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Sequence of structural phase transitions of CsInF4 crystal
Solid State Communications 129 (2004) 539–543 www.elsevier.com/locate/ssc
Sequence of structural phase transitions of CsInF4 crystal C.W.A. Paschoala,*, A.P. Ayalab, I. Guedesb, R.L. Moreirac, J.-Y. Geslandd a
Departamento de Fı´sica, CCET, Universidade Federal do Maranha˜o, Sa˜o Luis, 65085-580 Maranha˜o, Brazil b Departamento de Fı´sica, Universidade Federal do Ceara´, C.P. 6030, 60455-760 Fortaleza, Ceara´, Brazil c Departamento de Fı´sica, ICEx, Universidade Federal de Minas Gerais, C. P. 702, 30161-970 Belo Horizonte, Minas Gerais, Brazil d Universite´ du Maine-Cristalloge´ne`se, UMR 807, 72085 Le Mans CEDEX 9, France Received 21 April 2003; received in revised form 21 October 2003; accepted 7 November 2003 by A. Pinczuk
Abstract In this work we employ calorimetric and dielectric techniques to study the sequence of structural phase transitions (SPTs) of CsInF4 crystal in the temperature range from 450 to 250 K. Our results show three first-order SPTs. Based on these results and on direct interferometric observation of the domain patterns, we discuss the elastic state of CsInF4 phases. q 2004 Elsevier Ltd. All rights reserved. PACS: 77.80.Bh; 77.22. 2 d Keywords: A. CsInF4; D. Phase transitions
1. Introduction The layered compounds AþM3þF4, where Aþ is usually an alkaline ion and M3þ a metallic ion, have been extensively studied in the last years [1 –12]. The main interest in these materials is that they have a bidimensional layered structure and exhibit several structural phase transitions (SPTs) [3]. According to Bulou [3], all members of this family have an aristotype structure, although for some compounds this structure is virtual. The observed SPTs are in general of displacive character, due to MF6 octahedra tiltings. This is the case for RbAlF4 [4], TlAlF4 [5], RbFeF4 [6], CsScF4 [7] and RbVF4 [8], among others. Two exceptions are: (NH4)AlF4, that exhibits an order– disorder SPT at 150 K [9]; and KAlF4, which exhibits a martensitic SPT at around 250 K [10]. Most of these materials have one of two basic layered aristotype structures 1. The ideal tetragonal D14h ðP4=mmmÞ structure, which was * Corresponding author. Tel.: þ55-98-2178291; fax: þ 55-982178201. E-mail address: [email protected] (C.W.A. Paschoal). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.11.013
first described by Brosset for TlAlF4 [1]. In this structure, MF6 octahedra are centered in a square-based parallelepiped, with Aþ ions at the corners; the octahedra are linked to each other in the (001) plane and disconnected along the [00l] axis, giving rise to the appearance of MF6 octahedra sheets in the (00l) planes. 2. The orthorhombic D17 2h ðBmmbÞ structure exhibited by KFeF4 [2]. This structure is similar to the previous one, but the layers of octahedra are now displaced by half of a basic translation perpendicular to the c-axis; parallel to either a or b-axis: In these compounds, MF6 octahedra play an important role in driving the mechanism of the SPTs, as they do in typical perovskites. This fact has led some authors to label these compounds as layered perovskites. A consequence of this layered structure is the presence of cleavage planes, perpendicular to the c-axis: Besides CsScF4, three other CsM3þF4 crystals have been studied, namely, CsVF4 [11], CsFeF4 [12] and CsInF4 [13]. Although there exists a good set of data characterizing the other crystals, as far as we know the only information available on the sequence of SPTs undergone by CsInF4 was reported by Laurat [13]. From differential scanning calorimetry (DSC) measurements, Laurat showed that
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C.W.A. Paschoal et al. / Solid State Communications 129 (2004) 539–543
CsInF4 exhibits two SPTs in the temperature range from 300 to 407 K. He also used electron paramagnetic resonance (EPR) spectra to get information on the possible crystal system for each phase. By comparing the EPR spectra with those obtained for similar crystals, he proposed the following symmetries for the observed phases: (i) phase I ðT . 403 KÞ is tetragonal belonging to the point group D4h ; (ii) phase II ð374 , T , 403 KÞ is also tetragonal ðD4h Þ; and (iii) phase III ð300 , T , 374 KÞ is orthorhombic belonging to the space group D13 2h ðPmmnÞ with Z ¼ 4: The aim of this work is to present a more complete description of the sequence of SPTs of CsInF4 in the temperature range between 250 and 450 K using several techniques. In addition, direct interferometric measurement and observation of ferroelastic domain patterns is used to discuss the ferroelastic characteristics of the CsInF4 phases.
2. Experimental Large transparent and colorless crystals of CsInF4 were grown using the Czochralski method by melting CsF and InF3 in an argon/CF4/HF atmosphere. The crystals melt congruently at 880 ^ 20 8C. Thermal measurements were performed with a Mettler (TA10-DSC30) apparatus, at linear rates of 10 K/min with controlled flux of nitrogen, in the range of 250– 450 K. Typical sample weights were 50 mg. For dielectric measurements, plates of CsInF4 were oriented and cut perpendicular to the principal axes [001] and [100] of the room temperature structure. Typical samples for measurements perpendicular to the [001] axis were plates of 5 £ 6 £ 1 mm3. Cutting thin plates in a plane containing the c-axis is very difficult, since there are cleavage planes perpendicular to it. Thus, along this axis, the samples were plates of 5 £ 6 £ 3 mm3. Silver paste electrodes were used to connect the samples to the holders in a controlled cryostat-furnace under nitrogen atmosphere. A HP4192A impedance analyzer was used to carry out measurements at 50 kHz under continuous linear heating and cooling rates of 2 K/min, between 250 and 450 K. Interference on ferroelastic domain walls was performed using a JDS Uniphase Helium – Neon gas laser, model 15070. The interference patterns were projected onto a blank screen and collected with a VCR digital camera. The observations of ferroelastic domains were performed using a polarizing microscope. The samples, with dimensions of 5 £ 5 £ 0.5 mm3, were put inside a cryostat or a furnace between crossed polarizers. The photographs of domains and interference patterns were taken in the (001) plane and acquired through a digital video board.
3. Results and discussion Fig. 1 shows DSC thermograms of CsInF4, where three
Fig. 1. DSC thermograms presenting the SPTs undergone by CsInF4.
enthalpic reversible peaks are observed at around 280, 373 and 412 K on cooling and 284, 383 and 415 K on heating. The critical temperatures determined from the onset of the enthalpic peaks, which are insensitive to the scan rate used [14], and the transition enthalpy are shown in Table 1. These results indicate that CsInF4 undergoes three SPTs in the temperature range investigated. The observation of enthalpic peaks as well as the hysteresis in the transition temperatures suggests that these SPTs are of first order. Note the presence of an additional anomaly at 430 K on cooling, but absent on heating: since other experimental techniques show no phase transition at this temperature, this anomaly is probably due to instabilities in the cooling. According to Ref. [15], the ratio DS=Rln 2; where DS is the entropy jump and Rln 2 is the number of ferroic states per mol, indicates the nature of the SPT: DS=Rln 2 , 1 indicates an order – disorder SPT; DS=Rln 2 # 0:1 indicates a displacive SPT. For values between 0.1 and 1, the SPT is said to have a mixed displacive/order –disorder character. The last column of Table 1 shows the DS=Rln 2 obtained from Fig. 1, suggesting that the last two SPTs (373 and 412 K) have a displacive character, while the first (280 K) has a mixed character. The displacive character of the hightemperature SPTs agrees well with results for other layered perovskites [4 –8]. According to Laurat [13] and using the Glazer– Bulou notation [4,5,16], the octahedral tiltings Table 1 Calorimetric data obtained for CsInF4: transition temperatures, enthalpy and entropy jumps of the three SPT’s Transition
TIV!III TIII!II TII!I
T (K) Cooling
Heating
280 373 412
284 383 415
H (J/g)
DS=Rln 2
1.47 0.083 0.40
0.29 0.01 0.05
C.W.A. Paschoal et al. / Solid State Communications 129 (2004) 539–543
driving the SPTs follow the path: a oa oc 2 for phase I and þ þ aþ p bp c for phase III. The tilting system for phase II remains undetermined. The sequence of SPTs was verified by measuring the dielectric permittivities along the c-axis; e 33 ; and perpendicular to the c-axis; e 11 ; at 50 kHz. Fig. 2(a) and (b) show the temperature dependence of the real part of dielectric permittivities e 033 and e 011 ; respectively. Fig. 2(a) shows three jumps at 277, 371 and 404 K on cooling, and at 281, 378 and 407 K on heating. However, Fig. 2(b) shows only jumps at 280 and 370 K on heating. The abrupt jumps indicate that CsInF4 indeed undergoes three first-order phase transitions. Laurat [13] proposes that the room temperature phase (Phase III) belongs to the D2h point group, while the two high temperature phases belong to the same point group D4h : In a non-ferroic phase transition the translational symmetry is broken without changing the point symmetry [17,18], which is the case for SPT I-II. On the other hand, SPT II-III corresponds to one of the 94 pure ferroelastic species studied by Aizu [19] and Toledano and Toledano [20]. Although no crystallographic data are yet available for the phases of CsInF4, Laurat’s proposal on their symmetry can be investigated, at least for the point group symmetry, by looking for ferroelastic domains. In a paraelastic phase no domain walls are expected to be observed. If a ferroic
Fig. 2. Real part of dielectric permittivity, e 0 ; of CsInF4as a function of temperature. Measurements were performed at 50 kHz along the (a) c-axis and (b) a-axis: The cooling and heating runs in (a) are indicated by the arrows.
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(paraelastic to ferroelastic) transition takes place, domain walls should be observed. In order to look for ferroelastic domains we investigated the interference of laser light propagating along the c-axis from domain walls. Light diffracts from domain walls when the domain size is smaller than the illuminated region. Fig. 3 shows the interference patterns observed in each phase. Only phase III shows a cross-shaped diffraction pattern. The other phases show just a single point (the laser spot accompanied by speckle points), indicating that no diffraction has occurred. These results are consistent with Laurat’s proposal: if phase I is tetragonal with symmetry D4h ; which is a paraelastic point group, no domain should be observed; if the crystal remains in a paraelastic phase after SPT I-II, no domains should be formed, the point group is preserved and therefore the SPT is non-ferroic; and if phase III is orthorhombic with symmetry D2h ; domains should indeed be observed. Note that the interference patterns of Fig. 3(c) are oriented at 458 with respect to the crystalline axes of the high temperature phase. According to Sapriel [21], the orientation of the domain walls is determined by the symmetries of both ferro and para-elastic phases. The SPT II-III is ferroic of the type 4/mmmFmmm(p), where F denotes the symmetry operation connecting both strain states of ferroelastic phase, and p, denotes that the orientation of the highest symmetry axis is invariant under the phase transformation. Following the results of Ref. [21], one can conclude that the domain walls should be along the x ^ y directions. These lines correspond to the planes ðx þ yÞz and ðx 2 yÞz which are the sd symmetry planes of the tetragonal D4h phase, lost after the phase transition takes place.
Fig. 3. Interference patterns obtained at various temperatures: (a) 420 K, (b) 390 K, (c) 300 K and (d) 270 K. The laser propagates along the c-axis:
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Fig. 4. Images of polarized optical microscopy performed at various temperatures: (a) 420 K, (b) 390 K, (c) 300 K and (d) 270 K.
The domain pattern of each phase observed by polarizing microscopy is shown in Fig. 4. The tetragonal c-axis is perpendicular to the plane of the photographs. As in Fig. 3, domain patterns are observed only in phase III (Fig. 4(c)), where the domain walls are indeed oriented at 458 with respect to the x and y-axes of the tetragonal phase. Unfortunately, no information on the symmetry of phase IV is available. If the orientation of the highest symmetry axis of phase III is maintained, one could say that SPT IIIIV, it is also ferroic, since no domains are observed. We have recently investigated the III – IV transition using Raman spectroscopy [22]. We identified the changes in the phonon spectrum, but were unable to obtain information on the point symmetry of phase IV. X-ray measurements are being carried out and the results will be reported soon.
4. Conclusions Thermal, dielectric and interferometric investigations of CsInF4 single crystals were performed. Thermal and dielectric measurements show three first order SPTs. The SPTs occurring at 412 and 373 K (on cooling) are of displacive character, while the SPT at around 280 K is of a mixed displacive and order– disorder character. Measurements of domain-walls interference patterns were used to investigate Laurat’s proposal for the point symmetry of phases I, II and III. Since a ferroic phase transition changes the elastic state of a given system, our results together with the theoretical predictions made by Sapriel [21] and Aizu [19], are consistent with Laurat’s proposal. The path of phase transformations followed by CsInF4 is very similar to
other crystals belonging to this family, and is drawn in the following diagram.
Acknowledgements This work was partially supported by the Brazilian (CNPq, FINEP, FUNCAP and FAPEMIG) and French (CNRS) funding agencies. Advice and helpful discussions with Dr J. Mendes Filho are gratefully acknowledged, and we thank Dr A. Donegan for a critical reading of the manuscript.
References [1] C. Brosset, Z. Anorg. Allg. Chem. 235 (1937) 139 –147. [2] G. Heger, R. Geller, D. Babel, Solid State Commun. 9 (1971) 335 –340. [3] A. Bulou, Transitions de phases structurales et dynamique du reseau des tetrafluoroaluminates bidimensionnels AAlF4 (A ¼ Rb, Tl, K, NH4), PhD Thesis, Universite´ Pierre et Marie Curie; Paris VI, 1985. [4] A. Bulou, J. Nouet, J. Phys. C: Solid State 15 (1982) 183–196. [5] A. Bulou, J. Nouet, J. Phys. C: Solid State 20 (1987) 2885–2900.
C.W.A. Paschoal et al. / Solid State Communications 129 (2004) 539–543 [6] M.C. Mo´ron, A. Bulou, C. Pique, J.L. Fourquet, J. Phys.: Condens. Matter 2 (1990) 8269–8275. [7] K.S. Aleksandrov, V.N. Voronov, A.I. Kruglik, S.B. Mel’nikovaand, I.N. Flerov, Sov. Phys. Solid State 30 (1988) 1911–1913. [8] M. Hidaka, K. Inoue, B.J. Garrard, B.M. Wanklyn, Phys. Status Solidi A 72 (1982) 809 –816. [9] A. Leble´, J.J. Rousseau, J.C. Fayet, J.L. Fourquet, R. de Pape, Ferroelectrics 36 (1981) 323– 326. [10] J.M. Launay, A. Bulou, A.W. Hewat, A. Gibaud, J.Y. Laval, J. Nouet, J. Phys. 46 (1985) 771–782. [11] M. Hidaka, H. Fujii, B.J. Garrard, B.M. Wanklyn, Phys. Status Solidi A 96 (1986) 415–423. [12] M. Hidaka, H. Fujii, B.J. Garrard, B.M. Wanklyn, Phys. Status Solidi A 95 (1986) 413–421. [13] P. Laurat, Phenomenes critiques des transitions structurales des perovskites en couches AMF4: influences des anisotropies
[14]
[15] [16] [17] [18] [19] [20] [21] [22]
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et de la structure en couches, PhD Thesis, Universite´ du Maine; 1996. G.W.H. Ho¨hne, W. Hemminger, H.-J. Flammersheim, Differential Scanning Calorimetry: An Introduction for Practioners, Springer, Berlin, 1996. B.A. Strukov, A.P. Levanyuk, Ferroelectric Phenomena in Crystals: Physical Foundations, Springer, New York, 1997. A.M. Glazer, Acta Crystallogr., Sect. A 31 (1975) 756 –762. J.C. Toledano, P. Toledano, The Landau Theory of Phase Transitions, World Scientific, Singapore, 1987. P. Toledano, J.C. Toledano, Phys. Rev. B 25 (1982) 1946–1964. K. Aizu, Phys. Rev. B 2 (1970) 754–772. J.C. Toledano, P. Toledano, Phys. Rev. B 21 (1980) 1139–1172. J. Sapriel, Phys. Rev. B 12 (1975) 5128–5140. C.W.A. Paschoal, A.P. Ayala, I. Guedes, J.-Y. Gesland, Solid State Commun. 122 (2002) 549–551.
Sequence of structural phase transitions of CsInF4 crystal C.W.A. Paschoala,*, A.P. Ayalab, I. Guedesb, R.L. Moreirac, J.-Y. Geslandd a
Departamento de Fı´sica, CCET, Universidade Federal do Maranha˜o, Sa˜o Luis, 65085-580 Maranha˜o, Brazil b Departamento de Fı´sica, Universidade Federal do Ceara´, C.P. 6030, 60455-760 Fortaleza, Ceara´, Brazil c Departamento de Fı´sica, ICEx, Universidade Federal de Minas Gerais, C. P. 702, 30161-970 Belo Horizonte, Minas Gerais, Brazil d Universite´ du Maine-Cristalloge´ne`se, UMR 807, 72085 Le Mans CEDEX 9, France Received 21 April 2003; received in revised form 21 October 2003; accepted 7 November 2003 by A. Pinczuk
Abstract In this work we employ calorimetric and dielectric techniques to study the sequence of structural phase transitions (SPTs) of CsInF4 crystal in the temperature range from 450 to 250 K. Our results show three first-order SPTs. Based on these results and on direct interferometric observation of the domain patterns, we discuss the elastic state of CsInF4 phases. q 2004 Elsevier Ltd. All rights reserved. PACS: 77.80.Bh; 77.22. 2 d Keywords: A. CsInF4; D. Phase transitions
1. Introduction The layered compounds AþM3þF4, where Aþ is usually an alkaline ion and M3þ a metallic ion, have been extensively studied in the last years [1 –12]. The main interest in these materials is that they have a bidimensional layered structure and exhibit several structural phase transitions (SPTs) [3]. According to Bulou [3], all members of this family have an aristotype structure, although for some compounds this structure is virtual. The observed SPTs are in general of displacive character, due to MF6 octahedra tiltings. This is the case for RbAlF4 [4], TlAlF4 [5], RbFeF4 [6], CsScF4 [7] and RbVF4 [8], among others. Two exceptions are: (NH4)AlF4, that exhibits an order– disorder SPT at 150 K [9]; and KAlF4, which exhibits a martensitic SPT at around 250 K [10]. Most of these materials have one of two basic layered aristotype structures 1. The ideal tetragonal D14h ðP4=mmmÞ structure, which was * Corresponding author. Tel.: þ55-98-2178291; fax: þ 55-982178201. E-mail address: [email protected] (C.W.A. Paschoal). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.11.013
first described by Brosset for TlAlF4 [1]. In this structure, MF6 octahedra are centered in a square-based parallelepiped, with Aþ ions at the corners; the octahedra are linked to each other in the (001) plane and disconnected along the [00l] axis, giving rise to the appearance of MF6 octahedra sheets in the (00l) planes. 2. The orthorhombic D17 2h ðBmmbÞ structure exhibited by KFeF4 [2]. This structure is similar to the previous one, but the layers of octahedra are now displaced by half of a basic translation perpendicular to the c-axis; parallel to either a or b-axis: In these compounds, MF6 octahedra play an important role in driving the mechanism of the SPTs, as they do in typical perovskites. This fact has led some authors to label these compounds as layered perovskites. A consequence of this layered structure is the presence of cleavage planes, perpendicular to the c-axis: Besides CsScF4, three other CsM3þF4 crystals have been studied, namely, CsVF4 [11], CsFeF4 [12] and CsInF4 [13]. Although there exists a good set of data characterizing the other crystals, as far as we know the only information available on the sequence of SPTs undergone by CsInF4 was reported by Laurat [13]. From differential scanning calorimetry (DSC) measurements, Laurat showed that
540
C.W.A. Paschoal et al. / Solid State Communications 129 (2004) 539–543
CsInF4 exhibits two SPTs in the temperature range from 300 to 407 K. He also used electron paramagnetic resonance (EPR) spectra to get information on the possible crystal system for each phase. By comparing the EPR spectra with those obtained for similar crystals, he proposed the following symmetries for the observed phases: (i) phase I ðT . 403 KÞ is tetragonal belonging to the point group D4h ; (ii) phase II ð374 , T , 403 KÞ is also tetragonal ðD4h Þ; and (iii) phase III ð300 , T , 374 KÞ is orthorhombic belonging to the space group D13 2h ðPmmnÞ with Z ¼ 4: The aim of this work is to present a more complete description of the sequence of SPTs of CsInF4 in the temperature range between 250 and 450 K using several techniques. In addition, direct interferometric measurement and observation of ferroelastic domain patterns is used to discuss the ferroelastic characteristics of the CsInF4 phases.
2. Experimental Large transparent and colorless crystals of CsInF4 were grown using the Czochralski method by melting CsF and InF3 in an argon/CF4/HF atmosphere. The crystals melt congruently at 880 ^ 20 8C. Thermal measurements were performed with a Mettler (TA10-DSC30) apparatus, at linear rates of 10 K/min with controlled flux of nitrogen, in the range of 250– 450 K. Typical sample weights were 50 mg. For dielectric measurements, plates of CsInF4 were oriented and cut perpendicular to the principal axes [001] and [100] of the room temperature structure. Typical samples for measurements perpendicular to the [001] axis were plates of 5 £ 6 £ 1 mm3. Cutting thin plates in a plane containing the c-axis is very difficult, since there are cleavage planes perpendicular to it. Thus, along this axis, the samples were plates of 5 £ 6 £ 3 mm3. Silver paste electrodes were used to connect the samples to the holders in a controlled cryostat-furnace under nitrogen atmosphere. A HP4192A impedance analyzer was used to carry out measurements at 50 kHz under continuous linear heating and cooling rates of 2 K/min, between 250 and 450 K. Interference on ferroelastic domain walls was performed using a JDS Uniphase Helium – Neon gas laser, model 15070. The interference patterns were projected onto a blank screen and collected with a VCR digital camera. The observations of ferroelastic domains were performed using a polarizing microscope. The samples, with dimensions of 5 £ 5 £ 0.5 mm3, were put inside a cryostat or a furnace between crossed polarizers. The photographs of domains and interference patterns were taken in the (001) plane and acquired through a digital video board.
3. Results and discussion Fig. 1 shows DSC thermograms of CsInF4, where three
Fig. 1. DSC thermograms presenting the SPTs undergone by CsInF4.
enthalpic reversible peaks are observed at around 280, 373 and 412 K on cooling and 284, 383 and 415 K on heating. The critical temperatures determined from the onset of the enthalpic peaks, which are insensitive to the scan rate used [14], and the transition enthalpy are shown in Table 1. These results indicate that CsInF4 undergoes three SPTs in the temperature range investigated. The observation of enthalpic peaks as well as the hysteresis in the transition temperatures suggests that these SPTs are of first order. Note the presence of an additional anomaly at 430 K on cooling, but absent on heating: since other experimental techniques show no phase transition at this temperature, this anomaly is probably due to instabilities in the cooling. According to Ref. [15], the ratio DS=Rln 2; where DS is the entropy jump and Rln 2 is the number of ferroic states per mol, indicates the nature of the SPT: DS=Rln 2 , 1 indicates an order – disorder SPT; DS=Rln 2 # 0:1 indicates a displacive SPT. For values between 0.1 and 1, the SPT is said to have a mixed displacive/order –disorder character. The last column of Table 1 shows the DS=Rln 2 obtained from Fig. 1, suggesting that the last two SPTs (373 and 412 K) have a displacive character, while the first (280 K) has a mixed character. The displacive character of the hightemperature SPTs agrees well with results for other layered perovskites [4 –8]. According to Laurat [13] and using the Glazer– Bulou notation [4,5,16], the octahedral tiltings Table 1 Calorimetric data obtained for CsInF4: transition temperatures, enthalpy and entropy jumps of the three SPT’s Transition
TIV!III TIII!II TII!I
T (K) Cooling
Heating
280 373 412
284 383 415
H (J/g)
DS=Rln 2
1.47 0.083 0.40
0.29 0.01 0.05
C.W.A. Paschoal et al. / Solid State Communications 129 (2004) 539–543
driving the SPTs follow the path: a oa oc 2 for phase I and þ þ aþ p bp c for phase III. The tilting system for phase II remains undetermined. The sequence of SPTs was verified by measuring the dielectric permittivities along the c-axis; e 33 ; and perpendicular to the c-axis; e 11 ; at 50 kHz. Fig. 2(a) and (b) show the temperature dependence of the real part of dielectric permittivities e 033 and e 011 ; respectively. Fig. 2(a) shows three jumps at 277, 371 and 404 K on cooling, and at 281, 378 and 407 K on heating. However, Fig. 2(b) shows only jumps at 280 and 370 K on heating. The abrupt jumps indicate that CsInF4 indeed undergoes three first-order phase transitions. Laurat [13] proposes that the room temperature phase (Phase III) belongs to the D2h point group, while the two high temperature phases belong to the same point group D4h : In a non-ferroic phase transition the translational symmetry is broken without changing the point symmetry [17,18], which is the case for SPT I-II. On the other hand, SPT II-III corresponds to one of the 94 pure ferroelastic species studied by Aizu [19] and Toledano and Toledano [20]. Although no crystallographic data are yet available for the phases of CsInF4, Laurat’s proposal on their symmetry can be investigated, at least for the point group symmetry, by looking for ferroelastic domains. In a paraelastic phase no domain walls are expected to be observed. If a ferroic
Fig. 2. Real part of dielectric permittivity, e 0 ; of CsInF4as a function of temperature. Measurements were performed at 50 kHz along the (a) c-axis and (b) a-axis: The cooling and heating runs in (a) are indicated by the arrows.
541
(paraelastic to ferroelastic) transition takes place, domain walls should be observed. In order to look for ferroelastic domains we investigated the interference of laser light propagating along the c-axis from domain walls. Light diffracts from domain walls when the domain size is smaller than the illuminated region. Fig. 3 shows the interference patterns observed in each phase. Only phase III shows a cross-shaped diffraction pattern. The other phases show just a single point (the laser spot accompanied by speckle points), indicating that no diffraction has occurred. These results are consistent with Laurat’s proposal: if phase I is tetragonal with symmetry D4h ; which is a paraelastic point group, no domain should be observed; if the crystal remains in a paraelastic phase after SPT I-II, no domains should be formed, the point group is preserved and therefore the SPT is non-ferroic; and if phase III is orthorhombic with symmetry D2h ; domains should indeed be observed. Note that the interference patterns of Fig. 3(c) are oriented at 458 with respect to the crystalline axes of the high temperature phase. According to Sapriel [21], the orientation of the domain walls is determined by the symmetries of both ferro and para-elastic phases. The SPT II-III is ferroic of the type 4/mmmFmmm(p), where F denotes the symmetry operation connecting both strain states of ferroelastic phase, and p, denotes that the orientation of the highest symmetry axis is invariant under the phase transformation. Following the results of Ref. [21], one can conclude that the domain walls should be along the x ^ y directions. These lines correspond to the planes ðx þ yÞz and ðx 2 yÞz which are the sd symmetry planes of the tetragonal D4h phase, lost after the phase transition takes place.
Fig. 3. Interference patterns obtained at various temperatures: (a) 420 K, (b) 390 K, (c) 300 K and (d) 270 K. The laser propagates along the c-axis:
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Fig. 4. Images of polarized optical microscopy performed at various temperatures: (a) 420 K, (b) 390 K, (c) 300 K and (d) 270 K.
The domain pattern of each phase observed by polarizing microscopy is shown in Fig. 4. The tetragonal c-axis is perpendicular to the plane of the photographs. As in Fig. 3, domain patterns are observed only in phase III (Fig. 4(c)), where the domain walls are indeed oriented at 458 with respect to the x and y-axes of the tetragonal phase. Unfortunately, no information on the symmetry of phase IV is available. If the orientation of the highest symmetry axis of phase III is maintained, one could say that SPT IIIIV, it is also ferroic, since no domains are observed. We have recently investigated the III – IV transition using Raman spectroscopy [22]. We identified the changes in the phonon spectrum, but were unable to obtain information on the point symmetry of phase IV. X-ray measurements are being carried out and the results will be reported soon.
4. Conclusions Thermal, dielectric and interferometric investigations of CsInF4 single crystals were performed. Thermal and dielectric measurements show three first order SPTs. The SPTs occurring at 412 and 373 K (on cooling) are of displacive character, while the SPT at around 280 K is of a mixed displacive and order– disorder character. Measurements of domain-walls interference patterns were used to investigate Laurat’s proposal for the point symmetry of phases I, II and III. Since a ferroic phase transition changes the elastic state of a given system, our results together with the theoretical predictions made by Sapriel [21] and Aizu [19], are consistent with Laurat’s proposal. The path of phase transformations followed by CsInF4 is very similar to
other crystals belonging to this family, and is drawn in the following diagram.
Acknowledgements This work was partially supported by the Brazilian (CNPq, FINEP, FUNCAP and FAPEMIG) and French (CNRS) funding agencies. Advice and helpful discussions with Dr J. Mendes Filho are gratefully acknowledged, and we thank Dr A. Donegan for a critical reading of the manuscript.
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