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Soft mode behavior in the crystal Sn2P2Se6
August 2000
Materials Letters 45 Ž2000. 12–14 www.elsevier.comrlocatermatlet
Soft mode behavior in the crystal Sn 2 P2 Se 6 Yung Park ) Department of Materials Science and Metallurgy, UniÕersity of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Received 22 July 1999; accepted 20 January 2000
Abstract A study of the dispersion of the dielectric function in the crystal Sn 2 P2 Se 6 has revealed some new, thermally unstable lattice excitations. These excitations suggest structural phase transitions in Sn 2 P2 Se 6 at 193 K and, possibly, near 220 K. q 2000 Elsevier Science B.V. All rights reserved. PACS: 63.20.Dj; 64.70.Kb; 77.90.q k Keywords: Sn 2 P2 Se 6 ; Lattice excitations; Dielectric functions
In the Sn 2 P2 Se 6 crystal exhibiting proper uniaxial ferroelectrics, an intermediate incommensurate phase exists and two successive phase transitions are observed: the second-order phase transition from a paraelectric phase to a ferroelectric one at Ti s 220 K and the lock-in phase transition of first order from the incommensurate phase to the ferroelectric one at Tc s 193 K w1,2x. In different experiments, Tc features characteristic of transitions of displacive type and of order–disorder ones were observed. This led to controversial conclusions about the character of the phase transitions. The measured values of the entropy of the phase transition are quite high Ž10.0 J P Ky1 moly1 ., which is more typical for order–disorder transitions w3x. The soft mode softening to be observed at frequency n ) 0.5 THz by neutron scattering reveals that the transition is mainly displacive
)
Tel.: q44-1223-334-342; fax: q44-1223-334-567. E-mail address: [email protected] ŽY. Park..
with a minor order–disorder component w4x. It has been well accepted that the pure displacive soft mode behavior presupposes a zero value at a transition point. The changes in the structure between the paraelectric and ferroelectric phases have been well studied for Sn 2 P2 Se 6 by X-ray structure determinations w5– 7x. Throughout the paper, Sn 2 P2 Se 6 has the pseudo˚ b s 7.679 orthorhombic symmetry w8; a s 9.652 A, ˚ c s 6.810 A, ˚ a s g s 908, b s 91.48 at 293 K.. A, The structure includes two wP2 Se 6 x 4y ionic units, each consisting of two trigonal PSe 3 pyramids, rotated about the connecting phosphor pair. The two wP2 Se 6 x 4y units are related by a glide plane Žan a–c plane. in both phases. In the paraelectric phase, the four Sn atoms occupy equivalent general positions and are eight-coordinated with the Se atoms. Upon transition to the ferroelectric phase, the Sn atoms move in phase, approximately along the a-axis Ž0.32 ˚ for Sn ŽI. and 0.28 A˚ for Sn ŽII. and with opposite A ˚ . relative to the rigid phase along the b-axis Ž0.04 A P2 Se 6 groups, destroying the inversion symmetry
00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 0 . 0 0 0 6 4 - 1
Y. Park r Materials Letters 45 (2000) 12–14
and the twofold axis. The displacements correspond to B u symmetry and result in the appearance of a dielectric polarisation in the a–c plane at an angle of 108 to the a-axis. Recently, Eijt et al. w4x reported the relationship between the lattice dynamics and the phase transition sequence using neutron scattering. In ferroelectric phase, the TO mode Ž Px polarisation. shows a considerable softening as the incommensurate phase approached from below. It is suggested that the combined inelastic line-shapes could all be analysed in the light of a coupled-mode damped harmonic oscillator model. In this letter, we report a study of Sn 2 P2 Se 6 at frequencies in the range 4–23 cmy1 , similar to those of Sn 2 P2 Se 6 in Ref. w9x, by submillimeter dielectric spectroscopy w10. Using an Epsilon-2 backwardwave-tube spectrometer, we recorded the frequency dependence of the real ´ X Ž n . and imaginary ´ Y Ž n . parts of the dielectric function of plane-parallel Sn 2 P2 Se 6 samples over a broad temperature range, from room temperature down to 150 K. The samples were oriented in such a manner that the field E was parallel to the mounting plane Žwe observed no anisotropy of the dielectric properties of the crystal in this plane.. The experimental results are shown in Fig. 1. Some curves of ´ X Ž n . and ´ Y Ž n ., which are easily distinguishable, are shown to illustrate the spectra actually recorded on the spectrometer. Curves 1–11 are numbered in accordance with the monotonic cooling of the crystal. The most important results found from these spectra are as follows. Ži. At frequencies n F 20 cmy1 , there is an intense polar lattice oscillation of a resonance type in Sn 2 P2 Se 6 with all the characteristics of a soft mode: As the temperature is lowered, its frequency Ž; 14 cmy1 at room temperature. falls off in Fig. 1a. Žii. The temperature region near 220 K is a special one for Sn 2 P2 Se 6 : As the crystal is being cooled, it is at these temperatures that the nature of the dielectric dispersion of the crystal begins to change from resonant to relaxational. The effect can be clearly seen in the spectra of Sn 2 P2 Se 6 at frequencies ; 7–10 cmy1 , where the signs of both ´ X and its derivative with respect to the frequency change Žcurves 4–7. in Fig. 1a.
13
Fig. 1. Submillimeter dielectric spectra of Sn 2 P2 Se 6 for various temperatures. Ža. 1 to 7 — 298, 250, 230, 222, 218, 205, and 195 K, and Žb. 7 to 11 — 195, 193, 170, 160, and 150 K, respectively. ´ X and ´ Y correspond to the real and imaginary parts of the dielectric function.
Žiii. At 193 K, the dynamic properties of Sn 2 P2 Se 6 change abruptly Žcurves 7 and 8 in Fig. 1b.. A new high-quality factor absorption line appears at ; 14 cmy1 . Fig. 2 shows the temperature dependence of the characteristics of the soft mode according to leastsquares calculations from the ´ X ŽT . and ´ Y ŽT . spectra in a damped-oscillator model. It is clear from these results that we are dealing with a typical soft ferroelectric mode. The square of its frequency is a linear function of the temperature; the dielectric con-
14
Y. Park r Materials Letters 45 (2000) 12–14
Fig. 2. Characteristics of the soft mode n , G, and D ´ : the frequency, damping, and dielectric contribution, respectively.
tribution D ´ ŽT . exhibits an approximately Curie– Weiss temperature dependence with a constant C s 5.5 = 10 3 K; and it exhibits a damping which depends comparatively weakly on the temperature. The point at which the mode frequency reaches minimum with non zero value, according to an extrapolation of the n 2 ŽT . dependence, is 193 " 1 K and thus coincident with the temperature of the sharp change in the spectra. All these results imply that a ferroelectric phase transition of the displacement type with a minor order–disorder one occurs at 193 K in Sn 2 P2 Se 6 . In recording the curves of ´ X ŽT . and ´ Y ŽT ., we observed a thermal hysteresis DT ; 0.5 K at 193 K; the hysteresis suggests that this is a first-order transition. The same conclusion follows from an analysis of the behavior of the soft mode below 193 K: The frequency of this mode changes essentially abruptly near 193 K. There is yet another important point to be noted with regard to the phase transition at 193 K. Judging from the change in the nature of the dielectric dispersion, from resonant to relaxational, at ; 220–193 K, what is happening at 193 K is apparently not a simple phase transition from the paraelectric to the ferroelectric phase. The appearance of relaxational excitations in crystals exhibiting displacive phase transitions is typical of ferroelectric crystals with incommensurate phases. One has observed a similar behavior in the dielectric properties of several other
ferroelectrics Že.g., in thiourea w11x, SCŽNH 2 . 2 .. In the case of Sn 2 P2 Se 6 the transition to the ferroelectric phase at 193 K is preceded by a phase transition ŽT ; 220 K. to a state with a spatially modulated structure, i.e., incommensurate phase. It can be suggested that the soft mode splits into two components of amplitudon and phason, even though neutron scattering present the evidence of amplitudon w4x. An attempt might also be made to interpret the appearance of frequency relaxation in microwave, low frequency, and infrared regions. Measurements of phason in incommensurate phase would appear to be important for a final resolution of dielectric dispersion w12,13x.
References w1x A.V. Gomonnai, A.A. Grabar, Yu.M. Vysochanskii, A.D. Belyaev, V.F. Machulin, M.I. Gurzan, V.Yu. Slivka, Sov. Phys. Solid State 23 Ž1981. 2093. w2x Yu.M. Vysochanskii, V.Yu. Slivka, Sov. Phys. Usp. 35 Ž1992. 123. w3x K. Moriya, H. Kuniyoshi, K. Tashita, Y. Ozaki, S. Yano, T. Matsuo, J. Phys. Soc. Jpn. 69 Ž1998. 525. w4x S.W.H. Eijt, R. Currat, J.E. Lorenzo, P. Saint-Gregoire, S. ´ Katano, T. Janssen, B. Hennion, Yu.M. Vysochanskii, J. Phys.: Condens. Matter 10 Ž1998. 4811. w5x R. Israel, ¨ R. de Gelder, J.M.M. Smits, P.T. Beurskens, S.W.H. Eijt, Th. Rasing, H. van Kempen, M.M. Maior, S.F. Motrija, Z. Kristallogr. 213 Ž1998. 34. w6x Yu.V. Voroshilov, M.N. Potorii, L.A. Seikovskaya, A.V. Yatsenko, I.P. Prits, Kristallografiya 33 Ž1988. 1282. w7x Yu.V. Voroshilov, M.N. Potorii, L.A. Seikovskaya, A.V. Yatsenko, I.P. Prits, Sov. Phys.-Crystallogr. 33 Ž1988. 761. w8x V.M. Rizak, Yu.M. Vysochanskii, A.A. Grabar, V.Yu. Slivka, Sov. Phys. Solid State 31 Ž1990. 1185. w9x A.A. Volkov, G.V. Kozlov, N.I. Afanas’eva, Yu.M. Vysochanskii, A.A. Graber, V.Yu. Slivka, Sov. Phys. Solid State 25 Ž1983. 1482. w10x A.A. Volkov, G.V. Kozlov, S.P. Lebedev, Sov. Phys. JETP 52 Ž1980. 722. w11x A.A. Volkov, Y. Ishibashi, G.V. Kozlov, S.P. Lebedev, J. Petzelt, A.M. Prokhorov, J. Phys. Soc. Jpn., Suppl. 49B Ž1980. 78. w12x J. Ollivier, J. Etrillard, B. Toudic, C. Ecolivet, P. Bourges, A.P. Levanyuk, Phys. Rev. Lett. 81 Ž1998. 3667. w13x M.M. Maior, Yu.M. Vysochanskii, V.P. Bovtun, Yu.M. Poplavko, B.M. Koperles, Sov. Phys. Solid State 27 Ž1985. 765.
Materials Letters 45 Ž2000. 12–14 www.elsevier.comrlocatermatlet
Soft mode behavior in the crystal Sn 2 P2 Se 6 Yung Park ) Department of Materials Science and Metallurgy, UniÕersity of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Received 22 July 1999; accepted 20 January 2000
Abstract A study of the dispersion of the dielectric function in the crystal Sn 2 P2 Se 6 has revealed some new, thermally unstable lattice excitations. These excitations suggest structural phase transitions in Sn 2 P2 Se 6 at 193 K and, possibly, near 220 K. q 2000 Elsevier Science B.V. All rights reserved. PACS: 63.20.Dj; 64.70.Kb; 77.90.q k Keywords: Sn 2 P2 Se 6 ; Lattice excitations; Dielectric functions
In the Sn 2 P2 Se 6 crystal exhibiting proper uniaxial ferroelectrics, an intermediate incommensurate phase exists and two successive phase transitions are observed: the second-order phase transition from a paraelectric phase to a ferroelectric one at Ti s 220 K and the lock-in phase transition of first order from the incommensurate phase to the ferroelectric one at Tc s 193 K w1,2x. In different experiments, Tc features characteristic of transitions of displacive type and of order–disorder ones were observed. This led to controversial conclusions about the character of the phase transitions. The measured values of the entropy of the phase transition are quite high Ž10.0 J P Ky1 moly1 ., which is more typical for order–disorder transitions w3x. The soft mode softening to be observed at frequency n ) 0.5 THz by neutron scattering reveals that the transition is mainly displacive
)
Tel.: q44-1223-334-342; fax: q44-1223-334-567. E-mail address: [email protected] ŽY. Park..
with a minor order–disorder component w4x. It has been well accepted that the pure displacive soft mode behavior presupposes a zero value at a transition point. The changes in the structure between the paraelectric and ferroelectric phases have been well studied for Sn 2 P2 Se 6 by X-ray structure determinations w5– 7x. Throughout the paper, Sn 2 P2 Se 6 has the pseudo˚ b s 7.679 orthorhombic symmetry w8; a s 9.652 A, ˚ c s 6.810 A, ˚ a s g s 908, b s 91.48 at 293 K.. A, The structure includes two wP2 Se 6 x 4y ionic units, each consisting of two trigonal PSe 3 pyramids, rotated about the connecting phosphor pair. The two wP2 Se 6 x 4y units are related by a glide plane Žan a–c plane. in both phases. In the paraelectric phase, the four Sn atoms occupy equivalent general positions and are eight-coordinated with the Se atoms. Upon transition to the ferroelectric phase, the Sn atoms move in phase, approximately along the a-axis Ž0.32 ˚ for Sn ŽI. and 0.28 A˚ for Sn ŽII. and with opposite A ˚ . relative to the rigid phase along the b-axis Ž0.04 A P2 Se 6 groups, destroying the inversion symmetry
00167-577Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X Ž 0 0 . 0 0 0 6 4 - 1
Y. Park r Materials Letters 45 (2000) 12–14
and the twofold axis. The displacements correspond to B u symmetry and result in the appearance of a dielectric polarisation in the a–c plane at an angle of 108 to the a-axis. Recently, Eijt et al. w4x reported the relationship between the lattice dynamics and the phase transition sequence using neutron scattering. In ferroelectric phase, the TO mode Ž Px polarisation. shows a considerable softening as the incommensurate phase approached from below. It is suggested that the combined inelastic line-shapes could all be analysed in the light of a coupled-mode damped harmonic oscillator model. In this letter, we report a study of Sn 2 P2 Se 6 at frequencies in the range 4–23 cmy1 , similar to those of Sn 2 P2 Se 6 in Ref. w9x, by submillimeter dielectric spectroscopy w10. Using an Epsilon-2 backwardwave-tube spectrometer, we recorded the frequency dependence of the real ´ X Ž n . and imaginary ´ Y Ž n . parts of the dielectric function of plane-parallel Sn 2 P2 Se 6 samples over a broad temperature range, from room temperature down to 150 K. The samples were oriented in such a manner that the field E was parallel to the mounting plane Žwe observed no anisotropy of the dielectric properties of the crystal in this plane.. The experimental results are shown in Fig. 1. Some curves of ´ X Ž n . and ´ Y Ž n ., which are easily distinguishable, are shown to illustrate the spectra actually recorded on the spectrometer. Curves 1–11 are numbered in accordance with the monotonic cooling of the crystal. The most important results found from these spectra are as follows. Ži. At frequencies n F 20 cmy1 , there is an intense polar lattice oscillation of a resonance type in Sn 2 P2 Se 6 with all the characteristics of a soft mode: As the temperature is lowered, its frequency Ž; 14 cmy1 at room temperature. falls off in Fig. 1a. Žii. The temperature region near 220 K is a special one for Sn 2 P2 Se 6 : As the crystal is being cooled, it is at these temperatures that the nature of the dielectric dispersion of the crystal begins to change from resonant to relaxational. The effect can be clearly seen in the spectra of Sn 2 P2 Se 6 at frequencies ; 7–10 cmy1 , where the signs of both ´ X and its derivative with respect to the frequency change Žcurves 4–7. in Fig. 1a.
13
Fig. 1. Submillimeter dielectric spectra of Sn 2 P2 Se 6 for various temperatures. Ža. 1 to 7 — 298, 250, 230, 222, 218, 205, and 195 K, and Žb. 7 to 11 — 195, 193, 170, 160, and 150 K, respectively. ´ X and ´ Y correspond to the real and imaginary parts of the dielectric function.
Žiii. At 193 K, the dynamic properties of Sn 2 P2 Se 6 change abruptly Žcurves 7 and 8 in Fig. 1b.. A new high-quality factor absorption line appears at ; 14 cmy1 . Fig. 2 shows the temperature dependence of the characteristics of the soft mode according to leastsquares calculations from the ´ X ŽT . and ´ Y ŽT . spectra in a damped-oscillator model. It is clear from these results that we are dealing with a typical soft ferroelectric mode. The square of its frequency is a linear function of the temperature; the dielectric con-
14
Y. Park r Materials Letters 45 (2000) 12–14
Fig. 2. Characteristics of the soft mode n , G, and D ´ : the frequency, damping, and dielectric contribution, respectively.
tribution D ´ ŽT . exhibits an approximately Curie– Weiss temperature dependence with a constant C s 5.5 = 10 3 K; and it exhibits a damping which depends comparatively weakly on the temperature. The point at which the mode frequency reaches minimum with non zero value, according to an extrapolation of the n 2 ŽT . dependence, is 193 " 1 K and thus coincident with the temperature of the sharp change in the spectra. All these results imply that a ferroelectric phase transition of the displacement type with a minor order–disorder one occurs at 193 K in Sn 2 P2 Se 6 . In recording the curves of ´ X ŽT . and ´ Y ŽT ., we observed a thermal hysteresis DT ; 0.5 K at 193 K; the hysteresis suggests that this is a first-order transition. The same conclusion follows from an analysis of the behavior of the soft mode below 193 K: The frequency of this mode changes essentially abruptly near 193 K. There is yet another important point to be noted with regard to the phase transition at 193 K. Judging from the change in the nature of the dielectric dispersion, from resonant to relaxational, at ; 220–193 K, what is happening at 193 K is apparently not a simple phase transition from the paraelectric to the ferroelectric phase. The appearance of relaxational excitations in crystals exhibiting displacive phase transitions is typical of ferroelectric crystals with incommensurate phases. One has observed a similar behavior in the dielectric properties of several other
ferroelectrics Že.g., in thiourea w11x, SCŽNH 2 . 2 .. In the case of Sn 2 P2 Se 6 the transition to the ferroelectric phase at 193 K is preceded by a phase transition ŽT ; 220 K. to a state with a spatially modulated structure, i.e., incommensurate phase. It can be suggested that the soft mode splits into two components of amplitudon and phason, even though neutron scattering present the evidence of amplitudon w4x. An attempt might also be made to interpret the appearance of frequency relaxation in microwave, low frequency, and infrared regions. Measurements of phason in incommensurate phase would appear to be important for a final resolution of dielectric dispersion w12,13x.
References w1x A.V. Gomonnai, A.A. Grabar, Yu.M. Vysochanskii, A.D. Belyaev, V.F. Machulin, M.I. Gurzan, V.Yu. Slivka, Sov. Phys. Solid State 23 Ž1981. 2093. w2x Yu.M. Vysochanskii, V.Yu. Slivka, Sov. Phys. Usp. 35 Ž1992. 123. w3x K. Moriya, H. Kuniyoshi, K. Tashita, Y. Ozaki, S. Yano, T. Matsuo, J. Phys. Soc. Jpn. 69 Ž1998. 525. w4x S.W.H. Eijt, R. Currat, J.E. Lorenzo, P. Saint-Gregoire, S. ´ Katano, T. Janssen, B. Hennion, Yu.M. Vysochanskii, J. Phys.: Condens. Matter 10 Ž1998. 4811. w5x R. Israel, ¨ R. de Gelder, J.M.M. Smits, P.T. Beurskens, S.W.H. Eijt, Th. Rasing, H. van Kempen, M.M. Maior, S.F. Motrija, Z. Kristallogr. 213 Ž1998. 34. w6x Yu.V. Voroshilov, M.N. Potorii, L.A. Seikovskaya, A.V. Yatsenko, I.P. Prits, Kristallografiya 33 Ž1988. 1282. w7x Yu.V. Voroshilov, M.N. Potorii, L.A. Seikovskaya, A.V. Yatsenko, I.P. Prits, Sov. Phys.-Crystallogr. 33 Ž1988. 761. w8x V.M. Rizak, Yu.M. Vysochanskii, A.A. Grabar, V.Yu. Slivka, Sov. Phys. Solid State 31 Ž1990. 1185. w9x A.A. Volkov, G.V. Kozlov, N.I. Afanas’eva, Yu.M. Vysochanskii, A.A. Graber, V.Yu. Slivka, Sov. Phys. Solid State 25 Ž1983. 1482. w10x A.A. Volkov, G.V. Kozlov, S.P. Lebedev, Sov. Phys. JETP 52 Ž1980. 722. w11x A.A. Volkov, Y. Ishibashi, G.V. Kozlov, S.P. Lebedev, J. Petzelt, A.M. Prokhorov, J. Phys. Soc. Jpn., Suppl. 49B Ž1980. 78. w12x J. Ollivier, J. Etrillard, B. Toudic, C. Ecolivet, P. Bourges, A.P. Levanyuk, Phys. Rev. Lett. 81 Ž1998. 3667. w13x M.M. Maior, Yu.M. Vysochanskii, V.P. Bovtun, Yu.M. Poplavko, B.M. Koperles, Sov. Phys. Solid State 27 Ž1985. 765.