Ferroelectric properties of the [N(CH3)4]2CoCl2Br2 compound

5
Ferroelectric properties of the [N(CH 3 ) 4 ] 2 CoCl 2 Br 2 compound Abdallah Ben Rhaiem a,, Fathi Jomni b , Karim Karoui a , Kamel Guidara a a University of Sfax, Faculty of Sciences, Laboratory of Solid State, BP 1171, 3000 Sfax, Tunisia b Laboratory for Materials, Organization and Properties (LMOP), Campus Universitaire-El Manar, 2092 Tunis, Tunisia highlights " Spectroscopic properties of DMBA and MMBA were examined by FT-IR, FT-Raman and NMR techniques by DFT method. " Simulated and observed vibrational spectra are agreed well. " 1 H and 13 C NMR chemical shifts have been compared with experimental values. " HOMO and LUMO energies showed the charge transfer. " The first static hyperpolarizability have been calculated and compared. article info Article history: Received 23 July 2012 Received in revised form 25 August 2012 Accepted 4 September 2012 Available online 13 September 2012 Keywords: Calorimetric study Dielectric permittivity AC conductivity abstract Synthesis, X-ray powder and Raman description are reported for [N(CH 3 ) 4 ] 2 CoCl 2 Br 2 compound. The calo- rimetric study shows three endothermic peaks at 289 K, 323 K and 408 K. The compound crystallizes in the orthorhombic system, space group Pnma with a = 12.384 Å, b = 9.058 Å and c = 15.647 Å. The dielec- tric spectra were measured in the frequency range 10 1 –10 6 Hz and temperature interval from 200 to 305 K. The dielectric permittivity shows that this compound exhibits a ferroelectric–paraelectric phase transition at 290 K. The frequency dependent permittivity is interpreted in the non-Debye model. The temperature dependence of the low frequency limit of the bulk AC conductivity r dc is well described by the Arrhenius equation: r dc = r 0 exp(E a /kT). Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Hybrid materials of general formula A 2 MX 4 (A: organic cation, M: metal = Co, Cu, and Zn, X: halogen = Cl, Br, I) have attracted con- siderable interest due to their multiple phase transitions related to the dynamics of the organic cations and inorganic anions. Interest in these compounds is rapidly increasing, as some of them exhibit interesting structural and physical properties like ferro-electricity, ferro-elasticity and low dimensional magnetism [1–10]. In particular, [N(CH3) 4 ] 2 CoCl 4 crystals undergo six phase transi- tions, at 122, 192, 276, 277.6, 280.1, and 293 K and [N(CH 3 ) 4 ] 2 CoBr 4 compound undergoes only one second order phase transition from the normal orthorhombic phase Pnma to the monoclinic ferroelastic phase P2 1 /a at 287.2 K [11,12]. At room temperature these com- pounds belong to the orthorhombic system, Pnma space group, with the unit cell dimensions a = 12.276 Å; b = 9.001 Å and c = 15.539 Å [5] for [N(CH 3 ) 4 ] 2 CoCl 4 and a = 12.683 Å, b = 9.247 Å, c = 16.052 Å for the [N(CH 3 ) 4 ] 2 CoBr 4 compound [13,14]. In this course of a sys- tematic investigation of these compounds, we have synthesized the new mixed crystal of composition [N(CH 3 ) 4 ] 2 CoCl 2 Br 2 . The aim of this paper is to study the electrical and dielectrical propriety at low temperature in order to investigate the ferro-paraelectric phase transition for this compound. 2. Experimental procedure The crystals of [N(CH 3 ) 4 ] 2 CoCl 2 Br 2 compound were synthesized starting from (N(CH 3 ) 4 )Br and CoCl 2 precursors of high purity (more than 99.9%), which were weighed in the stoichiometric pro- portion conforming to the equation 2ðNðCH 3 Þ 4 ÞBr þ CoCl 2 NðCH 3 Þ 4 2 CoCl 2 Br 2 then dissolved in the minimum amount of water and finally mixed. The mixture was slowly evaporated at room temperature. After a few days, the product compound was obtained. The purity and the composition of the synthesized compound were checked by atomic absorption. X-ray powder diffraction pattern was recorded using a Philips PW 1710 diffractometer operating with copper radiation K a = 1.5418 Å. Units cells parameters of the synthesized compound have been refined by the least square method from the powder data. 0022-2860/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molstruc.2012.09.009 Corresponding author. Tel.: +216 20 917074. E-mail addresses: [email protected] (A. Ben Rhaiem), karouikari- [email protected] (K. Karoui), [email protected] (K. Guidara). Journal of Molecular Structure 1035 (2013) 140–144 Contents lists available at SciVerse ScienceDirect Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc

Transcript of Ferroelectric properties of the [N(CH3)4]2CoCl2Br2 compound

Page 1: Ferroelectric properties of the [N(CH3)4]2CoCl2Br2 compound

Journal of Molecular Structure 1035 (2013) 140–144

Contents lists available at SciVerse ScienceDirect

Journal of Molecular Structure

journal homepage: www.elsevier .com/locate /molstruc

Ferroelectric properties of the [N(CH3)4]2CoCl2Br2 compound

Abdallah Ben Rhaiem a,⇑, Fathi Jomni b, Karim Karoui a, Kamel Guidara a

a University of Sfax, Faculty of Sciences, Laboratory of Solid State, BP 1171, 3000 Sfax, Tunisiab Laboratory for Materials, Organization and Properties (LMOP), Campus Universitaire-El Manar, 2092 Tunis, Tunisia

h i g h l i g h t s

" Spectroscopic properties of DMBA and MMBA were examined by FT-IR, FT-Raman and NMR techniques by DFT method." Simulated and observed vibrational spectra are agreed well."

1H and 13C NMR chemical shifts have been compared with experimental values." HOMO and LUMO energies showed the charge transfer." The first static hyperpolarizability have been calculated and compared.

a r t i c l e i n f o

Article history:Received 23 July 2012Received in revised form 25 August 2012Accepted 4 September 2012Available online 13 September 2012

Keywords:Calorimetric studyDielectric permittivityAC conductivity

0022-2860/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.molstruc.2012.09.009

⇑ Corresponding author. Tel.: +216 20 917074.E-mail addresses: [email protected] (A.

[email protected] (K. Karoui), [email protected]

a b s t r a c t

Synthesis, X-ray powder and Raman description are reported for [N(CH3)4]2CoCl2Br2 compound. The calo-rimetric study shows three endothermic peaks at 289 K, 323 K and 408 K. The compound crystallizes inthe orthorhombic system, space group Pnma with a = 12.384 Å, b = 9.058 Å and c = 15.647 Å. The dielec-tric spectra were measured in the frequency range 10�1–106 Hz and temperature interval from 200 to305 K. The dielectric permittivity shows that this compound exhibits a ferroelectric–paraelectric phasetransition at 290 K. The frequency dependent permittivity is interpreted in the non-Debye model. Thetemperature dependence of the low frequency limit of the bulk AC conductivity rdc is well describedby the Arrhenius equation: rdc = r0 exp(�Ea/kT).

� 2012 Elsevier B.V. All rights reserved.

1. Introduction the new mixed crystal of composition [N(CH3)4]2CoCl2Br2. The aim

Hybrid materials of general formula A2MX4 (A: organic cation,M: metal = Co, Cu, and Zn, X: halogen = Cl, Br, I) have attracted con-siderable interest due to their multiple phase transitions related tothe dynamics of the organic cations and inorganic anions. Interestin these compounds is rapidly increasing, as some of them exhibitinteresting structural and physical properties like ferro-electricity,ferro-elasticity and low dimensional magnetism [1–10].

In particular, [N(CH3)4]2CoCl4 crystals undergo six phase transi-tions, at 122, 192, 276, 277.6, 280.1, and 293 K and [N(CH3)4]2CoBr4

compound undergoes only one second order phase transition fromthe normal orthorhombic phase Pnma to the monoclinic ferroelasticphase P21/a at 287.2 K [11,12]. At room temperature these com-pounds belong to the orthorhombic system, Pnma space group, withthe unit cell dimensions a = 12.276 Å; b = 9.001 Å and c = 15.539 Å[5] for [N(CH3)4]2CoCl4 and a = 12.683 Å, b = 9.247 Å, c = 16.052 Åfor the [N(CH3)4]2CoBr4 compound [13,14]. In this course of a sys-tematic investigation of these compounds, we have synthesized

ll rights reserved.

Ben Rhaiem), karouikari-(K. Guidara).

of this paper is to study the electrical and dielectrical propriety atlow temperature in order to investigate the ferro-paraelectric phasetransition for this compound.

2. Experimental procedure

The crystals of [N(CH3)4]2CoCl2Br2 compound were synthesizedstarting from (N(CH3)4)Br and CoCl2 precursors of high purity(more than 99.9%), which were weighed in the stoichiometric pro-portion conforming to the equation

2ðNðCH3Þ4ÞBrþ CoCl2 ! ½NðCH3Þ4�2CoCl2Br2

then dissolved in the minimum amount of water and finally mixed.The mixture was slowly evaporated at room temperature. After afew days, the product compound was obtained. The purity andthe composition of the synthesized compound were checked byatomic absorption.

X-ray powder diffraction pattern was recorded using a PhilipsPW 1710 diffractometer operating with copper radiationKa = 1.5418 Å. Units cells parameters of the synthesized compoundhave been refined by the least square method from the powderdata.

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5 10 15 20 25 30 35 40 45 50 55 600

2000

4000

6000

8000

10000

Inte

nsité

(au

)

2θ (°)

153

112 43

505

123

653152

2142

035

306

040

421 51

1420

323

314

132

205

322

411

410

223

401

40030

320

411

422

121

310

400

430

112

121

201

320

2

200

102

002

Fig. 1. X-ray diffractogram of the [N(CH3)4]2CoCl2Br2 compound.

200 220 240 260 280 300 320 340 360 380 400 420 440T (K)

endo

ther

mic

Fig. 2. Differential scanning calorimetry of [N(CH3)4]2CoCl2Br2.

tens

ity (

a.u.

)

A. Ben Rhaiem et al. / Journal of Molecular Structure 1035 (2013) 140–144 141

The Raman spectrum of monocrystal sample was performed inthe 50–3200 cm�1 range employing a Hololab 5000R instrumentusing the 514.5 nm line of a spectra-physics argon ion laser.

e0 and e0 0 dielectric measurement, and Z0, Z0 0 electric impedancewere performed over a broad frequency window, 10�1 < f(Hz) < 4 � 105 in a temperature range 223 < T (K) < 393 using a Sal-arton 1260 system integrating ALFA dielectric interface.

3200 2800 2400 2000 1600 1200 800 400 0

Rel

ativ

e in

wevernumber (cm-1)

Fig. 3. Raman spectra of [N(CH3)4]2CoCl2Br2 at room temperature.

3. X-ray powder analysis

Room temperature X-ray diffraction pattern of the [N(CH3)4]2-

CoCl2Br2 compound is shown in Fig. 1. All the reflection peaks wereindexed in the orthorhombic symmetry with Pnma space group. Thelattice parameters of the selected unit cell were refined using theleast-squares sub-routine of a standard computer program. Theserefined lattice parameters are a = 12.384(2) Å, b = 9.058(2) Å,c = 15.647(3) Å and V = 1755.190(4) Å3 with estimated standarddeviation in parenthesis. The compound structure is isotype to[N(CH3)4]2CoCl4, and [N(CH3)4]2CoBr4 [13,14]. In the [N(CH3)4]2-

CoCl4�xBrx series (x = 0, 2 and 4), we can correlate the volume perunit molecular formula of these materials with x (Table 1). Thevolume v is found to augment with increasing x.

The crystal structure consists of alternate organic–inorganic½ðNðCH3Þ4Þ

þ=CoX2�

4 � (X = Cl or Br) layers and organic sheets(N(CH3)4)+. Organic and inorganic groups are not disordered. Itsmain geometrical features are those commonly observed in theatomic arrangements of [N(CH3)4]2CoCl4 and [N(CH3)4]2CoBr4

[13,14].

4. Calorimetric study

Differential scanning calorimetry measurements were per-formed on heating the sample from 235 to 420 K using a Netzsch-DSC 204 calorimeter. The DSC diagram is presented in Fig. 2. Threeendothermic peaks are present at 289 K, 323 K and 408 K, confirm-ing the availability of four phases denoted I, II, III and IV.

Table 1Unit cell volume of [N(CH3)4]2CoCl4�xBrx series (x = 0, 2 and 4).

Formula x V(Å3)

[N(CH3)4]2CoCl4 0 1717.002[N(CH3)4]2CoCl2Br2 2 1755.190[N(CH3)4]2CoBr4 4 1882.573

5. Raman spectrum at room temperature

The Raman spectrum of [N(CH3)4]2CoCl2Br2 (Fig. 3) was inter-preted on the basis of the similar compounds [14–22]. We notethat there is no band in the 1500–2800 cm�1 spectral region. Gen-erally the observed bands in this region are overtones or combina-tions. The bands corresponding to the internal vibrational modes ofthe anions: m1, m2, m3 and m4 (CoX4) (where X = Cl and Br) appear inthe spectral region below 300 cm�1. The band observed at277 cm�1 was assigned to the m3(CoCl4) mode, while the band ob-served at 116 cm�1 was assigned to the m4(CoCl4) mode. Finally, theband appearing at 197 cm�1 was assigned to the m3(CoBr4) modecan be used to confirm the presence of the CoBr4 group in this com-pound [23].

For cations, the assignment of the bands was made by compar-ing the Raman spectra of the compound with those of (CH3)4NCl,[(CH3)4N]2SbCl4 and [(CH3)4N]2SiF6 [22,24]. The band observed at453 cm�1 arises from the deformation vibration m4(NC4) of thetetramethylammonium cation. The deformation mode m2(NC4)appears blow 749 cm�1. The two bands observed around 945 and1115 cm�1 were assigned to m3 and m1(NC4) stretching modes,respectively, while the weak bands observed at 1168 and1297 cm�1 were assigned to the qr(CH3) methyl rocking modes.The band observed at 1452 cm�1 was assigned to the da(CH3) bend-ing mode of the moiety. In the frequency region above 2800 cm�1,

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200 220 240 260 280 300 320 340 360 380 400

0,0

5,0x106

1,0x107

1,5x107

2,0x107

2,5x107

3,0x107

ε' r

T (K)

f = 0.1Hz f = 0.25Hz f = 1Hz f = 10Hz

200 220 240 260 280 300 320 340 360 380 400-1x105

0

1x105

2x105

3x105

4x105

5x105

6x105

7x105

8x105

9x105

1x106

ε' r

T (K)

f = 100Hz f = 251Hz f = 1000Hz f = 10000Hz

Fig. 4. Temperature dependence of dielectric constant e0r for [N(CH3)4]2CoCl2Br2.

200 220 240 260 280 300 320 340 360 380 400-2,0x105

0,0

2,0x105

4,0x105

6,0x105

8,0x105

1,0x106

1,2x106

1,4x106

1,6x106

ε " r

T (K)

f = 100Hz f = 251Hz f = 1000Hz f = 10000Hz

Fig. 5. Temperature dependence of dielectric constant e00r for [N(CH3)4]2CoCl2Br2.

220 240 260 280 300 320 340 3600,0000

0,0005

0,0010

0,0015

0,0020

0,0025

0,00301/

ε' r

T (K)

f = 100000Hz f = 10000Hz

Fig. 6. Temperature variation of 1/er at some frequency for the [N(CH3)4]2CoCl2Br2

compound.

142 A. Ben Rhaiem et al. / Journal of Molecular Structure 1035 (2013) 140–144

the bands corresponding to the methyl C–H stretching modes, thebands corresponding to overtones, as well as the bands corre-sponding to Fermi resonance between methyl stretching and bend-ing overtones modes appear [24]. More particularly, the bandsobserved near 2976 and 3018 cm�1 were assigned to the ms(CH3)and ma(CH3) stretching modes, respectively.

6. Dielectrical study

6.1. Temperature dependence of dielectrical study

The temperature dependence of the real (e0) and imaginary (e0 0)parts of the dielectric permittivity of [N(CH3)4]2CoCl2Br2 com-pound for different frequencies is shown in Figs. 4 and 5. Our mea-surements were done in the 223–393 K temperature range. Thesespectra present a prominent dielectric peak at T = 290 K associatedto a ferroelectric–paraelectric phase transition. However the[N(CH3)4]2MX4 compound family exhibits ferroelectric proprieties[9–12], particularly the parental compound [N(CH3)4]2CoBr4 is fer-roelectric below 287.2 K [12]. This transition occurs in the vicinityof that detected by DSC technique (Fig. 2). The value of the ferro-electric–paraelectric temperature phase transition does not changewith the increasing frequency. In fact, this result suggests that thissample does not present any type of dielectric relaxation in theinvestigated frequency range [25].

In addition, the thermal variation of 1=e0r (Fig. 6) in the paraelec-tric state is of the Curie–Weiss type:

1=e0r ¼ ðT � T0Þ=C ð1Þ

where C is the Curie–Weiss constant and T0 is the Curie–Weisstemperature.

The Curie–Weiss plot 1/er versus temperature gives a straightline with the X-axis intercept at T0. For the classical ferroelectrics,the order of the ferroelectric–paraelectric phase transition can bedetermined from the value of T0. In the case T0 – Tc, the phase tran-sition is of the first order. If T0 = Tc, this transition is of second ordertype [8]. In our study, these values are 293 K at 100 Hz, 1000 Hzand 10,000 Hz (Fig. 6) which are close to Tc = 290 K suggesting thatthis transition is of the second order type [26,27].

6.2. Frequency dependence of dielectrical studies

The dielectric relaxation is described by a non-Debye modelwhich gives the frequency dependent complex permittivity inthe form [28]:

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2,5 3,0 3,5 4,0 4,5-8

-7

-6

-5

-4

-3

-2

EA=0.13eV

ln (σ

dc*T

(Ω-1cm

-1K

)

1000/T(K)

EA=0.31eV

Fig. 8. Temperature dependence of ln (rdcT).

A. Ben Rhaiem et al. / Journal of Molecular Structure 1035 (2013) 140–144 143

e�ðxÞ ¼ e1 þes � e1

1þ ðixs1Þ1�a þrdc

je0xð2Þ

where rdc represents the specific conductivity, es is the static per-mittivity and s1 is the relaxation time of the Debye process.

The imaginary part of the e�is:

e00ðxÞ ¼ðes � e1Þðxs1Þ1�a sin ð1�aÞp

2

� �

1þ 2ðxs1Þ1�a cos ð1�aÞp2

� �þ ðxs1Þ2ð1�aÞ

þ rdc

e0xð3Þ

The first part in Eq. (3) is related to the thermal polarization andthe second one to the electrical conductivity. Fig. 7 shows the fre-quency dependence of the imaginary part of the dielectric constantfrom fitting Eq. (3). There are no appreciable relaxation peaks inthe frequency range employed in this study. The dielectric loss risesharply at low frequency indicating that electrode polarization andspace charge effects have occurred confirming non-Debye depen-dence [29,30]. The dielectric loss increases at higher temperaturesdue to the higher charge carrier density.

The temperature dependence in electrical conductivity rdc cal-culated from fitting e00r to Eq. (3) is well described by an Arrheniusequation of the form:

Trdc ¼ r0 expð�Ea=kTÞ ð4Þ

10-1

100

101

102

103

104

105

106

107

0,0

4,0x107

8,0x107

1,2x108

1,6x108

2,0x108

a T = 223K T = 243K T = 253K T = 263K T = 273K Fit

ε"r

ω (rad/s)

10-1 100 101 102 103 104 105 106 107

0

100000

200000

300000

400000

500000

600000b T = 373K

T = 353K T = 333K T = 303K Fit

ε"r

ω (rad/s)

Fig. 7. Variation of the imaginary part of dielectric constant versus frequency; (a)ferroelectric phase and (b) paraelectric phase.

where r0 is the pre-exponential factor, k the Boltzmann constantand Ea the apparent activation energy for the ion migration. Onthe basis of Eq. (1), ln (rdcT) versus 1000/T is presented in Fig. 8.The phase transition is confirmed by the change of the slope ofthe curve at 290 K. Following the Arrhenius law, the obtained acti-vation energy of the sample crystal are Ea = 0.31 eV in the ferroelec-tric phase and Ea = 0.13 eV in the paraelectric phase [9,10,31].

7. Conclusion

The present work reports the results of our investigation on thedielectric properties of the [N(CH3)4]2CoCl2Br2 compound. The var-iation of e0r and e00r versus temperature at different frequenciesshows a ferroelectric–paraelectric phase transition at 290 K ofthe second order type. The frequency dependence permittivity isinterpreted in the non-Debye model. rdc is analyzed by the Arrhe-nius equation: rdc T = r0 exp(�Ea/kT). The activation energy Ea

jumps from 0.31 eV in the ferroelectric phase to 0.13 eV in theparaelectric phase.

References

[1] K. Gesi, Ferroelectrics 137 (1992) 209.[2] P.S. Peercy, D. Morosin, Phys. Lett. A 36 (1971) 409.[3] T. Tsang, D.B. Utton, J. Chem. Phys. 57 (1976) 3780.[4] Y. Mlik, M. Couzi, J. Phys. C: Solid State Phys. 15 (1982) 6891.[5] T. Levola, R. Laiho, Solid State Commun. 66 (1988) 557.[6] G. Aguirre-Zamalloa, V. Rodriguez, M. Couzi, F. Sayetat, P. Ferty, J. Phys.:

Condens. Matter 9 (1997) 937.[7] A. Ben Rhaiem, N. Zouari, K. Guidara, M. Gargouri, A. Daoud, J. Alloys Comp. 38

(7) (2005) 1.[8] K. Karoui, A. Ben Rhaiem, F. Hlel, M. Arous, K. Guidara, Mater. Chem. Phys. 133

(2012) 1.[9] K. Karoui, A. Ben Rhaiem, K. Guidara, Physica B 407 (2012) 489.

[10] K. Horiuchi, A. Weiss, J. Mol. Struct. 345 (1995) 97.[11] K. Hasebe, H. Mashyama, S. Tanisaki, K. Gesi, J. Phys. Soc. Jpn. 53 (1984) 1866.[12] K. Gesi, J. Phys. Soc. Jpn. 51 (1968) 1.[13] BY J.R. Wiesner, R.C. Srivatava, C.H.L. Kennard, M. Divaira, E.C. Lingafelter, Acta

Cryst. 23 (1967) 565.[14] Y. Nishihata, A. Sawada, Acta Cryst. CA9 (1993) 1939.[15] M. Gosniowska, Z. Ciuik, G. Bator, R. Jakubas, J. Baran, J. Mol. Struct. 555 (2000)

243.[16] J. Barn, M. Sledz, M. Drozd, A. Pietraszko, A. Haznar, H. Ratajczak, J. Mol. Struct.

526 (2000) 361.[17] M.A. Kandhaswamy, V. Srinivasan, Bull. Mater. Sci. 25 (1) (2002) 41.[18] J.R. Durig, C. Zheng, G.A. Guirgis, H. Zhen, A.S. Drew, D.T. Durig, J. Mol. Struct.

786 (2006) 9.[19] M. Herstedt, W.A. Henderson, M. Smironov, L. Ducasse, L. Sevant, D. Talga, J.C.

Lass‘egues, J. Mol. Struct. 783 (2006) 145.[20] Y. Abid, M. Kamoun, A. Daoud, F. Romain, J. Raman Spectrosc. 21 (1990) 709.[21] Y. Abid, A. Daoud, M. Couzi, Phys. Stat. Sol. (a) 52 (1979) 175.

Page 5: Ferroelectric properties of the [N(CH3)4]2CoCl2Br2 compound

144 A. Ben Rhaiem et al. / Journal of Molecular Structure 1035 (2013) 140–144

[22] A. Ouasri, A. Rhandour, M.C. Dhamelincourt, P. Dhamelincout, A. Mazzah,Spectochim. Acta Part A 58 (2002) 2779.

[23] P.H.M. van Loosdrecht, A. Janner, J. Phys.: Condens. Matter 3 (1991) 8113.[24] W. Von der Ohe, J. Chem. Phys. 62 (1975) 3933.[25] H. Khemakhem, T. Mhiri, A. Daoud, Solid State Ion. 117 (1999) 337.[26] S. Triebwasser, Phys. Rev. 101 (1989) 993.

[27] S. Triebwasser, IBM J. Res. Dev. 2 (1958) 212.[28] F. Alvarez, A. Alegría, J. Colmenero, Phys. Rev. B47 (1993) 125.[29] H. Kolodziej, L. Sobczyk, Acta Phys. Polon. A39 (1971) 59.[30] X. Qian, N. Gu, Z. Cheng, X. Yang, S. Dong, Electronichim. Acta 46 (2001)

1829.[31] S. Kumar, K.B.R. Varma, Solid State Commun. 146 (2008) 137.