Structural phase transition, ionic conductivity, and dielectric investigations in K3H(SO4)2 single crystals

Structural phase transition, ionic conductivity, and dielectric investigations in K3H(SO4)2 single crystals

Journal of Physics and Chemistry of Solids 64 (2003) 553–563 www.elsevier.com/locate/jpcs Structural phase transition, ionic conductivity, and dielec...

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Journal of Physics and Chemistry of Solids 64 (2003) 553–563 www.elsevier.com/locate/jpcs

Structural phase transition, ionic conductivity, and dielectric investigations in K3H(SO4)2 single crystals R.H. Chena,*, R.Y. Changa,1, C.S. Sherna, T. Fukamib b

a Department of Physics, National Taiwan Normal University, 88 Sec.4 Ting-Chou Rd, Taipei 117, Taiwan, ROC Department of Physics and Earth Sciences, College of Science, University of the Ryukyus, Okinawa 903-0213, Japan

Received 5 February 2002; revised 31 May 2002; accepted 1 July 2002

Abstract Optical observation, differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) measurements have been carried out on K3H(SO4)2 crystal in the temperature range between 25 and 300 8C. Domain structures of K3H(SO4)2 were observed at room temperature which are the same as those observed in other member of A3H(XO4)2 which show ferroelasticity. Two endothermic peaks of DSC were found at around 206 and 269 8C. In this temperature range, the result of TGA indicate the loss of weight. It supports that partial dehydration is most probable. The first peak can be accounted for the dehydration reaction on the surface of crystals, and the second peak corresponds to the melting of the sample crystal. The impedance measurements were performed as a function of both temperature and frequency. The electrical conductivity increases with increasing temperature and the sample crystal becomes a fast ionic conductor at the temperatures above 206 8C. The high conductivity of the crystal is caused by the increases of the defects due to the dehydration. The dielectric properties of the sample crystal were studied by the impedance spectroscopy. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: A. Inorganic compounds; C. Differential scanning calorimetry; C. Thermogravimetric analysis; D. Electrical conductivity; D. Dielectric properties

1. Introduction Crystals in the family of A3H(XO4)2 (A ¼ NH4, K, Rb, Cs, and X ¼ S and Se) exhibit a great interest because of their series of structural phase transitions with the temperature [1– 4]. At room temperature, most of them belong to monoclinic system with the space group A2/a, except that Cs3H(SeO4)2 crystal is A2/m [4] and (NH4)3H(SeO4)2 crystal is P1 [5]. The crystals of (NH4) 3H(SeO4) 2, (NH 4)3H(SO4) 2, Rb 3H(SeO4) 2 and K3H(SeO4)2 are found to be ferroelastic in the room temperature phase and have transformed to paraelastic  [6 – 10]. The crystal phase with the space group R3m structure of tripotassium hydrogen disulfate, K3H(SO4)2, * Corresponding author. Tel.: þ886-2-934-6620; fax: þ 886-9326408. E-mail address: [email protected] (R.H. Chen). 1 Present address: The Affiliated Senior High School of National Taiwan Normal University, Taipei 116, Taiwan, ROC.

at room temperature was determined by X-ray diffraction [11]. It also belongs to the space group A2/a, with the  bm ¼ 5:674ð1Þ A;  unit cell parameters am ¼ 9:777ð1Þ A;  cm ¼ 14:667ð4Þ A and b ¼ 102:97ð2Þ8: The hydrogen bond length between two nearest SO4 group is ˚ . The hydrogen atom is disordered over two 2.493(1) A symmetry-equivalent minima [11]. K3H(SO 4)2 is isostructural with the other member of A3H(XO4)2, hence a similar high temperature phase transition is expected. It was mentioned that crystal of K3H(SO4)2 decomposed at 172 ^ 5 8C before taking the phase transition [11]. Recently, the physical properties of the K3H(SO4)2 were studies by Chisholm and Haile [12]. A new high temperature structure has been found by X-ray powder diffraction, and the structure was quit different from the other A3H(XO4)2 compounds. The electrical properties of A3H(XO4)2 crystal are studied extensively [3,4,13,14]. The crystals in this family exhibit superprotonic conduction in the high temperature

0022-3697/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 3 6 9 7 ( 0 2 ) 0 0 3 1 0 - 4

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 paraelastic phase (space group R3m). The mechanism of high ionic conductivity in these crystals is proposed and studied [3,4,13 – 15]. In the present paper, we report the results of DSC, thermogravimetric analysis (TGA), and impedance spectroscopy measurement in K3H(SO4)2 single crystal. The temperature and frequency dependence of electrical conductivity and the dielectric properties of the sample crystal are studied.

2. Experimental Single crystals of K3H(SO4)2 were grown at room temperature by slow evaporation from a mixed aqueous solutions containing 4:3 mole fraction of K2SO4 and H2CO3. Transparent plates with the dominant face of (001) were obtained. The sample crystal under a microscope is heated up to 300 8C. The temperature was controlled using a heating stage THMS600 (Linkam). Differential scanning calorimetry (DSC) was performed on K3H(SO4)2 crystal with a DSC2920 TA instrument in the temperature range 25– 300 8C. Thermogravimetric (TG) and differential thermogravimetric (DTG) measurements are performed using a TA Instrument TGA2500 analyzer (Instrumentation center, National Taiwan Univ.). Dry nitrogen was used with a flow of 60 ml/min and heating rate is 5 8C/min. A crystal of 6 £ 6 mm2 with thickness 0.3 mm was used in the electrical measurement. The complex impedance measurements were measured using a HP4194A impedance analyzer for the frequency range between 100 Hz and 7 MHz under 1 atm pressure. The temperature of the sample crystal was controlled using Huber high-temperature attachment from 30 to 250 8C. The sample crystals were pasted with silver plaster on the (001) plate as electrodes. Owing to the shape of the sample crystal, the measurement in other directions is difficult to perform.

3. Results and discussion 3.1. Optical, DSC, and TGA studies Fig. 1 shows grow twins observed under the polarizing microscope. Although the number of domain boundaries is different in an individual, three distinct orientations of 1208 apart were observed. The morphology of growth twins and twin boundaries is the same as observed by Parry and Glasser [16]. Two kinds of domain walls (W and W0 [17]) are observed, one perpendicular to the hexagonal edges of the crystal, while the other parallel to the crystal edges. The orientations of domains and domain walls are similar to the crystal of (NH4)3H(SO4)2, Rb3H(SeO4)2, and K3H(SeO4)2 which exhibit the characteristic of the ferroelastic species of  3mF2=m [8,10,18]. Hence, it is expected that they have the similar elastic properties and the crystal would undergoes the structural phase transition from monoclinic to trigonal

paraelastic phase. A detail analysis of the ferroelastic domain structure in this species was given in Ref. [8]. In order to decide the transition temperature where the crystal change symmetry, a crystal with four domains was chosen to heat up on the heating stage. After raising the temperature to 206 8C, the crystal becomes turbid gradually and microcracks have been observed on portion of the surface. The crystal changes from transparent colorless to opaqueness under a microscope (as shown in Fig. 2). The shape of the crystal started to deform at around 250 8C. The optical observation with the turbid crystal has the difficulty to judge any structure phase transition at the high temperature. However, the studies of X-ray powder diffraction of K3H(SO4)2 done by Chisholm and Haile indicates that the sample crystal at and above 210 8C has structure and is different from the room-temperature phase [12]. The structure in the high temperature phase cannot be identified as trigonal or hexagonal [12]. The obtained DSC curve of K3H(SO4)2 crystals with heating rate 5 8C/min is shown in Fig. 3(a). Two endothermic peaks was observed at 206.2 and 269.1 8C. For the first peak, the enthalpy change is DH ¼ 18:4 kJ mol21 : The corresponding entropy change is DS ¼ 38:4 J mol21 K21 ( ¼ 4.6R, where R is the gas constant), which is much larger than the entropy change of the structural phase transition from monoclinic to trigonal ðR ln3 ¼ 1:099RÞ as observed in Rb3H(SeO4)2 crystal [3]. Comparing with the optical observation, this transition is rather due to the onset of partial dehydration at particular localities on the surface. When the crystal is heated above 206 8C, the constitutional water on the surface that produced during growth is evaporated. The DSC curve also shows a smeared out transition with the peak temperatures between 242 and 269.1 8C by the enthalpy change ¼ 5.64 kJ mol21. As temperatures reach above 240 8C, the chemical decomposition in the bulk and premelting start on or near the surface of the crystal at the same time. The corresponding behavior can be compared with the optical observation as shown in Fig. 2. The TG and DTG measurements show the mass variation recorded during the heating. The results are shown in curve (b) and (c) in Fig. 3. The obtained DTG curve shows some sudden loss of weight at temperature above 203.8 8C. Hence the DSC endothermic peak at 206.2 8C was identified as an onset of thermal dehydration at the surface rather than a structural phase transition. We believe that the water is released in the dehydration process on the surface of the samples and its consequences, such as microcracks, can be seen on the surface under microscope. When the crystal was heated up to 222.1 8C, the chemical decomposition process takes place all over the surface of the crystal. The smeared endothermic peak at around 242 8C is related by this process of chemical decomposition also in the bulk and the premelting of the crystal on the surface started at the same time. Two processes keep on going up to 300 8C. The DSC and TGA measurements on K3H(SO4)2 were also reported by Chisholm and Haile [12]. Two

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Fig. 1. Different kinds of domain morphologies of K3H(SO4)2 crystals observed under the polarizing microscope at room temperature. Three distinct orientational domains are detected easily by applying a tint plate. Two kinds of domain boundary, W and W0 , are observed.

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Fig. 2. Optical observation of crystal of K3H(SO4)2 under heating on the heating stage.

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Fig. 3. DSC thermogram, thermogravimetric analysis (TGA) and derivative TGA for K3H(SO4)2 on heating. Heating rate is 5 8C/min21.

endothermic peak temperatures at 190 and 227 8C were observed by their studies. The slightly different observed temperatures are probably attributed to different heating rate in the measurements. The accompany enthalpy of transition observed in these measurements are very close to each other. The result of TGA supports the lost of weight at the temperatures above 204 8C. Comparing it with the optical observation under the microscope, the observed peaks are attributed to the decomposition on surface and premelting of the sample crystal. The high temperature behavior of sample crystal on heating above 206 8C is similar to that observed for the NH4H2AsO4, NH4H2PO4, and KHSO4 compounds [19 – 21]. A new structure phase observed at and above 210 8C in the X-ray powder diffraction done by Chisholm and Haile [12] need to interpret as a product compound resulting from the decomposition reaction. 3.2. Ionic conductivity and dielectric properties The complex resistivity of the sample crystals are evaluated from the measured complex impedance. The Cole –Cole Complex resistivity diagrams (2r00 verses r0 ) at several temperatures are shown in Fig. 4. The impedance spectra show semicircles. The sample crystal can be treated as a parallel combination of resistance and capacitance in the electrical circuit. The dielectric constant (e ) and electrical conductivity (s ) have also been evaluated from

the measured complex impedance. The temperature dependence of the dielectric constant at several frequencies is given in Fig. 5. The dielectric constant is about 60 at the temperatures up to 205 8C. It increases rapidly with increasing temperature at around 206 8C and is frequency dependent. The DC resistivity of the sample crystal was extracted from the Cole – Cole plot to zero frequency. The DC conductivity, sð0Þ is the reciprocal of the DC resistivity. It is in the order around 1 £ 1029 V21 cm21 at room temperature. It increases rapidly with increasing temperature. At 213 8C, the DC conductivity is 3.6 £ 10 24 V21cm 21 and it increases smoothly to 1.1 £ 10 22 V21cm21 at 250 8C. The temperature variation of the DC conductivity (logsð0ÞT vs. 1000/T ) is shown in Fig. 6. A generally accepted form of Arrhenius relation is approximately obeyed and it suggests the mobile carriers are thermally activated. Despite the variation of the activation energy with the temperature, the straight lines (a) and (b) approximate the experimental data are assigned to the extrinsic and intrinsic regions, respectively. A discontinuous change takes place again at temperature above 206 8C in the (c) region. This temperature is close to the dehydration temperature of the sample crystal as it is observed under the microscope. The DC activation energies determined from Fig. 6 for (a) and (b) regions are 0.37 and 1.34 eV, respectively. The evolution of

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Fig. 4. The complex Cole– Cole plot of resistivity for K3H(SO4)2 single crystal at various temperatures.

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Fig. 5. Temperature dependence of the dielectric constant for K3H(SO4)2 at various frequency.

Fig. 6. Arrhenius plot of DC conductivity of K3H(SO4)2. The straight lines (a) and (b) are assigned to the extrinsic and intrinsic regions, respectively. The crystal in the region (c) is in the fast ionic phase due to the dehydration of the crystal.

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Fig. 7. The variation of AC conductivity with frequency over the temperature range 30–250 8C for K3H(SO4)2.

Fig. 8. Thermal variation of the exponents for K3H(SO4)2.

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Fig. 9. Frequency dependence of the (a) real and (b) imaginary part of electric modulus for K3H(SO4)2 at various temperatures. The lines are drawn as a guide for the eye.

conductivity with temperature is also in good agreement with the electrical data measured by Chisholm and Haile [12]. The obtained activation energy was slightly different from this report is due to the different temperature range chosen in two reports. However, the activation energy is in the same order of magnitude as the activation energy of the proton in the family of A3H(XO4)2 in the room temperature phase [3,4,13,14].

The crystal with s $ 1024 V21 cm21 is identified as a fast ionic conductor. Hence the crystal of K3H(SO4)2 at temperatures higher than 206 8C is in fast ionic conducting phase. Since the contribution to the conductivity is determined by the concentrations of vacant sites as well as the ion mobility in the most of ionic crystal. The contribution to the high conductivity is mainly due to the increasing of defects which were formed mainly by

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Fig. 10. Temperature dependence of relaxation time of K3H(SO4)2 single crystal.

the dehydration on or near the surface of the crystal. The activation energy as determined form Fig. 6 in the region (c) is 3.70 eV which would include both of the defect formation energy and migration energy of the mobile carriers. Since the different structural phase transition information is detected from the previous DSC measurement, the mechanism of conduction in the superprotonic phase is much different from the the other members of the crystal of A3H(XO4)2 [3,4,13 – 15], which involves a high temperature phase transition. The breaking of hydrogen bonds between the nearest XO4 and forming the new weaker hydrogen bonds between the reorientation and disorder of XO4 tetrahedra through the structural phase transition. The high conduction of those crystals is attributed to the hopping of protons among the increasing disordered vacant proton sites in this phase with little migration energy [3,4,13,14]. The frequency dependence of AC conductivity at various temperatures for the sample is shown in Fig. 7. The variation of s with frequency clearly shows a flat DC plateau at low frequencies and high temperatures. At low temperatures, s shows a strong function of frequency at high frequency end. In many ionic conducting glass, these phenomena of the conductivity dispersion is generally analyzed using Jonscher’s law [22]

sðvÞ ¼ sð0Þ þ Avn ;

ð1Þ

where sð0Þ is DC conductivity of the sample, A is a constant for a particular temperature, and n is the power law exponent. It has applied to many materials to analyze the AC conductivity behavior in glasses, amorphous, and

semiconductors [22 – 27]. This characteristic feature is well known in the disorder system. n represents the degree of interaction between mobile ions and the environments surrounding them. Many manifestations of the hopping models and experiments to give value of n in the range of 0.6– 1 have been given in Refs. [25,28,29]. The transport mechanism of it is explained by the thermally activated process for the mobile ions hop between two sites separated by an energy barrier. Recently, the relation of the frequency dependence of electrical conductivity has been applied to single crystals [10,14,30,31]. The Jonscher universality of AC conductivity is not limited to the case of glasses but extends to cover single crystals. The values of n in Eq. (1) are obtained from the plot of logðsðvÞ 2 sð0ÞÞ versus log(v )(not shown here). An approximate linear relationship is obtained at all temperatures. The temperature dependence of n-values obtained from the experiment is plotted in Fig. 8. It decreases from 1.3 to 0.2 smoothly with increasing temperature. The temperature dependence of n suggests that the hopping of the ions between defect sites is involved in the conduction mechanism. Although n greater than 1 is excluded out in the theory, but it has been found in the experimental analysis of the crystals of K2SO4 [30], Rb3H(SO4)2 [31], Rb3H(SeO4)2 [31] and K3H(SeO4)2 [10]. The frequency dispersion behavior is attributed to the Coulomb interaction effects between the mobile ions as well as the ions with the environment within materials. The values of n are around 0.2 at temperatures above 200 8C. This temperature is close to the dehydration temperature of the sample crystal as seen under the microscope.

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The dielectric relaxation was often studied by electric modulus which is defined as M ; 1=e [32]. The variation of the real and imaginary parts of the electric modulus with the frequency at various temperatures is shown in Fig. 9. The interfacial effects tend to eliminated in modulus representation [32]. It can be seen that the peak positions shift with temperature. As temperature increases higher, the modulus peak maxima (vm ) move toward higher frequency. The relaxation time, t, is determined by the relation vm t ¼ 1: The temperature dependence of the obtained relaxation time is plotted in Fig. 10. It shows that the relaxation time is well described by Arrhenius relation t ¼ t0 expðEm =ðkB TÞÞ; where t0 is the pre-exponential factor, Em is the activation energy for the dielectric relaxation, kB the Boltzmann’s constant, and T is the absolute temperature. The relaxation peaks cannot be obtained at temperatures above 204 8C due to the uncovered high frequencies in this measurement. The activation energy Em obtained from the modulus spectra is 1.34 eV in the room temperature phase. This value is same as determined from the conductivity measurement.

4. Conclusion Domain structure is observed in K3H(SO4)2. The DTG shows the loss of weight at temperature around 204 8C. The crystal is thermally dehydrated on heating at and above 206.2 8C. The DSC endothermic peaks were interpreted as an onset of thermal dehydration on the surface and later on melting at higher temperatures. The electrical conductivity increases with increasing temperature and the crystal becomes a superprotonic conductor at temperatures above 206 8C. The high conductivity is explained by the motion of mobile ions among the increasing of defects due to the loss of water. Before dehydration, the conductivity of the crystal increases as a power of frequency and this behavior is expected for most of the hopping type of ionic conductors and could be attributed to an interaction involving mobile ions and the neighboring group ions within crystal. The values of the exponent n are greater than 1.0 for the sample crystal at temperatures below 130 8C. The exponents n decrease smoothly to 0.2 with increasing temperature.

Acknowledgments This research was supported by the National Science Council of ROC under grant number NSC 89-2112-M-003030 and NSC 90-2112-M-003-025.

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