Ferroelastic phase transition and twin structure by 133 Cs NMR in a CsPbCl 3 single crystal

Transcription

1 Physica B 304 (2001) Ferroelastic phase transition and twin structure by 133 Cs NMR in a CsPbCl 3 single crystal Ae Ran Lim a, *, Se-Young Jeong b a Department of Physics, Jeonju University, Jeonju , South Korea b Department of Physics, Pusan National University, Pusan , South Korea Received 18 August 2000; received in revised form 20 December 2000; accepted 23 January 2001 Abstract The temperature dependence of the 133 Cs nuclear magnetic resonance (NMR) in a ferroelastic CsPbCl 3 single crystal has been investigated using a FT NMR spectrometer. The rotation patterns of the 133 Cs NMR spectra were obtained in three mutually perpendicular planes under an applied magnetic field of 9.4 T. Two sets of seven-line structures were obtained instead of a simple seven-line structure of the 133 Cs(I= 7 2 ) nucleus in CsPbCl 3 crystal. From these results, the NMR parameters were obtained. These showed the same magnitudes of quadrupole coupling constants and asymmetry parameters for resonance lines of the two sets, but with different orientations. It is known that two different orientations in phases II IV occurred in ferroelastic domains. The domain wall makes an angle of 458 with respect to the [1 0 0] axis in phases II IV. At the transition point of 478C, one signal from the 133 Cs resonance line indicates that a phase transition takes place to a new phase with higher symmetry than tetragonal. There is no EFG tensor at the Cs site in phase I. The parameters obtained from the 133 Cs NMR spectra were based on the occurrence of first-order phase transitions at 378C and 478C, and a second-order phase transition at 428C. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Ferroelectrics (ferroelastics); Crystal growth; Phase transitions; Nuclear resonances; Twin structure 1. Introduction The phase transitions in CsPbCl 3 were first reported by Moller in 1959 [1]. The CsPbCl 3 single crystal undergoes three successive structural phase transitions at 478C, 428C, and 378C. From the high temperature cubic phase (phase I), it transforms to phase II, tetragonal, then to phase III, orthorhombic, and finally to phase IV, monoclinic *Corresponding author. Tel.: ; fax: address: aeranlim@hanmail.net (A.R. Lim). [2 5]. The structural phase transitions of CsPbCl 3 are attributed to changes in the orientations of PbCl 6 octahedra [6]. The three structural phase transitions between 478C and 378C, from a hightemperature cubic phase to a monoclinic phase, are ferroelastic phase transitions. The results of experimental investigations such as X-ray diffraction [7], neutron scattering [8], EPR [9,10], nuclear magnetic resonance (NMR) [11], optical property [12,13], and sound velocity [14] have been reported for the CsPbCl 3 single crystal. Domains occur in all ferroelastic crystals as a result of the reduction in symmetry between the /01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S (01)

2 80 A.R. Lim, S.-Y. Jeong / Physica B 304 (2001) high- and low-temperature phases [15,16]. The loss of symmetry elements in the cubic prototypic phase results in a very complicated domain structure in the room temperature monoclinic phase. CsPbCl 3 belongs to the m3mf2/m(p) species and has 12 domains and 45 domain walls at room temperature, making it one of the most complicated ferroelastic species. The ferroelasticity of the CsPbCl 3 crystal was investigated by Chabin and Gilletta [17,18]. The domains present at room temperature remain unchanged up to 478C, at which point the crystal structure becomes cubic [2]. The twin configuration can easily be changed by mechanical stress and the crystal can be transformed to a single domain state by external stress. The ferroelastic character of CsPbCl 3 crystals was established by direct observation using a transmission electron microscope [18], optical polarizing microscope [19], and stress strain hysteresis [20]. Our present work reports on the temperature dependence of the 133 Cs NMR in CsPbCl 3 single crystals grown by the Bridgman method. The temperature dependence of the quadrupole coupling constant, the asymmetry parameter, and the direction of the principal axes of the electric field gradient (EFG) tensor of 133 Cs(I= 7 2 ) in CsPbCl 3 single crystals were determined by experimental data obtained with a pulse NMR spectrometer. Also, we examine the twin structure of 133 Cs NMR in ferroelastic CsPbCl 3 crystals. Based on these results, we discuss the phase transition and the ferroelastic property of a CsPbCl 3 crystal. 2. Crystal structure The CsPbCl 3 single crystal undergoes a firstorder phase transition at T C =478C, a secondorder phase transition at T C =428C and another first-order phase transition at T C =378C. This crystal has the ideal cubic perovskite structure with space group Pm3 m O 1 h in phase I. The lattice constants are a=b=c=5.605 A. ( Phase II is tetragonal with space group P4/mbm D 5 4h. Phase III is orthorhombic with space group Cmcm (D 17 2h) and the unit cell volume is octupled with eight formula units of CsPbCl 3. The space group of phase IV is P2 1 /m (C 2 2h) and the monoclinic unit cell contains four formula units of CsPbCl 3. The crystal structures in phases II IV are shown in Fig. 1. The lattice constants in phase IV are a=7.993 A, ( b= A, ( c=7.803 A ( and b= When the Pbions are placed on the z=0 plane, the Cs ions drawn with closed and open circles, are placed on the z=1/4a and z= 1/4a planes, respectively [21]. 3. Experimental procedure Single crystals of CsPbCl 3 were grown by melting a mixture of CsCl and PbCl 2 powders using the Bridgman method. At room temperature, the crystal is pale yellow in color and transluscent. The crystal shows a clear cleavage parallel to the original cubic (1 0 0) plane. The Fig. 1. Projections of the structure of CsPbCl 3 along the [0 0 1] plane at each phases.

3 A.R. Lim, S.-Y. Jeong / Physica B 304 (2001) orientations of the crystal were identified using an optical polarizing microscope. The angular dependences of the NMR spectra were measured on the crystallographic ab-, bc-, and ca-planes, respectively. Nuclear magnetic resonance signals of 133 Cs in the CsPbCl 3 single crystal were measured using a Bruker DSX 400 FT NMR spectroscopy at the Korea Basic Science Institute in Taejon. The static magnetic field was 9.4 T and the central RF frequency was set at o o =2p= MHz. The NMR spectra of 133 Cs were recorded with a sequence of one 908 pulse, 8192 scans, and a pulse width of 0.5 ms. A ring-down delay time of 3 ms was used to remove the effect of the pulse. The temperature-dependent NMR measurements were taken by the previously reported method [22]. 4. Results and analysis The Hamiltonian for NMR used to analyze the experimental results was the general equation H ¼ H Z þ H Q ; ð1þ where H Z is the nuclear Zeeman term and H Q describes the nuclear quadrupole interaction of the 133 Cs nucleus, which has the nuclear spin I= 7 2 with 100% natural abundance. The Zeeman interaction is given by [23 25] H Z ¼ g n b n B I; ð2þ where g n is the nuclear g-factor, b n is the nuclear magneton, B is the magnetic field and I is the nuclear spin. The quadrupole Hamiltonian in the principal axis system of the electric field gradient tensor is described by H Q ¼ e 2 qq=4ið2i 1Þ 3IZ 2 IIþ ð 1 Þþ 1 2 Z I þ 2 þ I 2 ; ð3þ where e 2 qq=h is the quadrupole coupling constant and Z is the asymmetry parameter. The conventional X, Y, and Z axes are such that jv XX j4 jv YY j4jv ZZ j ¼ eq; then 04Z41. The matrix form of the spin Hamiltonian of Eq. (3) is employed to calculate the resonance fields with the magnetic field applied along a general direction. All resonance spectra and parameters were calculated by numerically diagonalizing the matrix using a computer program. Rotation patterns in three mutually perpendicular directions are required to determine the quadrupole interaction completely. The rotation patterns of the 133 Cs NMR spectra measured in the crystallographic planes at room temperature are displayed in Fig. 2. The satellite lines show the angular dependence of 3 cos 2 y 1, where the polar angle y is the direction of the magnetic field with respect to the c-axis, whereas the central line is angle independent. Fig. 2 shows interchanged ab-, bc-, and ca-planes for one set of crystals and ba-, ac-, and cb-planes for the other. Notably, when the external magnetic field is applied along the c-axis, the two sets of resonance lines coincide with one set of domains. Because the resonance field of the central line is almost constant and the spacings between adjacent lines are equal, the first-order perturbation of H Q with respect to H Z should be sufficient for analysis [23]. From these results, the nuclear quadrupole coupling constant and asymmetry parameter for the two groups of 133 Cs nucleus in a CsPbCl 3 crystal were observed, with the same magnitude at room temperature; the quadrupole coupling constant, e 2 qq=h=207 khz and the asymmetry parameter, Z=0.38, were determined at room temperature. The maximum separation resulting from quadrupole interaction was observed when the magnetic field was applied along the b-axis of the crystal. This direction is found by analysis to be the Z-axis of the EFG tensor. The direction of the principal EFG tensor of the 133 Cs nucleus is parallel to the crystallographic c-, a-, and b-axes of CsPbCl 3 crystal. The EFG tensor for the two Cs ions was found to be related through a rotation of 908 around the X- axis, and the principal axes systems are simply related, as shown schematically in Fig. 3. The X 1 axis of one group is coincident with that of the other (X 2 ), but the Z 1 axis corresponds to the negative Y 2 axis, and vice versa, where the subscript 1(2) refers to the first (second) group. This indicates that this crystal has the characteristics of twin structure. Moreover, the twin structure is the bisector of the ab-plane, where the angle g= is only slightly different from 908. This plane is shown in Fig. 4. The NMR

4 82 A.R. Lim, S.-Y. Jeong / Physica B 304 (2001) Fig. 2. The rotation pattern of 133 Cs NMR for the ab-, bc-, and ca-plane at the room temperature. ferroelastic species m3mf2/m(p) classification, and the spontaneous monoclinic distortion takes the following form [27]: 0 1 a d 0 B 0 b 0 A ¼ 0 0 c 0 ðe 11 þ e 22 þ 2e 12 Þ=2 ðe 22 e 11 Þ=2 0 0 ðe 11 þ e 22 2e 12 Þ= e 33 1 C A; Fig. 3. The relation between the two principal axes of the EFG tensor of the two sets. results show that the domain wall of CsPbCl 3 crystal makes an angle of 458 with respect to the [1 0 0] axis. This result can be explained by Sapriel theory [26]. The CsPbCl 3 crystal belongs to the ð4þ where e 11, e 22, e 33, and e 12 are determined from the monoclinic (m) and cubic (c) lattice parameters measured at temperature T as follows: pffiffi p ffiffiffi e 11 ¼ a m a c 2 =a c 2 ; pffiffi p ffiffiffi e 22 ¼ c m a c 2 =a c 2 ; e 33 ¼ ðb m 2a c Þ=2a c ; e 12 ¼ 1=2 p=2 b m : ð5þ Using the spontaneous strain tensors given by Aizu [27] and the formulae proposed by Sapriel [26], we can evaluate the domain wall orientations.

5 In the case of the transition from m3m to 2/m symmetry, the domain wall orientations are expressed by the following equations: x ¼ y and x ¼ y; y ¼ z and y ¼ z; z ¼ x and z ¼ x; x ¼ 0 and y ¼ 0 and z ¼ 0; A.R. Lim, S.-Y. Jeong / Physica B 304 (2001) ða cþðx þ yþþ2dz ¼ 0 and ðb cþðy þ zþþ2dx ¼ 0; ða cþðx þ yþ 2dz ¼ 0 and ðb cþðy þ zþ 2dx ¼ 0; ða cþðx yþþ2dz ¼ 0 and ðb cþðy zþþ2dx ¼ 0; ða cþðx yþ 2dz ¼ 0 and ðb cþðy zþ 2dx ¼ 0; ðb cþðx þ yþþ2dz ¼ 0 and ða cþðz þ xþþ2dy ¼ 0; ðb cþðx þ yþ 2dz ¼ 0 and ða cþðz þ xþ 2dy ¼ 0; ðb cþðx yþþ2dz ¼ 0 and ða cþðz xþþ2dy ¼ 0; ðb cþðx yþ 2dz ¼ 0 and ða cþðz xþ 2dy ¼ 0; ða cþðy þ zþþ2dx ¼ 0 and ðb cþðz þ xþþ2dy ¼ 0; ða cþðy þ zþ 2dx ¼ 0 and ðb cþðz þ xþ 2dy ¼ 0; ða cþðy zþþ2dx ¼ 0 and ðb cþðz xþþ2dy ¼ 0; ða cþðy zþ 2dx ¼ 0 and ðb cþðz xþ 2dy ¼ 0; x ¼ ny and y ¼ nz and z ¼ nx; x ¼ nz and y ¼ nx and z ¼ ny; x ¼ ny and y ¼ nz and z ¼ nx; x ¼ nz and y ¼ nx and z ¼ ny n with n ¼ 2d þ 4d 2 þ ðc bþ 1=2 o = ðc bþ: ð6þ Fig. 4. The proposed twin structure for the twin structure of CsPbCl 3 crystal. These directions lie along the crystallographically prominent W wall as well as the non-prominent S wall [26]. The NMR results show that the domain wall of the CsPbCl 3 crystal makes an angle of 458 with respect to the [1 0 0] axis; this (1 1 0) domain wall is the prominent W wall with y ¼ z and y ¼ z. The 133 Cs NMR spectra were measured in the temperature ranges of phase I through phase IV. The temperature dependence of the 133 Cs NMR spectrum is shown in Fig. 5. At phases II IV, two groups of resonance lines are obtained instead of the seven resonance lines of the 133 Cs (I= 7 2 ) nucleus. The signal intensity of one group is stronger than that of the other. The 133 Cs NMR spectrum consists of only one line for all orientations of the crystal in the external magnetic field at phase I. The splitting of 133 Cs resonance lines changed slightly in the temperature range between phases IV and I, which includes the PI PII, PII PIII, and PIII PIV transitions; the splitting between lines was found to increase as the temperature decreased. The rotation patterns of the 133 Cs NMR spectra measured at phases II and III are similar with those shown in Fig. 2. These rotation patterns, as well as that in phase IV, show interchanged ab-, bc-, and ca-plane for one set of crystals and ba-, ac- and cb-plane for the other. The obtained results can be explained by the existence of two kinds of ferroelastic domains, rotated with respect to each other by 908 around

6 84 A.R. Lim, S.-Y. Jeong / Physica B 304 (2001) Fig. 5. The temperature dependence of 133 Cs NMR spectra for the each phases. The zero point corresponds to the resonance frequency MHz of the 133 Cs nucleus. the X-axis, as well as the phase IV rotation. The NMR results show that the domain wall of the CsPbCl 3 crystal makes an angle of 458 with respect to the [1 0 0] axis at temperatures up to 478C. The temperature dependence of e 2 qq=h and Z in the temperature range of phases I IV is shown in Fig. 6. Near the transition point of 378C, the parameters of the 133 Cs NMR change abruptly demonstrating a change in the caesium site symmetry, and the asymmetry parameter Z which changes from 0.50 at 388C to 0.39 below 388C. The 133 Cs quadrupole coupling constant decreases to a value of 185 khz near the transition point of 378C. This means that the PIV PIII transition is a firstorder phase transition. The values of e 2 qq=h above 378C were constant, while the value of Z was found to decrease as a function of increasing temperature. Above 428C, the 133 Cs NMR spectra had only continuous quantitative changes in the quadrupole splitting distances, without any pattern changes or abrupt changes. This means, then, Fig. 6. The temperature dependence of (a) the nuclear quadrupole coupling constants, e 2 qq=h, and (b) asymmetry parameters, Z, for 133 Cs in a CsPbCl 3 single crystal. that PIII PII transition is a second-order phase transition. From the experimental data, the maximum separation resulting from the quadrupole interaction was observed when the magnetic field was applied along the b-axis of the crystal. This direction was found by analysis to be the Z-axis of the EFG tensor. Also, the principal axes of the Cs ion in phases II and III are consistent with those of phase IV. At the transition point of 478C, the 133 Cs NMR lines superpose into one line. One signal of the 133 Cs resonance line indicates that a phase transition takes place to a new phase with higher symmetry than tetragonal. There is no EFG tensor at the Cs site in phase I because of the site symmetry m3m. Here, the PII PI transition is a first-order phase transition. 5. Discussion and conclusion The phase transitions of a ferroelastic CsPbCl 3 single crystal grown by the Bridgman method have

7 A.R. Lim, S.-Y. Jeong / Physica B 304 (2001) been investigated using 133 Cs nuclear magnetic resonance. Due to quadrupole interaction, two sets of seven-line NMR signals were obtained instead of a simple seven-line structure. From the experimental data, the quadrupole coupling constant, asymmetry parameter, and the direction of EFG tensor were determined in the temperature range from the phase I to phase IV. At phases II IV, two parameters were observed with the same magnitudes of the quadrupole coupling constant and the asymmetry parameter. The principal axes X, Y, and Z of the EFG tensor for the 133 Cs were found to lie along the crystallographic c-, a- andb-axis for one set, and the Y and Z axes were interchanged for the other. Therefore, the boundary of these two grains, shown in Fig. 4, makes an angle of 458 with respect to the a-axis. This indicates that this crystal has the characteristics of twin structure, and confirms that the crystallographic a- and b-axis of one grain are interchanged for the other. The twin domain crystal grown by our group has prominent W domain walls with y ¼ z and y ¼ z. This result is consistent with the domain wall proposed by Sapriel theory [26]. Based on our experimental results, the two resonance lines were analyzed in a ferroelastic domain. In the temperature range between 258C and 468C, which includes the PIV PIII and PIII PII transitions, there is no change in the number of 133 Cs resonance lines. The e 2 qq=h and Z of the 133 Cs nucleus decrease with increasing temperature when going through the PIII PII transition. The principal axes corresponding to the largest principal value of all the 133 Cs EFG tensors were parallel to the cubic b-axis in the temperature range from room temperature to 478C. At the transition point of 378C, the parameters of the 133 Cs NMR abruptly changed, indicating a change in the caesium site symmetry. The values of 133 Cs NMR parameters above 378C were found to decrease as a function of increasing temperature. Above 428C, the 133 Cs NMR spectra had only continuous quantitative changes in the quadrupole splitting distances, without any pattern changes or abrupt changes. At the transition point of 478C, the 133 Cs NMR lines superpose into one line. Based on these results, we can conclude that the parameters obtained from the 133 Cs NMR spectra were based on the occurrence of first-order phase transitions at 378C and 478C and a second-order phase transition at 428C. Acknowledgements This work was supported by Korea Research Foundation Grant (KRF sp0130). References [1] C.K. Moller, Mat. Fys. Medd. Danske Vindensk Selsk (1959) 32. [2] S. Hirotsu, S. Sawada, Phys. Lett. A 28 (1969) 762. [3] S. Hirotsu, J. Phys. Soc. Japan 31 (1972) 552. [4] H. Ohta, J. Harada, S. Hirotsu, Solid State Commun. 13 (1973) [5] Y. Fujii, S. Hoshino, Y. Yamada, G. Shirane, Phys. Rev. B 9 (1974) [6] S. Hirotsu, Y. Kunii, J. Phys. Soc. Japan 50 (1981) [7] K.S. Alexandrov, B.V. Beznosikov, L.A. Posdnjakova, Ferroelectrics 12 (1976) 197. [8] J. Harada, M. Sakata, S. Hoshino, S. Hirotsu, J. Phys. Soc. Japan 40 (1976) 212. [9] J.A. Cape, R.A. White, R.S. Feigelson, J. Appl. Phys. 40 (1969) [10] Y. Vaills, J.Y. Buzare, J. Phys. Chem. Solids 48 (1987) 363. [11] S. Plesko, R. Kind, J. Roos, J. Phys. Soc. Japan 45 (1978) 553. [12] K. Heidrich, H. Kunzel, J. Treusch, Solid State Commun. 25 (1978) 887. [13] L.N. Amitin, A.T. Anistratov, A.I. Kuznetsov, Sov. Phys. Solid State 21 (1979) [14] S. Hirotsu, T. Suzuki, J. Phys. Soc. Japan 44 (1978) [15] K. Aizu, J. Phys. Soc. Japan 27 (1969) 387. [16] C. Boulesteix, Phys. Stat. Sol. A 86 (1984) 11. [17] M. Chabin, F. Gilletta, J. Appl. Crystallogr. 13 (1980) 533. [18] M. Chabin, F. Gilletta, J. Appl. Crystallogr. 13 (1980) 539. [19] E.J. Shin, H.T. Jeong, H.K. Kim, S.Y. Jeong, J. Korean Assoc. Cryst. Growth 7 (1997) 117. [20] A.R. Lim, S.Y. Jeong, Physica B 245 (1998) 277. [21] S.L. Mair, Acta Crystallogr. A 38 (1982) 790. [22] A.R. Lim, S.H. Choh, S.Y. Jeong, J. Phys.: Condens. Matter 8 (1996) [23] A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, Oxford, [24] C.P. Slichter, Principles of Magnetic Resonance, Springer, Berlin, [25] S.H. Choh, Z. Naturforsch 51a (1996) 591. [26] J. Sapriel, Phys. Rev. B 12 (1975) [27] K. Aizu, J. Phys. Soc. Japan 28 (1970) 706.