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EPR study of the low temperature ferroelectric phase transition in Cu2+ doped Rb2ZnCl4 single crystals
Solid State Communications 127 (2003) 695–698 www.elsevier.com/locate/ssc
EPR study of the low temperature ferroelectric phase transition in Cu2þ doped Rb2ZnCl4 single crystals Mariana Stefana,b,*, Sergiu V. Nistora,b, Dirk Schoemakerb, Ioan Ursuc a
National Institute for Materials Physics, Laboratory 190, P.O. Box MG-7 Magurele, Bucuresti RO-77125, Romania b Physics Department, University of Antwerp (UIA), B-2610 Antwerp, Wilrijk, Belgium c Romanian Academy, Calea Victoriei no.125, Bucuresti, Romania Received 18 June 2003; accepted 18 July 2003 by D.E. Van Dyck
Abstract Temperature dependent EPR measurements on copper doped Rb2ZnCl4 single crystals allowed us to evidence and study the P21 cn $ C1c1 structural phase transition that takes place in this compound at 74.6 K. From the two types of Cu2þ centers localized at different anionic sites, called Cu2þ(I) and Cu2þ(II), which are formed in this compound, only the Cu2þ(II) centers exhibit observable changes in their EPR spectra, attributable to the symmetry lowering. The observed changes have been related to the soft-mode responsible for the structural phase transition. q 2003 Elsevier Ltd. All rights reserved. PACS: 76.30.Fc; 77.80.Bh Keywords: A. Ferroelectrics; D. Phase transitions; E. Electron paramagnetic resonance; C. Point defects
1. Introduction Previous electron paramagnetic resonance (EPR) and optical experiments carried out on copper doped Rb2ZnCl4 single crystals revealed the presence of two Cu2þ centers, differing in concentration, production properties and localization [1]. The Cu2þ(I) centers, found in higher concentration, consist of Cu2þ ions localized substitutionally at Zn2þ sites. In the case of the lower concentration Cu2þ(II) centers, the Cu2þ ions substitute the Rbþ ions, with electric charge compensation at distance. The EPR spectra of both types of centers were observed up to 135 K, in a temperature range corresponding to the two low temperature ferroelectric phases of Rb2ZnCl4, namely P21 cn and C1c1 [2]. The P21 cn symmetry phase, occurring between 192 and 74.6 K, is characterized by the tripling of the unit cell along the c axis with respect to the paraelectric
Pmcn phase. Below TM ¼ 74:6 K; in the monoclinic C1c1 phase, the unit cell is further doubled along the a and b axes. The literature data about this phase are very scarce, and, to our knowledge, only one EPR study of the P21 cn $ C1c1 structural phase transition (SPT), using the Tl2þ and Tl0 centers as paramagnetic probes [3] has been reported so far. The different localization of the two types of copper centers brings into focus the possibility to obtain complementary information about the SPT mechanism and related lattice dynamics. This work presents an evaluation of the two copper centers’ sensitivities to the local crystal field variation induced by the P21 cn $ C1c1 phase transition, as well as the actual information concerning the microscopic phase transition mechanism that could be extracted from their EPR spectra.
2. Experimental * Corresponding author. Address: National Institute for Materials Physics, Laboratory 190, P.O. Box MG-7 Magurele, Bucuresti RO77125, Romania. Tel.: þ 40-21-493-0047; fax: þ40-21-493-0267. E-mail address: [email protected] (M. Stefan). 0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0038-1098(03)00649-5
The copper doped Rb2ZnCl4 single crystals used in our experiments were grown from the melt by the Czochralski method, as described in Refs. [1,4]. In order to increase the
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M. Stefan et al. / Solid State Communications 127 (2003) 695–698
concentration of the Cu2þ centers, the samples were further X-ray irradiated (50 mA, 50 kV, W-cathode) at room temperature. The EPR measurements were performed in the 140– 2.5 K temperature range, on an X-band Bruker ESP-300E spectrometer, equipped with a continuous-flow cryostat (Oxford ESR910). Due to the large, uncontrollable temperature gradient present in such a cooling system, the temperature was measured in two points, above and below the sample, using two Chromel – AuFe (0.07%) thermocouples. For such measurements we used a specially built sample holder, with a thermocouple fixed at 1 cm above the sample’s center and its reference junction kept in liquid nitrogen. The other thermocouple, which was part of the variable temperature system, did measure the temperature in the cold helium flow path, at about 1 cm below the sample. The experimental temperature was determined as the average of the two measured temperatures, with an estimated accuracy of ^1.5 degrees.
3. Results and discussion The EPR spectra of the two copper centers, which have been recorded for the magnetic field rotated in the three (ab), (bc) and (ca) main crystal planes, were clearly separated only for the magnetic field parallel to the a and b crystalline axes [1]. Along any other direction a clear identification of the lines belonging to the lower intensity Cu2þ(II) centers was practically impossible due to the strong overlap of the two spectra. The spectra of both centers along the a direction consist of single broad lines [1] which do not exhibit any change attributable to the SPT. On the other hand, the spectra measured along the b direction exhibited clear differences in the two low temperature phases. Fig. 1 shows several EPR spectra measured along the b axis, at various temperatures in the two structural phases. The selected temperatures correspond to significant changes in the EPR spectra. The Cu2þ(I) spectrum consists of a single broad line, which does not exhibit any difference in the two structural phases, neither in the line position nor in the linewidth. Apparently, for these centers, the SPT induced changes in the local environment are very small and probably buried in the large linewidth. In the case of the Cu2þ(II) centers, the spectrum in the P21 cn phase consists of four hyperfine lines of equal intensity, with a separation of , 4.3 mT and constant equal linewidths (, 2.2 mT) up to 90 K. Below 50 K, in the C1c1 phase, the Cu2þ(II) spectrum exhibits a five components structure with an intensity ratio of 1:2:2:2:1, having the same separation and linewidths as in the P21 cn phase. This five components structure seems to arise from the overlap of the spectra of two distinct Cu2þ(II)-like centers, induced by the symmetry decrease in the C1c1 phase.
Fig. 1. Temperature variation of the Cu2þ(I) and Cu2þ(II) EPR spectra in the two low temperature ferroelectric phases of Rb2ZnCl4, for the magnetic field orientated along the b crystal axis. The intensity of the spectra recorded at various temperatures was adjusted in order to present similar amplitudes in the figure.
The change from the four components structure to the five components one takes place continuously as the temperature decreases in the C1c1 phase. A similar behavior has been previously observed for the EPR spectra of Tl0 centers in Rb2ZnCl4 [3]. The continuous variation with the temperature of the Tl0 spectra in the C1c1 phase was associated to a dynamic process related to the lattice modes. Fig. 2 shows the experimental spectra measured at 76, 63 and 44 K, chosen to exemplify the four lines, intermediate and five lines structures, respectively, of the Cu2þ(II) spectra. The simulations of these spectra, calculated [5] in the hypothesis of the presence of two Cu2þ(II) centers in the C1c1 phase, are also displayed with dotted lines. The simulation of the Cu2þ(I) spectrum was made with the effective g ¼ 2:3094 and A ¼ 2:72 mT parameters values, resulted by projecting the spin-Hamiltonian parameters (Table 1 from Ref. [1]) on the b direction. The spectrum was considered to arise from four Gaussian-shaped components, each with a 6 mT linewidth. For the Cu2þ(II)-like spectra, the simulations were carried out with a hyperfine splitting value A ¼ 4:26 mT determined from the early reported (Table 1 from Ref. [1]) spin-Hamiltonian parameters and the following effective gvalues; as determined from the corresponding experimental spectra presented in Fig. 2: (a) g ¼ 2:177; (b) g1 ¼ 2:184; g2 ¼ 2:171 and (c) g1 ¼ 2:185; g2 ¼ 2:159; respectively.
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Fig. 3. Temperature dependence of the Dg difference of the effective g1 and g2 -values of the two Cu2þ(II)-type centers, measured along the b crystalline axis in the C1c1 phase of Rb2ZnCl4. Dotted line: the result of the fitting with formula (1) and the parameters given in the text. Inset: the temperature dependence of the effective g1 and g2 values.
fitted to the expression [7]: kPðtÞlðTÞ ¼ P0 Fig. 2. Experimental (continuous line) and simulated (dotted line) EPR spectra of the Cu2þ(I) and Cu2þ(II) centers, measured along the b crystalline axis, at significant temperatures in the ferroelectric phases of Rb2ZnCl4: (a) T ¼ 76 K; in the P21 cn phase; (b) T ¼ 63 K and (c) T ¼ 44 K in the C1c1 phase. The hyperfine transitions of the two Cu2þ(II)-type of centers are marked in the figure.
The hyperfine component lines of the Cu2þ(II) spectra were considered to be each Gaussian-shaped, with a constant 2.2 mT linewidth. The resulting simulated spectra (Fig. 2) show that the model of two inequivalent Cu2þ(II) centers gives an accurate description of the observed EPR spectra. Moreover, the analysis of the experimental spectra at other temperatures in the C1c1 phase shows that the pattern of the Cu2þ(II) spectra can be reasonably well reproduced by changing only the effective g-values of the inequivalent centers. The difference Dg ¼ g1 2 g2 of the effective g-values; which decreases continuously with increasing temperature, reaching the value zero at TM ; can thus be taken as an observable for the description of the phase transition. Fig. 3 shows the temperature dependence of Dg in the C1c1 phase. The calculated g1 and g2 -values at different temperatures are also given in the inset. The steep decrease of the Dg observable near the transition temperature can be attributed to the influence of the lattice modes [6] that soften at TM : Using a simple model for the soft-mode dispersion, v2q ðTÞ ¼ aðTc 2 TÞg þ b2 q2 ; where a and b are material constants, g is the critical exponent and q is the soft-mode wave vector, the temperature dependence of Dg could be
"
lT 2 Tc lg=2 21 C tan þ P1 T 1 2 C lT 2 Tc lg=2
# ð1Þ
Here P stands for Dg £ 102 ; P0 is a term related to the static distribution of the ligands and the second term gives the soft-mode induced temperature dependence, with C ¼ ða=b1=2 ÞQ; where Q is the Brillouin zone cut-off. The transition temperature was fixed at the Tc ¼ 74 K value and the mean field value g ¼ 1 was taken for the critical exponent. Due to the high experimental errors in determining the transition fields close to the transition temperature, the value of g in the critical region could not be determined with a higher accuracy by directly fitting the experimental data. The resulting fitting parameters are: P0 ¼ 3:19 ^ 0:14; P1 ¼ 20:05 ^ 0:02 K21 and C ¼ 9:68 ^ 1:49; the fitting curve being shown in Fig. 3 with dotted line. It should be mentioned that the value of the resulting material constant C is of the same order of magnitude as the one determined for the thallium centers [3]. The errors involved in the evaluation of the Dg values and the approximations used in this very simple soft-mode model impose a limit on the amount of information about the phase transition mechanism. However, several important conclusions can be drawn from these results: Firstly, our study reveals the importance of the localization of the paramagnetic centers in the crystal lattice in monitoring the SPT. The different sensitivities of the Cu2þ(I) and Cu2þ(II) centers to the P21 cn $ C1c1 transition can be explained by their different position in the crystal lattice, in the Zn2þ and Rbþ sites, respectively. As known from structural data [8], the ZnCl4 tetrahedra behave like rigid bodies at the transition, being rotated but not
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deformed. Consequently, the effects of these rotations on the EPR parameters can be enough small to be covered by the large linewidth of the Cu2þ(I) spectrum. On the other hand, the rotations and translations of the ZnCl4 tetrahedra at the phase transition determine important modifications in the local crystalline field at the Rbþ sites, by changing the relative Rbþ—neighboring Cl2 distances. These stronger effects are reflected in the observation of different EPR spectra from the Cu2þ(II) centers in the two low temperature phases. Secondly, the presence of the two inequivalent Cu2þ(II) centers in the C1c1 phase corresponds to the unit cell doubling along the b direction. The continuous variation with temperature of their spectra in this structural phase allowed us to evidence the soft-mode mechanism of the P21 cn $ C1c1 phase transition.
Acknowledgements This work was performed in the frame of the bilateral
Flemish-Romanian scientific research project BIL 00/72, with support from the CERES scientific project no. 31/2001 of the Romanian Ministry of Education and Research.
References [1] M. Stefan, S.V. Nistor, N.M. Grecu, D. Schoemaker, Phys. Status Solidi B 202 (1997) 999. [2] H.Z. Cummins, Phys. Rep. 185 (1990) 211. [3] M. Stefan, S.V. Nistor, D. Schoemaker, Rad. Eff. Def. Sol. 157 (2002) 695. [4] M. Stefan, S.V. Nistor, D.C. Mateescu, A.M. Abakumov, J. Cryst. Growth 200 (1999) 148. [5] Computer Program EPRNMR, Department of Chemistry, University of Saskatchewan, Canada, 1996. [6] M. Wada, A. Sawada, Y. Ishibashi, J. Phys. Soc. Jpn 50 (1981) 531. [7] N.M. Grecu, V.V. Grecu, F.F. Popescu, Ferroelectrics 20 (1978) 239. [8] M. Quilichini, J. Pannetier, Acta Crystallogr., Sect. B 39 (1983) 657.
EPR study of the low temperature ferroelectric phase transition in Cu2þ doped Rb2ZnCl4 single crystals Mariana Stefana,b,*, Sergiu V. Nistora,b, Dirk Schoemakerb, Ioan Ursuc a
National Institute for Materials Physics, Laboratory 190, P.O. Box MG-7 Magurele, Bucuresti RO-77125, Romania b Physics Department, University of Antwerp (UIA), B-2610 Antwerp, Wilrijk, Belgium c Romanian Academy, Calea Victoriei no.125, Bucuresti, Romania Received 18 June 2003; accepted 18 July 2003 by D.E. Van Dyck
Abstract Temperature dependent EPR measurements on copper doped Rb2ZnCl4 single crystals allowed us to evidence and study the P21 cn $ C1c1 structural phase transition that takes place in this compound at 74.6 K. From the two types of Cu2þ centers localized at different anionic sites, called Cu2þ(I) and Cu2þ(II), which are formed in this compound, only the Cu2þ(II) centers exhibit observable changes in their EPR spectra, attributable to the symmetry lowering. The observed changes have been related to the soft-mode responsible for the structural phase transition. q 2003 Elsevier Ltd. All rights reserved. PACS: 76.30.Fc; 77.80.Bh Keywords: A. Ferroelectrics; D. Phase transitions; E. Electron paramagnetic resonance; C. Point defects
1. Introduction Previous electron paramagnetic resonance (EPR) and optical experiments carried out on copper doped Rb2ZnCl4 single crystals revealed the presence of two Cu2þ centers, differing in concentration, production properties and localization [1]. The Cu2þ(I) centers, found in higher concentration, consist of Cu2þ ions localized substitutionally at Zn2þ sites. In the case of the lower concentration Cu2þ(II) centers, the Cu2þ ions substitute the Rbþ ions, with electric charge compensation at distance. The EPR spectra of both types of centers were observed up to 135 K, in a temperature range corresponding to the two low temperature ferroelectric phases of Rb2ZnCl4, namely P21 cn and C1c1 [2]. The P21 cn symmetry phase, occurring between 192 and 74.6 K, is characterized by the tripling of the unit cell along the c axis with respect to the paraelectric
Pmcn phase. Below TM ¼ 74:6 K; in the monoclinic C1c1 phase, the unit cell is further doubled along the a and b axes. The literature data about this phase are very scarce, and, to our knowledge, only one EPR study of the P21 cn $ C1c1 structural phase transition (SPT), using the Tl2þ and Tl0 centers as paramagnetic probes [3] has been reported so far. The different localization of the two types of copper centers brings into focus the possibility to obtain complementary information about the SPT mechanism and related lattice dynamics. This work presents an evaluation of the two copper centers’ sensitivities to the local crystal field variation induced by the P21 cn $ C1c1 phase transition, as well as the actual information concerning the microscopic phase transition mechanism that could be extracted from their EPR spectra.
2. Experimental * Corresponding author. Address: National Institute for Materials Physics, Laboratory 190, P.O. Box MG-7 Magurele, Bucuresti RO77125, Romania. Tel.: þ 40-21-493-0047; fax: þ40-21-493-0267. E-mail address: [email protected] (M. Stefan). 0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0038-1098(03)00649-5
The copper doped Rb2ZnCl4 single crystals used in our experiments were grown from the melt by the Czochralski method, as described in Refs. [1,4]. In order to increase the
696
M. Stefan et al. / Solid State Communications 127 (2003) 695–698
concentration of the Cu2þ centers, the samples were further X-ray irradiated (50 mA, 50 kV, W-cathode) at room temperature. The EPR measurements were performed in the 140– 2.5 K temperature range, on an X-band Bruker ESP-300E spectrometer, equipped with a continuous-flow cryostat (Oxford ESR910). Due to the large, uncontrollable temperature gradient present in such a cooling system, the temperature was measured in two points, above and below the sample, using two Chromel – AuFe (0.07%) thermocouples. For such measurements we used a specially built sample holder, with a thermocouple fixed at 1 cm above the sample’s center and its reference junction kept in liquid nitrogen. The other thermocouple, which was part of the variable temperature system, did measure the temperature in the cold helium flow path, at about 1 cm below the sample. The experimental temperature was determined as the average of the two measured temperatures, with an estimated accuracy of ^1.5 degrees.
3. Results and discussion The EPR spectra of the two copper centers, which have been recorded for the magnetic field rotated in the three (ab), (bc) and (ca) main crystal planes, were clearly separated only for the magnetic field parallel to the a and b crystalline axes [1]. Along any other direction a clear identification of the lines belonging to the lower intensity Cu2þ(II) centers was practically impossible due to the strong overlap of the two spectra. The spectra of both centers along the a direction consist of single broad lines [1] which do not exhibit any change attributable to the SPT. On the other hand, the spectra measured along the b direction exhibited clear differences in the two low temperature phases. Fig. 1 shows several EPR spectra measured along the b axis, at various temperatures in the two structural phases. The selected temperatures correspond to significant changes in the EPR spectra. The Cu2þ(I) spectrum consists of a single broad line, which does not exhibit any difference in the two structural phases, neither in the line position nor in the linewidth. Apparently, for these centers, the SPT induced changes in the local environment are very small and probably buried in the large linewidth. In the case of the Cu2þ(II) centers, the spectrum in the P21 cn phase consists of four hyperfine lines of equal intensity, with a separation of , 4.3 mT and constant equal linewidths (, 2.2 mT) up to 90 K. Below 50 K, in the C1c1 phase, the Cu2þ(II) spectrum exhibits a five components structure with an intensity ratio of 1:2:2:2:1, having the same separation and linewidths as in the P21 cn phase. This five components structure seems to arise from the overlap of the spectra of two distinct Cu2þ(II)-like centers, induced by the symmetry decrease in the C1c1 phase.
Fig. 1. Temperature variation of the Cu2þ(I) and Cu2þ(II) EPR spectra in the two low temperature ferroelectric phases of Rb2ZnCl4, for the magnetic field orientated along the b crystal axis. The intensity of the spectra recorded at various temperatures was adjusted in order to present similar amplitudes in the figure.
The change from the four components structure to the five components one takes place continuously as the temperature decreases in the C1c1 phase. A similar behavior has been previously observed for the EPR spectra of Tl0 centers in Rb2ZnCl4 [3]. The continuous variation with the temperature of the Tl0 spectra in the C1c1 phase was associated to a dynamic process related to the lattice modes. Fig. 2 shows the experimental spectra measured at 76, 63 and 44 K, chosen to exemplify the four lines, intermediate and five lines structures, respectively, of the Cu2þ(II) spectra. The simulations of these spectra, calculated [5] in the hypothesis of the presence of two Cu2þ(II) centers in the C1c1 phase, are also displayed with dotted lines. The simulation of the Cu2þ(I) spectrum was made with the effective g ¼ 2:3094 and A ¼ 2:72 mT parameters values, resulted by projecting the spin-Hamiltonian parameters (Table 1 from Ref. [1]) on the b direction. The spectrum was considered to arise from four Gaussian-shaped components, each with a 6 mT linewidth. For the Cu2þ(II)-like spectra, the simulations were carried out with a hyperfine splitting value A ¼ 4:26 mT determined from the early reported (Table 1 from Ref. [1]) spin-Hamiltonian parameters and the following effective gvalues; as determined from the corresponding experimental spectra presented in Fig. 2: (a) g ¼ 2:177; (b) g1 ¼ 2:184; g2 ¼ 2:171 and (c) g1 ¼ 2:185; g2 ¼ 2:159; respectively.
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Fig. 3. Temperature dependence of the Dg difference of the effective g1 and g2 -values of the two Cu2þ(II)-type centers, measured along the b crystalline axis in the C1c1 phase of Rb2ZnCl4. Dotted line: the result of the fitting with formula (1) and the parameters given in the text. Inset: the temperature dependence of the effective g1 and g2 values.
fitted to the expression [7]: kPðtÞlðTÞ ¼ P0 Fig. 2. Experimental (continuous line) and simulated (dotted line) EPR spectra of the Cu2þ(I) and Cu2þ(II) centers, measured along the b crystalline axis, at significant temperatures in the ferroelectric phases of Rb2ZnCl4: (a) T ¼ 76 K; in the P21 cn phase; (b) T ¼ 63 K and (c) T ¼ 44 K in the C1c1 phase. The hyperfine transitions of the two Cu2þ(II)-type of centers are marked in the figure.
The hyperfine component lines of the Cu2þ(II) spectra were considered to be each Gaussian-shaped, with a constant 2.2 mT linewidth. The resulting simulated spectra (Fig. 2) show that the model of two inequivalent Cu2þ(II) centers gives an accurate description of the observed EPR spectra. Moreover, the analysis of the experimental spectra at other temperatures in the C1c1 phase shows that the pattern of the Cu2þ(II) spectra can be reasonably well reproduced by changing only the effective g-values of the inequivalent centers. The difference Dg ¼ g1 2 g2 of the effective g-values; which decreases continuously with increasing temperature, reaching the value zero at TM ; can thus be taken as an observable for the description of the phase transition. Fig. 3 shows the temperature dependence of Dg in the C1c1 phase. The calculated g1 and g2 -values at different temperatures are also given in the inset. The steep decrease of the Dg observable near the transition temperature can be attributed to the influence of the lattice modes [6] that soften at TM : Using a simple model for the soft-mode dispersion, v2q ðTÞ ¼ aðTc 2 TÞg þ b2 q2 ; where a and b are material constants, g is the critical exponent and q is the soft-mode wave vector, the temperature dependence of Dg could be
"
lT 2 Tc lg=2 21 C tan þ P1 T 1 2 C lT 2 Tc lg=2
# ð1Þ
Here P stands for Dg £ 102 ; P0 is a term related to the static distribution of the ligands and the second term gives the soft-mode induced temperature dependence, with C ¼ ða=b1=2 ÞQ; where Q is the Brillouin zone cut-off. The transition temperature was fixed at the Tc ¼ 74 K value and the mean field value g ¼ 1 was taken for the critical exponent. Due to the high experimental errors in determining the transition fields close to the transition temperature, the value of g in the critical region could not be determined with a higher accuracy by directly fitting the experimental data. The resulting fitting parameters are: P0 ¼ 3:19 ^ 0:14; P1 ¼ 20:05 ^ 0:02 K21 and C ¼ 9:68 ^ 1:49; the fitting curve being shown in Fig. 3 with dotted line. It should be mentioned that the value of the resulting material constant C is of the same order of magnitude as the one determined for the thallium centers [3]. The errors involved in the evaluation of the Dg values and the approximations used in this very simple soft-mode model impose a limit on the amount of information about the phase transition mechanism. However, several important conclusions can be drawn from these results: Firstly, our study reveals the importance of the localization of the paramagnetic centers in the crystal lattice in monitoring the SPT. The different sensitivities of the Cu2þ(I) and Cu2þ(II) centers to the P21 cn $ C1c1 transition can be explained by their different position in the crystal lattice, in the Zn2þ and Rbþ sites, respectively. As known from structural data [8], the ZnCl4 tetrahedra behave like rigid bodies at the transition, being rotated but not
698
M. Stefan et al. / Solid State Communications 127 (2003) 695–698
deformed. Consequently, the effects of these rotations on the EPR parameters can be enough small to be covered by the large linewidth of the Cu2þ(I) spectrum. On the other hand, the rotations and translations of the ZnCl4 tetrahedra at the phase transition determine important modifications in the local crystalline field at the Rbþ sites, by changing the relative Rbþ—neighboring Cl2 distances. These stronger effects are reflected in the observation of different EPR spectra from the Cu2þ(II) centers in the two low temperature phases. Secondly, the presence of the two inequivalent Cu2þ(II) centers in the C1c1 phase corresponds to the unit cell doubling along the b direction. The continuous variation with temperature of their spectra in this structural phase allowed us to evidence the soft-mode mechanism of the P21 cn $ C1c1 phase transition.
Acknowledgements This work was performed in the frame of the bilateral
Flemish-Romanian scientific research project BIL 00/72, with support from the CERES scientific project no. 31/2001 of the Romanian Ministry of Education and Research.
References [1] M. Stefan, S.V. Nistor, N.M. Grecu, D. Schoemaker, Phys. Status Solidi B 202 (1997) 999. [2] H.Z. Cummins, Phys. Rep. 185 (1990) 211. [3] M. Stefan, S.V. Nistor, D. Schoemaker, Rad. Eff. Def. Sol. 157 (2002) 695. [4] M. Stefan, S.V. Nistor, D.C. Mateescu, A.M. Abakumov, J. Cryst. Growth 200 (1999) 148. [5] Computer Program EPRNMR, Department of Chemistry, University of Saskatchewan, Canada, 1996. [6] M. Wada, A. Sawada, Y. Ishibashi, J. Phys. Soc. Jpn 50 (1981) 531. [7] N.M. Grecu, V.V. Grecu, F.F. Popescu, Ferroelectrics 20 (1978) 239. [8] M. Quilichini, J. Pannetier, Acta Crystallogr., Sect. B 39 (1983) 657.