(NaCl) x (KCl) y-x (KBr) 1-y single crystals: study of the ac conductivity activation energy.

Transcription

1 (NaCl) x (KCl) y-x (KBr) 1-y single crystals: stuy of the ac conuctivity ivation energy. Vassiliki Katsika-Tsigourakou * Department of Soli State Physics, Faculty of Physics, University of Athens, Panepistimiopolis, Zografos, Greece Abstr Ac electrical measurements have been reporte for alkali halie mixe crystals that were melt grown from NaCl, KCl an KBr starting materials. They showe a nonlinear variation of all the electrical parameters with the bulk composition. Here, we show that these mixe systems, epening on their major constituent, are classifie into three categories in each of which, the ivation energy for the ac conuctivity increases linearly with B, where B is the isothermal bulk moulus an the mean volume per atom. PACS: Bb; Ji; Fv; Keywors: Alkali halies; Mixe crystals; Multiphase systems; Activation energies; Bulk moulus; Gibbs energy *vkatsik@phys.uoa.gr 1

2 1. Introuction Since it was realize [1] that alkali halie mixe crystals have the potential for important applications in optical, optoelectronic an electronic evices, the interest on unerstaning their properties has been largely intensifie, thus a large boy of experimental stuies have recently appeare [2-15]. This large amount of experimental ata allowe the investigation of the correctness of early theoretical stuies [16-20] the basic aim of which was to calculate the physical properties of a mixe system in terms of the corresponing properties of its en members. This recent investigation alreay gave some answers to some points summarize below. First, Katsika-Tsigourakou an Vassilikou-Dova [21] showe that the compressibility of the multiphase mixe crystals, grown by the melt metho using the miscible NaBr an KCl, can be reliably estimate in terms of the elastic ata of the en members alone. This mae use of the compressibility of the efect formation volume calculate on the basis of a thermoynamical moel [22-24], terme cb moel (see also below), that interconnects the Gibbs energy for the formation an migration of efects in solis with bulk properties. Subsequently, the same authors [25] showe that the large temperature variation of the static ielectric constant of the binary mixe crystal (NaCl) (KBr) can quantitatively reprouce by using the interconnection between the ionic polarizability an the isothermal bulk moulus B( 1 ) propose in Ref. [26]. In aition, in a later stuy [27], Katsika- Tsigourakou an Vassilikou-Dova showe that in four out of five mixe systems, forme when using NaBr an KCl as the starting materials, the ivation energy for their conuctivity process varies linearly with B, where is the mean volume per 2

3 atom. The same was foun to hol [28] for the mixe crystals of NaBr an KBr that where also prepare from melt [29]. The aforementione stuies left open the question whether the cb moel [22-24, 30-32] conforms with experimental ata when ealing with more complex mixe crystals, i.e., melt grown from three starting materials. Fortunately, such a case has appeare by Mahaevan an Jayakumari [33]. They presente electrical measurements on multiphase (NaCl) x (KCl) y-x (KBr) 1-y single crystals that were melt grown from NaCl, KCl an KBr starting materials extening the investigation reporte in B Ref. [34]. They foun a nonlinear variation of all electrical parameters they stuie with the bulk composition. In view of this nonlinearity it is worthwhile to investigate in this short paper whether the linear interrelations between the physical properties that are preicte by the cb moel still hol in these multiphase (NaCl) x (KCl) y-x (KBr) 1-y single crystals. 2. Investigation on the existence of a linear interrelation among the properties of (NaCl) x (KCl) y-x (KBr) 1-y single crystals The so calle cb moel suggests that for the efect Gibbs energy g, for a given thermally ivate process, is given by: g c B (1) where c is a constant inepenent of temperature an pressure. The value of c, however, oes epen on the host material as well as on the type of the efect process uner investigation. By inserting Eq. (1) into the relation s g T P, where 3

4 s enotes the ivation entropy, we can calculate the corresponing ivation enthalpy h through the relation h g Ts, which finally gives: B h c B T B T T P (2) where is the thermal volume expansion coefficient. When the conuctivity varies with temperature in a way so that the plot n( T) vs 1 T is a straight line, the ivation enthalpy h coincies with the so calle ivation energy E [35-37], thus: E h (3) The valiity of Eqs (1) an (2) has been checke in various categories of solis, incluing the complex case of the efects that give rise to the emission of electric signals when ionic crystals are subjecte to a time epenent stress. (This may provie the basis for the explanation [38] of the electric signals that precee earthquakes [39-43]). A review of a large variety of applications can be foun in Ref. [44]. In the low temperature range, Ts is significantly smaller than h, thus we can approximate g h, an then Eqs (1) an (2) simplify to h c B which alternatively reas: E c B (4) In view of this expectation we plot in Fig. 1 the ivation energies obtaine from the ac conuctivity measurements of Mahaevan an Jayakumari [33] versus B. The relevant values are given in Table 1, for all the 20 mixe systems that were melt grown from three (i.e., NaCl, KCl an KBr) starting materials stuie in Ref. [33]. The values of B are taken from the compressibilities ( 1 B) reporte in 4

5 Ref. [2] an the values have been calculate as follows: We consier a mixe system A x B y-x C 1-y where the three en members A, B an C will be equivalently labele as the pure components (1), (2) an (3) an volumes 1, 2 an 3 per molecule respectively [43]. We assume that the pure component (1) is the major component in the aforementione mixe system A x B y-x C 1-y an the volume 1 per molecule is smaller than the volumes 2 an 3 of the pure components (2) an (3). Now, let V1 N1, V2 N2 an V3 N3 enote the corresponing molar volumes (where N stans for Avogaro s number). We efine a efect volume 2,1 as the increase in the volume V 1 if one molecule of type (1) is replace by one molecule of type (2) an 3,1 the increase in the volume V 1 if one molecule of type (1) is replace by one molecule of type (3). Thus the aition of one molecule of type (2) to a crystal containing N molecules of type (1) will increase its volume by 2,1 1, while an aition of one molecule of type (3) by 3,1 1. If 2,1 an 3,1 are inepenent of composition, the volume VN n2 n of a crystal containing N molecules of type (1), n 3 2 molecules of type (2) an n 3 molecules of type (3) shoul be equal to: V N n ( ) n ( ). In the har-spheres moel, the efect N n2 n , ,1 1 volumes 2,1 an 3,1 can be approximately etermine from: 2,1 2 1 an 3, Finally, the mean volume per atom ( VN n ) 2n N, is then calculate 3 from: n N n N ac E At first glance, an inspection of Fig. 1 oes not reveal any systematic of E ac vs B. Disregaring, however the four points (i.e., numbers 4, 9, 11 an 17), that strongly eviate from the others, the remaining 16 points can be classifie as follows: First, the four points 5, 6, 7 an 12 which correspon to the mixe systems that have 5

6 NaCl as the major constituent. These are plotte in Fig. 2 an more or less follow a linear tren. A least squares fit to a straight line (which is rawn in Fig. 2) gives a slope an an intercept ev. Repeating the same proceure for the four mixe systems that have KCl as a major constituent (Fig. 3), we fin a straight line with slope an an intercept ev. Finally, the remaining eight systems that have KBr as a major constituent (Fig. 4), result in an almost linear behavior with slope an an intercept ev. Since the latter slope seems to be markely smaller than those euce in Figs 2 an 3, we further investigate that case an foun the following: If we just isregar the point N o 20, all the other seven points in Fig. 4, i.e., N o 10, 13, 14, 15, 16, 18, an 19, lea to a slope (an an intercept ev) which is almost the same with the slopes obtaine from Figs 2 an 3. This correspons to the straight line rawn in Fig. 4. In other wors, for the vast majority (i.e., seven out of eight) of the mixe systems that have KBr as a major constituent, we may say that they result in a straight line having a slope almost equal to that euce from the mixe systems that have NaCl or KCl as a major constituent. 3. Discussion The ex reason why in Fig. 1 some of the points eviate strongly from the others is not clear. A tentative reason coul be guesse if we consier that the conuctivity plot n( T) vs 1 T of alkali halies mainly consists of three almost linear segments as follows. Assuming for simplicity that the cation vacancies are appreciably more mobile than the anion vacancies, the segment corresponing to the higher temperature range (close to the melting point), terme intrinsic region, has a h h k 2 B where f m slope equal to the f h is the formation enthalpy per Schottky 6

7 efect an m h the cation vacancy migration enthalpy. In the intermeiate temperature range, terme extrinsic region, the slope is equal to h m k, while in the lowest B temperature range, terme association region, the slope becomes larger, i.e. equal to m ass ( h h ) k B where ass h is the issociation enthalpy. This is so, because the crystal usually contains ivalent cation impurities which, for the sake of charge neutrality, prouce extrinsic cation vacancies that have negative effective charge. At low temperatures, a portion of these vacancies are attre by the ivalent impurities, thus forming electric ipoles, terme complexes. The quantity ass h is just the heat necessary to issociate these complexes (thus giving free cation vacancies that contribute to conuctivity). Since the measurements of Mahaevan an Jayakumari [33] were carrie out at temperature ranging from 308 to 423 K, the following might have happene. Some points in Fig. 1, may correspon to systems that are in the extrinsic region of their conuctivity plot, while the others to the issociation region. Hence, the former systems may have ivation energies equal to thus the m h while the others equal to h m ass h, E ac values plotte in Fig. 1 o not correspon to the same process an hence some of them naturally eviate significantly from the others. This is might also explain why one of the points (i.e., N o 20) in Fig. 4 oes not fully conform with the straight line resulte from the other seven points, which as mentione- has almost the same slope with the straight lines rawn in Figs 2 an 3. The following remark might be worthwhile to be ae: The straight lines rawn in Figs 2, 3 an 4 o not pass through the origin of the axis, as emane by Eq. (4). The ex reason is yet unknown, although it might be attribute in general to experimental uncertainties in the etermination of E ac. 7

8 4. Conclusion Inspire from the so calle cb moel, in this short paper, we stuie the multiphase (NaCl) x (KCl) y-x (KBr) 1-y single crystals. We fin that, when consiering mixe crystals that have the same major constituent, i.e., NaCl or KCl or KBr, the ivation energy for the ac conuctivity process seems to increase linearly versus B. It is challenging that the resulting three straight lines (comprising four, four an seven systems, respectively) have almost the same slope, i.e., aroun

9 References [1] D. B. Sireshmukh, L. Sireshmukh, K. G. Subhara, Alkali Halies-A Hanbook of Physical Properties, Springer Series in Materias Science, Vol. 49, Springer, Berlin [2] K. Jayakumari, C. Mahaevan, J. Phys. Chem. Solis 66 (2005) [3] S. Perumai, C. K. Mahaevan, Physica B 369 (2005) 89. [4] S. Perumai, C. K. Mahaevan, Physica B 367 (2005) 172. [5] G. Selvarayan, C. K. Mahaevan, J. Mater. Sci. 41 (2006) [6] G. Selvarayan, C. K. Mahaevan, J. Mater. Sci. 41 (2006) [7] A. E. Corero-Borboa, R. R. Mijangos, P. S. Schabes- Retchkiman, J Mater. Sci. 41 (2006) [8] N. Neelakana Pillai, C. K. Mahaevan, Mater. Manuf. Processes 22 (2007) 393. [9] C. M. Pama, C. K. Mahaevan, Mater. Manuf. Processes 22 (2007) 362. [10] M. Priya, C. K. Mahaevan, Physica B 403 (2008) 67. [11] C. M. Pama, C. K. Mahaevan, Physica B 403 (2008) [12] N. Neelakana Pillai, C. K. Mahaevan, Physica B 403 (2008) [13] C. K. Mahaevan, NICE J. Emerging Technol. 3 (2008) 39. [14] M. Priya an C. K. Mahaevan, Cryst. Res. Technol. 43 (2008) [15] M. Priya an C. K. Mahaevan, Cryst. Res. Technol. 44 (2009) 92. [16] P. Varotsos, Phys. Stat. Sol. B 100 (1980) K133. [17] P. Varotsos, K. Alexopoulos, J. Phys. Chem. Solis 41 (1980) [18] P. Varotsos, J. Phys. Chem. Solis 42 (1981) 405. [19] P. Varotsos, K. Alexopoulos, J. Phys. Chem. Solis 41 (1980)

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12 FIGURE CAPTIONS Figure 1. The ivation energy for the ac conuctivity, as measure by Mahaevan an Jayakumari [33], versus the quantity B for all multiphase (NaCl) x (KCl) y- x(kbr) 1-y single crystals. The numbers refer to those use in Table 1. 12

13 Figure 2. The ivation energy for the ac conuctivity, as measure by Mahaevan an Jayakumari [33], versus the quantity B for those multiphase (NaCl) x (KCl) y- x(kbr) 1-y single crystals for which NaCl is the major component. A least squares fit to a straight line results in the line rawn in the figure. The numbers refer to those use in Table 1. 13

14 Figure 3. The ivation energy for the ac conuctivity, as measure by Mahaevan an Jayakumari [33], versus the quantity B for those multiphase (NaCl) x (KCl) y- x(kbr) 1-y single crystals for which KCl is the major component. A least squares fit to a straight line results in the line rawn in the figure. The numbers refer to those use in Table 1. 14

15 Figure 4. The ivation energy for the ac conuctivity, as measure by Mahaevan an Jayakumari [33], versus the quantity B for those multiphase (NaCl) x (KCl) y- x(kbr) 1-y single crystals for which KBr is the major component. The line rawn in the figure is foun by a least squares fit to a straight line of the seven points 10, 13, 14, 15, 16, 18, an 19 (i.e., the point N o 20 has been isregare, see the text). The numbers refer to those use in Table 1. 15

16 Table 1. The values of the ivation energy for the ac conuctivity E ac (as reporte in Ref. [33]), the compressibility (as reporte in Ref. [2]) an B for the (NaCl) x (KCl) y-x (KBr) 1-y single crystals. The values of B are taken from the compressibilities ( 1 B) reporte in Ref. [2] an the values are calculate with the proceure explaine in the text. System a E ac J m N B J 1: (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) : (NaCl) (KCl) (KBr) a estimate bulk composition in the crystal [33] 16