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Conductivity and dielectric studies in Cs0.4Rb0.6H2PO4 mixed crystals
Journal of Molecular Structure 519 (2000) 143–151 www.elsevier.nl/locate/molstruc
Conductivity and dielectric studies in Cs0.4Rb0.6H2PO4 mixed crystals H. Naı¨li, N. Zouari, T. Mhiri*, A. Daoud Laboratoire de l’Etat Solide, Universite´ de Sfax 3038, Sfax, Tunisia Received 9 March 1999; received in revised form 7 May 1999; accepted 24 May 1999
Abstract The mixed caesium rubidium dihydrogen phosphate, Cs0.4Rb0.6H2PO4 (CRDP) crystallises in the monoclinic system P21/m at and b 108:268 10; room temperature with the following parameters: a 4:8183 9; b 6:2671 6; c 7:7620 10 A Z 2. A calorimetric study of the title compound shows two distinct endothermal peaks which are detected at 293 and 525 K. Samples were examined by impedance and modulus spectroscopy techniques. The first transition (293 K) is attributed to a ferroelectric–paraelectric type. A high temperature phase transition (525 K) leading to a superionic–protonic phase was found, characterised by an unusual high conductivity. The conductivity relaxation parameters associated with the high-disorder protonic conduction have been determined from analysis of the M 00 =M 00max spectrum measured in a wide temperature range. Transport properties in this material appear to be due to proton hopping mechanism. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Conductivity; Superprotonic phase; Ferroelectric–paraelectric transition; Relaxation parameters
1. Introduction The compounds of general formula MH2XO4 (where M is a monovalent cation: K 1, Rb 1, Cs 1,… and X is P or As) exhibit structural phase transitions and interesting physical properties [1–6]. Rubidium dihydrogen phosphate RbH2PO4 (RDP) which is an isomorphic substance of potassium dihydrogen phosphate KH2PO4 (KDP) undergoes a ferroelectric–paraelectric phase transition at Tc 147 K [7] and a superprotonic one at 395 K [8], while CsH2PO4 (CDP) is known to have one-dimensional ferroelectric order below Tc 154 K and a superionic transition at Tc 504 K [9]. In order to determine the influence of the partial * Corresponding author. Tel.: 1 216-4274088; fax: 1 2164274437.
substitution of the caesium by rubidium (Cs0.4Rb0.6H2PO4), we have undertaken an analysis of the frequency response of a.c. conductivity data in our material. This process is useful in determining the complex permittivity 1 p(v ) and the conductivity relaxation time. The complex modulus formalism, p M p 1=1p jvC0 Z p where j 21; v v 2pf is the angular frequency and C0 is the vacuum capacitance of the cell, has been adopted to determine the conductivity relaxation times. This formalism discriminates as a matter of fact against electrode polarisation and other interfacial effects in solid electrolytes [10]. In addition, a short description of the crystal structure at room temperature paraelectric phase is given. The dielectric spectrum at temperatures ranging from 130 to 310 K and for the frequencies 10 4, 2 × 10 4, 5 × 10 4 and 10 5 Hz will also be examined. Furthermore, we compare in this work the
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Fig. 1. Differential scanning calorimetry of Cs0.4Rb0.6H2PO4 between 223 and 600 K.
conductivity behaviour at high temperature between CRDP with those in CDP and RDP.
2. Experimental and structure description 2.1. Experimental Single crystals of CRDP were prepared by slow evaporation of an aqueous solution containing stoichiometric quantities of Cs2CO3/Rb2CO3 /H3PO4 with the following reaction: 1 2 xCs2 CO3 1 xRb2 CO3 1 2H3 PO4 ! 2Cs12x Rbx H2 PO4 1 CO2 1 H2 O Upon maintaining the solution at a temperature of approximately 300 K, parallelepipedic crystals with a size of about 0:30 × 0:40 × 0:43 mm3 , formed after 10–15 days. Caesium, rubidium and phosphate contents were checked by chemical analysis. In fact, the single crystals so formed correspond to the composition Cs0.4Rb0.6H2PO4. The analysis of the frequency response of ac conductivity data is used to determine the electrical characteristics of protonic conductors. The crystal compounds of CRDP were crushed and carried out
on pellets at 200 MPa stress. Dense translucent pellets (10 mm in diameter; 1–2 mm in thickness) were obtained. Argent electrodes were deposited. Electrical properties were determined by impedance and modulus method using a frequency response analyser (Hewlett-Packard 4192 A LF automatic bridge monitored by a HP Vectra microcomputer). The frequency range was 100 Hz to 1 MHz and measurements were carried out in vacuum between 130 and 573 K. At each interval, the sample temperature was maintained by a Herrrmann-Moritz 28480 Chassant (using a Chromel/Alumel couple) controller for 0.5 h before collecting data; the stability was ^18C. 2.2. Structure description The cell structure of Cs0.4Rb0.6H2PO4 was determined by Naı¨li et al. [11], a monoclinic cell was obtained with the following parameters: ˚ a 4:8183 9; b 6:2671 6; c 7:7620 10 A and b 108:26 108, Z 2. The structure is built from Cs and Rb atoms coordinated by O atoms belonging to PO4 tetrahedra. Each Cs 1 and Rb 1 ion is bonded to 12 oxygen atoms, the bond distances ˚ and averages range from 3.012(4) to 3.544(2) A ˚ 3.30 A. In this structure, two oxygens designated as O(1) and O(2) are found to be located just in the plane
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hydrogen atoms over two symmetry-equivalent positions with a half occupancy around an inversion centre [11]. 3. Calorimetric studies The differential scanning calorimetry (DSC) measurements were performed on heating CRDP from 100 to 600 K on a DSC Mettler TA 4000 with scan speeds of 58 min 21. The thermogram shows three endothermal peaks at T1 293, T2 525 and T3 575 K (Fig.1). The first transition is considered to be of an order–disorder structure phase transition, the second one seems to be a superionic–protonic type and the latter one is attributed to the melting point of the product. The calculated transition enthalpy and entropy at the first transition T1 293 K were DH1 7:7 J g21 and DS1 26:28 × 1023 J g21 K21 , at the second transition T2 525 K were DH2 68:7 J g21 and DS2 13 × 1022 J g21 K21 . These results can be confirmed by electrical measurements using impedance spectroscopy. 4. Electrical properties Fig. 2. Thermal evolution of dielectric constant 1 0r in the frequency range 10–100 KHz.
y 3=4, and the remaining two oxygens O(3) and O(4) as mirror image with respect to this plane. In PO4 tetrahedron, we note that the bond length P– ˚ (type PyO and the P–O(1) O(2) is 1.471(5) A ˚ (type P–O(h)) while the P– distance is 1.564(4) A O(3) and P–O(4) distances which are equivalents ˚ (type P–O(h/2); with an average of 1.519(4) A where O(h) represents a hydroxyl oxygen and O(h/ 2) when the H atoms are distributed in a double minimum potential over two symmetry-equivalent positions between two oxygen atoms [11]. The PO4 tetrahedra are linked into two chains by two different ˚ ) links hydrogen bonds. The shorter bond (2.453(7) A the phosphate groups into chains running along the b˚ ) which is always axis and the longer one (2.488(6) A ordered, cross-links the chains to form the (0 0 1) layers. The shorter hydrogen bond is disordered, this disorder is due to a statistical distribution of the
4.1. Dielectric study The electrical data measured as an impedance, Z p, have been converted into permittivity, 1 p, using the relation
1p 1=iwC0 Z p where C0 is the vacuum capacitance [12]. Temperature dependence of the dielectric constant 1 0r was presented at various frequencies in Fig. 2. These spectra present a prominent dielectric peak at Tc 293 K characterising the ferroelectric–paraelectric phase transition which is observed by differential scanning calorimetry. The evolution of this dielectric constant as a function of frequency shows an increase of 1 0r with decreasing frequencies. This phenomenon characterises the presence of dispersion character in this material. The values of paraelectric–ferroelectric temperature phase transition does not change with increasing frequency, this suggests that this compound does not present a dipolar-type relaxation in this frequency
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Fig. 3. Complex plane plots of Cs0.4Rb0.6H2PO4 at various temperatures.
Fig. 4. Conductivity plots log10 sT f 103 =T for CRDP compound.
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Fig. 5. Variation of log10 s 0 with log f at different temperatures for a sample of CRDP.
range. The dielectric data in the paraelectric state obey quite well the Curie–Weiss law:
1 0r C=T0 2 Tc where C is the Curie–Weiss constant and T0 is the Curie–Weiss temperature for the paraelectric state. The strong decrease of 1 0r with increasing frequency observed in Fig. 2 is nothing but a dispersion without loss of peak resulting from charge carriers present in the material. This phenomenon is usually referred to as low-frequency dispersion (LFD) [13,14] where the charge carrier contribution is significant. 4.2. Protonic conductivity The crystals of CRDP have been reported to demonstrate high protonic conductivity in the high temperature phase. Our measurements were achieved in the temperature range 300–573 K. Some complex impedance diagrams 2Z 00 versus Z 0 at various temperatures are given in Fig. 3, and show that
CRDP follows the Cole–Cole law. The difference between the Cole–Cole and Deby law is determined from the precedent figure a 0:18. The bulk ohmic resistance relative to experimental temperature is the intercept on the real axis of the zero-phase angle extrapolation of the highest-frequency curve. These results are used elsewhere to show the evolution of the conductivity versus inverse temperature log10 sT f 103 =T for CRDP compound (Fig. 4). In the temperature range 339–573 K, the experimental points are located on both sides of a line above and below 525 K. An Arrhenius-type law sT s0 exp 2Ea =kT characterise the low and the high temperature domain with a sudden sharp increase of the conductivity upon 525 K. The activation energy of the title compound at low temperature is 0.30 eV and the conductivity increases sharply from 525 K s 2:92 × 1022 V21 cm21 at 525 K to 4:14 × 1021 V21 cm21 at 549 K). This result confirms the presence of a superprotonic phase transition observed previously at the same
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Fig. 6. Plots of log M 0 versus log f for Cs0.4Rb0.6H2PO4 at various temperatures.
temperature by differential scanning calorimetry measurements. The detected transition corresponds to the structural transformation between the monoclinic phase and the superprotonic phase, and leads to fast proton conduction. The structural mechanisms of proton conductivity on the CRDP compound is similar to that in the KDP-family. Therefore, occupation of the interstitial proton site should be possible and the proton migration from one oxygen atom of the PO4 group to another is accompanied by the formation of a new hydrogen bond. In order to explain the abrupt change in the conductivity at 525 K in CRDP crystals, we have compared these conductivity studies with those obtained in CDP crystals by Baranov et al. [15], who assumed that at the phase transition to the superprotonic phase, the crystal symmetry rises (from monoclinic to cubic) and some interstitial proton sites become structurally equivalent to normal proton sites. Hence, the proton will dynamically disorder between sites, because the number of these sites will exceed the number of protons. This will lead to the high proton conductivity in the cubic phase of CDP.
In Fig. 5 we show log s 0 (f) (real part of the complex conductivity) plots for CRDP material at different temperatures. At low frequencies dc conductivity plots are observed above and below the superionic–protonic phase transition which occurs at 525 K. Dc conductivity increases with increasing temperature. At high frequencies, these curves show an increasing hard segment length. This is due to the fact that charge-carrier motion occurs mostly through the soft segment phase. The increasing of the protonic conductivity is due to an increasing disorder of the hydrogen atoms among partly occupied symmetryequivalent positions. Therefore, we have included in this work the modulus formalism M p 1=1p jwC0 Z p ; to understand the proton conduction mechanism. 4.3. Modulus spectroscopy analysis A plot of log M 0 and of the normalised M 00 =M 00max imaginary part of the complex modulus versus log f is given in Figs. 6 and 7 at various temperatures for
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Fig. 7. Plots of normalised modulus M 00 =M 00max versus log f for CRDP at various temperatures.
CRDP compound. At all temperatures, the value of M 0 reaches at high frequencies, a constant value M 0∞ 1=1∞ . At low frequencies, it approaches zero, which indicates that the electrode polarisation phenomena make a negligible contribution to M p and may be ignored when the electric data are analysed in this form [16]. The M 00 =M 00max relative to a temperature given shows an asymmetrical peak approximately centred in the dispersion region of M* (Fig. 7). The region to the left of the peak is where the H 1 ions are mobile over long distances, the region to the right is where the ions are spatially confined to their potential wells. The frequency range where the peak occurs is indicative of the transition from short-range to longrange mobility at decreasing frequency and is defined by the condition vts 1, where t s is the most probable ion relaxation time [17]. The M 00 =M 00max curves are asymmetric, in agreement with the non-exponential behaviour of the electrical function, that is well described by the empirical stretched exponential Kohlrausch function w t exp2 t=ts b [18–19]. The full-width at half-height (FWHH) of the
M 00 =M 00max spectrum is clearly wider than the breadth of a Debye-peak (1.14 decades) [20] and it results in a value b 0:46 for the Kohlrausch parameter. When temperature increases, modulus peak maxima shift to higher frequencies (Fig. 7). Fig. 8 gives the temperature dependencies of log(s T) and log(fp) where fp fp 1=2pts is the frequency relative to M 00max peak corresponding to the bulk relaxation. An Arrheniustype law is shown with a high jump at about 525 K and confirm the superionic–protonic transition already observed by conductivity measurements and DSC at the same temperature. The conductivity variations are reported in Fig. 8. Both lines observed in the temperature studied above and below 525 K are quasiparallel, the activation energies issued from the impedance (DEs ) and modulus (DEf) spectra are very close (DEs 0:30 eV; DEf 0:31 eV in the temperature range 339–525 K), suggesting that the protonic conduction in the CRDP material is probably due to a hopping mechanism [21]. On the other hand, the (FWHH) width of peaks corresponding to various measurement temperatures is approximately close to
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Fig. 8. Temperature dependencies of log s T and log fp, where fp is the M 00max peak frequency for CRDP at various temperatures.
2.5 decades. Consequently, b may be considered as independent of temperature in the temperature range studied. The value of the b parameter, is clearly smaller than 1, can be attributed to the existence of a distribution of relaxation times in the material. Such an interpretation has been adopted for many solid electrolytes [22,23].
5. Conclusion The synthesis and structure determination of the salt CRDP were described in a monoclinic system. The physical properties and phase transitions of this compound were examined by different methods. The differential scanning calorimetry shows three anomalies at 293, 525 and 575 K corresponding, respectively, to paraelectric–ferroelectric, superionic–
protonic phase transitions and to the melting point. Based on a.c.-impedance measurements, we have analysed the low-frequency dispersion phenomena in this compound in the 130–310 K temperature range. The ordering effect of protons in the short hydrogen bonds is the key factor responsible for ferroelectricity in CRDP compound. The transition from the ferroelectric phase to the paraelectric phase in CRDP exhibits first-order transition characteristics. However, the first-order character of the phase transition is difficult to explain. This behaviour seems to be sensitive particularly to the detailed interaction between neighbouring protons. The relaxation conductivity is well described by the empirical stretched exponential Kohlrausch function w t exp2 t=ts b . The value of the b parameter 0 , b , 1 represents for the conductivity relaxation the departure from the linear exponential b 1. The
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M 00max
fp frequency relative to fp 1=2pts is defined by the condition vts 1, where t s is the most probable ion relaxation time, fp increases with increasing temperature and the temperature dependence of fp is of Arrhenius type fp fp0 exp 2DEf =kT: Information about charge carrier transport mechanism is obtained by comparison of DEf with DEs . These activation energies for CRDP compound which issued from the impedance and modulus spectra are very close, suggesting that the protonic transport above and below the superionic–protonic phase transition (525 K) is probably due to a hopping mechanism. On the other hand, in the temperature range studied, b may be considered as independent of temperature. The value of this parameter, clearly smaller than 1, shows the existence of a distribution of relaxation times in the CRDP material and confirms the validity of this model for protonic conducting in the KDP family. References [1] R. Blinc, J. Phys. State. Sol. (b) 67 (1975) 689. [2] Crystallography reports 42 (1997) 3.
[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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A.V. Belushkin, M.A. Adams, Physica B 234 (1997) 37. N.S.J. Kennedy, R.J. Nelmes, J. Phys. C 13 (1980) 4841. U. Efron, I. Pelech, H. Zafrir, J. Chem. Phys. 55 (1970) 3599. F. Romain, A. Novak, J. Mol. Struct. 263 (1991) 69. P.S. Peercy, G.A. Samara, Phys. Rev. B 8 (1973) 2033. B. Baranowski, M. Friesel, A. Lunden, Z. Naturforsch. A 41 (1986) 981. W. Bronowska, Solid State Commun. 76 (1990) 293. D.P. Almond, A.R. West, Solid State Ionics 11 (1983) 57. H. Naı¨li, T. Mhiri, A. Daoud, Phase Transitions, submitted for publication. I.M. Hodge, M.D. Ingram, A.R. West, J. Electroanal. Chem. 74 (1976) 125. A.K. Jonsher, J. Mater. Sci. 24 (1989) 372. A.K. Jonsher, Chelse a dielectric Press, London, 1983. A.I. Baranov, V.P. Khiznichenko, L.A. Shuvalov, Ferroelectrics 100 (1989) 136. F.S. Howell, R.A. Bose, P.B. Maado, C.T. Moynihan, J. Phys. Chem. 78 (1974) 639. H.K. Patel, S.W. Martin, Phys. Rev. B 45 (1992) 10292. G. Williams, D.C. Watts, Trans. Faraday Soc. 23 (1970) 625. K.L. Ngai, S.W. Martin, Phys. Rev. B 40 (1989) 10550. S.W. Martin, C.A. Angel, J. Non-Cryst. Solids 83 (1986) 185. B.V.R. Chowdari, R. Gopalakrishnan, Solid State Ionics 23 (1987) 225. J. Kawamura, M. Shimoji, Mater. Chem-Phys. 23 (1989) 72. C. Lin, H.G.K. Sundar, C.A. Angel, Solid State Ionics 18–19 (1986) 442.
Conductivity and dielectric studies in Cs0.4Rb0.6H2PO4 mixed crystals H. Naı¨li, N. Zouari, T. Mhiri*, A. Daoud Laboratoire de l’Etat Solide, Universite´ de Sfax 3038, Sfax, Tunisia Received 9 March 1999; received in revised form 7 May 1999; accepted 24 May 1999
Abstract The mixed caesium rubidium dihydrogen phosphate, Cs0.4Rb0.6H2PO4 (CRDP) crystallises in the monoclinic system P21/m at and b 108:268 10; room temperature with the following parameters: a 4:8183 9; b 6:2671 6; c 7:7620 10 A Z 2. A calorimetric study of the title compound shows two distinct endothermal peaks which are detected at 293 and 525 K. Samples were examined by impedance and modulus spectroscopy techniques. The first transition (293 K) is attributed to a ferroelectric–paraelectric type. A high temperature phase transition (525 K) leading to a superionic–protonic phase was found, characterised by an unusual high conductivity. The conductivity relaxation parameters associated with the high-disorder protonic conduction have been determined from analysis of the M 00 =M 00max spectrum measured in a wide temperature range. Transport properties in this material appear to be due to proton hopping mechanism. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Conductivity; Superprotonic phase; Ferroelectric–paraelectric transition; Relaxation parameters
1. Introduction The compounds of general formula MH2XO4 (where M is a monovalent cation: K 1, Rb 1, Cs 1,… and X is P or As) exhibit structural phase transitions and interesting physical properties [1–6]. Rubidium dihydrogen phosphate RbH2PO4 (RDP) which is an isomorphic substance of potassium dihydrogen phosphate KH2PO4 (KDP) undergoes a ferroelectric–paraelectric phase transition at Tc 147 K [7] and a superprotonic one at 395 K [8], while CsH2PO4 (CDP) is known to have one-dimensional ferroelectric order below Tc 154 K and a superionic transition at Tc 504 K [9]. In order to determine the influence of the partial * Corresponding author. Tel.: 1 216-4274088; fax: 1 2164274437.
substitution of the caesium by rubidium (Cs0.4Rb0.6H2PO4), we have undertaken an analysis of the frequency response of a.c. conductivity data in our material. This process is useful in determining the complex permittivity 1 p(v ) and the conductivity relaxation time. The complex modulus formalism, p M p 1=1p jvC0 Z p where j 21; v v 2pf is the angular frequency and C0 is the vacuum capacitance of the cell, has been adopted to determine the conductivity relaxation times. This formalism discriminates as a matter of fact against electrode polarisation and other interfacial effects in solid electrolytes [10]. In addition, a short description of the crystal structure at room temperature paraelectric phase is given. The dielectric spectrum at temperatures ranging from 130 to 310 K and for the frequencies 10 4, 2 × 10 4, 5 × 10 4 and 10 5 Hz will also be examined. Furthermore, we compare in this work the
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Fig. 1. Differential scanning calorimetry of Cs0.4Rb0.6H2PO4 between 223 and 600 K.
conductivity behaviour at high temperature between CRDP with those in CDP and RDP.
2. Experimental and structure description 2.1. Experimental Single crystals of CRDP were prepared by slow evaporation of an aqueous solution containing stoichiometric quantities of Cs2CO3/Rb2CO3 /H3PO4 with the following reaction: 1 2 xCs2 CO3 1 xRb2 CO3 1 2H3 PO4 ! 2Cs12x Rbx H2 PO4 1 CO2 1 H2 O Upon maintaining the solution at a temperature of approximately 300 K, parallelepipedic crystals with a size of about 0:30 × 0:40 × 0:43 mm3 , formed after 10–15 days. Caesium, rubidium and phosphate contents were checked by chemical analysis. In fact, the single crystals so formed correspond to the composition Cs0.4Rb0.6H2PO4. The analysis of the frequency response of ac conductivity data is used to determine the electrical characteristics of protonic conductors. The crystal compounds of CRDP were crushed and carried out
on pellets at 200 MPa stress. Dense translucent pellets (10 mm in diameter; 1–2 mm in thickness) were obtained. Argent electrodes were deposited. Electrical properties were determined by impedance and modulus method using a frequency response analyser (Hewlett-Packard 4192 A LF automatic bridge monitored by a HP Vectra microcomputer). The frequency range was 100 Hz to 1 MHz and measurements were carried out in vacuum between 130 and 573 K. At each interval, the sample temperature was maintained by a Herrrmann-Moritz 28480 Chassant (using a Chromel/Alumel couple) controller for 0.5 h before collecting data; the stability was ^18C. 2.2. Structure description The cell structure of Cs0.4Rb0.6H2PO4 was determined by Naı¨li et al. [11], a monoclinic cell was obtained with the following parameters: ˚ a 4:8183 9; b 6:2671 6; c 7:7620 10 A and b 108:26 108, Z 2. The structure is built from Cs and Rb atoms coordinated by O atoms belonging to PO4 tetrahedra. Each Cs 1 and Rb 1 ion is bonded to 12 oxygen atoms, the bond distances ˚ and averages range from 3.012(4) to 3.544(2) A ˚ 3.30 A. In this structure, two oxygens designated as O(1) and O(2) are found to be located just in the plane
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hydrogen atoms over two symmetry-equivalent positions with a half occupancy around an inversion centre [11]. 3. Calorimetric studies The differential scanning calorimetry (DSC) measurements were performed on heating CRDP from 100 to 600 K on a DSC Mettler TA 4000 with scan speeds of 58 min 21. The thermogram shows three endothermal peaks at T1 293, T2 525 and T3 575 K (Fig.1). The first transition is considered to be of an order–disorder structure phase transition, the second one seems to be a superionic–protonic type and the latter one is attributed to the melting point of the product. The calculated transition enthalpy and entropy at the first transition T1 293 K were DH1 7:7 J g21 and DS1 26:28 × 1023 J g21 K21 , at the second transition T2 525 K were DH2 68:7 J g21 and DS2 13 × 1022 J g21 K21 . These results can be confirmed by electrical measurements using impedance spectroscopy. 4. Electrical properties Fig. 2. Thermal evolution of dielectric constant 1 0r in the frequency range 10–100 KHz.
y 3=4, and the remaining two oxygens O(3) and O(4) as mirror image with respect to this plane. In PO4 tetrahedron, we note that the bond length P– ˚ (type PyO and the P–O(1) O(2) is 1.471(5) A ˚ (type P–O(h)) while the P– distance is 1.564(4) A O(3) and P–O(4) distances which are equivalents ˚ (type P–O(h/2); with an average of 1.519(4) A where O(h) represents a hydroxyl oxygen and O(h/ 2) when the H atoms are distributed in a double minimum potential over two symmetry-equivalent positions between two oxygen atoms [11]. The PO4 tetrahedra are linked into two chains by two different ˚ ) links hydrogen bonds. The shorter bond (2.453(7) A the phosphate groups into chains running along the b˚ ) which is always axis and the longer one (2.488(6) A ordered, cross-links the chains to form the (0 0 1) layers. The shorter hydrogen bond is disordered, this disorder is due to a statistical distribution of the
4.1. Dielectric study The electrical data measured as an impedance, Z p, have been converted into permittivity, 1 p, using the relation
1p 1=iwC0 Z p where C0 is the vacuum capacitance [12]. Temperature dependence of the dielectric constant 1 0r was presented at various frequencies in Fig. 2. These spectra present a prominent dielectric peak at Tc 293 K characterising the ferroelectric–paraelectric phase transition which is observed by differential scanning calorimetry. The evolution of this dielectric constant as a function of frequency shows an increase of 1 0r with decreasing frequencies. This phenomenon characterises the presence of dispersion character in this material. The values of paraelectric–ferroelectric temperature phase transition does not change with increasing frequency, this suggests that this compound does not present a dipolar-type relaxation in this frequency
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Fig. 3. Complex plane plots of Cs0.4Rb0.6H2PO4 at various temperatures.
Fig. 4. Conductivity plots log10 sT f 103 =T for CRDP compound.
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Fig. 5. Variation of log10 s 0 with log f at different temperatures for a sample of CRDP.
range. The dielectric data in the paraelectric state obey quite well the Curie–Weiss law:
1 0r C=T0 2 Tc where C is the Curie–Weiss constant and T0 is the Curie–Weiss temperature for the paraelectric state. The strong decrease of 1 0r with increasing frequency observed in Fig. 2 is nothing but a dispersion without loss of peak resulting from charge carriers present in the material. This phenomenon is usually referred to as low-frequency dispersion (LFD) [13,14] where the charge carrier contribution is significant. 4.2. Protonic conductivity The crystals of CRDP have been reported to demonstrate high protonic conductivity in the high temperature phase. Our measurements were achieved in the temperature range 300–573 K. Some complex impedance diagrams 2Z 00 versus Z 0 at various temperatures are given in Fig. 3, and show that
CRDP follows the Cole–Cole law. The difference between the Cole–Cole and Deby law is determined from the precedent figure a 0:18. The bulk ohmic resistance relative to experimental temperature is the intercept on the real axis of the zero-phase angle extrapolation of the highest-frequency curve. These results are used elsewhere to show the evolution of the conductivity versus inverse temperature log10 sT f 103 =T for CRDP compound (Fig. 4). In the temperature range 339–573 K, the experimental points are located on both sides of a line above and below 525 K. An Arrhenius-type law sT s0 exp 2Ea =kT characterise the low and the high temperature domain with a sudden sharp increase of the conductivity upon 525 K. The activation energy of the title compound at low temperature is 0.30 eV and the conductivity increases sharply from 525 K s 2:92 × 1022 V21 cm21 at 525 K to 4:14 × 1021 V21 cm21 at 549 K). This result confirms the presence of a superprotonic phase transition observed previously at the same
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Fig. 6. Plots of log M 0 versus log f for Cs0.4Rb0.6H2PO4 at various temperatures.
temperature by differential scanning calorimetry measurements. The detected transition corresponds to the structural transformation between the monoclinic phase and the superprotonic phase, and leads to fast proton conduction. The structural mechanisms of proton conductivity on the CRDP compound is similar to that in the KDP-family. Therefore, occupation of the interstitial proton site should be possible and the proton migration from one oxygen atom of the PO4 group to another is accompanied by the formation of a new hydrogen bond. In order to explain the abrupt change in the conductivity at 525 K in CRDP crystals, we have compared these conductivity studies with those obtained in CDP crystals by Baranov et al. [15], who assumed that at the phase transition to the superprotonic phase, the crystal symmetry rises (from monoclinic to cubic) and some interstitial proton sites become structurally equivalent to normal proton sites. Hence, the proton will dynamically disorder between sites, because the number of these sites will exceed the number of protons. This will lead to the high proton conductivity in the cubic phase of CDP.
In Fig. 5 we show log s 0 (f) (real part of the complex conductivity) plots for CRDP material at different temperatures. At low frequencies dc conductivity plots are observed above and below the superionic–protonic phase transition which occurs at 525 K. Dc conductivity increases with increasing temperature. At high frequencies, these curves show an increasing hard segment length. This is due to the fact that charge-carrier motion occurs mostly through the soft segment phase. The increasing of the protonic conductivity is due to an increasing disorder of the hydrogen atoms among partly occupied symmetryequivalent positions. Therefore, we have included in this work the modulus formalism M p 1=1p jwC0 Z p ; to understand the proton conduction mechanism. 4.3. Modulus spectroscopy analysis A plot of log M 0 and of the normalised M 00 =M 00max imaginary part of the complex modulus versus log f is given in Figs. 6 and 7 at various temperatures for
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Fig. 7. Plots of normalised modulus M 00 =M 00max versus log f for CRDP at various temperatures.
CRDP compound. At all temperatures, the value of M 0 reaches at high frequencies, a constant value M 0∞ 1=1∞ . At low frequencies, it approaches zero, which indicates that the electrode polarisation phenomena make a negligible contribution to M p and may be ignored when the electric data are analysed in this form [16]. The M 00 =M 00max relative to a temperature given shows an asymmetrical peak approximately centred in the dispersion region of M* (Fig. 7). The region to the left of the peak is where the H 1 ions are mobile over long distances, the region to the right is where the ions are spatially confined to their potential wells. The frequency range where the peak occurs is indicative of the transition from short-range to longrange mobility at decreasing frequency and is defined by the condition vts 1, where t s is the most probable ion relaxation time [17]. The M 00 =M 00max curves are asymmetric, in agreement with the non-exponential behaviour of the electrical function, that is well described by the empirical stretched exponential Kohlrausch function w t exp2 t=ts b [18–19]. The full-width at half-height (FWHH) of the
M 00 =M 00max spectrum is clearly wider than the breadth of a Debye-peak (1.14 decades) [20] and it results in a value b 0:46 for the Kohlrausch parameter. When temperature increases, modulus peak maxima shift to higher frequencies (Fig. 7). Fig. 8 gives the temperature dependencies of log(s T) and log(fp) where fp fp 1=2pts is the frequency relative to M 00max peak corresponding to the bulk relaxation. An Arrheniustype law is shown with a high jump at about 525 K and confirm the superionic–protonic transition already observed by conductivity measurements and DSC at the same temperature. The conductivity variations are reported in Fig. 8. Both lines observed in the temperature studied above and below 525 K are quasiparallel, the activation energies issued from the impedance (DEs ) and modulus (DEf) spectra are very close (DEs 0:30 eV; DEf 0:31 eV in the temperature range 339–525 K), suggesting that the protonic conduction in the CRDP material is probably due to a hopping mechanism [21]. On the other hand, the (FWHH) width of peaks corresponding to various measurement temperatures is approximately close to
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Fig. 8. Temperature dependencies of log s T and log fp, where fp is the M 00max peak frequency for CRDP at various temperatures.
2.5 decades. Consequently, b may be considered as independent of temperature in the temperature range studied. The value of the b parameter, is clearly smaller than 1, can be attributed to the existence of a distribution of relaxation times in the material. Such an interpretation has been adopted for many solid electrolytes [22,23].
5. Conclusion The synthesis and structure determination of the salt CRDP were described in a monoclinic system. The physical properties and phase transitions of this compound were examined by different methods. The differential scanning calorimetry shows three anomalies at 293, 525 and 575 K corresponding, respectively, to paraelectric–ferroelectric, superionic–
protonic phase transitions and to the melting point. Based on a.c.-impedance measurements, we have analysed the low-frequency dispersion phenomena in this compound in the 130–310 K temperature range. The ordering effect of protons in the short hydrogen bonds is the key factor responsible for ferroelectricity in CRDP compound. The transition from the ferroelectric phase to the paraelectric phase in CRDP exhibits first-order transition characteristics. However, the first-order character of the phase transition is difficult to explain. This behaviour seems to be sensitive particularly to the detailed interaction between neighbouring protons. The relaxation conductivity is well described by the empirical stretched exponential Kohlrausch function w t exp2 t=ts b . The value of the b parameter 0 , b , 1 represents for the conductivity relaxation the departure from the linear exponential b 1. The
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M 00max
fp frequency relative to fp 1=2pts is defined by the condition vts 1, where t s is the most probable ion relaxation time, fp increases with increasing temperature and the temperature dependence of fp is of Arrhenius type fp fp0 exp 2DEf =kT: Information about charge carrier transport mechanism is obtained by comparison of DEf with DEs . These activation energies for CRDP compound which issued from the impedance and modulus spectra are very close, suggesting that the protonic transport above and below the superionic–protonic phase transition (525 K) is probably due to a hopping mechanism. On the other hand, in the temperature range studied, b may be considered as independent of temperature. The value of this parameter, clearly smaller than 1, shows the existence of a distribution of relaxation times in the CRDP material and confirms the validity of this model for protonic conducting in the KDP family. References [1] R. Blinc, J. Phys. State. Sol. (b) 67 (1975) 689. [2] Crystallography reports 42 (1997) 3.
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