow evaporation of saturated aqueous solution containing equimolecular amount of Li2SO4H2O and (NH4)2 SO4. Specimens in the form of thin slabs (0.5 cm x 0.5cm x 0.1 cm) were prepared with edges parallel to the crystallographic axes. The two largest surfaces opposite to each other were coated with silver conducting paint and the specimen was mounted on a sample holder having spring loaded circular copper electrodes provided with teflon insulating supports. Evacuated chambers in which a vacuum of iO~torr could be maintained were used for temperature variation studies. The temperature could be controlled from liquid nitrogen temperature to 350°Cwith a stability
3. RESULTS The three phases of LiNH4SO4 appearing successively while lowering temperature are denoted by phase I (T ~ 186.5°C)II (10~T ~ 186.5°C)and III (T ~ 10°C). The conductivity data were obtained on raising the temperature from that of liquid nitrogen to 290°Cand also on cooling. The results were found to be very well reproducible for different samples as well as for different heating and cooling runs. Curves denoted by (a) in Figs. I and 2 respectively show the conductivity plots for LINH4SO4 along a-axis (ferroelectric axis) and along b-axis. The curve for the c-axis is almost identical to that for b and ence i~ is not shown in the figure. The striking feature of the present result is that two A-type 899
900
D.C. ELECTRICAL CONDUCTIVITY IN LiNH4SO4
—7
-
Vol. 34, No. II
—
-8.
—9
—10
o
—~1
0
~-12
o
~
1.~
2.2
2.~
3.’O
a~4:24~6
A
5.0
1o~/
TK 3/T plot for UNH 2~,_r—i—. (d) doped Cu2t Fig. 1. Log a vs I 0 4SO4 single crystals along the ferroelectric axis (a-axis): . (a) purewith sample, (b) quenched from the upper transition temperature (c) doped with Zn —i—A—
conductivity anomalies are observed, one at 10°Cand the other at 186.5°C.The transition at 10°Cis quite abrupt and there is an enormous increase in conduc-
Thus the conductivity of the whole region except in the vicinity of the transition points can be written as: U
tivity of about two orders of magnitude, while the transition at 186.5°Cis rather gradual and the increase in conductivity is only about an order of magntiude. It is found that a slower rate of variation of temperature gives sharper peaks. Except in the vicinity of the transition points the plots have three distinct straight line regions characteristic of ionic crystals [6]. The linear regions of the curve denoted by (a) in Fig. 1, can be described by the following equations: a1 = 1.19 x 106 exp (— 17,265/T), (1) =
0111
=
1.09 x iO~exp (— 6714/T), 5.01 x 10_14 exp (— 287/T).
(2) (3)
=
U~+ U 11
+ a111.
(4)
The slopes of the three linear regions give activation energies of 1.51, 0.58, and 0.025 eV in phases I, II and III of the crystal respectively. The activation energy values are almost the same in the case of the other axes. In phase III (antiferroelectric phase) the rate of variation of conductivity is extremely small and the curve extends almost parallel to the x-axis. (region below 70°Cis not shown in the figure). The plot denoted by (b) in Fig. 1 for a crystal quenched from the upper transition temperature to room temperature does not retrace the original path, but shows a higher value of conductivity in phase II, corresponding to a low —
Vol. 34, No. 11
D.C. ELECTRICAL CONDUCTIVITY IN UNH4SO4
901
—7
-8
-9
‘-‘
-10
TE0 -c 0
-
~-12.
—13
—14
.
—15
___________________________________________________________________________
1.8
2.2
2.6
3.0
3.4
3.8
4.2
4.6
5.0
I 0’~/T°K Fig. 2. Log a vs 103/T plot for UNH~SO 2~, (c) doped with Zn dopedalong with the (~2+ 4single(d) crystals b-axis: (a) pure sample, —o—o— (b) doped with Fe activation energy of about 0.1 eV. The quenching also 4. DISCUSSION reduces the height of the upper A-type peak. Doping of the crystal with divalent cationic impurities It is well known that electrical conduction in ionic (Z2~,~2+ and Fe2~)have the general effect of reducing crystals is a defect controlled property. The defect the conductivity of the crystal (Figs. I and 2). The concentration increases exponentially with rise of effect is more pronounced in phase II. In phase 111 temperature and hence the electrical conduction doping reduces the conductivity slightly while in phase I enhances correspondingly. In ionic crystals containing it has a lower value up to 270°Cwhen compared with ammonium groups the possible types of point defects the conductivity value for the pure crystals. Above are: normal ionic and electronic defects as found in 270°C the curves for both pure and doped crystals alkali halides and conventional semiconductors and merge into a single line. The activation energies of the protomc defects [7]. As a result conductivity may be doped crystals show a significant increase in phases II ionic, electronic and/or protonic. Generally in ionic and I while it has no change in phase III. crystals, the electronic defects, viz, electrons and holes —A—A—-
~,
—~—&--
—.—-.—
902
D.C. ELECTRICAL CONDUCTIVITY IN LiNH4SO4
and the protonic defects which may be the hydrogen ions removed the small ammonium groups the mixing hydrogen ions from are very in number. Inor LiNH 4SO4 the ionic defects are lithium, ammonium and sulphate ions (both vacancies and interstitials). Our experimentally confirmed result is that the doping of the crystals with divalent cationic impurities has a general effect of reducing the electrical conductivity. To compensate the excess charge of the added divalent positive ion impurity, (Z2.F), positive ion vacancies, (V), or negative ion interstitials, (X), may be created. If the mechanism of electrical conduction in the crystal is by the migration of either of these defects, the conductivity must be enhanced. To account for the observed decrease in conductivity we should consider the effect of the above increase in number ofnegative carriers on the concentration of other defects such as negative ion vacancies, (V~)and positive ion interstitials, (X~).The concentration of positive ion vacancy, [V1, exists in equilibrium with the concentration of negative ion vacancy, [V~], and also with the concentration of positive ion interstitials, [X~J. Similarly the concentration of negative ion interstitials, [X], exists in equilibrium with that of negative ion vacancy, [V~]. This may be expressed by the following equations [6]: + [V ][V~] = exp(—g 5/KT) = XS, (5) 2
[Vi] [X~] [X - 1[V~J +
=
exp (— g~/KT) = 4,
(6)
=
2 exp(—g~~/KT)= XAF
(7)
where 5, F and AF stand for Schottky, Frenkel and Antifrenkel defects respectively, g for the free energy of formation of defects, and x for the concentration of either defects in pure crystal. It is understood from the expressions (5) to (7) that increase in [V] or [X1 results in the decrease of [V~J and/or [X~]. That is, the addition of divalent positive ion impurities into the lattice has the effect of decreasing the negative ion vacancies and/or positive ion interstitials. The conductivity will decrease if the process is mainly contributed by either anion vacancies or cation interstitials. On account of the larger size of the sulphate (sulphur— oxygen bond in sulphate ion is 1.44 A with oxygen having an ionic radius of 1.40 A) and ammonium ions (ionic radius 1 .43 A) occurrence of interstitial sulphate and ammonium ions is less likely [8]. Also the mobility of the above interstitials and their vacancies is far less. Hence it follows that cationic Frenkel disorder is the most predominant one and the conductivity is contributed mainly by the migration of interstitial lithium ions (ionic radius 0.68 A). The usual method of purification by repeated crystallisation was used to prepare the “pure” sample. (To prepare the “pure” sample, BDH Analar grade salt was
Vol. 34, No. 11
recrystallised five times). This sample is2~), known to conand divalent tam divalent positive ion impurities, 2), of the (Z order of iO~ negative ion impurities, (Z also consider the effect of molar fraction. One should association of these impurity ions with the more significant charge compensators, viz. (V~)and (X~)to form complexes (Z2~V~) and (Z2X~).In phase I both of these complexes will be entirely in dissociated states providing a greater number of mobile defects resulting in a higher conductivity. In phase II these complexes are only partly dissociated and hence the conductivity is comparatively smaller. In phase Ill the existing impurity content may exceed the solubility limit and the impurity may precipitate out as a separate phase. This leads to a reduction of the carriers which explains the lower portion of the curve. The part of the plot above 270°Ccan be considered as the intrinsic region since the curves merge into one another in this portion. Although the actual values of conductivity are different along a and b(c) directions the activation energies themselves are found to be mdependent of direction. Thus it appears that the mechanism of electrical conduction is the same for different directions in this crystal. The sharp rise in conductivity at the transition point from phase HI to II may be due to the large scale avail.
ability of the carriers released dunng the rearrangement process of the crystal lattice or due to the loosening of the same. As in the case of ammonium chloride [91, the ammonium ions m LiNH4SO4 may be assumed to change from a state of tortional oscillation to one of free rotation while the crystal undergoes transition from phase II to I. This may generate an enormous amount of protonic defects giving rise to the conductivity anomaly at 186.5°C.Quenching of the crystal from the transition point leads to freeze the excess carriers produced at the transition point and these frozen in defects [6] may be responsible for the increase in conductivity of the quenched sample. Hence the observed decrease in activation energy value of 0.1 eV should correspond to the migration of these frozen in carriers. Murti et aL [10] estimated the activation energy of protons in NH4CI to be 0.08 eV by a plastic deformation experiment. A reasonable assumption that the activation energy of protons in LiNH4SO4 is not widely different from this value leads to the conclusion that protonic conduction can be the phenomenon responsible for the conductivity anomaly at 186.5°C. .
5. CONCLUSIONS The migration of interstitial Li~ions is suggested to be the dominant mechanism of electrical transport in single crystals of LiNH4SO4. Activation energy measurements
Vol. 34, No. 11
D.C. ELECTRICAL CONDUCTIVITY IN LiNH4SO4
show that the conduction mechanism is the same for the different directions in the crystal. The conductivity anomaly at 10°Cis suggested to be due to the availability of excess carriers released during the rearrangement process of the crystal lattice or due to the loosening of the same. Pmotonic conduction can be responsible for the discontinuity observed at 186.5°C.
Acknowledgements The authors wish to thank Dr. j Ramakrishna of Indian Institute of Science, Bangalore for providing them with some crystal samples used in these studies. They are grateful to Dr. K. Sathianandan for his kind interest and encouragement during the progress of this work. Thanks are also due to University Grants Commission, New Delhi for providing a Junior Research Fellowship to one of the authors (U.S.P.) and for a research grant to the other. —
903
REFERENCES I. 2.
W.A. Dollase, Acta Crystallogr. B25, 2298 (1965). R. Pepinsky, K. Venam, Y. Okaya & S. Hosino, Phys. Rev. 111, 1467 (1958). 3. T. Mitsui, T. Oka, Y. Shiroishi, M. Takashige, K. ho & S. Sawada, J. Phys. Soc. Japan 39, 845 (1975). 4. A.V. R. Warner, Spectra of Crystals. Ph.D. Thesis, Indian Institute of Science, Bangalore (1966). 5. P. Kumamacharya & P.S. Narayanan, Indian J. Pure andAppi. Phys. 11, 514 (1973). 6. A.B. Lidiard, Handbuch der Physik 20, 246 (1957). 7. F.A. Kroger, J. Chem. Phys. 51, 4025 (1969). 8. N.F. Mott & R.W. Gurney, Electronic Process in Ionic Crystals, 2nd edn. p. 41(1964). 9. Y.V.G.S. Murty & S. Prasad, Proc. Nuclear Physics and Solid State Physics Symposium 17C, 67 (1974). 10. Y.V.G.S. Murti & P.S. Prasad, Solid State Commun. 15, 1619 (1974).
and accuracy better than ±0.2°C. The heating of the chamber was done by direct current and it was carefully shielded from stray electrical disturbances. Tern. perature measurements were carried out by two copper— constantan thermocouples arranged just above and below the specimen. The rate of the temperature change 1 in the the other regions. A potential of was ~ hr~in vicinity of the transitiondifference points and 10°ChrV was applied across the crystal from dry 50—100 batteries and the resulting current was measured by a ‘..
vibrating condenser electrometer (Electronic Corporation of India Umited, Model EA8I 1) and the same was checked by means of a d.c. Microvoltmeter (Marconi, Model TF 2655). No appreciable polarization effects were observed for the above voltage ranges, the value of current remaining constant for several minutes after applying the field. Electrical leakage current through the mount was bypassed to earth by grounding the mount so that the meter reading gives only the current through the crystal. Each of the samples was first annealed at 120°C for 2 Hr in vacuum by keeping the same on the conductivity mount itself so as to avoid surface conduction.
2. EXPERIMENTAL Single crystals of LiNH4SO4 were grown over a period of a week by slow evaporation of saturated aqueous solution containing equimolecular amount of Li2SO4H2O and (NH4)2 SO4. Specimens in the form of thin slabs (0.5 cm x 0.5cm x 0.1 cm) were prepared with edges parallel to the crystallographic axes. The two largest surfaces opposite to each other were coated with silver conducting paint and the specimen was mounted on a sample holder having spring loaded circular copper electrodes provided with teflon insulating supports. Evacuated chambers in which a vacuum of iO~torr could be maintained were used for temperature variation studies. The temperature could be controlled from liquid nitrogen temperature to 350°Cwith a stability
3. RESULTS The three phases of LiNH4SO4 appearing successively while lowering temperature are denoted by phase I (T ~ 186.5°C)II (10~T ~ 186.5°C)and III (T ~ 10°C). The conductivity data were obtained on raising the temperature from that of liquid nitrogen to 290°Cand also on cooling. The results were found to be very well reproducible for different samples as well as for different heating and cooling runs. Curves denoted by (a) in Figs. I and 2 respectively show the conductivity plots for LINH4SO4 along a-axis (ferroelectric axis) and along b-axis. The curve for the c-axis is almost identical to that for b and ence i~ is not shown in the figure. The striking feature of the present result is that two A-type 899
900
D.C. ELECTRICAL CONDUCTIVITY IN LiNH4SO4
—7
-
Vol. 34, No. II
—
-8.
—9
—10
o
—~1
0
~-12
o
~
1.~
2.2
2.~
3.’O
a~4:24~6
A
5.0
1o~/
TK 3/T plot for UNH 2~,_r—i—. (d) doped Cu2t Fig. 1. Log a vs I 0 4SO4 single crystals along the ferroelectric axis (a-axis): . (a) purewith sample, (b) quenched from the upper transition temperature (c) doped with Zn —i—A—
conductivity anomalies are observed, one at 10°Cand the other at 186.5°C.The transition at 10°Cis quite abrupt and there is an enormous increase in conduc-
Thus the conductivity of the whole region except in the vicinity of the transition points can be written as: U
tivity of about two orders of magnitude, while the transition at 186.5°Cis rather gradual and the increase in conductivity is only about an order of magntiude. It is found that a slower rate of variation of temperature gives sharper peaks. Except in the vicinity of the transition points the plots have three distinct straight line regions characteristic of ionic crystals [6]. The linear regions of the curve denoted by (a) in Fig. 1, can be described by the following equations: a1 = 1.19 x 106 exp (— 17,265/T), (1) =
0111
=
1.09 x iO~exp (— 6714/T), 5.01 x 10_14 exp (— 287/T).
(2) (3)
=
U~+ U 11
+ a111.
(4)
The slopes of the three linear regions give activation energies of 1.51, 0.58, and 0.025 eV in phases I, II and III of the crystal respectively. The activation energy values are almost the same in the case of the other axes. In phase III (antiferroelectric phase) the rate of variation of conductivity is extremely small and the curve extends almost parallel to the x-axis. (region below 70°Cis not shown in the figure). The plot denoted by (b) in Fig. 1 for a crystal quenched from the upper transition temperature to room temperature does not retrace the original path, but shows a higher value of conductivity in phase II, corresponding to a low —
Vol. 34, No. 11
D.C. ELECTRICAL CONDUCTIVITY IN UNH4SO4
901
—7
-8
-9
‘-‘
-10
TE0 -c 0
-
~-12.
—13
—14
.
—15
___________________________________________________________________________
1.8
2.2
2.6
3.0
3.4
3.8
4.2
4.6
5.0
I 0’~/T°K Fig. 2. Log a vs 103/T plot for UNH~SO 2~, (c) doped with Zn dopedalong with the (~2+ 4single(d) crystals b-axis: (a) pure sample, —o—o— (b) doped with Fe activation energy of about 0.1 eV. The quenching also 4. DISCUSSION reduces the height of the upper A-type peak. Doping of the crystal with divalent cationic impurities It is well known that electrical conduction in ionic (Z2~,~2+ and Fe2~)have the general effect of reducing crystals is a defect controlled property. The defect the conductivity of the crystal (Figs. I and 2). The concentration increases exponentially with rise of effect is more pronounced in phase II. In phase 111 temperature and hence the electrical conduction doping reduces the conductivity slightly while in phase I enhances correspondingly. In ionic crystals containing it has a lower value up to 270°Cwhen compared with ammonium groups the possible types of point defects the conductivity value for the pure crystals. Above are: normal ionic and electronic defects as found in 270°C the curves for both pure and doped crystals alkali halides and conventional semiconductors and merge into a single line. The activation energies of the protomc defects [7]. As a result conductivity may be doped crystals show a significant increase in phases II ionic, electronic and/or protonic. Generally in ionic and I while it has no change in phase III. crystals, the electronic defects, viz, electrons and holes —A—A—-
~,
—~—&--
—.—-.—
902
D.C. ELECTRICAL CONDUCTIVITY IN LiNH4SO4
and the protonic defects which may be the hydrogen ions removed the small ammonium groups the mixing hydrogen ions from are very in number. Inor LiNH 4SO4 the ionic defects are lithium, ammonium and sulphate ions (both vacancies and interstitials). Our experimentally confirmed result is that the doping of the crystals with divalent cationic impurities has a general effect of reducing the electrical conductivity. To compensate the excess charge of the added divalent positive ion impurity, (Z2.F), positive ion vacancies, (V), or negative ion interstitials, (X), may be created. If the mechanism of electrical conduction in the crystal is by the migration of either of these defects, the conductivity must be enhanced. To account for the observed decrease in conductivity we should consider the effect of the above increase in number ofnegative carriers on the concentration of other defects such as negative ion vacancies, (V~)and positive ion interstitials, (X~).The concentration of positive ion vacancy, [V1, exists in equilibrium with the concentration of negative ion vacancy, [V~], and also with the concentration of positive ion interstitials, [X~J. Similarly the concentration of negative ion interstitials, [X], exists in equilibrium with that of negative ion vacancy, [V~]. This may be expressed by the following equations [6]: + [V ][V~] = exp(—g 5/KT) = XS, (5) 2
[Vi] [X~] [X - 1[V~J +
=
exp (— g~/KT) = 4,
(6)
=
2 exp(—g~~/KT)= XAF
(7)
where 5, F and AF stand for Schottky, Frenkel and Antifrenkel defects respectively, g for the free energy of formation of defects, and x for the concentration of either defects in pure crystal. It is understood from the expressions (5) to (7) that increase in [V] or [X1 results in the decrease of [V~J and/or [X~]. That is, the addition of divalent positive ion impurities into the lattice has the effect of decreasing the negative ion vacancies and/or positive ion interstitials. The conductivity will decrease if the process is mainly contributed by either anion vacancies or cation interstitials. On account of the larger size of the sulphate (sulphur— oxygen bond in sulphate ion is 1.44 A with oxygen having an ionic radius of 1.40 A) and ammonium ions (ionic radius 1 .43 A) occurrence of interstitial sulphate and ammonium ions is less likely [8]. Also the mobility of the above interstitials and their vacancies is far less. Hence it follows that cationic Frenkel disorder is the most predominant one and the conductivity is contributed mainly by the migration of interstitial lithium ions (ionic radius 0.68 A). The usual method of purification by repeated crystallisation was used to prepare the “pure” sample. (To prepare the “pure” sample, BDH Analar grade salt was
Vol. 34, No. 11
recrystallised five times). This sample is2~), known to conand divalent tam divalent positive ion impurities, 2), of the (Z order of iO~ negative ion impurities, (Z also consider the effect of molar fraction. One should association of these impurity ions with the more significant charge compensators, viz. (V~)and (X~)to form complexes (Z2~V~) and (Z2X~).In phase I both of these complexes will be entirely in dissociated states providing a greater number of mobile defects resulting in a higher conductivity. In phase II these complexes are only partly dissociated and hence the conductivity is comparatively smaller. In phase Ill the existing impurity content may exceed the solubility limit and the impurity may precipitate out as a separate phase. This leads to a reduction of the carriers which explains the lower portion of the curve. The part of the plot above 270°Ccan be considered as the intrinsic region since the curves merge into one another in this portion. Although the actual values of conductivity are different along a and b(c) directions the activation energies themselves are found to be mdependent of direction. Thus it appears that the mechanism of electrical conduction is the same for different directions in this crystal. The sharp rise in conductivity at the transition point from phase HI to II may be due to the large scale avail.
ability of the carriers released dunng the rearrangement process of the crystal lattice or due to the loosening of the same. As in the case of ammonium chloride [91, the ammonium ions m LiNH4SO4 may be assumed to change from a state of tortional oscillation to one of free rotation while the crystal undergoes transition from phase II to I. This may generate an enormous amount of protonic defects giving rise to the conductivity anomaly at 186.5°C.Quenching of the crystal from the transition point leads to freeze the excess carriers produced at the transition point and these frozen in defects [6] may be responsible for the increase in conductivity of the quenched sample. Hence the observed decrease in activation energy value of 0.1 eV should correspond to the migration of these frozen in carriers. Murti et aL [10] estimated the activation energy of protons in NH4CI to be 0.08 eV by a plastic deformation experiment. A reasonable assumption that the activation energy of protons in LiNH4SO4 is not widely different from this value leads to the conclusion that protonic conduction can be the phenomenon responsible for the conductivity anomaly at 186.5°C. .
5. CONCLUSIONS The migration of interstitial Li~ions is suggested to be the dominant mechanism of electrical transport in single crystals of LiNH4SO4. Activation energy measurements
Vol. 34, No. 11
D.C. ELECTRICAL CONDUCTIVITY IN LiNH4SO4
show that the conduction mechanism is the same for the different directions in the crystal. The conductivity anomaly at 10°Cis suggested to be due to the availability of excess carriers released during the rearrangement process of the crystal lattice or due to the loosening of the same. Pmotonic conduction can be responsible for the discontinuity observed at 186.5°C.
Acknowledgements The authors wish to thank Dr. j Ramakrishna of Indian Institute of Science, Bangalore for providing them with some crystal samples used in these studies. They are grateful to Dr. K. Sathianandan for his kind interest and encouragement during the progress of this work. Thanks are also due to University Grants Commission, New Delhi for providing a Junior Research Fellowship to one of the authors (U.S.P.) and for a research grant to the other. —
903
REFERENCES I. 2.
W.A. Dollase, Acta Crystallogr. B25, 2298 (1965). R. Pepinsky, K. Venam, Y. Okaya & S. Hosino, Phys. Rev. 111, 1467 (1958). 3. T. Mitsui, T. Oka, Y. Shiroishi, M. Takashige, K. ho & S. Sawada, J. Phys. Soc. Japan 39, 845 (1975). 4. A.V. R. Warner, Spectra of Crystals. Ph.D. Thesis, Indian Institute of Science, Bangalore (1966). 5. P. Kumamacharya & P.S. Narayanan, Indian J. Pure andAppi. Phys. 11, 514 (1973). 6. A.B. Lidiard, Handbuch der Physik 20, 246 (1957). 7. F.A. Kroger, J. Chem. Phys. 51, 4025 (1969). 8. N.F. Mott & R.W. Gurney, Electronic Process in Ionic Crystals, 2nd edn. p. 41(1964). 9. Y.V.G.S. Murty & S. Prasad, Proc. Nuclear Physics and Solid State Physics Symposium 17C, 67 (1974). 10. Y.V.G.S. Murti & P.S. Prasad, Solid State Commun. 15, 1619 (1974).