0038-1098/9255.00 + .00 Pergamon Press Ltd
Solid State Communications, Vol. 82, No. 10, pp. 755-757, 1992. Printed in Great Britain.
IONIC CONDUCTIVITY IN LiKo.sNao.IS04 SINGLE CRYSTALS M.A.Pimenta, S.L.A.Vieira, F.O.V.Letelier, N.L.Speziali and M.S.Dantas Departamento de Fisica Universidade Federal de Minas Gerais CP 702 - 30161 Belo Horizonte/BRAZIL FAX-(5531)4481372 Electronic Mail - [email protected]
(Received 26 nov/91; in revised form 09 mar/92 by C.E.T. Gon~alves da Silva)
Electrical conductivity measurements have been performed in single crystals of LiKo.sNaoaS04 between 400°C and 650°C. A phase transition has been observed at 472°C accompanied by an increase of the electrical conductivity by a factor of 50. The temperature dependence of the conductivity data shows anomalies at about the phase transition temperatures of the pure compounds LiKS04 and LiNaS04. A model is proposed to calculate the evolution of the activation energy at high temperature.
phase transition in these compounds. Results for x = O.1 are presented here.
Compounds of the family LiAS04 (A = Li, Na, K, Ag, etc.) undergo a phase transition at high temperature accompanied by a jump in the electrical conductivity.l-4 The high temperature phase is characterized by a sulfate ion orientational disorder, typical of the plastic crystals, and a high cationic mobility. It has been proposed that the cationic mobility is related to the sulfate ions rotation by a paddle-wheel mechanism,s,s The electrical conductivity of these compounds can be large enoughto consider some of them as superionic conductors, as for example LiNaS04, Li2S04 and LiAgS04. Other sulfate crystals, such as LiKS04, present in their high temperature phase a significant cationic mobility, but not large enough to get the label of superionic. Lithium Sodium Sulfate (LiNaS04) undergoes a phase transition at 518°C accompanied by an increase of the electrical conductivity by a factor of 1000 and a volume change of 8%. 2 At room temperature LiNaS04 has a C~, (P31c) trigonal symmetry r and above the phase transition, a centered cubic symmetry s up to the melting point at 616°C. The sequence of high temperature phase transition in Lithium Potassium Sulfate (LiKS04) is quite particular. At room temperature it presents a C~ (P6s) hexagonal structure s and undergoes a phase transition at 435°C in which the electrical conductivity increases discontinuously by a factor of 20.4 Another phase transition occurs at 670°C and, above this temperature, the crystal adopts a D~h (P63/mmc) hexagonal structure characterized by an orientational disorder of the sulfate ions. The intermediate phase (435°C < T < 670°C) has a symmetry lower than hexagonal, probably due to the existence of an incommensurate structure) ° The melting point of LiKS04 is about 720°C. We are now studying the mixed compounds of the type Liko_~)Na~S04 for several values of x. Electrical conductivity measurements have been performed in order to investigate the mechanism of ionic conduction and the high temperature
Single crystals of Liko.sNaoaS04 have been grown by slow .evaporation of a saturated aqueous solution containing Li~SO4:H20, k2S04 and Na2S04 salts in molar ratios 1.0; 0.9; 0.1, at 40°C. X-ray precession photographs were obtained at room temperature with an untwined single crystal, using Moka radiation. Systematically absent reflections indicates C~ (P6s), C~h (P6a/,~) and D~ (P6322) as candidates for the space group symmetry. Cell dimensions were determined as a = 5.142(5)A and c = 8.602(5)A which give V/Z = 98.48~ s. For the sake of comparison, the cell parameters of LiKSO~ are a = 5.1452(2)~, and c = 8.6343~ (V/Z = 98.98ha) 9 and, for LiNaS04, a = 7.6270(7)A and c = 9.858(1)~t (V/Z = 82.77/~s). r The cell dimensions together with the space group possibilities indicate the predominance of LiKS04 in the mixed compound Liko.sNao.lS04. Thin plates (7ram x 5ram x 1ram), transparent and free of visible defects were cut parallel to the hexagonal axis. Silver paint has been used as metal electrodes. The electrical conductivity measurements have been performed using a GR1620 capacitance bridge at 1 KHz. The rate of heating was about 5°C/min. lowered to 1°C/rain. near the phase transition.
Figure 1 shows the temperature dependence of the electrical conductivity a. The usual log(aT) versus 1/T system of coordinates was used to present the data. It can be observed that the mixed crystal undergoes a phase transition at about 472°C accompanied by a change of the electrical conductivity by a factor of 50. It is interesting to observe that these values are intermediate between the transition temperature and the 755
600 °C 2
LiKI_ x Na x S04. X~O.I
aT = aoexp(-Eo/(ksT))
The activation energy E~ for a mobile ion can be obtained from measurements of the temperature dependence of the ionic conductivity by the Arrhenius relation,
Vol. 82, No. 10
LiK0.9Na0.1S04 SINGLE CRYSTALS
104IT (K 4)
Figure 1 - Temperature dependence of the electrical conductivity of Liko.sNao.tS04, me~ured perpendicular to the c-axis. The usual log (aT) versus 1/T system of coordinates has been used to present the data. In this figure we have used the decimal logarithm.
jump of the electrical conductivity in the pure compounds, i.e., T = 435°C with an increase of the electrical conductivity of 20 times for LiKS04 and T = 518°C with an increase of 1000 times for LiNaS04. Another important feature observed in figure 1 is the existence of different regions, each one defining approximately a straight line. Above the phase transition, the conductivity data show clearly three different regions, called regions III, IV and V. The division of the low temperature data in different regions is less pronounced. Considering the pretransitional effects already observed in the pure compound LiKS04 (which are discussed later), the low temperature data can be roughly divided in two regions, called regions I and II. The slopes of the straight lines are given in table I.
where kB is the Boltzmann constant and T the absolute temperature. Usually, the slope of the graph ln(aT) versus 1/T gives directly the value of the activation energy E,. This is not true if EL or a0 depend on temperature or if the conduction mechanism involves different reactions. In the present case, it is not reasonable to directly associate the slopes of the straight lines given in table I with the activation energies for these five regions. In fact, it is difficult to explain the increase of the activation energy with temperature, and moreover, an activation energy of 6.2 eV in the highest temperature region (V). To explain our results, we have to consider a temperature dependence of E, or a0 in eq.(1). Let us first consider the temperature dependence of EL. The possibility of a temperature effect on a0 will be discussed later. Strong pre-transitional effects have been observed in this family of compounds related to the onset of the sulfate ion orientational disorder./° It is well known that the ionic mobility is closely related with the sulfate ion motion. In this context of increasing disorder, the activation energy E, is expected to decrease with increasing temperature. This assumption has already been used to explain the conductivity data of LiKS04, which show a similar behavior just below its phase transition. 4 In particular, for regions I and III, it is reasonable to directly associate the values of the slopes of the straight lines, i.e., 1.6 eV and 1.2 eV respectively, with an activation energy EL. This assumption is supported by the facts that (i) in these regions, far below and just above the phase transition, the activation energy is expected to be independent of temperature and (ii) its values are compatible with those found in LiKS04 far below and above the phase transition, i.e., 1.80 eV and 1.35 eV respectively: The determination of the activation energy in regions II,
I II Ill IV V 1.6 2.1 1.2 1.9 6.2 A
Table I: Slopes of the straight lines observed in figure 1, in units of energy (eV). An increase of 8% is estimate for these values.
It is interesting to observe a close association between the slope changes in figure 1 and the phase transition temperatures in the pure compounds. For example, the increase of the slope from region I to region II occurs at about 440°C, which corresponds approximately to the phase transition in LiKS04. The increases of the slopes at about 514°C (IIIIV) and 619°C (IV-V) correspond to the superionic phase transition and the melting point in LiNaS04, respectively. The mixed crystal melts at 650°C and, here again, this temperature is intermediate between the melting points of pure crystals.
"-6 1.2 1.0
s6o Temperature (°C)
Figure 2 - Temperature dependence of the activation energy EL, calculated using equation 2. Temperature increases towards the left direction.
VO|. 82, NO. 10
LiK0.9Na0.1 $O 4 SINGLE CRYSTALS
IV and V requires a little more attention. Derivating eq.(1) with respect to T, we obtain - k
s ~ = E . - ~
Equation 2 shows that, when Eo depends on temperature, an increase of the modulus of the slope in the graph ln(aT) versus 1/T can be due to a decrease of Eo with temperature. It can explain the results obtained for regions II, IV and V. We can then calculate the evolution of the activation energy by solving eq.(2). Since the left side of eq.(2) is a constant in each one of these regions, the solutions axe those of a straight line whose equations are listed in table II. The temperature dependence of the activation energy calculated using eq.(2) is shown in fig.2. Region Activation Energy Eo I
Eo = 1.6 eV
II Ill IV V
Ea = Ea = Eo = E6 =
~.leV- 7.0 x 10-4T 1.2 eV 1.9 eV - 8.9 x 10-4 T 6.2 eV - 5.7 x 10 - s T
Table II: Temperature dependence of the activation energy in the five regions observed in figure 1.
Our experimental data could also be explained by considering the activation energy Ea to be a constant above and below the phase transition and by considering a temperature dependence of the prefactor ~o. In this case, the derivative of eq.(1) should be written as:
s d(---~- =E~+
ksT 2d(In(~°)) dY
Therefore, an increase of the modulus of the slope in the graph ln(~T) versus 1/T can also be due to an increase in ~o with temperature. The slope changes of figure 1 have been fitted using eq.(3) instead of eq.(2). We have estimated an increase of the prdactor ~0 of about 3 times in region IV and of about 12 times in region V. The increase of ¢0 with temperature is reasonable since the fraction of the cations which are disordered is expected to increase at high temperature. However, the values estimated above seem to be very high. In the same temperature ranges, according to eq.(2), the activation energy E. decreases approximately 10% and 15%, respectively. Even if ~0 increases with temperature, we believe that the main cause of the slope changes of figure 1 is
the decrease of E~ at high temperature. Let us now discuss the temperature dependence of the activation energy. It is proposed that the rotations of the sulfate ions enhance the ionic mobility in this family of compounds through a "paddle-wheel~ mechanism, s's Therefore, the height of a potential barrier over which the ions must jump is expected to decrease with increasing sulfate ion orientational disorder. The slight decrease of the activation energy E, observed in region II (of about 0.02 eV) can be related to the onset of an orientational disorder below the phase transition. This has already been proposed to explain the evolution of the conductivity data in the pure compound LiKS04. The discontinuities in the evolution of the activation energy above the phase transition, which occur approximately at the superionic transition and the melting point of the pure compound LiNaS04, can also be related to an extra enhancement of the sulfate ion orientational disorder. Experiments using different experimental techniques and with crystals having other concentrations of sodium are in progress.
Acknowledgements - This work has been supported by the Brazilian Agencies CNPq (Conselho Nacional de Desenvolvimento Cientlfico e Tecnol6gico) and FAPEMIG (Funda~go de Amparo g Pesquisa de Minas Gerais).
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