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Successive phase transitions in tetra(isopropylamine)decachlorotricadmate (II) [(CH3)2CH NH3]4Cd3Cl10] crystal – Dielectric and dilatometric studies
Current Applied Physics 12 (2012) 413e417
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Successive phase transitions in tetra(isopropylamine)decachlorotricadmate (II) [(CH3)2CH NH3]4Cd3Cl10] crystal e Dielectric and dilatometric studies B. Staskiewicz a, *, S. Dacko a, Z. Czapla a, b a b
Institute of Experimental Physics, University of Wrocław, M Borna 9, 50-204 Wrocław, Poland Department of Physics, Opole University of Technology, Ozimska 75, 45-271 Opole, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 May 2011 Received in revised form 15 July 2011 Accepted 19 July 2011 Available online 28 July 2011
Single crystal of a new [(CH3)2CHNH3]4Cd3Cl10 compound was grown and its properties have been characterized by dielectric and dilatometric investigations. Dielectric measurement evidenced the phase transitions at T1 ¼ 352.8 K, T2 ¼ 293.5 K and T3 ¼ 261.5 K on cooling run. Dilatometric measurement of thermal expansion showed clearly two successive phase transitions at T1 and at T2. No temperature hysteresis was observed for phase transitions at T1 and T2. Large temperature hysteresis was observed at T3 in dielectric studies. Transitions at T1 and T3 are classified as a first order and at T2 as a continuous one. Anomalies of electric permittivity and expansion connected with the transitions are observed at practically the same temperatures and close to those observed earlier in DSC (Differential Scanning Calorimetry) studies. Results of dilatometric studies were applied to estimate critical coefficient b for continuous phase transition at T1 which is equal to 0.40 0.01. Ó 2011 Elsevier B.V. All rights reserved.
Keywords: Phase transitions Electric permittivity Critical behaviour coefficient Thermal expansion
1. Introduction Organic-inorganic crystals containing different organic cations i.e.: pyridinium [1,2], imidazolium [3,4], dimethylammonium [5e7], tetramethylammonium [8,9] and isopropylammonium [10,11] and inorganic anions exhibit structural phase transitions of various type and they are a subject of numerous investigations [1e15]. The phase transitions mechanism in these crystals is usually connected with cationic units dynamics in the crystal lattice. Interesting crystals were found among complex organicinorganic crystals with cadmium chloride. Some cadmium salts show unusual anionic structure. i.e.: the crystal of the formula [(CH3)2NH2]5Cd3Cl11 where complex anions Cd3Cl11 was found [12]. This crystal exhibits interesting dielectric properties and structural phase transitions [5]. In some crystals infinite chains of cadmium with octahedral coordination are found [9]. There are known crystals with tetramethylammonium cations of the chemical formula [(CH3)4N]CdCl3 [13] and [(CH3)4N]CdBr3 [14] where ferroelastic and ferroelectric phase transitions were observed, respectively. Structural phase transitions are found in a crystal containing isopropylammonium cations and chemical formula [(CH3)2CHNH3]CdCl3 [10]. Recently, a new crystal of chemical formula [(CH3)2CHNH3]4Cd3Cl10 was synthesized and its * Corresponding author. E-mail address: [email protected] (B. Staskiewicz). 1567-1739/$ e see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2011.07.039
structure and phase transitions sequence has been described [15]. The sequence of phase transitions obtained from DSC measurement on cooling run and symmetry of particular phases obtained from X-ray studies are presented below: T1 ¼ 355 K
294 K
260 K
Cmca / Pbca / P21 21 21 / P21 =b I
II
III
IV
The crystal structure is built of two dimensional network of Cd3Cl10 units interconnected by isopropylammonium cations. Taking into account the observed sequence of phase transition we decided to grow the large crystal of the [(CH3)2CHNH3]4Cd3Cl10, study its dielectric properties and expansion in a broad temperature range to get some new detailed characteristics of particular phases and phase transitions. 2. Experimental The single crystals of [(CH3)2CHNH3]4Cd3Cl10 were obtained from saturated water solution containing isopropylamine hydrochloride and cadmium chloride in molar ratio 3:1 by slow evaporation method at constant temperature of 303 K. Dielectric measurements were carried out on platelets about 0.5 mm thick, cut out from a large crystal with the faces perpendicular to the a, b and c crystallographic directions. Silver paste was used as the electrodes. The capacitance of the samples was measured using an HP 4284A precision LCR meter at the frequency of 10 kHz.
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B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
The amplitude of measuring field was 4 V cm1. The measurements were performed on heating/cooling runs at a rate of 0.5 Kmin1. Dilatometric studies were performed by a capacitance quartz dilatometer. The crystal bars of a length of a few mm along the crystallographic directions a, b and c were used for elongation measurement. The capacitance was measured using an HP 4284A precision LCR meter at the frequency of 1000 kHz. Measurement were done at constant cooling/heating rate of 0.1 K/min.
Fig. 1. Temperature dependences of electric permittivity along three crystallographic axes for the [(CH3)2CHNH3]4Cd3Cl10 crystal; insets present the changes of permittivity around 261.5 K (T3).
3. Results and discussion Large and good quality crystals of [(CH3)2CHNH3]4Cd3Cl10 were obtained during about 4 weeks. The shape of the crystal is typical for orthorhombic symmetry. The crystal possesses excellent cleavage plane perpendicular to the b-axis. The results of dielectric studies are presented in Fig. 1. As shown in Fig. 1 on the temperature dependences of permittivity anomalies are observed at T1 ¼ 352.8 K, T2 ¼ 293.5 K and T3 ¼ 261.5 K on cooling. Anomalies are related to structural phase transitions. The behaviour of permittivity is different for particular crystallographic directions. The phase transitions are observed as changes of slope or jumps of permittivity values. The permittivity along the a-axis increases in phase I on cooling and a small jump like increase is observed at T1. In phase II permittivity increases down to T2 with decreasing temperature. At T2 the change of a slope is observed and in phase III permittivity decreases on cooling. The permittivity along the b-axis decreases in all three phases with decreasing temperature. At T1 small jump like decrease and at T2 the change of a slope are observed, respectively. Along the c-axis insignificant decrease of permittivity is observed in phase I and II on cooling. At T1 only a weak change and at T2 the clear change in a slope and next decrease of permittivity are observed in phase III with decreasing temperature. The character of permittivity changes along a- and b-axis is typical for the first order phase transitions at T1. The changes at T2 are characteristic for continuous phase transition along three crystallographic directions. At T3 an abrupt decrease of permittivity appeared along three crystallographic directions and evidenced strong first order transition. In phase IV permittivity decreases on cooling. Temperature hysteresis is not observed at T1 and T2 and also there are no changes of permittivity values. The hysteresis is observed at T3. This temperature of phase transition shifts at heating to about 270 K but the permittivity does not reach the same value as observed in phase III on cooling from phase II. It is connected with strong cracks of the samples after transition IIIeIV and IVeIII. In general the changes of permittivity a rather small but they are seen well at phase transition temperatures and in particular phases. Results of dilatometric measurements as temperature dependences of relative linear expansion Dl/l along three crystallographic axes are presented in Fig. 2. As shown in Fig. 2 Dl/l along the a-axis diminishes in phase I on cooling and at T1 small jump like decrease connected with the first order phase transition takes place. On further cooling nonlinear decrease of Dl/l in phase II is observed down to T2. At this temperature clear change of a slope and in phase III increase of Dl/l is observed with decreasing temperature. Dl/l along the b-axis shows decrease in phase I on cooling and jump like increase at T1. In
Fig. 2. Temperature dependences of relative expansion measured along three crystallographic directions for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
Fig. 3. Temperature dependences of expansion coefficients for three crystallographic directions for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
phase II increase of Dl/l is observed down to T2 with decreasing temperature. At T2 the change of a slope is seen and in phase III elongation diminishes on cooling; Dl/l along the c-axis diminishes in all three phases with decreasing temperature and at T1 and T2 the changes of elongation are extremely weak. Because of strong cracking of the samples connected with the transition at T3 measurements of dilatation were not done around this phase transition temperature. Anomalies of elongation connected with phase transitions are observed at the same temperatures as anomalies of permittivity. The changes of elongation at phase transition confirm the first order phase transition at T1 and continuous at T2. It is interesting to note that along the a-axis increase of permittivity in phases I and II corresponds to decrease of elongation but in phase III decrease of permittivity corresponds to increase of elongation. Jump like increase of permittivity at T1 corresponds to jump like decrease of elongation. Obtained from dilatometric measurement expansion coefficients aa, ab and ac are presented in Fig. 3. As shown in Fig. 3 the aa in negative in phase III and positive in phases II and I; the ab is positive in phase III, negative in phase II and again positive in phase I; the ac is positive in three phases. Anomalies of expansions coefficients are observed at T1 and near T2. Anomalies of elongation and expansion coefficients evidenced first order phase transition at T1 and continuous at T2. The obtained changes of samples dimensions along three crystallographic axes allowed us to calculate the relative changes of the crystal volume. The calculated dependences of relative volume expansion and the volume expansion coefficient av as function of temperature are illustrated in Fig. 4.
Fig. 4. Temperature dependences of relative volume expansion DV/V0 and relative volume expansion coefficient av for the [(CH3)2CNH3]4Cd3Cl10 crystal.
415
Fig. 5. Temperature dependences of relative expansion along the a-axis, expansion and extrapolated dependence of expansionfor the increment dDla/la [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
As it is shown in Fig. 4 the relative volume expansion decreases in all phases. At T1 the jump like decrease of DV/V0 is observed. At T2 clear change in the slope is observed. The coefficient av is positive in all phases and its anomalies are seen well at phase transitions temperatures. To get information related to the critical behaviour of order parameter in the case of continuous phase transition at T2 the following dependences were used:
dDl l
NðTc TÞ2b or
dD V V
NðTc TÞ2b
where dDl/land dDV/V - the increments ofrelative linear expansion, relative volume expansion connected with phase transition and b critical parameter, respectively. As it is shown in Fig. 2 very distinct changes of expansion are found along the a- and b-axes and in phase II and they are nonlinear function of temperature. The expansion increments connected with continuous phase transition at T2 ¼ Tc were obtained as subtraction of the extrapolated dependences of expansion in phase II to phase III from measured values around the phase transition. Results of applied procedure is illustrated in Fig. 5 for a-axis. In this case dDla/la values obtained after subtraction were used directly to obtain the log-log dependence of expansion increment vs. (T2T) presented in Fig. 6. The changes of relative expansion and extrapolated dependences for the b-axis are presented in Fig. 7.
Fig. 6. The logelog dependence of dDla/la vs. (T2T) for the [(CH3)2CNH3]4Cd3Cl10 crystal.
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B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
Fig. 7. Temperature dependences of relative elongation Dlb/lb and extrapolated dependence for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
Fig. 8. Temperature dependences of expansion increment d0 Dlb/lb after subtracting, extrapolated dependence and expansion increment dDlb/lb after subtracting of fluctuation part presented as the “mirror image” for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
Along this direction the character of the dependence is a little different. In some range of temperature above T2 the fluctuation of order parameter is observed and it gives stronger deviation of the dependence in the vicinity of phase transition, in comparison with higher temperature range. Therefore, extrapolated dependence was obtained from experimental one observed at temperature range 300e320 K. The obtained d0 Dlb/lb is presented in Fig. 8.
Fig. 10. Temperature dependences of relative volume expansion DV/V0, extrapolated dependence and expansion increment after subtraction for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
Fig. 11. The logelog dependence of dDV/V0 vs. (T2T) for the [(CH3)2CNH3]4Cd3Cl10 crystal.
In Fig. 8 fluctuation part is seen clearly in phase II. To get more real increment the fluctuation part presented as “mirror image” in phase III is subtracted from d0 Dlb/lb. This difference dDlb/lb is also shown in Fig. 8. The slope of log-log dependences of expansion increment vs. (T2T) for b- axis is presented in Fig. 9. This way of calculation was not done along the c-axis as the changes are much smaller and estimation of dDlc/lc is expected to be burdened with bigger uncertainty. The same procedure applied to the changes of volume expansion is presented in Figs. 10 and 11. The values of the b coefficient obtained from elongation and volume expansion are similar and its average value is equal to 0.40 0.01. Usually the values of the b coefficient obtained in different crystals and different experimental methods ranges in 0.3e0.4 for continuous phase transitions in comparison to theoretical value of 0.5. 4. Summary and conclusions Presented above results one can summarize as follows:
Fig. 9. The logelog dependence of dDlb/lb vs. (T2T) for the [(CH3)2CNH3]4Cd3Cl10 crystal.
1. Detailed dielectric studies showed evidences for the phase transitions of the first order at T1 ¼ 352.8 K and T3 ¼ 261.5 K; continuous phase transitions was found at T2 ¼ 293.5 K. 2. Dilatometric studies confirmed clearly the phase transitions at T1 and T2.
B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
3. The expansions coefficients obtained along three crystallographic directions and expansion volume coefficient showed anomalies at T1 and T2. 4. The results of dilatometric studies were used to estimate the critical coefficient b ¼ 0.4 for continuous phase transition at T2. References [1] P. Czarnecki, W. Nawrocik, Z. Paja˛ k, J. Wa˛ sicki, Phys. Rev. B. 49 (1994) 1511. [2] Z. Czapla, S. Dacko, B. Kosturek, Z. Naturf. A 55 (2000) 891. ska, H. Ma1uszyn ska, Z. Fojud, Phys. Rev. B. 69 [3] Z. Paja˛ k, P. Czarnecki, B. Szafran (2004) 132102. [4] Z. Czapla, S. Dacko, B. Kosturek, A. Waskowska, Phys. Status Solidi B. 242 (2005) R122eR124.
417
[5] Z. Czapla, S. Dacko, U. Krzewska, A. Waskowska, Solid State Commun. 71 (1989) 139. [6] L.J. Kirpichnikova, A. Pietraszko, W. Bednarski, S. Waplak, A.U. Sheleg, Crystallogr. Rep. 49 (2004) 1. [7] Z. Czapla, Yu. Eliyashevskyy, S. Dacko, Ferroelectrics Lett. 33 (2006) 1e6. [8] S. Mulla-Osman, D. Michel, G. Voelkel, Z. Czapla, Phys. Stat. Sol. B. 219 (2000) 9. [9] I. Peral, G. Madariaga, A. Pérez-Etxebarria, T. Breczewski, Acta Cryst. B. 56 (2000) 215e225. [10] U. Krzewska, R. Jakubas, S. Dacko, Z. Czapla, A. Waskowska, Acta Phys. Pol. A 81 (1992) 379. [11] R. Jakubas, G. Bator, P. Cia˛ pa1a, J. Zaleski, J. Baran, J. Lefebvre, J. Phys. Condens. Matter 7 (1995) 5335. [12] A. Waskowska, T. Lis, U. Krzewska, Z. Czapla, Acta Cryst. C 46 (1990) 1768. [13] T. Asahi, K. Hasebe, K. Gesi, Acta Cryst. C 46 (1990) 2252e2253. [14] T. Asahi, K. Hasebe, K. Gesi, Acta Cryst. C 47 (1991) 1208e1211. [15] A. Gagor, A. Waskowska, Z. Czapla, S. Dacko, Acta Cryst. B. 67 (2011) 122e129.
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Successive phase transitions in tetra(isopropylamine)decachlorotricadmate (II) [(CH3)2CH NH3]4Cd3Cl10] crystal e Dielectric and dilatometric studies B. Staskiewicz a, *, S. Dacko a, Z. Czapla a, b a b
Institute of Experimental Physics, University of Wrocław, M Borna 9, 50-204 Wrocław, Poland Department of Physics, Opole University of Technology, Ozimska 75, 45-271 Opole, Poland
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 May 2011 Received in revised form 15 July 2011 Accepted 19 July 2011 Available online 28 July 2011
Single crystal of a new [(CH3)2CHNH3]4Cd3Cl10 compound was grown and its properties have been characterized by dielectric and dilatometric investigations. Dielectric measurement evidenced the phase transitions at T1 ¼ 352.8 K, T2 ¼ 293.5 K and T3 ¼ 261.5 K on cooling run. Dilatometric measurement of thermal expansion showed clearly two successive phase transitions at T1 and at T2. No temperature hysteresis was observed for phase transitions at T1 and T2. Large temperature hysteresis was observed at T3 in dielectric studies. Transitions at T1 and T3 are classified as a first order and at T2 as a continuous one. Anomalies of electric permittivity and expansion connected with the transitions are observed at practically the same temperatures and close to those observed earlier in DSC (Differential Scanning Calorimetry) studies. Results of dilatometric studies were applied to estimate critical coefficient b for continuous phase transition at T1 which is equal to 0.40 0.01. Ó 2011 Elsevier B.V. All rights reserved.
Keywords: Phase transitions Electric permittivity Critical behaviour coefficient Thermal expansion
1. Introduction Organic-inorganic crystals containing different organic cations i.e.: pyridinium [1,2], imidazolium [3,4], dimethylammonium [5e7], tetramethylammonium [8,9] and isopropylammonium [10,11] and inorganic anions exhibit structural phase transitions of various type and they are a subject of numerous investigations [1e15]. The phase transitions mechanism in these crystals is usually connected with cationic units dynamics in the crystal lattice. Interesting crystals were found among complex organicinorganic crystals with cadmium chloride. Some cadmium salts show unusual anionic structure. i.e.: the crystal of the formula [(CH3)2NH2]5Cd3Cl11 where complex anions Cd3Cl11 was found [12]. This crystal exhibits interesting dielectric properties and structural phase transitions [5]. In some crystals infinite chains of cadmium with octahedral coordination are found [9]. There are known crystals with tetramethylammonium cations of the chemical formula [(CH3)4N]CdCl3 [13] and [(CH3)4N]CdBr3 [14] where ferroelastic and ferroelectric phase transitions were observed, respectively. Structural phase transitions are found in a crystal containing isopropylammonium cations and chemical formula [(CH3)2CHNH3]CdCl3 [10]. Recently, a new crystal of chemical formula [(CH3)2CHNH3]4Cd3Cl10 was synthesized and its * Corresponding author. E-mail address: [email protected] (B. Staskiewicz). 1567-1739/$ e see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2011.07.039
structure and phase transitions sequence has been described [15]. The sequence of phase transitions obtained from DSC measurement on cooling run and symmetry of particular phases obtained from X-ray studies are presented below: T1 ¼ 355 K
294 K
260 K
Cmca / Pbca / P21 21 21 / P21 =b I
II
III
IV
The crystal structure is built of two dimensional network of Cd3Cl10 units interconnected by isopropylammonium cations. Taking into account the observed sequence of phase transition we decided to grow the large crystal of the [(CH3)2CHNH3]4Cd3Cl10, study its dielectric properties and expansion in a broad temperature range to get some new detailed characteristics of particular phases and phase transitions. 2. Experimental The single crystals of [(CH3)2CHNH3]4Cd3Cl10 were obtained from saturated water solution containing isopropylamine hydrochloride and cadmium chloride in molar ratio 3:1 by slow evaporation method at constant temperature of 303 K. Dielectric measurements were carried out on platelets about 0.5 mm thick, cut out from a large crystal with the faces perpendicular to the a, b and c crystallographic directions. Silver paste was used as the electrodes. The capacitance of the samples was measured using an HP 4284A precision LCR meter at the frequency of 10 kHz.
414
B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
The amplitude of measuring field was 4 V cm1. The measurements were performed on heating/cooling runs at a rate of 0.5 Kmin1. Dilatometric studies were performed by a capacitance quartz dilatometer. The crystal bars of a length of a few mm along the crystallographic directions a, b and c were used for elongation measurement. The capacitance was measured using an HP 4284A precision LCR meter at the frequency of 1000 kHz. Measurement were done at constant cooling/heating rate of 0.1 K/min.
Fig. 1. Temperature dependences of electric permittivity along three crystallographic axes for the [(CH3)2CHNH3]4Cd3Cl10 crystal; insets present the changes of permittivity around 261.5 K (T3).
3. Results and discussion Large and good quality crystals of [(CH3)2CHNH3]4Cd3Cl10 were obtained during about 4 weeks. The shape of the crystal is typical for orthorhombic symmetry. The crystal possesses excellent cleavage plane perpendicular to the b-axis. The results of dielectric studies are presented in Fig. 1. As shown in Fig. 1 on the temperature dependences of permittivity anomalies are observed at T1 ¼ 352.8 K, T2 ¼ 293.5 K and T3 ¼ 261.5 K on cooling. Anomalies are related to structural phase transitions. The behaviour of permittivity is different for particular crystallographic directions. The phase transitions are observed as changes of slope or jumps of permittivity values. The permittivity along the a-axis increases in phase I on cooling and a small jump like increase is observed at T1. In phase II permittivity increases down to T2 with decreasing temperature. At T2 the change of a slope is observed and in phase III permittivity decreases on cooling. The permittivity along the b-axis decreases in all three phases with decreasing temperature. At T1 small jump like decrease and at T2 the change of a slope are observed, respectively. Along the c-axis insignificant decrease of permittivity is observed in phase I and II on cooling. At T1 only a weak change and at T2 the clear change in a slope and next decrease of permittivity are observed in phase III with decreasing temperature. The character of permittivity changes along a- and b-axis is typical for the first order phase transitions at T1. The changes at T2 are characteristic for continuous phase transition along three crystallographic directions. At T3 an abrupt decrease of permittivity appeared along three crystallographic directions and evidenced strong first order transition. In phase IV permittivity decreases on cooling. Temperature hysteresis is not observed at T1 and T2 and also there are no changes of permittivity values. The hysteresis is observed at T3. This temperature of phase transition shifts at heating to about 270 K but the permittivity does not reach the same value as observed in phase III on cooling from phase II. It is connected with strong cracks of the samples after transition IIIeIV and IVeIII. In general the changes of permittivity a rather small but they are seen well at phase transition temperatures and in particular phases. Results of dilatometric measurements as temperature dependences of relative linear expansion Dl/l along three crystallographic axes are presented in Fig. 2. As shown in Fig. 2 Dl/l along the a-axis diminishes in phase I on cooling and at T1 small jump like decrease connected with the first order phase transition takes place. On further cooling nonlinear decrease of Dl/l in phase II is observed down to T2. At this temperature clear change of a slope and in phase III increase of Dl/l is observed with decreasing temperature. Dl/l along the b-axis shows decrease in phase I on cooling and jump like increase at T1. In
Fig. 2. Temperature dependences of relative expansion measured along three crystallographic directions for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
Fig. 3. Temperature dependences of expansion coefficients for three crystallographic directions for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
phase II increase of Dl/l is observed down to T2 with decreasing temperature. At T2 the change of a slope is seen and in phase III elongation diminishes on cooling; Dl/l along the c-axis diminishes in all three phases with decreasing temperature and at T1 and T2 the changes of elongation are extremely weak. Because of strong cracking of the samples connected with the transition at T3 measurements of dilatation were not done around this phase transition temperature. Anomalies of elongation connected with phase transitions are observed at the same temperatures as anomalies of permittivity. The changes of elongation at phase transition confirm the first order phase transition at T1 and continuous at T2. It is interesting to note that along the a-axis increase of permittivity in phases I and II corresponds to decrease of elongation but in phase III decrease of permittivity corresponds to increase of elongation. Jump like increase of permittivity at T1 corresponds to jump like decrease of elongation. Obtained from dilatometric measurement expansion coefficients aa, ab and ac are presented in Fig. 3. As shown in Fig. 3 the aa in negative in phase III and positive in phases II and I; the ab is positive in phase III, negative in phase II and again positive in phase I; the ac is positive in three phases. Anomalies of expansions coefficients are observed at T1 and near T2. Anomalies of elongation and expansion coefficients evidenced first order phase transition at T1 and continuous at T2. The obtained changes of samples dimensions along three crystallographic axes allowed us to calculate the relative changes of the crystal volume. The calculated dependences of relative volume expansion and the volume expansion coefficient av as function of temperature are illustrated in Fig. 4.
Fig. 4. Temperature dependences of relative volume expansion DV/V0 and relative volume expansion coefficient av for the [(CH3)2CNH3]4Cd3Cl10 crystal.
415
Fig. 5. Temperature dependences of relative expansion along the a-axis, expansion and extrapolated dependence of expansionfor the increment dDla/la [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
As it is shown in Fig. 4 the relative volume expansion decreases in all phases. At T1 the jump like decrease of DV/V0 is observed. At T2 clear change in the slope is observed. The coefficient av is positive in all phases and its anomalies are seen well at phase transitions temperatures. To get information related to the critical behaviour of order parameter in the case of continuous phase transition at T2 the following dependences were used:
dDl l
NðTc TÞ2b or
dD V V
NðTc TÞ2b
where dDl/land dDV/V - the increments ofrelative linear expansion, relative volume expansion connected with phase transition and b critical parameter, respectively. As it is shown in Fig. 2 very distinct changes of expansion are found along the a- and b-axes and in phase II and they are nonlinear function of temperature. The expansion increments connected with continuous phase transition at T2 ¼ Tc were obtained as subtraction of the extrapolated dependences of expansion in phase II to phase III from measured values around the phase transition. Results of applied procedure is illustrated in Fig. 5 for a-axis. In this case dDla/la values obtained after subtraction were used directly to obtain the log-log dependence of expansion increment vs. (T2T) presented in Fig. 6. The changes of relative expansion and extrapolated dependences for the b-axis are presented in Fig. 7.
Fig. 6. The logelog dependence of dDla/la vs. (T2T) for the [(CH3)2CNH3]4Cd3Cl10 crystal.
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B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
Fig. 7. Temperature dependences of relative elongation Dlb/lb and extrapolated dependence for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
Fig. 8. Temperature dependences of expansion increment d0 Dlb/lb after subtracting, extrapolated dependence and expansion increment dDlb/lb after subtracting of fluctuation part presented as the “mirror image” for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
Along this direction the character of the dependence is a little different. In some range of temperature above T2 the fluctuation of order parameter is observed and it gives stronger deviation of the dependence in the vicinity of phase transition, in comparison with higher temperature range. Therefore, extrapolated dependence was obtained from experimental one observed at temperature range 300e320 K. The obtained d0 Dlb/lb is presented in Fig. 8.
Fig. 10. Temperature dependences of relative volume expansion DV/V0, extrapolated dependence and expansion increment after subtraction for the [(CH3)2CHNH3]4Cd3Cl10 crystal (cooling run).
Fig. 11. The logelog dependence of dDV/V0 vs. (T2T) for the [(CH3)2CNH3]4Cd3Cl10 crystal.
In Fig. 8 fluctuation part is seen clearly in phase II. To get more real increment the fluctuation part presented as “mirror image” in phase III is subtracted from d0 Dlb/lb. This difference dDlb/lb is also shown in Fig. 8. The slope of log-log dependences of expansion increment vs. (T2T) for b- axis is presented in Fig. 9. This way of calculation was not done along the c-axis as the changes are much smaller and estimation of dDlc/lc is expected to be burdened with bigger uncertainty. The same procedure applied to the changes of volume expansion is presented in Figs. 10 and 11. The values of the b coefficient obtained from elongation and volume expansion are similar and its average value is equal to 0.40 0.01. Usually the values of the b coefficient obtained in different crystals and different experimental methods ranges in 0.3e0.4 for continuous phase transitions in comparison to theoretical value of 0.5. 4. Summary and conclusions Presented above results one can summarize as follows:
Fig. 9. The logelog dependence of dDlb/lb vs. (T2T) for the [(CH3)2CNH3]4Cd3Cl10 crystal.
1. Detailed dielectric studies showed evidences for the phase transitions of the first order at T1 ¼ 352.8 K and T3 ¼ 261.5 K; continuous phase transitions was found at T2 ¼ 293.5 K. 2. Dilatometric studies confirmed clearly the phase transitions at T1 and T2.
B. Staskiewicz et al. / Current Applied Physics 12 (2012) 413e417
3. The expansions coefficients obtained along three crystallographic directions and expansion volume coefficient showed anomalies at T1 and T2. 4. The results of dilatometric studies were used to estimate the critical coefficient b ¼ 0.4 for continuous phase transition at T2. References [1] P. Czarnecki, W. Nawrocik, Z. Paja˛ k, J. Wa˛ sicki, Phys. Rev. B. 49 (1994) 1511. [2] Z. Czapla, S. Dacko, B. Kosturek, Z. Naturf. A 55 (2000) 891. ska, H. Ma1uszyn ska, Z. Fojud, Phys. Rev. B. 69 [3] Z. Paja˛ k, P. Czarnecki, B. Szafran (2004) 132102. [4] Z. Czapla, S. Dacko, B. Kosturek, A. Waskowska, Phys. Status Solidi B. 242 (2005) R122eR124.
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