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DIELECTRIC RELAXATION AND IONIC THERMO-CURRENT STUDIESA study of
impurity-vacancy complexes in SrCl2 doped with Na+, K+ or Rb+ ions by the ionic thermocurrent method
M. Jacquet, M. Bathier
To cite this version:
M. Jacquet, M. Bathier. DIELECTRIC RELAXATION AND IONIC THERMO-CURRENT STUD- IESA study of impurity-vacancy complexes in SrCl2 doped with Na+, K+ or Rb+ ions by the ionic thermocurrent method. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-447-C6-450.
�10.1051/jphyscol:19806116�. �jpa-00220023�
DIELECTRIC RELAXATION AND IONIC THERMO-CURRENT STUDIES.
A study of impurity-vacancy complexes in SrCl2
doped with Na
+, K
+or Rb
+ions by the ionic thermocurrent method
Abstract. — Above 79 K, SrCl2 crystals with low concentrations of Na+, K+ or Rb+ ions give a single ITC band for each dopant. When the samples are warmed up at a constant rate ATjdt — 0.07 K. s"', the band maxima are at 120.0, 107.7 and 88.0 K respectively. The kinetics of disorientation of the monovalent ion-Cl- vacancy complexes are of the first order. The depolarization activation energies with Na+, K+ and Rb+ are 0.345, 0.325 and 0.25 eV respectively.
1. Introduction. — Strontium chloride, SrCl2, has the fiuorite structure. Its cell edge is a = 6.963 A (25 °C). The intrinsic defects are anion Frenkel defects.
Conductivity measurements carried out by Gervais et al. [1] show that the electrical neutrality is preserved thanks to the formation of chlorine vacancies Cly when monovalent ions M+ (= Na + , K+ or R b+) are added. Dielectric loss measurements done by Pailloux et al. [2] show the presence of M + Cly pairs at low temperatures. It appears to us that the dipole relaxation phenomena can be interpreted by means of Wachtman's model [3] : M+ occupies a Sr2 + site and Cly is formed at one of the eight nearest-neighbour sites. However, the accuracy of absorption measu- rements is not very good; that is why one cannot assert that there are no other relaxation phenomena in the Debye bands which become wider when the concentration increases. The sensitivity of the ITC method will allow us to observe dipole relaxations for a few ppm of dopant and to separate neighbouring relaxation processes.
In the ITC method [4], one applies an electric field
£P at the temperature TP for an interval of time tP : the dipoles are polarized. Then the sample is cooled down to a temperature T0 low enough to freeze in the dipoles. The electric field is removed, then the dielectric is warmed up at a constant rate b = dT/dt and the depolarization current i(T) is recorded. For a single type of dipoles, the relaxation time at T is
where E is the activation energy, T0 the reciprocal
frequency factor and k Boltzmann's constant. For a depolarization kinetic of the first order, i(T) is pro- portional to the polarization P(T) and the current is represented by an asymmetric band with a maximum at a temperature 7V The area delimited by the band is :
where N is the dipole concentration, fi the dipole moment, 5 the area of the sample and P0 the total polarization. In order to determine E and T0, one plots the logarithm of
as a function of T \
2. Experimental techniques. — The SrCl2 single crystals were grown in our laboratory by the Stock- barger-Bridgman method [1]. The salt is purified by the zone melting technique, then it is placed under an atmosphere of HC1 in a silica envelope which is sealed off. The dopant (NaCl, KC1 or RbCl) is added to the polycrystalline material before melting. The parallel faces of the samples cut in the crystal are painted with a silver lac. The sample is introduced between the electrodes of the apparatus in a glove box. The sample JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 7, Tome 41, Juillet 1980, page C6-447
M. Jacquet a n d M. Bathier
Université de Clermont 2, UER des Sciences, Groupe de Physique des matériaux, BP 45, 63170 Aubière, France
Résumé. — Au-dessus de 79 K, les cristaux de SrCl2 faiblement dopés par N a+, K + ou Rb + donnent un seul pic ITC pour chaque dopant. Pour une vitesse de chauffage constante des échantillons âTjàt = 0,07 K . s- 1, les sommets des pics sont respectivement à 120,0, 107,7 et 88,0 K. La cinétique de désorientation des complexes lacune Cl"-ion monovalent est du premier ordre. Les énergies d'activation de la dépolarisation avec N a+, K+ et Rb+ sont respectivement 0,345, 0,325 et 0,25 eV.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19806116
C6-448 M. JACQUET AND M. BATHIER
container filled with purified helium is lowered into liquid nitrogen. The temperature is measured by means of a chromel-constantan thermocouple located in the grounded electrode. The other electrode, insu- lated by Kel-F, is connected either to the tension source or to a vibrating condenser electrometer which can detect currents as low as 3 x 10-l6 A. Dielectric loss is measured with a General Radio 1620 assembly.
3. Experimental results. - 3.1 ITC STUDY OF NON- DOPED CRYSTALS OR CRYSTALS WITH LOW CONCEN-
TRATIONS OF DOPANT. - 3.1.1 Non-doped SrCl,. - T / K
The depolarization current for one sample is shown in figure 1. The maximum of peak A is at
/
TpFig. 2. - ITC peak of SrC1, : Na+ (c = 150 ppm) :
TM = 120.2 f 0.5 K for b = 0.07 K . s - '
.
Ep = 4.7 x lo5 V.m-' , b = 0.070 K . S - ' ,T, = 120.0 K , E = 0.353 eV, 7, = 7 x 10-l4 s . The different samples give the following average
values : E = 0.35
+
0.02 eV; .ro between 2 and 70 x 10-l4 s. These values are the same as those of the peak of SrCl, : Na+ . Therefore, peak A is due to the presence of residual Na' ions ( a 5 ppm) in purified crystals.gK
I . . . . r . . ' . ".. 3. T I K110 lop $0 100 , r" II , '' ,9b
Fig. 1. - ITC spectrum of a non-doped SrCI, crystal :
E, = 6.0 x lo5 V.m-', b = 0.07 K.s-'. Peak A : TM = 120.2 K, Fig. 3. - ITC peak of SrC1, : K' ( c = 95 ppm) : E = 0.35 eV, T, = 1 x 10-l3 s. PeakB : TM = 97 K, E = 0.28 eV,
= 1 x 10-l3 s. E p = 5.5 x 105 V.m-' , b = 0.066 K.s-' ,
TM = 107.6 K , E = 0.326 eV , T, = 2.5 x 10-l4 s
.
The maximum of peak B is at TM=97.0
+
0.7 K for b = 0.07 K.s-' ; E = 0.27+
0.015 eV; z, bet-ween 1 and 100 x 10-l4 s. We noticed that this peak appears if we warm above 600 OC, in HCI, a sample superficially hydrated. This dipole relaxation may be due to the presence of 02- or OH- ions in the crystal.
There is no peak B in the crystals we grow now. 3.1 .2 SrC1, : Na+. - When the concentration of 16%
n
Na' increases, a single peak appears (Fig. 2); it corresponds to an increase of peak A. Measurements on annealed or quenched samples for concentrations
under 400 ppm give : TM = 120.0
+
0.3 K for TIK')
, , , , ,\>.
-- - - . -b = 0.07 K . s-
'
; E = 0.345+
0.015 eV ; T, between 804 and 70 x 10-l4 s. Fig. 4. - ITC peak of SrCI, : Rb' (c
-
60 ppm) :3.1.3 SrCI, : K'. - For c < 400 ppm , a single E~ = 7.9 x 10' v . m - l ;
peak appears (Fig. 31, with : TM = l07.7
*
0.3 K ; dashed line : b is not constant; full line : b = 0.055 K.s-' ;E = 0.325
+
0.007eV; 7, between 1 and 6 x 10-I4s. T, = 87.4 K, E = 0.26 ev, 7, = 5 x 10-l4 s.A STUDY OF IMPURITY-VACANCY COMPLEXES IN SrC1, DOPED WITH Na', K + OR Rb+ IONS C6-449
3.1 . 4 SrC1, : Rb'
.
- Above 79 K, there is a single peak due to the presence of Rbt (Fig. 4). For c < 4 0 0 p p m : T M = 8 8 . 0 + 0 . 5 K ; b =0.07K.sC1;E=0.25
+
0.015 eV; z0 between 2 and 100 x 10-l4 s.3.1 .5 Properties common to all peaks. - For every sample, the peak area is proportional to the applied field and the temperature of the maximum does not depend on the polarization temperature : the peaks are due to a dipole relaxation whose kinetics are of the first order. The polarization, Po, is approxi- mately proportional to the concentration of the dopant calculated from our conductivity measurements or dosed. The concentrations given in this paper have been calculated from the values of Po, with
where e is the elementary charge. For the different dopants, we do not note a systematic decrease of the activation energy when the concentration varies from 40 to 400 ppm.
3.2 ITC STUDY OF CRYSTALS WITH HIGH CONCEN- T R A n o N s OF DOPANT.
-
When the concentration of the dopant reaches 1 000 ppm, the corresponding peak becomes wider. No other peak appears. The temperature of the maximum remains practically equal to TM given in paragraph 3.1 if we polarize at Tp > TM. Crystals grown from certain non purified materials give widened peaks even for low concen- trations of dopant.shows the curves v, = f(TP1) for samples with
c > 200 ppm. The table shows that the results confirm the ITC values.
4. Discussion. - For each of the monovalent dopants added to SrCI,, one observes dipole relaxation phenomena, with a single relaxation time, above 79 K.
When the concentration increases, the ITC peaks become wider, which is due to a dipole-dipole inter- action; our dielectric loss studies suggested this interpretation. The polarization deduced from our measurements can be explained by the presence of Mf and C1; in nearest-neighbour positions : the eight-position model proposed by Wachtman gives a satisfactory interpretation of relaxation processes in SrC12 : Na+, SrC1, : K + and SrCl, : Rb'. The reciprocal frequency factor T, of M+Cl; complexes does not depend on the nature of the dopant :
T;
'
is of the order of magnitude of the Debye frequency of the lattice (5.22 x loi2 s-I) [5]. We note that the activation energy decreases when the ionic radius of the impurity increases : the potential barrier between two neighbouring sites of C1; vacancies is all the more lowered as the ionic radius of the associate impurity is greater. The values of the activation energy of M + C1, pairs fit in with the mobility enthalpies of the free vacancies deduced from the conductivity measure- ments (see Table). However, the average activation energy of the Na+Cl; is greater than the mobility enthalpy of the free vacancy (0.335 eV).3.3 RESULTS OF DIELECTRIC LOSS MEASUREMENTS. - Let vM be the frequency of the maximum of the di-
electric loss at T. We studied the dielectric absorption Table. - Activation energies (eV) of C1- vacancies in as a function of T for constant values of v. Figure 5 SrC1, doped with monol,(&nt ions.
Mobility enthalpies Activation energies of complexes of free vacancies
ITC Dielectric loss Conductivity measurements measurements measurements [l]
- - -
N a r 0.345 k 0.015 0.34 f 0.01 0.335 K + 0.325
+
0.007 0.32 f 0.01 0.336R b + 0.250
+
0.015 0.25 f_ 0.01 0.3365. Conclusion. - The ITC measurements show that associations in SrCI, doped with Na +, K + or Rb + can be interpreted by Wachtman's model. A theoretical study of the lowering of the potential barrier near the monovalent impurity could complete our experimental results.
Acknowledgments. - The authors are grateful to
Fig. 5. - v M vs. T - 1 forloss peaks : + SrC1,
.
Na+ ; SrC12 : K + ; P ~ o ~ ~ s s o ~ Chapelle who gave them l n f ~ r m a t i ~ n aboutSrCI, : ~ b + the zone melting technique of purification.
M. JACQUET A N D M. BATHIER
DISCUSSION
Question. - P. J . BENDALL. Reply. - M . BATHIER.
Our calculations on this system using the HADES The uncertainty of ' z; deduced from the adjust- program give values for the activation energies for ment of the ITC curves can be calculated from the reorientation of a vacancy around Na+ and K + values given in
$9
3.1.2, 3.1 . 3 and 3.1.4 .'of the ions both in the region of 0.3 eV. present paper. We see that our results fit in w:th theusual values mentioned in your question.
Reply. - M . BATHIER.
Our experimental results are in agreement with your calculated values. Moreover, we have found that the activation energy of the complexes decreases when the ionic radius increases.
Question. - A. S. NOWICK.
What is the uncertainty of your pre-exponential
2G1, and do you have any explanation for why it seems to be about 1 order of magnitude lower than usual ? (In the usual case an entropy factor tends to bring 7,' into the range 3 x 1013 to lOI4 s-I.)
Question. - H . W . DEN HARTOG.
You have compared your activation energies with those found from ionic conductivity measurements.
Do these latter activation energies correspond with the motion of free vacancies or with reorienting defects ?
Reply. - M . JACQUET.
Our A.C. conductivity measurements gave the activation energies of the free vacancies. Cf. refe- rence [I].
References
[l] GERVAIS, A,, JACQUET, M. and BATHIER, M., J. Phys. C 7 [3] WACHTMAN, J. B. Jr., Phys. Rev. 131 (1963) 517.
(1976) 281. [4] BUCCI, C., FIESCHI, R. and GUIDI, G., Phys. Rev. 148 (1966) 816.
[2] PAILLOUX, M., GERVAIS, A., JACQUET, M. and BATHIER, M., [5] HISANO, K., OHAMA, N. and MATUMURA, O., J. Phys. Soc.
C. R. Hebd. Skan. Acad. Sci. 274B (1972) 991. Japan 20 (1965) 2294.
