Ferroelectrics Physical Effects Part 5 pdf

Ferroelectrics – Physical Effects 150 The crack length increased with increasing hydrogen concentration in the samples. Therefore, the cracks can also grow with the prolongation of dwell time during indentation test in a pre- charged sample since the hydrogen concentration will increase at the indentation crack tips by stress-induced diffusion. The experimental results indicate that the longer the indentation load hold, the larger the indentation crack length is, and the smaller fracture toughness, K IC (H,t) measures, as shown in Figure 14 (Zhang et al., 2008). Under a constant load, the HIDC can occur by the stress-induced hydrogen diffusion and enrichment. Fig. 14. The normalized fracture toughness K IC (H,t)/K IC versus the logarithm of the dwell time during the indentation test for the charged sample (Zhang et al., 2008) 5.3 Hydrogen-induced delayed cracking in ferroelectric ceramics During single-edge-notched-tensile sample of PZT ferroelectric ceramics hydrogen charging dynamically in 0.2mol/l NaOH+0.25 g/l As 2 O 3 solution, hydrogen-induced delayed cracking (HIDC) can occur (Wang et al., 2003a) and depends on the relative orientation between notch plane and the polarization vector, i.e., the HIDC also shows anisotropy in ferroelectric ceramics, as shown in Figure 15 (Wang et al., 2003b). Hydrogen concentration C H under different charging current densities is given in Table 2. The curve of K IH /K IC vs i or C H can plot based on Table 2 and one can find a linear relationship between K IH /K IC and the lnC H (Wang et al., 2003b) aabb IH IC IH IC //KKKK =0.4-0.15lnC H (5) where superscript a and b denote polarization vector parallel and perpendicular to the crack plane, respectively. a IC K =1.53 MPam 1/2 and b IC K =1.12 MPam 1/2 for PZT ferroelectric Hydrogen in Ferroelectrics 151 i (mA/cm 2 ) 0.05 0.5 5 50 300 C H ( ppm) 0.92 2.61 4.8 7.16 9.84 a IH K (MPam 1/2 ) 0.54 0.34 0.28 0.13 0.01 b IH K (MPam 1/2 ) 0.36 0.26 0.17 0.08 - aa IH IC /KK 0.40 0.25 0.21 0.10 0.01 bb IH IC /KK 0.40 0.28 0.19 0.09 - Table 2. The threshold stress intensity factors of HIDC corresponding to various hydrogen concentrations (Wang et al., 2003b) 0 20406080100 0.0 0.2 0.4 0.6 0.8 1.0 Parallel 0.05 mA/cm 2 0.5 mA/cm 2 5 mA/cm 2 50 mA/cm 2 300 mA/cm 2 K I /K IC Time to fracture, h (a) 0 20406080100 0.0 0.2 0.4 0.6 0.8 1.0 0.05 mA/cm 2 0.5 mA/cm 2 5 mA/cm 2 50 mA/cm 2 K I /K IC Time to fracture, h Perpendicular (b) Fig. 15. The normalized stress intensity factor vs time to fracture during dynamically charging with various i (the arrows mean no fracture within 100 h). (a) Polarization direction parallel to the crack plane; (b) Polarization direction perpendicular to the crack plane (Wang et al., 2003b) Ferroelectrics – Physical Effects 152 ceramics. Eq.5 suggests that the t anisotropy of K IH is entirely caused by the anisotropy of fracture toughness. 6. Conclusion In this chapter, the effects of hydrogen on main properties of ferroelectric materials are reviewed. Even if a little amount of hydrogen enters a ferroelectric material, the ferroelectricity and dielectric properties would be degraded, such as hydrogen causes hysteresis loop narrower, reduces remnant polarization, increases leakage current, etc. If great amount hydrogen is charged into ferroelectrics, hydrogen fissure and hydrogen- induced delayed cracking can occur. Fortunately, hydrogen can escape from the hydrogenated ferroelectric materials and properties can restore after a heat treatment. Therefore, outgassing treatment is an effectual method to prevent hydrogen damage. Although most of reports about hydrogen in ferroelectrics proved that hydrogen has negative influence, hydrogen can’t be consider completely harmful to the ferroelectric materials. For example, a very small amount of hydrogen can enhance the ferroelectricity. Now, the mechanism of enhancement effect is not clear yet, but this phenomenon enough to absorb more interests to develop the potential role of hydrogen in ferroelectric materials. 7. Acknowledgment Authors acknowledge support from the National Nature Science Foundation of China under grants 51072021 and 50632010 and from Beijing Municipal Commission of Education under YB20091000801 grant. 8. References Aggarwal, S.; Perusse, S. R.; Tipton, C. W.; Ramesh, R.; Drew, H. D.; Venkatesan, T.; Romero, D. B.; Podobedov, V. B. & Weber, A. (1998). Effect of hydrogen on Pb(Zr,Ti)O 3 -based ferroelectric capacitors. Applied Physics Letters, Vol.73, No.14, pp. 1973-1975, ISSN 0003-6951 Chen, F.; Chen, W. P.; Wang, Y.; Hu, Y. M.; Shen, Z. J. & Chan, H. L. W. (2011). Effects of forming gas annealing on LiNbO3 single crystals. Physica B: Condensed Matter, Vol. 406, No.3, pp. 683-686, ISSN 0921-4526 Chen, W. P.; Li, L. T.; Qi, J Q. & Gui Z. L. (1998). Effect of electrochemical hydrogen charging on Ba1-xPbxTiO3-Based semiconducting ceramics. Journal of Materials Science Letters, Vol.17, No.11, pp.899-900, ISSN 0261-8028 Joo, H. J.; Lee, S. H.; Kim, J. P.; Ryu, M. K. & Jang, M. S. (2002). Effect of hydrogen on the electrical and optical properties in ferroelectric Pb(Zr,Ti)O 3 thin films. Ferroelectrics, Vol.272, No.1, pp.149-154, ISSN 1563-5112 Han, J. P. & Ma, T. P. (1997). Electrode dependence of hydrogen-induced degradation in ferroelectric Pb(Zr,Ti)O 3 and SrBi 2 Ta 2 O 9 thin films. Applied Physics Letters, Vol.71, No.9, pp. 1267-1269, ISSN 0003-6951 Huang, H. Y.; Chu, W. Y.; Su, Y. J.; Qiao, L. J. & Gao, K. W. (2005). Combined effect of electric field and residual stress on propagation of indentation cracks in a PZT-5H Hydrogen in Ferroelectrics 153 ferroelectric ceramic. Materials Science and Engineering B, Vol. 122, No.1, pp. 1-6, ISSN 0921-5107 Huang, H. Y.; Chu, W. Y.; Su, Y. J.; Li, J. X.; Qiao, L. J. & Shi, S. Q. (2006). Experiment and first principles investigation on the hydrogen-hindered phase transition of ferroelectric ceramics. Applied Physics Letters, Vol.89, No.142904, ISSN 0003-6951 Huang, H. Y.; Chu, W. Y.; Su, Y. J.; Gao, K. W.; Li, J. X. & Qiao, L. J. (2007). Hydrogen- induced semiconductor transformation of PZT ferroelectric ceramics. Journal of the American Ceramics Society, Vol. 90, No.7, pp. 2062 –2066, ISSN 0002-7820 Ikarashi, N. (1998) Analytical transmission electron microscopy of hydrogen-induced degradation in ferroelectric Pb(Zr,Ti)O 3 on a Pt Electrode. Applied Physics Letters, Vol.73, No.14, pp.1955-1957, ISSN 0003-6951 Katz, L. E. (1988). In: VLSI Technology (2nd ed), S. M. Sze (Ed), pp. 127, McGraw-Hill, ISBN 978-007-0627-35-2, New York Kushida-Abdelghafar, K.; Miki, H.; Torii, K. & Fujisaki, Y. (1996). Electrode-induced degradation of Pb(Zr x Ti 1−x )O 3 (PZT) polarization hysteresis characteristics in Pt/PZT/Pt ferroelectric thin-film capacitors. Applied Physics Letters, Vol.69, No.21, pp. 3188-3190, ISSN 0003-6951 Pen, X.; Su, Y. J.; Gao, K. W.; Qiao, L. J. & Chu, W. Y. (2004). Hydrogen fissure in PZT ferroelectric ceramic, Materials Letters, Vol.58, No.15, pp. 2073-2075, ISSN 0167- 577x Shimamoto, Y.; Kushida-Abdelghafar, K.; Miki, H. & Fujisaki, Y. (1997). H 2 damage of ferroelectric Pb(Zr,Ti)O 3 thin-film capacitors-The role of catalytic and adsorptive activity of the top electrode. Applied Physics Letters, Vol.70, No.23, pp. 3096-3097, ISSN 0003-6951 Tamura, T.; Matsuura, K.; Ashida, H.; Kondo, K. & Otani, S. (1999). Hysteresis variations of (Pb,La)(Zr,Ti)O3 capacitors baked in a hydrogen atmosphere. Applied Physics Letters, Vol.74, No. 22, pp.3395-3397, ISSN 0003-6951 Wang, Y.; Chu, W. Y.; Qiao, L. J. & Su, Y. J. (2003a). Hydrogen-induced delayed fracture of PZT ceramics during dynamic charging under constant load ，Materials Science and Engineering B, Vol. 98, No.1, pp. 1-5, ISSN 0921-5107 Wang, Y.; Chu, W. Y.; Su, Y. J.; Qiao, L. J. & Gao, K. W. (2003b) ，Hydrogen-induced cracking and its anisotropy of a PZT ferroelectric ceramics ，Science in China E, Vol.46, No.3, pp.318-325, ISSN 1674-7321 Wu, M.; Huang, H. Y.; Jiang, B.; Chu, W. Y.; Su, Y. J.; Li, J. X & Qiao, L. J. (2009). Experiments and first principles calculations on the effects of hydrogen on the optical properties of ferroelectric materials. Journal of Materials Science, Vol. 44, No.21, pp. 5768-5772, ISSN 0022-2461 Wu, M. (2009). Study of effect of hydrogen on the properties of ferroelectric ceramics. Doctoral dissertation, University of Science and Technology Beijing. Wu, M.; Huang, H. Y.; Chu, W. Y.; Guo, L. Q.; Qiao, L. J.; Xu, J. Y. & Zhang, T. Y. (2010). Tuning the ferroelectric and piezoelectric properties of 0.91Pb(Zn 1/3 Nb 2/3 )O 3 - 0.09PbTiO 3 single crystals and lead zirconate titanate ceramics by doping hydrogen. Journal of Physical Chemistry C, Vol.114, No.21, pp. 9955-9960, ISSN 1932-7447 Ferroelectrics – Physical Effects 154 Zhang, H.; Su, Y. J.; Qiao, L. J. & Chu, W. Y. (2008). The Effect of Hydrogen on the Fracture Properties of 0.8(Na 1/2 Bi 1/2 )TiO 3 -0.2(K 1/2 Bi 1/2 )TiO 3 Ferroelectric Ceramics. Journal of Electronic Materials, Vol.37, No. 3, pp.368-372, ISSN 0361-5235 7 Thermal Conduction Across Ferroelectric Phase Transitions: Results on Selected Systems Jacob Philip Department of Instrumentation and STIC, Cochin University of Science and Technology India 1. Introduction A ferroelectric phase transition represents a special class of structural phase transition characterized by the appearance of a spontaneous polarization in the material. Above the Curie temperature the transition often follows a diverging differential dielectric response or permittivity  , which varies with temperature in an approximate Curie-Weiss manner  = C/(T-T 0 ), where T 0 is the Curie-Weiss temperature, which is equal to the Curie temperature T c for a continuous transition. The crystalline phase which undergoes transformation to the ferroelectric form at T c is the paraelectric one. Below T c , in the absence of an applied field, there are at least two directions along which a spontaneous polarization can develop. To minimize the depolarizing fields different regions of the crystal polarize in each of these directions, each volume of uniform polarization being called a domain. The resulting domain structure usually results in a near complete compensation of polarization and the crystals consequently exhibit very small pyroelectric effects until they are poled by the application of a field. A ferroelectric transition is usually associated with the condensation of a soft (or low- frequency) mode of lattice motion at the Brillouin-zone centre. Structural transitions triggered by zone-centre soft modes are generally termed ferrodistortive, and in this sense ferroelectrics constitute a subgroup of the class of ferrodistortive transitions. This subgroup involves the condensation of a polar or optically active mode whose condensation causes the appearance of a long rage polar order. If the transition is strongly first order then mode softening may not occur to a significant degree, and in this situation, there is also a possibility that the large polarization which sets in discontinuously at T c may not be reversible, or the low temperature phase may be pyroelectric only. Ferroelectric transitions are categorized as being either displacive or order-disorder in character. This distinction is generally made in terms of whether the paraelectric phase is microscopically nonpolar (displacive) or only nonpolar in a macroscopic or thermally averaged sense (order-disorder). The displacive or order-disorder character is often defined in terms of the dynamics of the phase transition, as to whether the soft mode is a propagating or diffusive type respectively. The displacive or propagating soft mode is a damped optic phonon, representing small quasi-harmonic motion about the mean position, while the diffusive soft mode represents large amplitude thermal hopping motion between the domain wells. Although most ferroelectrics are ferrodistortive (common examples being barium titanate, sodium nitrite, and triglycine sulphate) some are not. To understand this it is necessary to recognize that, because of the existence of coupling between modes, it is not a necessary Ferroelectrics – Physical Effects 156 condition for ferroelectricity that a zone centre polar mode should be driving the instability. Sometimes a driving antidistortive mode can couple directly or indirectly to a zone centre polar mode and upon condensation induce a small spontaneous polarization in an indirect fashion. In this case the primary order parameter is antidistortive in character while the spontaneous polarization is said to be a secondary order parameter of the transition. There can of course be only one primary order parameter (at least for a continuous or near continuous transition), but there may be many induced or secondary order parameters resulting from couplings to the primary order parameter. All the known antiferroelectrics (examples: lead zirconate, ammonium dihydrogen phosphate etc.) are intrinsically antidistortive, although one can conceive of a ferrodistortive antiferroelectric as one having an antiparallel arrangement of electric dipoles occurring within a primitive cell of the higher-symmetry phase. Such a phase is characterized by the condensation of an antipolar zone-centre soft mode. Once the importance of coupling between polar modes and other modes has been recognized it is clear that, via the piezoelectric interaction (or coupling to acoustic modes), a spontaneous strain will be virtually a universal characteristic of ferroelectrics since all ferroelectrics are piezoelectric. If this strain can be switched by application of stress then an obvious parallel in elastic terms exists with ferroelectricity. This property is termed ferroelasticity, and a crystal is said to be ferroelastic when it has two or more orientation states in the absence of mechanical stress (and electric field) and can be shifted from one to another of these states by mechanical stress. Intrinsic ferroelastic transitions are associated with the condensation of long-wavelength acoustic phonons and many are known. The optical and acoustic phonon modes involved in ferroelectric and ferroelastic phase transitions can be probed with Brillouin light scattering and ultrasonic techniques. When phonon modes soften, the involved elastic constants undergo anomalous variations which get reflected in ultrasound velocity and attenuation. Elaborate reviews on these subjects have appeared in literature (Luthi & Rehwald, 1980; Cummins, 1990). Other popular techniques used to probe modes in ferroelectrics are dielectric spectroscopy (Grigas, 1996) and neutron scattering (Dorner, 1981). A number of books and reviews on these subjects have appeared in literature (Lines & Glass, 1977). Though technique like measurement of thermal conductivity across phase transition can reveal information about the coupling between ferroelectric soft modes and thermal phonons, not many measurements have appeared in literature on this. The few measurements that have appeared in literature have used the well established steady-state methods of measuring thermal conductivity (Dettmer et al., 1989). There are several ferroelectrics that undergo successive phase transitions with incommensurate phases (I-phase) from a symmetrical paraelectric to an incommensurate phase at Ti and then from the incommensurate phase to a commensurate polar phase at T c (Cummins, 1990, Blinc & Levanyuk, 1986). This phase transition sequence can be qualitatively described in terms of the phenomenological Landau theory of phase transitions (Toledano & Toledano, 1987). The appearance of an I-modulated structure can be observed experimentally as satellite peaks in X-ray or neutron diffraction patterns. In the I-phase, at temperatures close to Ti, the I-modulation wave is harmonic, but as the temperature approaches Tc, the ideal crystal can be considered as a system of equally spaced commensurate constant-phase domains separated by narrow phase varying regions, i.e., phase solitons. The presence of these modulation waves can influence heat conduction in ferroelectric crystals in two distinctive ways. As has been shown earlier, an interaction Thermal Conduction Across Ferroelectric Phase Transitions: Results on Selected Systems 157 manifested in sound attenuation exists between the acoustical waves and the I-modulation waves in the I-phase (Levanyuk et al., 1992; Lebedev et al., 1992). The usual expression for the thermal conductivity in an insulating crystal is given by 1 3 Cvl   (1) where C, v and l denote the specific heat, group velocity, and mean free path for phonons, respectively (Ashcroft & Mermin, 1976). The incommensurate modulation waves can affect the mean free path and, consequently, can cause an anomalous variation of thermal conductivity in the I-phase. Another possibility is that the modulation waves may participate directly in heat conduction as carriers. In this case, one would expect the modulation waves to enhance the thermal conductivity by the sliding motion in addition to causing the usual phonon scattering effect. The effect of sliding modulation waves on thermal conductivity has been investigated earlier within a phenomenological approach (Levanyuk et al., 1992). In spite of the fact that measurement of thermal properties across transition points is highly relevant to understand the coupling between modes, only limited experimental work has appeared on this in literature. 2. Overview of thermal properties across ferroelectric phase transitions In the few measurements of the variations of thermal conductivity near ferroelectric phase transitions reported in literature, steady state methods have been employed. One of the first measurements was on BaTiO 3 by Mante & Volger (1967). Their results show dips in thermal conductivity at temperatures corresponding to phase transition points. The results are explained in terms of mode conversion near the transition points. The low lying temperature dependant optical phonon branches can get zero energy at zero wave-vector, which causes permanent polarization of the crystal. Near the transition temperature the optical branches have energies comparable to those of the acoustic branches which usually transport the heat. This influences the number of scattering processes in which optical phonons participate, resulting in a reduction of the conductivity due to acoustic branches. In case transverse optical phonon branch shows enough dispersion and is not scattered too much, one can expect additional conductivity which might compensate for the effect of decreased conduction by the acoustic phonons. Thermal conductivities and specific heat capacities of a wide spectrum of ferroelectrics, BaTiO 3 , PbTiO 3 , KNbO 3 , KTaO 3 , NaNbO 3 and Pb(Mg 1/3 Nb 2/3 )O 3 (PMN) single crystals have been measured from 2 to 390 K (Tachibana et al., 2008). Pronounced jumps are found at structural transitions in BaTiO 3 and KNbO 3 . A low-temperature anomaly from soft optical phonons is observed in KTaO 3 . For PMN and NaNbO 3 , glass-like behaviour is observed in both thermal conductivity and heat capacity measurements. The glass-like behaviour in NaNbO 3 is associated with the phase separation phenomena which have been reported in earlier studies. Thermal analysis techniques such as differential scanning calorimetry (DSC) have been employed by several researchers to probe ferroelectric phase transitions (Setter & Cross, 1980, Podlojenov et al., 2006). Belov & Jeong (1998) have reported thermal conductivity measurements for two ferroelectric crystals, (NH4) 2 BeF 4 and Rb 2 ZnCl 4 , with incommensurate phases. It is found that anomalies exist in the thermal conductivities of these crystals in the I-phases. I-modulation waves cause anomalies in the heat transport processes by scattering of heat carrying phonons Ferroelectrics – Physical Effects 158 rather than by their direct participation as heat carriers. They have employed the steady- state technique for their measurements. Comparatively large samples, of size typically greater than 5 mm 3 , are needed for these techniques in order to avoid boundary effects. Moreover, comparatively large rises in temperature are often necessary to obtain a reasonably high signal to-noise ratio, which lead to considerable temperature gradients being set up in the sample. These drawbacks make these techniques unsuitable for studying critical thermal conductivity behaviour near phase transitions. Thermal wave measurements based on a photothermal effect, such as the photothermal deflection technique, photoacoustic method and photopyroelectric measurement do not disturb the thermal equilibrium of the sample during transitions. In these techniques one measures the thermal diffusivity, rather than thermal conductivity. Thermal diffusivity measurements do not suffer from heat losses from the sample during measurements and hence are more accurate than a direct measurement of thermal conductivity by the steady state method. With a proper choice of boundary conditions, photothermal techniques make a simultaneous measurement of thermal diffusivity and thermal effusivity possible, from which the thermal conductivity and specific heat capacity can be extracted. The photopyroelectric technique has been used earlier to measure the variations of thermal conductivity and heat capacity of a few crystalline solids as they undergo phase transitions with temperature (Marinelli et al., 1990; Zammit et al., 1988; Mandelis et al., 1985). 3. The photopyroelectric technique Complete characterization of the thermal properties of a material requires the determination of the thermal transport properties such as the thermal conductivity as well as the specific heat capacity. Techniques for high resolution measurement of specific heat capacity are well established (Kasting et al., 1980; Thoen et al., 1982). It has been shown that photothermal techniques allow simultaneous measurement of specific heat capacity c p and thermal conductivity λ s (Marinelli et al., 1990). The photoacoustic technique has been used for the simultaneous determination of the thermal diffusivity, thermal conductivity and heat capacity of liquid-crystalline compounds (Zammit et al., 1988). A somewhat similar technique has been used for measuring the thermal diffusivity and heat capacity of solids at room temperature using a photopyroelectric (PPE) detector (Mandelis et al., 1985; John et al., 1986). This technique enables simultaneous determination of thermal diffusivity, thermal effusivity, thermal conductivity and heat capacity as a function of temperature. Moreover, this technique allows studies of critical behaviours of thermal parameters when the material undergoes a transition. Marinelli et al. (1990) developed a technique to determine thermal diffusivity, thermal conductivity and heat capacity simultaneously at low temperatures with a pyroelectric detector kept in vacuum. At temperatures above room temperature, the boundary conditions involved in the theory of this method are not easy to satisfy, so that application of the method can lead to errors in measurement. A photothermal technique for the simultaneous determination of the thermal conductivity and specific heat capacity near solid state phase transitions using a pyroelectric detector kept in contact with a thermally thick backing medium has been developed by Menon & Philip (2000). The PPE technique has some distinct advantages, such as its simplicity, good sensitivity and ability to perform nondestructive probing, over other photothermal methods. In this measurement the sample is heated by a modulated light source on one side and the temperature oscillations on the opposite side of the sample are detected with a [...]... Ferroelectrics – Physical Effects been shown that the enhancement in thermal conductivity is related to the excess specific heat ce due to order parameter fluctuation as (   bg ) T (7)  ce 4 .5 1 .50 -2 -2 2 -1 Thermal Diffusivity (x10 cm s ) 1 .55 1. 45 4.0 1.40 3 .5 1. 35 1.30 3.0 1. 25 1.20 -2 -1 -1/2 5. 0 Thermal Effusivity (x10 Jcm K s ) 1.60 2 .5 80 100 120 140 160 180 200 Temperature (K) 0.42 5. 4... 104.8) I n =5 Cr 71.3 SmC* 75. 2 SmA 101.1 I n=6 Cr 71.4 SmC* 75. 1 SmA 97.1 I C6H13 (S) (6.m.n) 180 Ferroelectrics – Physical Effects n=7 Cr 67.2 SmC* 78.2 SmA 95. 7 I m=6 n=1 Cr 70.6 (SmC* 69.8) SmA 98.8 I n=2 Cr 54 .6 (SmC*A 43.0) SmC* 74.4 SmA 96.1 I n=3 Cr 76.0 (SmC*A 58 .0 SmC* 75. 1) SmA 89.0 I n=4 Cr 76.2 (SmC*A 68.0 SmC* 74.9) SmA 87.2 I n =5 Cr 64.9 (SmC*A 57 .0) SmC* 73.0 SmA 84.6 I n=6 Cr 54 .9 SmC*A... transition temperature This was in agreement with thermal diffusivity measurements along these axes reported earlier (Gaffar et al., 1987) 162 Ferroelectrics – Physical Effects 5. 5 5. 0 4 .5 PPE Amplitude (mV) 4.0 3 .5 a-axis b-axis c-axis 3.0 2 .5 2.0 1 .5 1.0 0 .5 0.0 -0 .5 0 100 200 300 400 Modulation Frequency (Hz) Fig 3 (a) Frequency dependence of the photo-pyroelectric amplitudes along the three principal... n=7 Cr 49 .5 (SmI* 25. 0) SmC*A 89.9 SmC* 91.9 SmA 1 05. 4 I m=6 n=1 Cr 66.7 (SmC*A 48.0) SmC* 104.9 SmA 117.3 I n=2 Cr 58 .1 SmC*A 95. 2 SmC* 103 .5 SmA 112.2 I n=3 Cr 61.0 SmC*A 87 .5 SmC* 98.1 SmA 104 .5 I n=4 Cr 64.8 SmC*A 93.3 SmC* 96.2 SmA 101.7 I n =5 Cr 68.4 SmC*A 87.6 SmC* 93.9 SmA 99 .5 I n=6 Cr 68 .5 SmC*A 89.8 SmC* 91.7 SmA 97 .5 I n=7 Cr 70.4 SmC*A 85. 9 SmC* 89.9 SmA 96.9 I Phase diagrams for all compounds... lead propionate Ca2Pb (C2H5COO)6: Determination of critical exponent below the ferroelectric phase transition and comparison with EPR studies on Ca2Ba(C2H5COO)6 and Ca2Sr(C2H5COO), Phy Rev B 39, 2041-2 050 Tachibana, M.; Kolodiazhnyi, T & Takayama-Muromachi, E (2008) Thermal conductivity of perovskite ferroelectrics, Appl Phys Letters 93, 092902 176 Ferroelectrics – Physical Effects Takashige, M.; Hirotsu,... 25 Badarinath, K V S & Radhakrishna, S (1984) Studies on the ferroelectric-paraelectric transition of dicalcium lead propionate, J Mat Sci Lett 3, 57 5 -57 7 Belov, A & Jeong, Y H (1998) Anomalous heat conduction in ferroelectric crystals with incommensurate phases, J Korean Phys Society 32, 452 - 455 Bhat, S V.; Dhar, V & Srinivasan, R (1981) ESR studies on phase transitions in double propionates, Ferroelectrics. .. the phase transitions in Ferroelectric Ca2Sr (C2H5COO)6 and Ca2Pb(C2H5COO)6, J Phys Soc Jpn 39, 10261031 Goldsmith, G J & White, J G (1 959 ) Ferroelectric behavior of Thiourea, J Chem Phys 31, 11 75- 1187 Grigas, J (1996) Microwave dielectric spectroscopy of ferroelectrics and related materials (Gordon and Breach Publishers) 174 Ferroelectrics – Physical Effects Gupta, S S.; Karan, S & Gupta, S P S (2000)... n=7 Cr 50 .5 SmC*A 60.3 SmC* 71.7 SmA 82 I CnH2n+1COO(CH2)mO COO COO C*H C6H13 (S) (7.m.n ) CH3 m=3 n=1 Cr 62.6 (SmI* 52 .7) SmA 129.7 I n=2 Cr 77.3 (SmI* 49.2) SmC*A 88.2 SmA 123.6 I n=3 Cr 66.6 (SmI* 43.0) SmC*A 92.4 SmA 117.3 I n=4 Cr 62.2 (SmI* 31.9) SmC*A 92.8 SmA 111.7 I n =5 Cr 73.6 (SmI* 26.3) SmC*A 92 .5 SmA 109.1 I n=6 Cr 69.2 (SmI* 22.0) SmC*A 91.0 SmC* 92.2 SmA 106.6 I n=7 Cr 49 .5 (SmI* 25. 0)... properties of Dicalcium lead propionate, J Phys Soc Jpn 45, 55 8 -56 4 Terauchi, H; Takenaka, H & Shimaoka, K (19 75) Structural Phase Transition in K2SeO4, J Phys Soc Japan 39, 4 35- 39 Thoen, T; Marynissen, H & Van Dael, W.(1982) Temperature dependence of the enthalpy and the heat capacity of the liquid-crystal octylcyanobiphenyl (8CB) Phys Rev A 26, 2886-29 05 Toledano, J & Toledano, P (1987) The Landau theory... temperatures T1 = 7 45 K, T2 = 129 .5 K and T3 = 93 K (Aiki et al 1969) The crystal exhibits hexagonal structure in phase I, with space group D46h (P63/mmc) (Shiozaki et al 1977), which changes to an orthorhombic structure (phase II) with space 168 Ferroelectrics – Physical Effects 0.72 -2 -1 -1 -1 0.37 Thermal conductivity (x10 Wcm s ) 0.74 -1 0.76 0.38 Specific heat capacity (Jg K ) 0.39 0.36 0.70 0. 35 0.68 0.34 . reported earlier (Gaffar et al., 1987). Ferroelectrics – Physical Effects 162 0 100 200 300 400 -0 .5 0.0 0 .5 1.0 1 .5 2.0 2 .5 3.0 3 .5 4.0 4 .5 5.0 5. 5 PPE Amplitude (mV) Modulation Frequency. 20406080100 0.0 0.2 0.4 0.6 0.8 1.0 Parallel 0. 05 mA/cm 2 0 .5 mA/cm 2 5 mA/cm 2 50 mA/cm 2 300 mA/cm 2 K I /K IC Time to fracture, h (a) 0 20406080100 0.0 0.2 0.4 0.6 0.8 1.0 0. 05 mA/cm 2 0 .5 mA/cm 2 5 mA/cm 2 50 mA/cm 2 K I. ceramics by doping hydrogen. Journal of Physical Chemistry C, Vol.114, No.21, pp. 9 955 -9960, ISSN 1932-7447 Ferroelectrics – Physical Effects 154 Zhang, H.; Su, Y. J.; Qiao, L. J. &