Ferroelectrics Physical Effects Part 15 potx

Localized States in Narrow-Gap Ferroelectric-Semiconductor PbSnTe: Injection Currents, IR and THz Photosensitivity, Magnetic Field Effects 549 traps, the charging processes of the various traps will proceed simultaneously without emergence of notable current oscillations. The latter situation refers to the case of high voltages at which a reduction of the current oscillation amplitude and, then, complete vanishing of oscillations were observed in the experiment. Thus, involvement of the mechanism of current decrease due to trapping-induced reduction of free-electron concentration, on the one hand, and involvement of the mechanism of current increase owing to recharging-induced change of trap polarizability, on the other hand, can result in an oscillating dynamics of the current decay to a steady-state value of the current. 7. Conclusions The object under study being solid solution Pb-Sn-Te with a substantial (up to a few atomic per cents) In content, this object has to be considered as a disordered system presenting a solid without long-range ordering, with the potential energy of charge carriers no longer being a periodic function of coordinates. The violation of long-range ordering is related to the fact that any chosen site of the metal sublattice may contain, with certain probability, any of the three components. Electronic processes in such systems, namely, in amorphous germanium and silicon, and also in chalcogenide glasses, were considered in (Mott & Davis, 1979). Such properties of PbSnTe:In as the Fermi-level pinning, the absence of an EPR signal, and deviations from linearity in the temperature dependence ( ) log 1 f T σ = are similar to chalcogenide properties. J. Marshall and A.E. Owen (Marshall & Owen, 1976) considered a state density model assuming that the forbidden band of PbSnTe contains deep donors with energy levels below the acceptor energy (see Figure 18). Fig. 18. Density of states in a non-crystalline semiconductor. VB – valence band; CB – conduction band; E F - Fermi level; D – donors; A – acceptors; E V , E C – mobility edges; E B – valence-band ceiling; E A – conduction-band bottom. Shaded are localized states. The states in the forbidden band of PbSnTe pin the Fermi level at the middle of the energy gap, thus leading to decreased conductivity. If the deep acceptor and donor states do not overlap, then unpaired electrons, normally causing an EPR signal, are lacking, except for those due to magnetic impurities. Without going into details, we can state that the model by I.A. Drabkin and B.Ya. Moizhes (Drabkin & Moizhes, 1981) mentioned in Section 1 closely follows the theory by P.W. Anderson (Anderson, 1975). The unique possibility of creating injecting contacts to PbSnTe:In has allowed researchers to examine charge transport processes related to the recharging phenomena of localized states Ferroelectrics – Physical Effects 550 in PbSnTe:In both under conditions with screened background radiation and under sample illumination in a broad spectral range, from IR to THz radiation. The fact that PbSnTe:In is a ferroelectric has widened available possibilities in studying the effect of magnetic field on the charge transport due to electrons. Of course, the data described in the present publication present no final results; yet, we believe that space-charge-controlled limitation of the electric current, and also capture of electrons into localized traps and their emission from those traps, which affect sample polarizability, are factors that need to be taken into account in developing theoretical models. 8. Acknowledgments This work was supported by the Programs of Russian Academy of Sciences No. 5.4, 21.20 and, 21.34. 9. References Akimov A.N., Erkov V.G., Klimov A.E., Molodtsova E.L., Suprun S.P. & Shumsky V.N. (2005). Injection currents in narrow-gap (Pb 1-x Sn x Te):In insulators, Semiconductors, Vol. 39, No. 5, pp. 533-538, ISSN 1063-7826 Akimov A. N., Erkov V. G., Kubarev V. V., Molodtsova E. L., Klimov A. E. & Shumski V. N. (2006). Photosensitivity of Pb 1–x Sn x Te:In films in the terahertz region of the spectrum, Semiconductors, Vol. 40, No. 2, pp. 164–168, ISSN 1063-7826 Akimov B.A., Brandt N.B., Bogoslovskii S.A., Riabova L.I. & Choudnev S.M. (1979). Non- equilibrium metal state in Pb 1-x Sn x Te(In) alloys. JETP Letters, Vol. 29, No. 1, pp. 9- 12, ISSN 0021-3640 Akimov B.A., Ryabova L.I., Shumsky V.N. & Petikov N.I. (1993). An operating regime based on switching effect for photodetectors of PbSnTe<In> MBE films, Infrared Phys., Vol. 34, No. 4, pp. 375-378, ISSN 1350-4495 Anderson W. W. (1975). Model for the electronic structure of amorphous semiconductors, Phys Rev Lett., Vol. 34, pp. 953-955, ISSN 0031-9007 Anderson W.W. (1980). Tunnel contribution to Hg 1-x Cd x Те and Рb 1-x Sn x Те p-n junction diode characteristics, Infrared Phys., Vol. 20, pp. 353-361, ISSN 1350-4495 Bonch-Bruevich V.L. (1974). Electronic dielectric susceptibility of a disordered semiconductor, JETP Letters, Vol. 19, No. 4, p. 122, ISSN: 0370-274X Bonch-Bruevich V.L. & Kalashnikov G . (1965). On possible recombination instability in semiconductors, Fizika Tverdogo Tela (in Russian), Vol. 7, No. 3, pp. 750-758, ISSN 0367-3294 Borodin V.V., Klimov A.E. & Shumsky V.N. (1997). Photocurrent oscillations in PbSnTe<In> films, In: Narrow Gap Semiconductors, Shen S.C., Tang D.V., Zheng G.V., Bauer G., pp. 365-368, World Scientific Borodin V.V., Klimov A.E., Shumsky V.N. (1997). Recombination in PbSnTe <In> at low temperatures, In: Narrow Gap Semiconductors, Shen S.C., Tang D.V., Zheng G.V., Bauer G., pp. 361-364, World Scientific Drabkin I. A. & Moizhes B. Ya. (1981). Spontaneous dissociation of neutral impurity states to positive and negative charge states, Fizika i Tekhnika Poluprovodnikov (in Russian), Vol. 15, No. 4, pp. 625-647, ISSN 0015-3222 Localized States in Narrow-Gap Ferroelectric-Semiconductor PbSnTe: Injection Currents, IR and THz Photosensitivity, Magnetic Field Effects 551 Drabkin I.A. & Moizhes B.Ya. (1983). On the photoconductivity of Pb 1-x Sn x Te doped with In. Fizika i Tekhnika Poluprovodnikov (in Russian), Vol. 17, No. 6, pp. 969-972, ISSN 0015-3222 Emtage P.R. (1976). Auger recombination and junction resistance in lead-tin-telluride, J. 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Giant light-modulated permittivity of Pb 0.74 Sn 0.26 Te<In> narrow band-gap isolator: new approach to relaxation processes and potential applications, Proceedings of International Semiconductor Device Research Symposium (ISDRS 2001), Washington, USA, December 2001 Klimov A. E. & Shumsky V.N. (2003). Photocapacitance effect in narrow band gap PbSnTe<In>, Proceedings SPIE, Vol. 5126, pp. 341-346, ISSN 0277-786X Klimov A., Shumsky V. & Kubarev V. (2007). Terahertz sensitivity of Pb 1-x Sn x Te:In, Ferroelectrics, Vol. 347, pp. 111-119, ISSN 0015-0193 Klimov A.E. & Shumsky V.N. (2008), Photosensitivity of Pb 1–x Sn x Te:In films in the region of intrinsic absorption, Semiconductors, Vol. 42, No. 2, pp. 149–15, ISSN 1063-7826 Klimov A., Sherstyakova V. & Shumsky V. (2009). Giant magnetoresistance in narrow-gap ferroelectric-semiconductor PbSnTe:In, Ferroelectrics, Vol. 378, pp. 101-110, ISSN 0015-0193 Klimov A.E. & Shumsky V.N. (2009). Shallow traps and the space-charged-induced limitation of the injection current in PbSnTe:In narrow-gap ferroelectric, Physica B, Vol. 404, No. 23-24, pp. 5028–5031, ISSN 0921-4526 Lampert M.A. & Mark P. (1970). Current injection in solids, Academic Press, N.Y London. Lishka K., Durstberger R., Lindermann G., Staudinger H. ( 1984). Defect states in Рb 1-x Sn x Те, Phys. Stat. Sol (a)., Vol. 123, pp. 319–324, ISSN 0031-8965 Marshall J. & Owen A.E., (1976). Field-effect measurements in disordered As 30 Te 48 Si 12 Ge 10 and As 2 Te 3 , Philosophical Magazine, Vol. 33, p. 457, ISSN 1478-6435 Mitsuru I. & Ruiping W. (2000). Quantum ferroelectricity in SrTiO 3 induced by oxygen isotope exchange, Appl. Phys. Lett., Vol. 76, pp. 221–223, ISSN 0003-6951 Mott N.F. & Davis E.A. (1979). Electron processes in non-crystalline materials, Clarendon Press. Oxford Nasybbulin R. A., Girshberg Ya. N., Trunov N. N., Kalimullin R. H., Kukharskii A. A., Kharionovskii Yu. S., Shapkin V. V. & Bursian E. V. (1983). Non-monotone dependence on composition of the ferroelectric phase transition temperature in Ferroelectrics – Physical Effects 552 Pb 1−x Sn x Te, Fizika Tverdogo Tela (in Russian), Vol. 25, No. 4, pp. 784–788, ISSN 0367- 3294 Romcevic N., Popovic Z.V., Khokhlov D., Nikorich A.V. & Konig W. (1991). Far-infrared study of In doped Pb 0,75 Sn 0,25 Te single crystals, Infrared Phys., Vol. 31, No. 3, pp. 225-230, ISSN 1350-4495 Suris R.A. & Fuks B.I. (1975). Sample impedance of compesated material under the conditions of the space-re-charge wave exitation, Fizika i Tekhnika Poluprovodnikov (in Russian), Vol. 9, No. 1717-1727, ISSN 0367-3294 Van Rooesbroeck W. & Shockley W. (1954). Photon-radiative recombination of electrons and holes in germanium, Phys. Rev., Vol. 94, No. 6, pp. 1558-1560, ISSN 0031-899X Vinogradov V. S. , Voronova I. D., Kalyuzhnaya G. A. , Ragimova T. Sh. & Shotov A. P. (1980). Hall effect and photoconductivity of Pb 1-x Sn x Te with indium, JETP Letters, Vol. 32, No. 1, pp. 20-24, ISSN 0021-3640 Vinogradov V.S. & Kucherenko I.V. (1991). Ferroelectric properties of Pb 1-x Sn x Te (x=0.25) crystals doped with indium. Fizika Tverdogo Tela (in Russian), Vol. 33, No. 9, pp. 2572-2578, ISSN 0367-3294 Volkov B. A. & and Pankratov O. A. (1980). Yan-Teller instability of crystal environment of point defects in A 4 B 6 semiconductors, Doklady Akademii Nauk (in Russian), Vol. 255, No. 1, pp. 93-97, ISSN 0869-5652 Volkov B. A. & Ruchaiski O. M. (1995). Intracenter Coulomb correlations, charge states, and spectrum of group-III impurities in IV-VI narrow-gap semiconductors, JETP Lett., Vol. 62, No. 3, pp. 217-222, ISSN 0021-3640 Volkov B.A., Ryabova L.I. & Khokhlov D.R. (2002). Mixed-valence impurities in lead telluridebased solid solutions. Physics Uspekhi, Vol. 45, No. 8, p. 819-846, ISSN 1063- 7869 Vul B.M., Voronova I.D., Kaliuzhnaya G.A., Mamedov T.S. & Rakhimova T.Sh. (1979). Peculiarities of transport phenomena in Pb 0.78 Sn 0.22 Te with large content of indium. JETP Letters, Vol. 29, No. 1, pp. 18-22, ISSN 0021-3640 Zasavitskii I.I., Matvienko A.V., Matsonoshvili B.N. & Trofimov V.T. (1986). Photoconductivity spectrum of Pb 1-x SnxTe:In epitaxial layers, Fizika i Tekhnika Poluprovodnikov (in Russian) , Vol. 20, No. 2, pp. 214-220, ISSN 0015-3222 24 Piezo-optic and Dielectric Behavior of the Ferroelectric Lithium Heptagermanate Crystals A. K. Bain 1 , Prem Chand 1 and K. Veerabhadra Rao 2 1 Department of Physics, Indian Institute of Technology Kanpur 2 Advanced Center for Materials Science, Indian Institute of Technology Kanpur India 1. Introduction It is well known that piezo-optic and electro-optic effects in crystals find wide ranging applications in laser devices. The photoelastic behavior of crystals forms a necessary prelude to study the electro-optical effect of ferroelectric crystals. Lithium heptagermanate Li 2 Ge 7 O 15 (LGO) is regarded as a weak ferroelectric and its curie point T c is 283.5K (Wada et al., 1981, 1983). Due to its intermediate behaviour between order-disorder and displacive types in a conventional grouping of ferroelectric materials LGO remains a subject of interest from both the theoretical and the application point of view. The paraelectric phase above T c is orthorhombic 14 2h D ~ pbcn and below T c the ferroelectric phase is 5 2v C ~ pbc2 1 with four formula units in a unit cell in both the phases. Below T c LGO shows dielectric hysteresis loop and the permittivity shows a sharp peak at T c (Preu, 1982; Wada et al., 1981, 1983). The Raman scattering spectrum shows a shoft mode whose frequency tends to zero as T c is approached from below (Wada & Ishibashi, 1983). Below T c the spontaneous polarization appears along the c-axis. The nature of the second order phase transition is not simple because according to Raman spectra the transition is suggested to be a displacive phase transition. But the temperature dependence of the permittivity ε is indicative of the order disorder character of the phase transition (Preu, 1982; Wada et al., 1981, 1983) and does not agree with the behaviour expected of a displacive phase transition. Many interesting physical properties of LGO such as birefringence (Kaminsky & HaussÜhl, 1990), elastic (Hauss Ühl et al., 1980), thermal expansion (Wada & Ishibashi, 1983), dielectric susceptibility (Preu, 1982; Kudzin, 1994a, 1995b), electron paramagnetic resonance (EPR) of doped ions Mn 2+ and Cr +3 (Trubitsyn et al., 1992; Bain, 1994) and photoluminescence (Bain, 1994) exhibit strong anomalies around T c . However, the optical properties vary only to such a small degree that the transition could not be detected with the aid of a standard polarization microscope (Kaminsky & Hauss Ühl, 1990). Interestingly with the help of a high resolution polarization device, Kaminsky and Hauss Ühl (Kaminsky & HaussÜhl, 1990) studied the birefringence in LGO near T c and observed anomalies at the phase transition. The study of piezo-optic dispersion of LGO (un-irradiated and irradiated) in the visible region of the spectrum of light at room temperature (RT=298 K) shows an optical zone/window in between 5400Å and 6200Å with an enhanced piezo-optical behavior (Bain et al., 2008). The temperature dependence of the photoelastic coefficients of the ferroelectric Ferroelectrics – Physical Effects 554 crystals Li 2 Ge 7 O 15 (both un-irradiated and x-irradiated) in a cooling and a heating cycle between room temperature and 273K shows an interesting observation including the lowering of the T c under uniaxial stress contrary to the increase of T c under hydrostatic pressure and observation of thermal photoelastic hysteresis similar to dielectric behavior (Bain et al., 2009). The study of a.c. electrical impedance (Z) along the c-axis of the crystals LGO in the temperature range 283.5 K to 573 K at the frequency range 10kHz – 10,000 kHz shows a sharply decrease of the magnitude of ǀZǀ with increasing frequency and tends to zero value at about the frequency 10,000kHz. This chapter will include basic properties of the ferroelectric Lithium heptagermanate (Li 2 Ge 7 O 15 ) crystals, related experimental studies on this crystal including growth of single crystals, agreement and disagreement between the results of different experimental investigations. The brief description on the theory of photoelasticity, fabrication process of the ferroelectric Li 2 Ge 7 O 15 crystals, experimental methods of the photoelastic coefficients of LGO (un-irradiated and irradiated) at different wave length and temperatures around the phase transition temperature T c and also the practical applications of the LGO crystals in the opto-electronic devices will be discussed. 1.1 Growth and structure of Li 2 Ge 7 O 15 crystals Single crystals of Li 2 Ge 7 O 15 are grown in an ambient atmosphere by Czochralski method from stoichiometric melt, employing a resistance heated furnace. Stoichiometric mixture of powdered Li 2 CO 3 and GeO 2 in the ratio of 1.03 and 7.0 respectively was heated at 1100 K for 24 hours to complete the solid state reaction for the raw material for the crystal growth. The crystals were grown by rotating the seed at the rate of 50 rpm with a pulling rate of 1.2 mm/hour. The cooling rate of temperature in the process of growth was 0.8-1.2 K/hour. The crystals grown were colorless, fully transparent and of optical quality. The crystal axes were determined by x-ray and optical methods. The desired impurities such as Cr +3 , Mn +2 , Bi +2 and Eu +2 etc are also introduced in desired concentration by mixing the appropriate amount of the desired anion salt in the growth mixture. The crystal structure of LGO above T c is orthorhombic (psedohexagonal) with the space group 14 2h D (Pbcn). The cell parameters are a: 7.406 Å, b: 16.696 Å, c: 9.610 Å, Z = 4 and b~√3c. Below T c a small value of spontaneous polarization occurs along c-axis and the ferro-phase belongs to 5 2v C (Pbc2 1 ) space group. The crystal structure contains strongly packed layers of GeO 4 tetrahedra linked by GeO 8 -octahedra to form a three dimensionally bridged frame work in which Li atoms occupy the positions in the vacant channels extending three dimensionally (Hauss Ühl et al., 1980; Wada et al., 1984, 1988; Iwata et al., 1987). The size of the unit cell (Z = 4) does not change at the phase transition and ferroelectric phase transition is associated with a relaxational mode as well as the soft phonon (Wada, 1988). 1.2 Theory of photoelasticity If a rectangular parallelepiped with edges parallel to x[100], y[010] and z[001] axes is stressed along z-axis and observation is made along y-axis, as shown in Fig.1, then the path retardation δ zy introduced per unit length due the stress introduced birefringence is given by δ zy = (Δn z – Δn x ) = C zy P zz (1) Piezo-optic and Dielectric Behavior of the Ferroelectric Lithium Heptagermanate Crystals 555 where Δn z and Δn x are the changes in the corresponding refractive indices, (Δn z – Δn x ) is the corresponding stress induced birefringence, P zz is the stress along z-axis and C zy is a constant called the Brewster constant or the relative photoelastic coefficient. In general the Brewster constant is related to the stress optical and strain optical tensors of forth rank (Narasimhamurty, 1981) and is a measure of the stress induced (piezo-optic) birefringence. It is conveniently expressed in the unit of 10 -13 cm 2 /dyne per cm thickness along the direction of observation is called a Brewster (Narasimhamurty, 1981). Fig. 1. A solid under a linear stress of stress-optical measurements (P zz is the applied stress and LL is the direction of light propagation and observation). 1.3 Experimental method of determining the photoelastic constants To study the piezo-optical birefringence the experimental set up consists of a source of light (S), a lens (L) to render the rays parallel, a polarizer (P), an analyzer Polaroid (A), a Babinet compensator (B) and a detector (D), as shown in Fig.2. The P and A combination are adjusted for optimal rejection of light. The sample with stressing arrangement and a Babinet compensator are placed between P and A. A monochromator and a gas flow temperature controlling device are used to obtain the piezo-optic coefficients (C λ ) at different wavelengths and temperature. The subscript λ in the symbol C λ denotes that the piezo-optic coefficient depends on the wavelength of light used to measure it. The experiments are carried out for different wavelengths using white light and a monochromator and the monochromatic sodium yellow light. An appropriate stress along a desired direction of the sample is applied with the help of a stressing apparatus comprising a mechanical lever and load. Fig. 2. A schematic diagram of the experimental setup for the measurement of photoelastic constants of the crystals at room temperature. Source of light (S), Lense (L), Polarizer (P), Crystals (C) under stress, Babinet Compensator (B), Analyzer (A) and Detector (D). Ferroelectrics – Physical Effects 556 To start with, the Babinet compensator is calibrated and the fringe width is determined for different wavelengths of light in the visible region. The crystal specimen is placed on the stressing system so that the stress could be applied along vertical axis and observation made along horizontal axis. A load on the crystal shifts the fringe in the Babinet compensator and this shift is a measure of the piezo-optic behavior. The piezo-optic coefficients (C  ) are now calculated using the calibration of the Babinet compensator. The experiment is repeated for other orientations of the crystals and the results are obtained. 1.4 Piezo-optic dispersion of Li 2 Ge 7 O 15 crystals The experimental procedure for the piezo-optic measurements is described in section 1.3. The polished optical quality samples worked out to dimensions i) 5.9 mm, 9.4 mm and 5.0 mm; ii) 3.17 mm, 5.88 mm and 6.7 mm, along the crystallographic a, b and c axes respectively. The stress was applied with an effective load of ~23 kg in each case (Bain et al., 2008). The values of C λ thus obtained at different wavelengths are given in Table 1 and the results are plotted in Fig. 3. Here C pq is the piezo-optic coefficient with the stress direction being p and observation direction being q. The results show an interesting piezo-optic behavior. A survey of literature indicates that the piezo-optic behavior of materials studied till now shows a reduction of C λ with increasing wavelength in the visible region (Narasimhamurty, 1981). In the present case, C λ decreases with wavelength up to a certain wavelength as in other normal materials and then suddenly shows a peak and later on the usual behavior of reduction in the values of piezo-optic coefficients is observed. Wavelenghts Obs. C pq 4358Å 4880Å 5390Å 5890Å 6140Å 1 C x y 4.024 3.819 3.722 4.328 3.677 2 C xz 5.243 4.895 4.770 5.552 4.451 3 C y x 4.084 3.525 3.092 3.562 2.913 4 C y z 4.353 4.118 3.946 4.261 3.866 5 C z y 4.179 2.814 3.177 3.713 3.172 6 C zx 3.312 2.991 2.650 4.190 2.618 Table 1. Stress optical coefficients c pq (in Brewster) for Li 2 Ge 7 0 15 at different wave lenghts. To the best knowledge of the authors this behavior is unique to the LGO crystals. For the sake of convenience we denote C λ measured at λ = 5890 Å as C 5890 and so on. The results show that sometimes the value of C 5890 is even higher than that at C 4400 , the value of piezo- optic coefficient obtained at the lowest wavelength studied here. This is the case with C xy , C zx and C xz . For other orientations the value is lower than that at 4400 Å. Further, C λ is found to have increased to more than 50% in the case of stress along [001] and observation along [100]. Also, it is interesting to note that the value of C 6140 , is less than that of C 5390 , in tune with usual observation of piezo-optic dispersion. Thus one can see an “optical window” in between 5400 Å and 6200 Å. The height of this optical window is different for various orientations, though the width seems approximately the same. The maximum height of about 1.5 Brewster was found for C zx followed by C xz with about 0.9 Brewster. It should be noted here that Z-axis is the ferroelectric axis for LGO. It is also interesting to note that the change in height is more in the former while the actual value of C λ , is less compared to that of the latter. The percentage dispersion also is different for various orientations. It is very high, as high as 25% for C zy , while it is just 10% for C xy . Piezo-optic and Dielectric Behavior of the Ferroelectric Lithium Heptagermanate Crystals 557 Fig. 3. Stress optical dispersion of Li 2 Ge 7 0 15 crystals with wavelength at room temperature (298 K). Figure 4 shows the variation of C zx (λ) at the temperatures ranging from 298K to 283K on cooling process of the sample LGO. It is clear from the figure that the distinct peak of C zx (λ) appears only at the sodium yellow wavelength of 5890 Å for the whole range of temperatures (298 K–283 K) investigated. It is also interesting to note that a temperature anomaly is also observed around 283 K. LGO undergoes a second order phase transition at 283.5 K from the high temperature paraelectric phase to the low temperature ferroelectric phase. So this anomaly is related to this phase transition of the LGO crystal. The observed peculiarity of piezo-optic behavior could be due to many factors, viz., i) anomalous behavior of refractive index or birefringence ii) anomalous ferroelastic transformation at some stage of loading iii) shift of absorption edge due to loading. The following have been done to identify the reasons for this peculiar behaviour. Birefringence dispersion has been investigated in the visible region and no anomalies in its behavior has been observed. This rules out the first of the reasons mentioned. The reason due to ferroelastic behavior also is ruled out since the effect would be uniform over all the wavelengths investigated. It was not possible to investigate the effect of load on the absorption edge. Hence an indirect experiment has been performed. If there is a shift in the absorption edge due to loading the sample, the peak observed now at sodium yellow light would shift with load. No clear shift of the peak could be observed within the experimental limits. Another interesting experiment was done to identify the source of the anomaly. It is well known that T c of LGO changes under uniaxial stress. The measurements were made near T c under different stress (loads). Although T c was found to shift a little with load the Ferroelectrics – Physical Effects 558 dispersion peak did not show any discernible shift. No particular reason could be established as to why a dispersion peak appears around sodium yellow region. Another interesting work in this direction is on Gd 2 (Mo0 4 ) 3 — where an anomalous peak was recorded in spontaneous birefringence at 334.7 nm (Saito et al., 1994), an observation made for the first time. Fig. 4. The variation of C zx (λ) at the temperatures ranging from 298 K to 283 K on cooling process of the sample Li 2 Ge 7 0 15 . It is well known that the photoelasticity in crystals arises due to change in number of oscillators, effective electric field due to strain and the polarisability of the ions. In the present case, as the wavelength approaches around 5400 Å , the ionic polarisability seems to be changing enormously. There is no optical dispersion data available on LGO. We haveconducted an experiment on transmission spectra of LGO along x, y and z-axes, which shows a strong absorption around 5400 Å . The observed anomaly in the piezo-optic dispersion may be attributed to the absorption edge falling in this region. This explanation needs further investigation in this direction. It is also known that the strain optical dispersion arises due to the shift in absorption frequencies and a change in the oscillator strength caused by the physical strain in the crystal. 1.5 Irradiation effect on Piezo-optic dispersion of Li 2 Ge 7 O 15 crystals The ferroelectric single crystals Li 2 Ge 7 O 15 was irradiated by x-ray for one hour and the experimental processes described in section 1.4 were repeated for the crystal (irradiated) LGO in order to understand the radiation effect on piezo-optical birefringence dispersion(Bain et al., 2008). The values of C  of the crystal (irradiated) LGO thus obtained at different wavelengths are given in Table 2 and the results are plotted in Fig. 5. [...]... Transition in Li2Ge7O15 J Phys Soc Jpn., Vol 50, No 9, (July 10, 1981), pp 2785-2786, ISSN 0031 9 015 Wada, M & Ishibashi, Y (1983) Ferroelectric Phase Transition in Li2Ge7O15 J.Phys Soc Jpn., Vol 52, No 1, (July 29, 1982), pp 193-199, ISSN 0031 9 015 578 Ferroelectrics – Physical Effects Wada, M.; Swada, A & Ishibashi, Y (1984) The Oscillator Strength of the Soft Mode in Li2Ge7O15 J Phys Soc Jpn., Vol... ISFD-2, Nantes Vanishri, S & Bhat, H L (2005) Irradiation Effects on Ferroelectric Glycine Phosphite Single  Crystal,  Ferroelectrics, Vol 323, No 1, (August 2005), pp 151 -156 , ISSN 0 015- 0193 Wada, M.; Swada, A & Ishibashi, Y (1981) Ferroelectricity and Soft Mode in Li2Ge7O15 J.Phys Soc.Jpn., Vol 50, No.6, (March 20, 1981), pp 1811-1812, ISSN 0031 9 015 Wada, M.; Orihara, H ; Midorikawa, M.; Swada A & Ishibashi,Y... 0 015- 0193 Bain, A.K.; Chand, P ; Rao, K.V.; Yamaguchi, T & Wada, M (2008) Irradiation Effect on Piezo-optic Dispersion of Li2Ge7O15 Crystals , Ferroelectrics, Vol 377, No 1, (December 2008), pp 86-91, ISSN: 0 015- 0193 Bain, A.K.; Chand, P ; Rao, K.V.; Yamaguchi, T & Wada, M (2009) Anomalous Temperature Dependence of Piezo-optic Birefrigence in Li2Ge7O15 Crystals Ferroelectrics, Vol 386, No 1, pp 152 -160,... ISSN: 0 015- 0193 Bain, A.K & Chand, P (in print) Study of Impedance in Ferroelectric Li2Ge7O15 Crystals, Integrated Ferroelectrics Bain, A.K & Chand, P (in print) Irradiation Effect on Photoelastic Coefficients in Ferroelectric Li2Ge7O15 Crystals, Integrated Ferroelectrics Haussühl, S & Albers, J.(1977) Elastic and thermoelastic constants of triglycine sulphate (TGS) in the paraelectric phase Ferroelectrics, ... Stress optical dispersion of Li2Ge7 015 crystals (un-irradiated and irradiated) with Wavelength at room temperature (298 K) Irradiation of crystals can change physical properties of the crystals Irradiation brings about many effects in the crystal such as creating defects, internal stress and electric fields etc These irradiation effects in turn are supposed to affect the physical properties of the irradiated... with the increase of constant electric field Fig.8 shows the dielectric constant ε of Li2Ge7O15:0.7%Bi measured on cooling at 1 MHz as a function of temperature for different values of constant electric field 562 Ferroelectrics – Physical Effects Fig 8 The temperature dependence of dielectric constant ε of Li2Ge7O15:0.7%Bi at 1 MHz on cooling for different values of constant electric field The spontaneous... phase Ferroelectrics, Vol 15, No 1, pp 73-75, ISSN 0 0150 193 Haussühl, S.; Wallrafen, F.; Recker, K & Eckstein, J (1980) Growth, Elastic Properties and Phase Transition of Orthorombic Li2Ge7O15 Z.krist, Vol 153 , pp 329-337, ISSN 0044 2968 Iwata, Y.; Shibuya, I.; Wada, M.; Sawada, A & Ishibashi, Y (1987) Neutron Diffraction study of structural Phase Transition in Ferroelectric Li2Ge7O15 J Phys Soc Jpn Vol... 9 015 James, A.R.; Balaji, S & Krupanidhi, S.B (1999) Impedance-fatigue correlated studies on SrBi2Ta2O9,Mater Sci Eng., B 64, No 3, pp 149 -156 , ISSN 0921-5107 Kholodenko, L P (1971) Thermodynamic Theory of Ferroelectrics of Barium Titanate Family (in Russian), Riga Kaminsky, W & Haussühl, S (1990) Faraday effect aid birefringence in orthorhombic Li2Ge7O15 near the ferroelectric phase transition Ferroelectrics. .. Lines, M E & Glass, A M (2004) Principles and Applications of Ferroelectrics and Related Materials, Clarendon press, ISBN 0-19-850778-X, Oxford Morioka, Y.; Wada, M & Swada, A (1988) Hyper-Raman Study of Ferroelectric Phase Transition of Li2Ge7O15 J.Phys Soc Jpn., Vol 57, No 9, (February 15, 1988), pp 3198-3203, ISSN 0031 9 015 Nye, J F (1957) Physical Properties of Crystals, Clarendon Press, ISBN 0-19-851165-5,... Li2Ge7O15 between 298 K and 273 K were determined and are shown in Fig 15 and Fig 16 The values of Cpq at 291 K and 278 K were reported in paper (Bain et.al., 1998) and it was observed that there were large changes in the values of Czy and Cyz at 278 K and 291 K as compared to other components and Czy did not show a peak in its temperature dependence between 291K and 278 K 568 Ferroelectrics – Physical Effects . dependence of the photoelastic coefficients of the ferroelectric Ferroelectrics – Physical Effects 554 crystals Li 2 Ge 7 O 15 (both un-irradiated and x-irradiated) in a cooling and a heating. T c was found to shift a little with load the Ferroelectrics – Physical Effects 558 dispersion peak did not show any discernible shift. No particular reason could be established as to why. constant ε of Li 2 Ge 7 O 15 :0.7%Bi measured on cooling at 1 MHz as a function of temperature for different values of constant electric field. Ferroelectrics – Physical Effects 562 Fig. 8.