Electrical measurements on multiphased (NaCl)x(KCl)y−x(KBr)1−y single crystals

Electrical measurements on multiphased (NaCl)x(KCl)y−x(KBr)1−y single crystals

ARTICLE IN PRESS Physica B 403 (2008) 3990–3996 Contents lists available at ScienceDirect Physica B journal homepage: www.elsevier.com/locate/physb ...

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ARTICLE IN PRESS Physica B 403 (2008) 3990–3996

Contents lists available at ScienceDirect

Physica B journal homepage: www.elsevier.com/locate/physb

Electrical measurements on multiphased (NaCl)x(KCl)yx(KBr)1y single crystals C.K. Mahadevan , K. Jayakumari Physics Research Centre, S.T. Hindu College, Nagercoil 629 002, Tamil Nadu, India

a r t i c l e in f o

a b s t r a c t

Article history: Received 11 February 2007 Received in revised form 20 July 2008 Accepted 29 July 2008

Alkali halide mixed crystals were melt grown from NaCl, KCl and KBr starting materials. DC and AC electrical measurements were carried out on the resulting ternary compositions at temperatures ranging from 308 to 423 K. Activation energies and mean jump frequencies were also estimated. The present study indicates an increase of DC and AC electrical conductivities and dielectric constant with the increase of temperature. Also, it indicates a nonlinear variation of all the electrical parameters (both DC and AC) with the bulk composition, which is explained to be due to the enhanced diffusion of charge carriers along dislocations and grain boundaries. & 2008 Published by Elsevier B.V.

Keywords: Alkali halides Mixed crystals Ionic crystals Single crystals Multiphased system Crystal growth Melt method DC conductivity Dielectric constant Activation energies Dielectric parameters Electrical properties

1. Introduction Alkali halides are useful for theoretical calculations of the energies for formation and migration of defects because of their electrostatic interactions. They are purely ionic conductors. Ionic conductivity studies provide valuable information on the state of point imperfections. Ionic conductivity measurements as a function of temperature have been done by a number of researchers on pure alkali halide crystals and also on impurity (anionic as well as cationic)-added ones. Various defect parameters such as activation energy for migration, formation energy, etc. have been evaluated from these studies. Though an extensive amount of work has been done on pure and impurity-added alkali halide crystals, the work on mixed crystals of alkali halides is very limited [1–4]. The dielectric constant is one of the basic electrical properties of solids. The measurement of the dielectric constant and the dielectric loss factor as a function of frequency and temperature is

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E-mail addresses: [email protected], [email protected] (C.K. Mahadevan). 0921-4526/$ - see front matter & 2008 Published by Elsevier B.V. doi:10.1016/j.physb.2008.07.041

of interest both from the theoretical point of view and from the applied aspects. Practically, the presence of a dielectric between the plates of a condenser enhances the capacitance. This effect makes materials with high dielectric constants useful in capacitor technology. There is limited work reported in the literature on the dielectric behaviour of alkali halide mixed (binary and ternary) crystals [2–5]. Mahadevan and co-workers [6] obtained larger and more stable crystals from (NaCl)x(KCl)0.9x(KBr)0.1 solutions than from NaxK1xCl solutions. They grew the crystals from aqueous solutions only. Though the miscibility problem was there, their study has illustrated that a KBr addition to the NaCl–KCl system may yield a new class of stable materials. The present work is a systematic addition to this previous study. A research programme on the growth and characterization of (NaCl)x(KCl)yx(KBr)1y single crystals was planned and investigations were undertaken. Details regarding the growth of crystals, determination of density and refractive index along with estimation of bulk composition, indexing the X-ray powder diffraction data along with determining the lattice parameters, determination of thermal parameters like the mean Debye–Waller factor, the mean square amplitude of vibration, the Debye temperature and the Debye frequency from the X-ray powder diffraction data,

ARTICLE IN PRESS C.K. Mahadevan, K. Jayakumari / Physica B 403 (2008) 3990–3996

determination of compressibility, mean sound velocity from the Debye temperature, etc. have been reported elsewhere [7]. The amount of substance in grams for preparing the required sample crystal of composition given by (NaCl)x(KCl)yx(KBr)1y may be obtained by using the following formula:

3991

(1/t) were determined through the DC electrical measurements. Dielectric constant (er), dielectric loss factor (tan d), AC electrical conductivity (sac) and AC activation energy (Eac) were determined through the AC electrical measurements. The results obtained are reported here.

P½ðxÞ  molecular weight of NaCl þ ðy  xÞ  molecular weight of KCl þ ð1  yÞ  molecular weight of KBr ¼ 100 P¼

100 ðxÞ  mol:wt: of NaCl þ ðy  xÞ  mol:wt: of KCl þ ð1  yÞ  mol:wt: of KBr

So; weight of NaCl to be taken ¼ P  ðxÞ  mol:wt: of NaCl weight of KCl to be taken ¼ P  ðy  xÞ  mol:wt: of KCl weight of KBr to be taken ¼ P  ð1  yÞ  mol:wt: of KBr It has been found that the density and refractive index values form a linear relationship with bulk composition for the binary mixed crystals [8]. Assuming that these values have linear relationships with composition for the ternary mixed crystals also, the following relations were considered [7]: d ¼ xd1 þ ðy  xÞd2 þ ð1  yÞd3 n ¼ xn1 þ ðy  xÞn2 þ ð1  yÞn3 Here d, d1, d2 and d3 represent the densities of mixed crystal, NaCl, KCl and KBr, respectively; n, n1, n2 and n3 represent the refractive indices of mixed crystal, NaCl, KCl and KBr, respectively. Compositions of the grown mixed crystals were estimated by solving the above two equations for x and y values. The initial compositions taken for the crystallization and the final estimated bulk composition in the crystal for all the ternary mixed systems considered [7] are given in Table 1. In the second part of the programme, DC and AC (with a fixed frequency of 1 kHZ) electrical measurements were carried out at various temperatures ranging from 308 to 423 K for all the 26 crystals grown [20 ternary mixed crystals, viz. (NaCl)x(KCl)yx(KBr)1y with x ¼ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7 and y ¼ 0.8, 0.6, 0.5, 0.4 and 0.2; three binary mixed crystals, viz. (NaCl)0.5(KCl)0.5, (NaCl)0.5(KBr)0.5 and (KCl)0.5(KBr)0.5; three end member crystals, viz. NaCl, KCl and KBr]. DC electrical conductivity (sdc), DC activation energy (Edc) and mean jump frequency Table 1 The initial composition taken for crystallization and the final estimated bulk composition in the crystal System (with composition taken for crystallization)

Estimated bulk composition in the crystal

(NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

(NaCl)0.078(KCl)0.724(KBr)0.198 (NaCl)0.159(KCl)0.641(KBr)0.200 (NaCl)0.282(KCl)0.524(KBr)0.194 (NaCl)0.389(KCl)0.418(KBr)0.193 (NaCl)0.479(KCl)0.319(KBr)0.202 (NaCl)0.595(KCl)0.218(KBr)0.187 (NaCl)0.704(KCl)0.091(KBr)0.205 (NaCl)0.063(KCl)0.541(KBr)0.396 (NaCl)0.159(KCl)0.453(KBr)0.388 (NaCl)0.292(KCl)0.029(KBr)0.419 (NaCl)0.361(KCl)0.212(KBr)0.427 (NaCl)0.505(KCl)0.039(KBr)0.457 (NaCl)0.133(KCl)0.363(KBr)0.504 (NaCl)0.230(KCl)0.274(KBr)0.493 (NaCl)0.261(KCl)0.231(KBr)0.508 (NaCl)0.389(KCl)0.075(KBr)0.536 (NaCl)0.110(KCl)0.293(KBr)0.597 (NaCl)0.240(KCl)0.159(KBr)0.602 (NaCl)0.272(KCl)0.103(KBr)0.625 (NaCl)0.104(KCl)0.079(KBr)0.817

2. Experimental The DC electrical conductivity measurements were carried out to an accuracy of 72% for all the 26 crystals grown using the two-probe technique at various temperatures ranging from 308 to 423 K in a way similar to that followed by Mahadevan and co-workers [2–4]. The sample crystal was kept between two parallel plates (silver electrodes) to form a parallel plate capacitor. The resistances of the crystals were measured using a million megohm meter (AEC mfs; Model MOM 2). The observations were made while cooling the sample. The temperature was controlled to an accuracy of 71 K. The samples (rectangular crystals) were cut parallel to the cleavage plane to the desired thickness of 1 and 2 mm using a sharp blade and polished using a soft emery paper. The samples were then etched with distilled water and dried to avoid the change taking place, if any, in the electrical properties of the surfaces of the crystals due to cutting and polishing. They were annealed for 2 h at 423 K to remove moisture content if present. Opposite faces of the sample crystals were coated with goodquality graphite to obtain a good conductive surface layer. The samples were again annealed in the holder assembly at 423 K before making observations. The dimensions of the crystals were measured using a travelling microscope (L.C. ¼ 0.001 cm). The DC electrical conductivity (sdc) of the crystal was calculated using the relation [2]

sdc ¼ d=ðRAÞ where R is the measured resistance, d is the thickness of the sample and A is the area of the face in contact with the electrode. Plots between ln(sdc) and 1000/T were found to be very nearly linear (not shown here). So, the sdc values were fitted with the relation [2]

sdc ¼ so exp½Edc =ðkTÞ where Edc is the DC activation energy, k is the Boltzmann constant, T is the absolute temperature and so is a parameter depending on the material. Edc values were estimated using the slopes of the above line plots (Edc ¼ (slope)k  1000). The mean jump frequency (1/t) was estimated using the Edc and Debye frequency (fD) values (taken from Ref. [7]) in a way similar to that followed by Selvarajan and Mahadevan [3]. The DC electrical conductivity is easily calculated [9] to be

sdc ¼ Ne2 a2 =ðkT tÞ where t is a mean jump time, perhaps different from that for dipolar orientation but still given by an equation [9] like   1 1 E ¼ exp kT t t0 where a is the distance of a jump. The factor 1/to ¼ oo (nearly equal to 2pfD where fD is the Debye frequency) is the ionic vibrational frequency around its equilibrium position and exp(E/(kT)) is the statistical Boltzmann factor. A jump is attempted with each vibration, but only a fraction succeeds, depending on the (activation) energy Edc required in order to squeeze through the barrier to the neighbouring equilibrium position. N stands for the number of perfect bonds or the number of charges per unit volume. The frequency 1/toE1013 s1.

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Also, 1/tp1011 s1 and 1/t will be much smaller than this at temperatures well below the melting temperature. The AC electrical (dielectric) measurements were carried out to an accuracy of 71.5% for all the 26 crystals grown using the parallel plate capacitor method with a fixed frequency of 1 kHz at various temperatures ranging from 308 to 423 K in a way similar to that followed by Mahadevan and co-workers [2–4]. The capacitance and dielectric loss factor were measured using an LCR meter (Systronis mfs; Sr. No. 7497). The observations were made while cooling the sample. Temperature was controlled to an accuracy of 71 K. The samples (rectangular crystals) were prepared and annealed in a way similar to that followed for the resistance measurements. Air capacitance was also measured. The dielectric constant of the crystal was calculated using the relation (as the crystal area was smaller than the plate area of the cell) [2]    C crys  C air ð1  Acrys =Aair Þ Aair r ¼ C air Acrys where Ccrys is the capacitance with the crystal (including air), Cair is the capacitance of air, Acrys is the area of the crystal touching the electrode and Aair is the area of the electrode. The AC conductivity (sac) was calculated using the relation [2]

on the material. Eac values were estimated using the slopes of the above line plots (Eac ¼ (slope)k  1000).

3. Results The sdc values observed in the present study are provided in Table 2. In order to reduce the size of the table, the values for temperatures 313, 333, 353, 373, 393 and 413 K are not given here. The values of 1/to and 1/t are presented along with the Edc values in Table 3. The er, tan d and sac values obtained in the present study are provided in Tables 4–6, respectively. In order to reduce the size of the tables, the values for temperatures 313, 333, 353, 373, 393 and 413 K are not given here. The low-frequency (static) dielectric permittivity, e(o), and high-frequency dielectric permittivity, eN, and Eac values are provided in Table 7. e(o) in Table 7 is the er value at 308 K for 1 kHz frequency (assumed to be low) from Table 4. eN was evaluated from the refractive index in the optical range (eN ¼ n2) reported previously [7]. Comparable literature values [10] are given in brackets.

4. Discussion

sac ¼ o r o tan d where eo is the permittivity of free space (8.85  1012 C2 N1 m2) and o is the angular frequency (o ¼ 2pf; f ¼ 1 kHz in the present study). Plots between ln(sac) and 1000/T were found to be very nearly linear (not shown here). So, the sac values were fitted with the relation [2]   Eac sac ¼ so exp kT where Eac is the activation energy, k is the Boltzmann constant, T is the absolute temperature and so is the parameter depending Table 2 DC electrical conductivities (  106 /m)

Table 3 Values of Edc (eV), 1/to (  1013 s1) and 1/t (  107 s1)

A

System (with composition taken for crystallization)

NaCl KCl KBr (NaCl)0.5(KCl)0.5 (NaCl)0.5(KBr)0.5 (KCl)0.5(KBr)0.5 (NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

The temperature range considered in the present study for the electrical measurements is well below the melting temperature, which is more than 900 K. Hence, the values of 1/to and 1/t obtained in the present study can be understood as comparing well with those expected by the model (see Section 2). The sdc values are found to increase with increasing temperature for all the 26 crystals measured. Results observed in the present study indicate that the composition has nonlinear influences on the values of sdc, Edc, 1/to and 1/t. The bulk composition (taken for crystallization) dependences of the sdc value at 308 K and Edc value are shown, as an illustration, in Figs. 1 and 2, respectively.

sdc for temperatures (K) 1/to

1/t

323

343

363

383

403

423

System (with composition taken for crystallization)

Edc

308 0.05 0.06 0.32 0.82 0.98 0.12 0.32 0.37 0.06 0.08 0.01 0.04 0.01 0.19 0.22 0.13 0.10 0.20 0.20 0.31 0.40 0.10 0.24 0.11 0.11 0.14

0.07 0.08 0.76 1.07 1.53 0.16 0.41 0.57 0.07 0.09 0.01 0.06 0.02 0.21 0.55 0.65 0.17 0.38 0.24 0.33 0.54 0.16 1.20 0.23 0.38 0.16

0.09 0.11 1.18 1.15 1.87 0.22 0.51 0.80 0.17 0.11 0.01 0.07 0.02 0.25 0.59 1.35 0.24 0.59 0.29 0.39 0.63 0.51 2.11 0.53 0.68 0.20

0.10 0.13 1.42 1.47 2.27 0.34 0.67 1.09 0.43 0.15 0.04 0.07 0.03 0.31 0.64 1.84 0.31 0.86 0.34 0.59 0.70 0.98 2.99 0.93 1.41 0.27

0.11 0.14 1.55 1.72 2.63 0.40 1.48 1.20 0.83 0.27 0.10 0.11 0.06 0.45 0.71 2.91 0.37 1.13 0.44 1.51 0.83 1.44 3.48 1.44 2.03 0.49

0.12 0.17 2.16 2.06 2.80 0.60 2.84 1.71 1.26 0.43 0.21 0.19 0.13 0.64 0.84 3.49 0.49 1.49 0.69 2.67 1.01 2.02 4.02 1.82 4.63 0.82

0.16 0.19 4.97 2.93 3.00 1.21 7.39 2.99 2.56 0.71 0.47 0.43 0.32 1.25 1.35 4.48 0.97 2.12 1.55 5.48 3.25 2.71 4.60 2.03 6.74 1.44

NaCl KCl KBr (NaCl)0.5(KCl)0.5 (NaCl)0.5(KBr)0.5 (KCl)0.5(KBr)0.5 (NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

0.09 0.10 0.20 0.11 0.10 0.20 0.28 0.17 0.39 0.22 0.53 0.19 0.29 0.18 0.09 0.29 0.17 0.21 0.25 0.29 0.15 0.34 0.22 0.28 0.39 0.23

3.11 2.74 2.39 3.41 2.64 2.39 2.53 2.93 2.65 2.82 2.81 2.84 2.66 2.29 2.87 2.87 3.00 2.37 2.40 2.37 2.60 2.39 2.94 2.43 2.31 2.49

106248.00 53598.60 1065.80 56049.50 61552.00 1164.07 50.06 4655.00 0.77 582.40 0.01 2162.89 30.75 2251.81 65698.00 38.58 4647.90 732.96 142.96 36.10 7064.87 3.71 488.70 41.30 0.74 350.10

ARTICLE IN PRESS C.K. Mahadevan, K. Jayakumari / Physica B 403 (2008) 3990–3996

3993

Table 4 Dielectric constants

Table 6 AC electrical conductivities (  106 /m)

System (with composition er for temperatures (K) taken for crystallization) 308 323 343 363

System (with composition taken for crystallization)

A

NaCl KCl KBr (NaCl)0.5(KCl)0.5 (NaCl)0.5(KBr)0.5 (KCl)0.5(KBr)0.5 (NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

4.34 3.52 4.27 17.32 29.43 6.53 11.99 14.49 17.83 18.80 8.92 28.02 40.33 18.01 19.42 13.91 14.81 15.70 8.91 35.71 23.46 28.90 42.63 24.19 43.41 7.41

5.08 3.87 5.05 28.73 35.91 6.86 17.29 28.33 29.12 31.30 13.82 36.03 52.21 19.20 21.19 15.71 16.72 17.31 11.40 49.20 40.36 38.28 51.40 34.65 56.60 11.80

383

403

6.56 7.68 8.79 9.54 4.19 4.51 4.83 5.31 6.02 6.50 7.15 7.79 41.91 54.11 63.15 67.28 39.04 45.09 53.25 62.52 7.18 7.67 8.01 8.16 29.80 43.06 55.18 64.27 39.96 54.27 69.62 87.65 40.21 55.20 72.14 94.81 42.50 64.10 86.61 110.92 22.50 30.92 38.84 45.76 51.61 81.04 104.63 131.54 75.77 103.62 132.05 153.08 20.61 22.92 25.10 26.24 23.09 31.16 36.27 38.41 17.18 18.16 20.94 25.03 18.61 21.32 34.21 47.46 20.70 25.17 38.52 57.40 14.82 17.31 20.31 22.43 66.81 79.94 89.63 100.72 64.65 100.64 141.76 166.12 58.57 86.42 138.34 191.50 59.12 65.31 71.01 77.04 42.71 50.88 58.18 64.71 61.42 77.41 100.65 103.69 18.24 23.64 31.32 36.93

423 10.28 5.95 8.12 68.66 72.71 8.32 85.49 106.26 128.83 132.60 50.79 169.32 176.64 28.63 39.00 26.21 57.44 77.88 23.90 105.90 170.14 243.22 80.71 71.57 114.55 38.39

Table 5 Dielectric loss tangents System (with composition taken for crystallization)

NaCl KCl KBr (NaCl)0.5(KCl)0.5 (NaCl)0.5(KBr)0.5 (KCl)0.5(KBr)0.5 (NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

NaCl KCl KBr (NaCl)0.5(KCl)0.5 (NaCl)0.5(KBr)0.5 (KCl)0.5(KBr)0.5 (NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

sac for temperatures (K) 308

323

343

363

383

403

423

0.01 0.04 0.18 2.49 30.10 0.04 0.61 0.86 1.44 1.15 0.68 1.70 1.68 0.57 1.23 0.42 0.44 0.42 0.25 1.73 5.88 6.65 1.33 0.80 2.46 0.07

0.03 0.06 0.21 5.65 37.10 0.05 0.86 1.64 2.94 1.83 1.70 2.32 2.70 0.67 1.57 0.70 0.58 0.82 0.37 2.52 10.25 8.74 1.66 1.19 3.37 0.47

0.04 0.08 0.25 12.02 41.20 0.06 1.31 2.13 4.20 2.32 4.15 3.27 3.91 0.99 1.80 1.28 1.08 1.75 0.53 3.90 16.64 12.53 2.00 1.57 4.44 1.11

0.09 0.10 0.29 20.33 48.11 0.07 1.65 2.56 5.95 3.03 7.90 4.46 4.84 1.24 2.52 2.84 1.73 2.33 0.65 5.51 26.46 15.61 2.36 2.15 5.85 1.57

0.12 0.13 0.34 29.48 57.40 0.09 1.72 3.02 8.01 3.80 11.71 5.17 5.58 1.74 3.02 5.69 2.85 3.02 0.82 7.12 39.47 17.91 2.76 2.62 6.93 2.14

0.15 0.15 0.55 37.17 68.10 0.10 2.14 3.46 11.54 4.68 14.78 6.14 6.04 2.83 3.46 11.02 4.00 4.28 0.95 9.46 49.76 21.29 3.25 3.06 8.58 2.71

0.18 0.18 0.58 49.30 80.00 0.12 3.09 4.08 18.18 5.38 21.02 7.72 6.48 3.50 4.27 17.77 5.26 5.66 1.09 11.36 58.15 27.17 3.63 3.58 10.69 3.28

Table 7 Activation energies (eV), low- and high-frequency dielectric permittivities and ol/ ot ( ¼ [e(o)/eN]1/2) tan d for temperatures (K) 308

323

343

363

383

403

423

0.02 0.22 0.74 2.59 18.40 0.11 0.92 1.17 1.46 1.10 1.38 1.09 0.75 0.57 1.14 0.54 0.53 0.48 0.51 0.87 4.51 4.14 0.56 0.60 1.02 0.16

0.10 0.28 0.73 3.54 18.60 0.13 0.89 1.04 1.82 1.05 2.21 1.16 0.93 0.63 1.34 0.80 0.62 0.85 0.58 0.92 4.57 4.11 0.58 0.62 1.07 0.72

0.12 0.34 0.75 5.16 19.00 0.15 0.79 0.96 1.88 0.98 3.32 1.14 0.93 0.66 1.40 1.35 1.04 1.52 0.64 1.05 4.63 3.85 0.61 0.66 1.30 1.10

0.20 0.38 0.79 6.76 19.20 0.17 0.69 0.85 1.94 0.85 4.60 0.99 0.84 0.97 1.46 2.82 1.46 1.67 0.68 1.24 4.73 3.25 0.65 0.76 1.36 1.20

0.24 0.47 0.86 8.40 19.40 0.19 0.56 0.78 2.00 0.79 5.43 0.89 0.76 1.25 1.50 4.90 1.50 1.41 0.73 1.43 5.01 2.33 0.70 0.81 1.24 1.23

0.29 0.52 1.26 9.94 19.60 0.21 0.60 0.71 2.19 0.76 5.82 0.84 0.71 1.94 1.62 7.93 1.52 1.34 0.76 1.69 5.39 2.00 0.76 0.85 1.49 1.32

0.31 0.54 1.28 12.92 19.80 0.25 0.65 0.69 2.54 0.73 7.46 0.82 0.66 2.20 1.97 12.20 1.65 1.31 0.82 1.93 6.15 2.01 0.81 0.90 1.68 1.54

System (with composition taken for crystallization)

Eac

e(o)

eN

ol/ot

NaCl KCl KBr (NaCl)0.5(KCl)0.5 (NaCl)0.5(KBr)0.5 (KCl)0.5(KBr)0.5 (NaCl)0.1(KCl)0.7(KBr)0.2 (NaCl)0.2(KCl)0.6(KBr)0.2 (NaCl)0.3(KCl)0.5(KBr)0.2 (NaCl)0.4(KCl)0.4(KBr)0.2 (NaCl)0.5(KCl)0.3(KBr)0.2 (NaCl)0.6(KCl)0.2(KBr)0.2 (NaCl)0.7(KCl)0.1(KBr)0.2 (NaCl)0.1(KCl)0.5(KBr)0.4 (NaCl)0.2(KCl)0.4(KBr)0.4 (NaCl)0.3(KCl)0.3(KBr)0.4 (NaCl)0.4(KCl)0.2(KBr)0.4 (NaCl)0.5(KCl)0.1(KBr)0.4 (NaCl)0.1(KCl)0.4(KBr)0.5 (NaCl)0.2(KCl)0.3(KBr)0.5 (NaCl)0.3(KCl)0.2(KBr)0.5 (NaCl)0.4(KCl)0.1(KBr)0.5 (NaCl)0.1(KCl)0.3(KBr)0.6 (NaCl)0.2(KCl)0.2(KBr)0.6 (NaCl)0.3(KCl)0.1(KBr)0.6 (NaCl)0.1(KCl)0.1(KBr)0.8

0.29 0.14 0.12 0.29 0.09 0.10 0.14 0.33 0.21 0.14 0.33 0.15 0.13 0.18 0.12 0.38 0.25 0.24 0.14 0.19 0.23 0.13 0.10 0.14 0.14 0.30

4.34 3.52 4.27 17.32 29.43 6.53 11.79 14.40 17.80 18.80 8.90 28.00 40.30 18.00 19.40 13.90 14.80 15.70 8.90 35.70 23.46 28.90 42.60 24.10 43.40 7.40

2.375 (2.3849) 2.233 (2.2222) 2.449 (2.4324) 2.286 2.396 2.349 2.277 2.290 2.308 2.324 2.340 2.355 2.376 2.311 2.333 2.361 2.373 2.377 2.355 2.368 2.376 2.400 2.373 2.394 2.405 2.422

1.35 1.26 1.32 2.75 3.51 1.67 2.28 2.51 2.78 2.84 1.95 3.45 4.12 2.79 2.88 2.43 2.50 2.57 1.94 3.88 3.14 3.47 4.24 3.17 4.25 1.75

Values given in brackets are taken from the literature [10].

Perumal and Mahadevan [2] have observed similar results with (KCl)x(KBr)yx(KI)1y single crystals: the sdc value increases with increasing temperature and the bulk composition has nonlinear influences on the values of sdc, Edc, 1/to and 1/t. In the case of (NaCl)x(KCl)yx(KBr)1y crystals considered here, their transparency is reduced when the crystals are cooled from

high to room temperature. The pulled crystal was allowed to cool naturally to room temperature over a 12 h period (i.e. the rate of cooling is very high at higher temperature). The observed lattice parameters indicated the existence of two phases in crystals with NaCl content greater than 0.1; one phase nearly corresponds to pure NaCl and the other corresponds to a mixed system [7].

ARTICLE IN PRESS C.K. Mahadevan, K. Jayakumari / Physica B 403 (2008) 3990–3996

0.45

Y = 0.8 Y = 0.6 y = 0.5

σdc

0.36 0.27 0.18 0.09 0 0.3

0.1

0.5

0.7

X Fig. 1. Composition dependence of sdc (  106 /m) at 308 K. A

0.54 0.45

Y = 0.8 Y = 0.6 y = 0.5

Εdc

0.36 0.27 0.18 0.09 0 0.1

0.3

0.5

0.7

X Fig. 2. Composition dependence of Edc (eV).

In the present study, AnalaR-grade samples of NaCl, KCl and KBr (with a minimum assay of 99.9% for NaCl and 99.5% for the others) were the starting materials for crystal growth. The dominant impurities present in NaCl are halides (bromide and iodide, 0.005%), potassium (0.01%) and divalent ions (barium 0.001%, calcium 0.002% and magnesium 0.002%). The dominant impurities present in KBr are halides (chloride 0.3% and iodide 0.05%), sodium (0.05%) and divalent ions (calcium 0.001% and magnesium 0.001%). No specific controls were provided to prevent these impurities from entering the crystals. The level of natural impurities present in the raw materials used in the present study is expected to cause precipitation effects even in the end-member crystals. Moreover, it is expected to have the well-known disturbing polarization effects in DC measurements in spite of annealing carefully to remove any moisture. Nadler and Rossel [11] have performed ionic conductivity measurements as a function of temperature between 373 and 1073 K for NaCl, KCl, KI and CsI single crystals. They determined the activation energy for the divalent cation-vacancy association in their lower temperature region to be 0.434–0.566 eV for undoped NaCl samples and 0.368 eV for an undoped KCl sample. The activation energies for mobility reported by Etzel and Maurer [12] for NaCl (0.85 eV) and Beniere et al. [13] for KCl (0.58–0.65 eV) are higher than the values reported by Nadler and Rossel. The measurements were made at higher temperature ranges. The activation energies observed in the present study for NaCl and KCl are, respectively, 0.087 and 0.101 eV, which are very

low when compared to those reported by the previous authors. The observed deviations can possibly be explained by impurity precipitation (expected to be more in the present study) and the different measurement methods. Also, the temperature range considered in the present study is not equivalent to those considered by the previous authors. The nonlinear variation with composition observed here for the NaCl–KCl–KBr mixed crystals can be explained in a similar way as done by Perumal and Mahadevan [2] for KCl–KBr–KI mixed crystals and may be attributed to the enhanced diffusion of charge carriers along dislocations and grain boundaries, which are expected to be more in the ternary mixed crystals investigated here. Sirdeshmukh and Srinivas [8], for the KCl–KBr system, indicate that there is excellent theoretical and experimental agreement on the dielectric constant data as a function of composition. The er value observed in the present study for (KCl)0.5(KBr)0.5 (6.53) is not in good agreement with the maximum theoretical value (4.937) [14]. This disagreement may be due to the defects created during cooling of the grown crystal from melting temperature to room temperature and natural impurities (available in the starting materials) getting into the crystal. Dielectric constants determined for the end-member crystals are of the same order as those obtained by previous authors [3–5,15]. The er values are found to increase with increase in temperature for the 26 crystals studied. This is similar to that observed for KCl–KBr [5], RbCl–RbBr [5], (KCl)x(KBr)yx(KI)1y [2], (NaCl)x(KBr)yx(KI)1y [3] and (NaCl)x(NaBr)yx(NaI)1y [4] mixed crystals (both single and poly crystals). The temperature has complicated influences on tan d and sac values for some of the crystals, and the increase in dielectric constant with the increase in temperature observed in the present study is large when compared to that of earlier workers. This may be due to the difference in the method and conditions used for the growth of single crystals and also to the thermal defects formed in the crystals while cooling them from melting temperature to room temperature. The bulk composition (taken for crystallization) dependences of er, tan d and sac values at 308 K and Eac value are shown as an illustration in Figs. 3–6, respectively. Results observed in the present study show that the bulk composition has complicated influences on the dielectric constant, tan d, sac and Eac values. This is similar to that observed for (KCl)x(KBr)yx(KI)1y single crystals [2]. As done for (KCl)x(KBr)yx(KI)1y single crystals, the nonlinear variation of these dielectric parameters with composition observed in the present study may be attributed to the enhanced diffusion of charge carriers along dislocations and grain boundaries.

εr

3994

43

Y = 0.8

38

Y = 0.6

33

y = 0.5

28 23 18 13 8

0.1

0.3

0.5 X

Fig. 3. Composition dependence of er at 308 K.

0.7

ARTICLE IN PRESS C.K. Mahadevan, K. Jayakumari / Physica B 403 (2008) 3990–3996

5 Y = 0.8 4

Y = 0.6 y = 0.5

tanδ

3 2 1 0

0.1

0.3

0.5

0.7

X Fig. 4. Composition dependence of tan d at 308 K.

7 Y = 0.8

6

Y = 0.6 y = 0.5

σac

5 4 3 2

3995

The value obtained for KBr (1.320) compares well with that obtained by earlier workers (1.39 [15]). The activation energy values (mobility enthalpies), Eac, obtained from dielectric measurements for the end-member crystals are 0.293, 0.138 and 0.117 eV for NaCl, KCl and KBr, respectively. Values available in the literature are significantly larger than these. Breckenridge [17] reported 0.65 eV for NaCl, 0.78 eV for KCl and 0.53 eV for KBr. If divalent foreign cations are present in a crystal, an equal number of cation vacancies are introduced to preserve electrical neutrality. It may be anticipated that a fraction of these foreign ions and vacancies will be present as pairs on adjacent sites because of the coulomb forces between them. Similarly, since elastic stresses in the lattice near a foreign ion may be partially relieved if the foreign ion is adjacent to a vacancy, it may be anticipated that pairs may be formed between vacancies and univalent foreign ions in the absence of coulomb forces; or complexes may be formed between foreign ions and vacancy pairs [17]. As mentioned earlier for the DC activation energy, the deviations in the AC activation energy can be explained by the presence of foreign ions (expected to be more here) and the different measurement methods. Breckenridge measured the dielectric constant and dielectric loss at a particular temperature for a range of frequencies and analysed the loss maximum values. In terms of utility, the ternary mixed crystals with high dielectric constants are expected to be more useful than the end member crystals.

1 0

5. Conclusions 0.1

0.3

0.5

0.7

X Fig. 5. Composition dependence of sac (  106 /m) at 308 K. A

0.6 Y = 0.8 Y = 0.6 y = 0.5

Εac

0.4

Acknowledgements

0.2

0

DC electrical conductivity measurements were carried out on (NaCl)x(KCl)yx(KBr)1y single crystals. Activation energies and mean jump frequencies were determined. Capacitance and tan d were measured, and er, sac and Eac were determined from the data obtained. The results indicate that bulk composition has complicated influences on the sdc, Edc, 1/to, er, tan d, sac and Eac values. This has been attributed to enhanced diffusion of charge carriers along dislocations and grain boundaries. The ternary mixed crystals are found to have large dielectric constants and are expected to be more useful than their end-member crystals.

0.1

0.3

0.5

0.7

X

One of the authors C.K.M. thanks the University Grants Commission, Hyderabad for the grant of a Minor Research Project and the Tamil Nadu State Council for Science and Technology, Chennai for the grant of a Major Research Project. The author K.J. thanks the University Grants Commission for the FDP Award.

Fig. 6. Composition dependence of Eac (eV).

References

ol/ot values were calculated using the Lyddane–Sachs–Teller (LST) relation [15,16] o21 ðoÞ ¼ 1 o2t which establishes a direct link between the frequencies of the two oscillation modes and the ‘‘static’’ and ‘‘optical’’ values of the dielectric permittivities [15]. These values are provided in Table 7.

[1] [2] [3] [4] [5] [6]

V. Haribabu, U.V. Subbarao, Prog. Crys. Growth Charact. 8 (1984) 189. S. Perumal, C.K. Mahadevan, Physica B 367 (2005) 172. G. Selvarajan, C.K. Mahadevan, J. Mater. Sci. 41 (2006) 8218. N. Neelakanda Pillai, C.K. Mahadevan, Mater. Manuf. Process. 22 (2007) 393. G. Sathaiah, Ph.D. Thesis, Kakatiya University, Warangal, 1988. X. Sahaya Shajan, K. Sivaraman, C. Mahadevan, D. Chandrasekharam, Cryst. Res. Technol. 27 (1992) K79. [7] K. Jayakumari, C. Mahadevan, J. Phys. Chem. Solids 66 (2005) 1705. [8] D.B. Sirdeshmukh, K. Srinivas, J. Mater. Sci. 21 (1986) 4117. [9] J.R. Reitz, F.J. Milford, R.W. Christy, Foundations of Electromagnetic Theory, Narosa Publishing House, New Delhi, 1990.

ARTICLE IN PRESS 3996

C.K. Mahadevan, K. Jayakumari / Physica B 403 (2008) 3990–3996

[10] D.B. Sirdeshmukh, L. Sirdeshmukh, K.G. Subhadra, Alkali Halides— A Handbook of Physical Properties, Springer Series in Materials Science, vol. 49, Springer, Berlin, 2001. [11] C. Nadler, J. Rossel, Phys. Stat. Sol. (a) 18 (1973) 711. [12] H.W. Etzel, R.J. Maurer, J. Chem. Phys. 18 (1950) 1003. [13] M. Beniere, M. Chemla, F. Beniere, J. Phys. Chem. Solids 37 (1976) 525.

[14] [15] [16] [17]

P. Varotsos, Phys. Stat. Sol. (b) 100 (1980) K133. I. Bunget, M. Popescu, Physics of Solid Dielectrics, Elsevier, New York, 1984. R.H. Lyddane, R.G. Sachs, E. Teller, Phys. Rev. 59 (1941) 673. R.G. Breckenridge, Relaxation effects in ionic crystals, in: W. Shockley, J.H. Hollomon, R. Maurer, F. Seitz (Eds.), Imperfections in Nearly Perfect Crystals, Wiley, New York, 1952.