- Email: [email protected]
Calculation of the Raman and IR frequencies as order parameters and the damping constant (FWHM) close to phase transitions in methylhydrazinium structures
Journal of Molecular Structure 1181 (2019) 488e492
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: http://www.elsevier.com/locate/molstruc
Calculation of the Raman and IR frequencies as order parameters and the damping constant (FWHM) close to phase transitions in methylhydrazinium structures M. Kurt a, H. Yurtseven b, *, A. Kurt c a b c
Department of Physics, Çanakkale 18 Mart University, 17100 Çanakkale, Turkey Department of Physics, Middle East Technical University, 06531 Ankara, Turkey _ _ MTAL High School, 17100 Çanakkale, Turkey Lapseki IÇDAS ¸ ÇIB
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 October 2018 Received in revised form 3 January 2019 Accepted 4 January 2019 Available online 7 January 2019
Temperature dependences of the frequencies for the Raman modes of n (NH2), ns (CH3), n1 (HCOO), nS (CNN) and IR mode of r (NH2) are calculated in particular, for MHyMn close to the phase transition temperature (TC ¼ 220 K) in the family of compounds CH3NH2NH2M(HCOO)3, MHyM with M ¼ Mn, Mg, Fe and Zn. By assuming Raman and infrared frequency as an order parameter, this calculation is performed from the molecular field theory by using the experimental data from the literature. We also calculate the damping constant (FWHM) from the order parameter (Raman and IR frequency of those modes) by using the pseudospin (MHyþ cations)-phonon coupled model (PS) and the energy-fluctuation model (EF) for methylhydrazinium metal formate frameworks. Expressions of the damping constant from both models are fitted to the observed FWHM data for the Raman and infrared modes studied for these metal formates. Our results show that the anomalous behaviour of the Raman and IR frequencies of those modes, except the nS (CH3) Raman mode which are associated with the phase transition can be described adequately by the molecular field theory in MHyM, as observed experimentally. Also, the damping constant calculated from the PS and EF models can explain the observed FWHM of those Raman and IR modes studied in methylhydrazinium metal formate frameworks. © 2019 Elsevier B.V. All rights reserved.
Keywords: Order parameter Damping constant Raman and IR modes Phase transition. MHyMn
1. Introduction Inorganic compounds which crystallize in a perovskite structure such as perovskite manganites, have been studied because of their coexistence of magnetic and ferroelectric ordering [1e3]. In particular, due to the multiferroic properties of dense metal organic framework (MOF) compound (CH3)2NH2Mn(HCOO)3 [4], this family of compounds has been studied to investigate their ferroelectric, magnetic, dielectric, vibrational and mechanical properties close to the structural phase transitions [5e10]. Within this family of perovskite-type metal formate frameworks, CH3NH2NH2M(HCOO)3, M ¼ Mn, Mg, Fe and Zn or MHyM exhibits two structural phase transitions. As pointed out in a recent study
* Corresponding author. E-mail addresses: [email protected] (H. Yurtseven), [email protected] (A. Kurt).
(M.
https://doi.org/10.1016/j.molstruc.2019.01.016 0022-2860/© 2019 Elsevier B.V. All rights reserved.
Kurt),
[email protected]
[3], the first transition occurs due to partial ordering of MHyþ cations and it changes the symmetry from nonpolar R3c to polar R3c, whereas the second low temperature transition is associated also with the ordering of the MHyþ cations and distortion of the metal formate framework. The MHyþ cations are disordered within six symmetrically equivalent positions above 309e372 K and trigonally disordered at room temperature according to X-ray data [3]. Also, it has been obtained experimentally that there occur two heat anomalies in these compounds at around 309e327 K range and 168e243 K upon heating, which are associated with the ordering of the MHyþ cations [3]. Additionally, temperature dependence of the magnetization of MHyFe and MHyMn at constant magnetic fields was measured under zero-field cooling (ZFC) and field-cooling (FC) conditions [3]. From the measurement of M, it was found that for MHyFe magnetization exhibits a pronounced anomaly at around Tm ¼ 21 K, whereas for MHyMn there exists a relatively small anomaly at about Tm ¼ 9 K [3]. In this study, we calculate the temperature dependence of
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Raman and IR frequency (wavenumber) and damping constant (FWHM) for various modes responsible for the phase transition (TC ¼ 220 K) in MHyMn by using experimental data [3]. Expressions for the frequency from the molecular field theory and for the damping constant from the pseudospin-phonon coupled (PS) model, are fitted to the observed data [3] and the fitted parameters are determined. Below, in section 2 we give our calculations and results. Sections 3 and 4 give discussion and conclusions, respectively.
2. Calculations and results The order parameter can be calculated as a function of temperature from the molecular field theory [11,12] according to the relation,
S ¼ 1 expð 2TC =TÞ ¼ ½3ð1 T=TC Þ1=2 ¼0
T < < TC
(1a)
0 < TC T < TC
(1b)
T > TC
(1c)
where TC is the transition temperature. By associating the order parameter (S) with the vibrational frequency (n) of the modes (Raman, IR) involving in the mechanism of phase transition, the damping constant (FWHM) of those modes can also be predicted for the pseudospin-phonon (sp) coupling systems
GSP ¼ G0 þ A 1 S2 ln
TC T TC 1 S2
(2)
and
"
GSP ¼ G0 0 þ A0
G0 ðG0 0 Þ denotes the background damping constant (FWHM) and AðA0 Þ is the amplitude. Then, below TC (Ss0) and above TC (S ¼ 0), the temperature dependence of the damping constant due to pseudospin-phonon interactions (GSP) can be calculated from both models (Eqs. (2) and (3)). Expressions for the damping constant Gsp (Eqs. (2) and (3)) were applied to KDP type of crystals by analyzing the temperature dependence of an internal mode previously [15,16]. We have also used Eqs. (2) and (3) to analyze the linewidths of some Raman modes in ammonium halides [17]. Regarding the metal organic frameworks (MOFs), we have used the molecular field theory to study the magnetic properties of DMMn and chromium-doped DMMn [18]. Also, using the observed [19] Raman frequencies and bandwidths (FWHM) of the two stretching modes of (CH2)2NH2Mg(HCOO)3 shortly, DMMg close to the phase transition (TC ¼ 270 K) were analyzed according to the PS (Eq. (2)) and EF (Eq. (3)) models very recently [20]. In this study, we calculated the temperature dependences of the frequency (Eq. (1)) and the damping constant (Eqs. (2) and (3)) for the Raman modes of n (NH2), ns (CH3), n1 (HCOO), ns (CNN) and IR mode of r (NH2) were calculated for MHyMn. The Raman and IR frequencies of those modes were assumed as an order parameter (S) and they were used to predict their damping constant (FWHM) for this methylhydrazinium metal formate framework (MHyMn). By normalizing the vibrational frequency with respect to the maximum value (n/nmax) since S varies from 0 to 1, the frequency was related to S according to the quadratic relation S ¼ a þ bðn=nmax Þ þ cðn=nmax Þ2
(4)
where a, b and c are constants. Also, quadratic variation of n/nmax with the temperature was assumed as
n=nmax ¼ a0 þ a1 T þ a2 T 2
#1=2
489
T 1 S2 T TC 1 S2
(3)
from the pseudospin-phonon coupled (PS) model [13] and the energy fluctuation (EF) model [14], respectively. In Eqs. (2) and (3),
(5)
with constants a0 ; a1 and a2 . We first calculated the order parameter S from the molecular field theory (Eq. (1a)) for MHyMn (TC ¼ 220 K). We then analyzed the Raman frequencies of the n and ns (CNN) modes, and the IR fre(NH2), ns (CH3), n1 (HCOO) quencies of the r (NH2) mode using the observed data [3] according
Table 1 Values of the parameters a0 ; a1 and a2 (Eq. (5)) and a, b and c (Eq. (4)) by using the experimental data [3] for the Raman and IR modes indicated within the temperature interval of 80 < T(K) < 230 below Tc for MHyMn. Maximum frequency values (observed) are also given (Tc ¼ 220 K). Modes
nmax (cm1)
a0
a1 106 ðK 1 Þ
a2 108 ðK 2 Þ
a
b
c
n(NH2) Raman ns (CH3) Raman n1(HCOO) Raman
3203.84 2964.38 2884.65 2873.26 2856.4 946.17 876.81
0.9989 0.9983 1.0002 1.0085 0.9994 1.0020 1.0005
19.674 3.5045 1.7514 5.1544 7.603 1.2256 4.8451
8.1066 0.0932 5.3892 0.4543 2.5885 18.005 0.9849
415729 e 8334.23 126845.2 e 13.28 72611.65
832096 e 16816.29 253510.9 e 8.30 145057.08
416368 e 8483.05 126664.68 e 22.55 72444.43
r(NH2) IR ns (CNN) Raman
Table 2 Values of the parameters a0 ; a1 and a2 (Eq. (5)) above Tc for the Raman and IR modes indicated within the temperature interval of 230 < T(K) < 400 for MHyMn. Maximum frequency values (observed) are also given (Tc ¼ 220 K). Modes
nmax (cm1)
a0 ðcm1 Þ
a1 106 ðK 1 Þ
a2 108 ðK 2 Þ
n(NH2) Raman ns (CH2) Raman n1(HCOO) Raman
3203.84 2964.38 2884.65 2856.4 946.17 876.81
0.9936 0.9975 1.0005 1.0002 0.9836 1.0031
1.5455 0.9329 1.820 1.2701 2.4827 1.7165
0.3845 0.8236 0.1915 5.3846 9.9796 0.7396
r(NH2) IR ns (CNN) Raman
490
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Fig. 1. Wavenumber calculated as a function of temperature for the n(NH2) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close to phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
to Eq. (5) with the parameters a0 ; a1 and a2 determined (Table 1). Calculated S was then fitted to the observed frequency (n/nmax) by using Eq. (4) and the parameters a, b and c were determined (Table 1). This was done below TC when Ss0 of MHyMn. Above TC (S ¼ 0), we simply, analyzed the observed frequency (n/nmax) data according to Eq. (5) with the parameters a0 ; a1 and a2 for MHyMn (Table 2). Figs. (1-5) give the wavenumber (frequency) calculated as a function of temperature for the Raman modes of n(NH2), ns (CH3), n1(HCOO), IR mode of r(NH2) and Raman mode of ns (CNN), respectively. Observed wavenumbers [3] are also given in these figures. We also analyzed the temperature dependence of the damping constant (FWHM) according to the pseudospin-phonon coupled model (PS) by means of Eq. (2) where the order parameter S (Eq. (1a)) was used for the Raman modes of ns (CNN) (877 cm1), ns (NH3) (2961 cm1) and the IR mode of r (NH2) (924 cm1) of MHyMn by using the experimental data [3], as plotted in Figs.(6-8), respectively.
Fig. 2. Wavenumber calculated below Tc as a function of temperature for the ns (CH3) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close to phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
Fig. 3. Wavenumber calculated as a function of temperature for the n1(HCOO) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close to phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
3. Discussion Frequency (wavenumber) and damping constant (FWHM) were calculated as a function of temperature by the molecular field theory (Eq. (1)) and the pseudospin-phonon coupled (PS) model (Eq. (2)) using the experimental data [3] for MHyMn. Frequencies of the Raman modes of n(NH2), ns (CH3), n1(HCOO) and ns (CNN) and the IR mode of r(NH2) were assumed as an order parameter S (Eq. (1a)), which were fitted to the observed wavenumbers [3] of those modes (Figs. 1e5). Pseudospin-phonon coupled (PS) model (Eq. (2)) was then fitted to the observed FWHM [3] of the Raman modes of ns (CNN) and ns (NH3), and the IR mode of r(NH2) (Figs. 6e8) for MHyMn. This analysis was carried out for the first phase transition as the temperature increases with the transition temperature TC2 ¼ 213 K (cooling) and 224 K (heating) in MHyMn [3]. There occurs a second phase transition in this compound as the
Fig. 4. Wavenumber calculated as a function of temperature for the r(NH2) IR mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Fig. 5. Wavenumber calculated as a function of temperature for the ns (CNN) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
Fig. 6. Damping constant calculated as a function of temperature for the ns (CNN) Raman mode according to Eq. (2) which was fitted to the observed FWHM [3] close to the transition temperature (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
temperature increases at TC1 ¼ 309 K (cooling) and TC1 ¼ 310 K (heating) [3]. It was found that the decreasing behaviour of the frequency with increasing temperature toward the transition temperature (TC z 220 K), was associated with the order parameter S for the Raman modes of n(NH2) (Fig. 1), n1(HCOO) (Fig. 3) and the IR mode of r (NH2) (Fig. 4) with the exception of the ns (CH3) Raman mode whose frequency increases (Fig. 2). For this reason, the observed [3] Raman frequencies of the ns (CH3) (Fig. 2) and also of the n1(HCOO) mode at 2856 cm1 (Fig. 3) were not fitted to the order parameter according to Eq. (4), which were excluded (Table 1) in MHyMn. Our results show that those Raman and IR modes whose frequencies are related to the order parameter, involve in the mechanism of phase transition (TC z 220 K) in MHyMn within the molecular field theory (Eq. (1a)). Regarding the temperature dependence of the damping
491
Fig. 7. Damping constant calculated as a function of temperature for the ns (NH3) Raman mode according to Eq. (2) which was fitted to the observed FWHM [3] close to the transition temperature (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
Fig. 8. Damping constant calculated as a function of temperature for the r(NH2) IR mode according to Eq. (2) which was fitted to the observed FWHM [3] close to the transition temperature (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
constant (FWHM) for the Raman modes of ns (CNN) (Fig. 6), ns (NH3) (Fig. 7) and the r (NH2) IR mode (Fig. 8), the pseudospinphonon coupled (PS) model (Eq. (2)) was satisfactory to explain the mechanism of phase transition (TC z 224 K) in MHyMn. In particular, the FWHM of the r (NH2) IR (924 cm1) mode varied largely with the temperature at TC, a discontinuous jump at ~13 cm1as observed experimentally [3] (Fig. 8). This difference in FWHM at TC was very small (~1.3 cm1) for the ns (CNN) (877 cm1) and ns (NH3) (2961 cm1) Raman modes as shown in Figs. (6) and (7), respectively, as also observed experimentally [3] in MHyMn. This sudden decrease in the FWHM of the r (NH2) IR mode for MHyMn just below TC (Fig. 8), is similar to that of the same mode (910 cm1) for DMMg due to the reorientational motions of the DMAþ cations at low temperatures [19]. It has been pointed out that for the NH2 group vibrations wavenumbers increase which indicates strengthening of the hydrogen bonds as a result of DMAþ
492
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Table 3 Values of the background FWHM (G0) and the amplitude A for the Raman and IR modes indicated according to the pseudospin-phonon coupled (PS) model (Eq. (2)) within the temperature intervals below and above Tc (¼220 K) for MHyMn. T>Tc
T
Wavenumber (cm1) 877
ns (CH3) Raman r(NH2) IR
G0 (cm1) 3.68
A (cm1) 2.098
Temperature Interval (K) 79.6 < T < 219.8
2961
5.19
10.407
78.6 < T < 219.8
924
8.53
12.899
80.4 < T < 220.9
ordering in DMMg [19]. Similarly, due to the r (NH2) IR mode the phase transitions are governed by dynamics of the hydrazinium ions at low temperatures in MHyMn as in the case HyM (M ¼ Mn, Zn, Fe) compounds [21]. Note that analysis of the observed FWHM for the ns (CNN), ns (NH3) Raman modes and the r (NH2) IR mode above Tc was performed in the two temperature regions for the fitting procedure (Eq. (2)) with the parameters determined (Table 3). We also fitted damping constant due to the energy fluctuation (EF) model (Eq. (3)) to the observed FWHM [3] for the Raman and IR modes studied. Below Tc, it was fitted as good as the PS model for the ns (CNN) and ns (NH3) Raman modes but not for the r (NH2) IR mode. Above Tc, it did not give any better compared to the PS model although they could have been fitted reasonably well if the fitting were completed within two temperature regions as we did by using the PS model (Figs. 6e8). This may be due to the fact that the EF model (Eq. (3)) is better validated close to Tc (just above Tc, S ¼ 0) for the damping constant varying with the temperature as Gsp fðT Tc Þ1=2 with the critical exponent ½ whereas in a wide temperature range between ~100 and 400 K, the PS model seems to work better for MHyMn. It has been pointed out that the low temperature (LT) phase transition is well depicted for all frequencies but the hightemperature (HT) phase is strongly affected by the relaxation process and some conductivity processes appear at high temperatures [3]. From the expressions of the damping constant GSP (Eqs. (2) and (3)) for both models (PS and EF), the temperature dependence of the relaxation time (tSP) can be extracted for MHyMn. tSP should be quite different for MHyMn as compared to the other compounds of MHyM with M ¼ Mg, Fe and Zn. This is because of the fact that a distinct anomaly appeared at the HT phase transition at low frequencies in the MHyMn compound although anomalies associated with the HT phase transition are difficult to detect experimentally due to the strong frequency dispersion, as also pointed out previously [3]. It has been reported that high-pressure Raman scattering studies of MHyMn revealed a pressure-induced reversible phase transition between 4.8 and 5.5 GPa, which leads to significant changes in both the manganese formate framework and the MHyþ structure [3]. By analyzing the pressure dependence of the frequency (wavenumber) of Raman modes involving the pressureinduced phase transition using the molecular field theory and also by analyzing their linewidths through the PS and EF models, the mechanism of order-disorder transition in MHyMn can be
G0 (cm1) 7.35 8.91 11.31 12.96 32.67 39.97
A0 (cm1) 1.12 3.10 1.227 4.064 3.438 15.589
Temperature Interval (K) 230.0 < T < 310.8 318.3 < T < 399.1 229.1 < T < 310.1 319.2 < T < 400 229.1 < T < 309.9 320.1 < T < 399.1
explained. 4. Conclusions Raman and IR frequencies of some modes involving phase transitions were calculated at various temperatures in MHyMn by the molecular field theory using the observed data. Raman and IR frequency was assumed as an order parameter which was fitted to the observed wavenumber of those modes studied in this compound. Damping constant from the pseudospin-phonon coupling model (PS) was also fitted to the observed FWHM of those Raman and IR modes below and above the transition temperature (Tc ¼ 220 K) for MHyMn. We found that molecular field theory and the PS model are satisfactory to explain the observed behaviour of the wavenumber and FWHM, respectively, close to the phase transitions in MHyMn. References [1] A.P. Ramirez, J. Phys. Condens. Matter 9 (1997) 8171. [2] K.M. Rabe, C.H. Ahn, J.M. Triscone, Physics of Ferroelectrics: a Modern Perspective, Springer-Verlag, Berlin, Heidelberg, 2007. [3] M. Maczka, A. Gagor, M. Ptak, W. Paraguassu, T.A. da Silva, A. Sieradzki, A. Pikul, Chem. Mater. 29 (2017) 2264. [4] P. Jain, V. Ramachandran, R.J. Clark, H.D. Zhou, B.H. Toby, N.S. Dalal, H.W. Kroto, A.K. Cheetham, J. Am. Chem. Soc. 131 (2009) 13625. [5] M. Sanchez- Anjujar, S. Presedo, S. Yanez-Vilar, S. Castro-Garcia, J. Shamir, M.A. Senaris-Rodriguez, Inorg. Chem. 49 (2010) 1510. [6] W. Wang, L.Q. Yan, J.Z. Cong, Y.L. Zhao, F. Wang, S.P. Shen, T. Zhou, D. Zhang, S.G. Wang, X.F. Han, Y. Sun, Sci. Rep. 3 (2013) 2024. [7] M. Maczka, A. Gagor, B. Macalik, A. Pikul, M. Ptuk, J. Hanuza, Inorg. Chem. 53 (2014) 457. [8] M. Kosa, D.T. Major, Cryst. Eng. Commun. 17 (2015) 295. [9] P. Jain, A. Stroppa, D. Nabok, A. Marino, A. Rubano, D. Paparo, M. Matsubara, H. Nakotte, M. Fiebig, S. Picozzi, E.S. Choi, A.K. Cheetham, C. Draxl, N.S. Dalal, V.S. Zapf, NPJ. Quantum Mater. 1 (2016) 16012. [10] H.D. Duncan, M.T. Dove, D.A. Keen, A.E. Phillips, Dalton Trans. 45 (2016) 4380. [11] R. Brout, PhaseTransitions, Chapter 2, Benjamin, New York, USA, 1965. [12] M. Matsushita, J. Chem. Phys. 65 (1976) 23. [13] G. Lahajnar, R. Blinc, S. Zumer, Phys. Condens. Matter 18 (1974) 301. [14] G. Schaack, V. Winterfeldt, Ferroelectrics 15 (1977) 35. [15] I. Laulicht, N. Luknar, Chem. Phys. Lett. 47 (1977) 237. [16] I. Laulitch, J. Phys. Chem. Solid. 39 (1978) 901. [17] H. Yurtseven, H. Karacali, Spectrochim. Acta 65 (2006) 421. [18] H. Yurtseven, E. Kilit Dogan, Polyhedron 154 (2018) 132. [19] K. Szymborska-Malek, M. Trzebiatowska-Gusowska, M. Maczka, A. Gagor, Spectrochim. Acta 159 (2016) 35. [20] H. Yurtseven, A. Aslan, Ferroelectrics 526 (2018) 9. [21] M. Maczka, K. Pasinska, M. Ptak, W. Paraguassu, T. Almeida da Silva, A. Sieradzki, A. Pikul, Phys. Chem. Chem. Phys. 18 (2016) 31653.
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: http://www.elsevier.com/locate/molstruc
Calculation of the Raman and IR frequencies as order parameters and the damping constant (FWHM) close to phase transitions in methylhydrazinium structures M. Kurt a, H. Yurtseven b, *, A. Kurt c a b c
Department of Physics, Çanakkale 18 Mart University, 17100 Çanakkale, Turkey Department of Physics, Middle East Technical University, 06531 Ankara, Turkey _ _ MTAL High School, 17100 Çanakkale, Turkey Lapseki IÇDAS ¸ ÇIB
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 October 2018 Received in revised form 3 January 2019 Accepted 4 January 2019 Available online 7 January 2019
Temperature dependences of the frequencies for the Raman modes of n (NH2), ns (CH3), n1 (HCOO), nS (CNN) and IR mode of r (NH2) are calculated in particular, for MHyMn close to the phase transition temperature (TC ¼ 220 K) in the family of compounds CH3NH2NH2M(HCOO)3, MHyM with M ¼ Mn, Mg, Fe and Zn. By assuming Raman and infrared frequency as an order parameter, this calculation is performed from the molecular field theory by using the experimental data from the literature. We also calculate the damping constant (FWHM) from the order parameter (Raman and IR frequency of those modes) by using the pseudospin (MHyþ cations)-phonon coupled model (PS) and the energy-fluctuation model (EF) for methylhydrazinium metal formate frameworks. Expressions of the damping constant from both models are fitted to the observed FWHM data for the Raman and infrared modes studied for these metal formates. Our results show that the anomalous behaviour of the Raman and IR frequencies of those modes, except the nS (CH3) Raman mode which are associated with the phase transition can be described adequately by the molecular field theory in MHyM, as observed experimentally. Also, the damping constant calculated from the PS and EF models can explain the observed FWHM of those Raman and IR modes studied in methylhydrazinium metal formate frameworks. © 2019 Elsevier B.V. All rights reserved.
Keywords: Order parameter Damping constant Raman and IR modes Phase transition. MHyMn
1. Introduction Inorganic compounds which crystallize in a perovskite structure such as perovskite manganites, have been studied because of their coexistence of magnetic and ferroelectric ordering [1e3]. In particular, due to the multiferroic properties of dense metal organic framework (MOF) compound (CH3)2NH2Mn(HCOO)3 [4], this family of compounds has been studied to investigate their ferroelectric, magnetic, dielectric, vibrational and mechanical properties close to the structural phase transitions [5e10]. Within this family of perovskite-type metal formate frameworks, CH3NH2NH2M(HCOO)3, M ¼ Mn, Mg, Fe and Zn or MHyM exhibits two structural phase transitions. As pointed out in a recent study
* Corresponding author. E-mail addresses: [email protected] (H. Yurtseven), [email protected] (A. Kurt).
(M.
https://doi.org/10.1016/j.molstruc.2019.01.016 0022-2860/© 2019 Elsevier B.V. All rights reserved.
Kurt),
[email protected]
[3], the first transition occurs due to partial ordering of MHyþ cations and it changes the symmetry from nonpolar R3c to polar R3c, whereas the second low temperature transition is associated also with the ordering of the MHyþ cations and distortion of the metal formate framework. The MHyþ cations are disordered within six symmetrically equivalent positions above 309e372 K and trigonally disordered at room temperature according to X-ray data [3]. Also, it has been obtained experimentally that there occur two heat anomalies in these compounds at around 309e327 K range and 168e243 K upon heating, which are associated with the ordering of the MHyþ cations [3]. Additionally, temperature dependence of the magnetization of MHyFe and MHyMn at constant magnetic fields was measured under zero-field cooling (ZFC) and field-cooling (FC) conditions [3]. From the measurement of M, it was found that for MHyFe magnetization exhibits a pronounced anomaly at around Tm ¼ 21 K, whereas for MHyMn there exists a relatively small anomaly at about Tm ¼ 9 K [3]. In this study, we calculate the temperature dependence of
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Raman and IR frequency (wavenumber) and damping constant (FWHM) for various modes responsible for the phase transition (TC ¼ 220 K) in MHyMn by using experimental data [3]. Expressions for the frequency from the molecular field theory and for the damping constant from the pseudospin-phonon coupled (PS) model, are fitted to the observed data [3] and the fitted parameters are determined. Below, in section 2 we give our calculations and results. Sections 3 and 4 give discussion and conclusions, respectively.
2. Calculations and results The order parameter can be calculated as a function of temperature from the molecular field theory [11,12] according to the relation,
S ¼ 1 expð 2TC =TÞ ¼ ½3ð1 T=TC Þ1=2 ¼0
T < < TC
(1a)
0 < TC T < TC
(1b)
T > TC
(1c)
where TC is the transition temperature. By associating the order parameter (S) with the vibrational frequency (n) of the modes (Raman, IR) involving in the mechanism of phase transition, the damping constant (FWHM) of those modes can also be predicted for the pseudospin-phonon (sp) coupling systems
GSP ¼ G0 þ A 1 S2 ln
TC T TC 1 S2
(2)
and
"
GSP ¼ G0 0 þ A0
G0 ðG0 0 Þ denotes the background damping constant (FWHM) and AðA0 Þ is the amplitude. Then, below TC (Ss0) and above TC (S ¼ 0), the temperature dependence of the damping constant due to pseudospin-phonon interactions (GSP) can be calculated from both models (Eqs. (2) and (3)). Expressions for the damping constant Gsp (Eqs. (2) and (3)) were applied to KDP type of crystals by analyzing the temperature dependence of an internal mode previously [15,16]. We have also used Eqs. (2) and (3) to analyze the linewidths of some Raman modes in ammonium halides [17]. Regarding the metal organic frameworks (MOFs), we have used the molecular field theory to study the magnetic properties of DMMn and chromium-doped DMMn [18]. Also, using the observed [19] Raman frequencies and bandwidths (FWHM) of the two stretching modes of (CH2)2NH2Mg(HCOO)3 shortly, DMMg close to the phase transition (TC ¼ 270 K) were analyzed according to the PS (Eq. (2)) and EF (Eq. (3)) models very recently [20]. In this study, we calculated the temperature dependences of the frequency (Eq. (1)) and the damping constant (Eqs. (2) and (3)) for the Raman modes of n (NH2), ns (CH3), n1 (HCOO), ns (CNN) and IR mode of r (NH2) were calculated for MHyMn. The Raman and IR frequencies of those modes were assumed as an order parameter (S) and they were used to predict their damping constant (FWHM) for this methylhydrazinium metal formate framework (MHyMn). By normalizing the vibrational frequency with respect to the maximum value (n/nmax) since S varies from 0 to 1, the frequency was related to S according to the quadratic relation S ¼ a þ bðn=nmax Þ þ cðn=nmax Þ2
(4)
where a, b and c are constants. Also, quadratic variation of n/nmax with the temperature was assumed as
n=nmax ¼ a0 þ a1 T þ a2 T 2
#1=2
489
T 1 S2 T TC 1 S2
(3)
from the pseudospin-phonon coupled (PS) model [13] and the energy fluctuation (EF) model [14], respectively. In Eqs. (2) and (3),
(5)
with constants a0 ; a1 and a2 . We first calculated the order parameter S from the molecular field theory (Eq. (1a)) for MHyMn (TC ¼ 220 K). We then analyzed the Raman frequencies of the n and ns (CNN) modes, and the IR fre(NH2), ns (CH3), n1 (HCOO) quencies of the r (NH2) mode using the observed data [3] according
Table 1 Values of the parameters a0 ; a1 and a2 (Eq. (5)) and a, b and c (Eq. (4)) by using the experimental data [3] for the Raman and IR modes indicated within the temperature interval of 80 < T(K) < 230 below Tc for MHyMn. Maximum frequency values (observed) are also given (Tc ¼ 220 K). Modes
nmax (cm1)
a0
a1 106 ðK 1 Þ
a2 108 ðK 2 Þ
a
b
c
n(NH2) Raman ns (CH3) Raman n1(HCOO) Raman
3203.84 2964.38 2884.65 2873.26 2856.4 946.17 876.81
0.9989 0.9983 1.0002 1.0085 0.9994 1.0020 1.0005
19.674 3.5045 1.7514 5.1544 7.603 1.2256 4.8451
8.1066 0.0932 5.3892 0.4543 2.5885 18.005 0.9849
415729 e 8334.23 126845.2 e 13.28 72611.65
832096 e 16816.29 253510.9 e 8.30 145057.08
416368 e 8483.05 126664.68 e 22.55 72444.43
r(NH2) IR ns (CNN) Raman
Table 2 Values of the parameters a0 ; a1 and a2 (Eq. (5)) above Tc for the Raman and IR modes indicated within the temperature interval of 230 < T(K) < 400 for MHyMn. Maximum frequency values (observed) are also given (Tc ¼ 220 K). Modes
nmax (cm1)
a0 ðcm1 Þ
a1 106 ðK 1 Þ
a2 108 ðK 2 Þ
n(NH2) Raman ns (CH2) Raman n1(HCOO) Raman
3203.84 2964.38 2884.65 2856.4 946.17 876.81
0.9936 0.9975 1.0005 1.0002 0.9836 1.0031
1.5455 0.9329 1.820 1.2701 2.4827 1.7165
0.3845 0.8236 0.1915 5.3846 9.9796 0.7396
r(NH2) IR ns (CNN) Raman
490
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Fig. 1. Wavenumber calculated as a function of temperature for the n(NH2) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close to phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
to Eq. (5) with the parameters a0 ; a1 and a2 determined (Table 1). Calculated S was then fitted to the observed frequency (n/nmax) by using Eq. (4) and the parameters a, b and c were determined (Table 1). This was done below TC when Ss0 of MHyMn. Above TC (S ¼ 0), we simply, analyzed the observed frequency (n/nmax) data according to Eq. (5) with the parameters a0 ; a1 and a2 for MHyMn (Table 2). Figs. (1-5) give the wavenumber (frequency) calculated as a function of temperature for the Raman modes of n(NH2), ns (CH3), n1(HCOO), IR mode of r(NH2) and Raman mode of ns (CNN), respectively. Observed wavenumbers [3] are also given in these figures. We also analyzed the temperature dependence of the damping constant (FWHM) according to the pseudospin-phonon coupled model (PS) by means of Eq. (2) where the order parameter S (Eq. (1a)) was used for the Raman modes of ns (CNN) (877 cm1), ns (NH3) (2961 cm1) and the IR mode of r (NH2) (924 cm1) of MHyMn by using the experimental data [3], as plotted in Figs.(6-8), respectively.
Fig. 2. Wavenumber calculated below Tc as a function of temperature for the ns (CH3) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close to phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
Fig. 3. Wavenumber calculated as a function of temperature for the n1(HCOO) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close to phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
3. Discussion Frequency (wavenumber) and damping constant (FWHM) were calculated as a function of temperature by the molecular field theory (Eq. (1)) and the pseudospin-phonon coupled (PS) model (Eq. (2)) using the experimental data [3] for MHyMn. Frequencies of the Raman modes of n(NH2), ns (CH3), n1(HCOO) and ns (CNN) and the IR mode of r(NH2) were assumed as an order parameter S (Eq. (1a)), which were fitted to the observed wavenumbers [3] of those modes (Figs. 1e5). Pseudospin-phonon coupled (PS) model (Eq. (2)) was then fitted to the observed FWHM [3] of the Raman modes of ns (CNN) and ns (NH3), and the IR mode of r(NH2) (Figs. 6e8) for MHyMn. This analysis was carried out for the first phase transition as the temperature increases with the transition temperature TC2 ¼ 213 K (cooling) and 224 K (heating) in MHyMn [3]. There occurs a second phase transition in this compound as the
Fig. 4. Wavenumber calculated as a function of temperature for the r(NH2) IR mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Fig. 5. Wavenumber calculated as a function of temperature for the ns (CNN) Raman mode according to Eq. (1a) which was fitted to the observed data [3] through Eq. (4) close phase transition (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
Fig. 6. Damping constant calculated as a function of temperature for the ns (CNN) Raman mode according to Eq. (2) which was fitted to the observed FWHM [3] close to the transition temperature (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
temperature increases at TC1 ¼ 309 K (cooling) and TC1 ¼ 310 K (heating) [3]. It was found that the decreasing behaviour of the frequency with increasing temperature toward the transition temperature (TC z 220 K), was associated with the order parameter S for the Raman modes of n(NH2) (Fig. 1), n1(HCOO) (Fig. 3) and the IR mode of r (NH2) (Fig. 4) with the exception of the ns (CH3) Raman mode whose frequency increases (Fig. 2). For this reason, the observed [3] Raman frequencies of the ns (CH3) (Fig. 2) and also of the n1(HCOO) mode at 2856 cm1 (Fig. 3) were not fitted to the order parameter according to Eq. (4), which were excluded (Table 1) in MHyMn. Our results show that those Raman and IR modes whose frequencies are related to the order parameter, involve in the mechanism of phase transition (TC z 220 K) in MHyMn within the molecular field theory (Eq. (1a)). Regarding the temperature dependence of the damping
491
Fig. 7. Damping constant calculated as a function of temperature for the ns (NH3) Raman mode according to Eq. (2) which was fitted to the observed FWHM [3] close to the transition temperature (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
Fig. 8. Damping constant calculated as a function of temperature for the r(NH2) IR mode according to Eq. (2) which was fitted to the observed FWHM [3] close to the transition temperature (Tc ¼ 220 K) in MHyMn. Vertical dotted lines denote the transition temperatures [3].
constant (FWHM) for the Raman modes of ns (CNN) (Fig. 6), ns (NH3) (Fig. 7) and the r (NH2) IR mode (Fig. 8), the pseudospinphonon coupled (PS) model (Eq. (2)) was satisfactory to explain the mechanism of phase transition (TC z 224 K) in MHyMn. In particular, the FWHM of the r (NH2) IR (924 cm1) mode varied largely with the temperature at TC, a discontinuous jump at ~13 cm1as observed experimentally [3] (Fig. 8). This difference in FWHM at TC was very small (~1.3 cm1) for the ns (CNN) (877 cm1) and ns (NH3) (2961 cm1) Raman modes as shown in Figs. (6) and (7), respectively, as also observed experimentally [3] in MHyMn. This sudden decrease in the FWHM of the r (NH2) IR mode for MHyMn just below TC (Fig. 8), is similar to that of the same mode (910 cm1) for DMMg due to the reorientational motions of the DMAþ cations at low temperatures [19]. It has been pointed out that for the NH2 group vibrations wavenumbers increase which indicates strengthening of the hydrogen bonds as a result of DMAþ
492
M. Kurt et al. / Journal of Molecular Structure 1181 (2019) 488e492
Table 3 Values of the background FWHM (G0) and the amplitude A for the Raman and IR modes indicated according to the pseudospin-phonon coupled (PS) model (Eq. (2)) within the temperature intervals below and above Tc (¼220 K) for MHyMn. T>Tc
T
Wavenumber (cm1) 877
ns (CH3) Raman r(NH2) IR
G0 (cm1) 3.68
A (cm1) 2.098
Temperature Interval (K) 79.6 < T < 219.8
2961
5.19
10.407
78.6 < T < 219.8
924
8.53
12.899
80.4 < T < 220.9
ordering in DMMg [19]. Similarly, due to the r (NH2) IR mode the phase transitions are governed by dynamics of the hydrazinium ions at low temperatures in MHyMn as in the case HyM (M ¼ Mn, Zn, Fe) compounds [21]. Note that analysis of the observed FWHM for the ns (CNN), ns (NH3) Raman modes and the r (NH2) IR mode above Tc was performed in the two temperature regions for the fitting procedure (Eq. (2)) with the parameters determined (Table 3). We also fitted damping constant due to the energy fluctuation (EF) model (Eq. (3)) to the observed FWHM [3] for the Raman and IR modes studied. Below Tc, it was fitted as good as the PS model for the ns (CNN) and ns (NH3) Raman modes but not for the r (NH2) IR mode. Above Tc, it did not give any better compared to the PS model although they could have been fitted reasonably well if the fitting were completed within two temperature regions as we did by using the PS model (Figs. 6e8). This may be due to the fact that the EF model (Eq. (3)) is better validated close to Tc (just above Tc, S ¼ 0) for the damping constant varying with the temperature as Gsp fðT Tc Þ1=2 with the critical exponent ½ whereas in a wide temperature range between ~100 and 400 K, the PS model seems to work better for MHyMn. It has been pointed out that the low temperature (LT) phase transition is well depicted for all frequencies but the hightemperature (HT) phase is strongly affected by the relaxation process and some conductivity processes appear at high temperatures [3]. From the expressions of the damping constant GSP (Eqs. (2) and (3)) for both models (PS and EF), the temperature dependence of the relaxation time (tSP) can be extracted for MHyMn. tSP should be quite different for MHyMn as compared to the other compounds of MHyM with M ¼ Mg, Fe and Zn. This is because of the fact that a distinct anomaly appeared at the HT phase transition at low frequencies in the MHyMn compound although anomalies associated with the HT phase transition are difficult to detect experimentally due to the strong frequency dispersion, as also pointed out previously [3]. It has been reported that high-pressure Raman scattering studies of MHyMn revealed a pressure-induced reversible phase transition between 4.8 and 5.5 GPa, which leads to significant changes in both the manganese formate framework and the MHyþ structure [3]. By analyzing the pressure dependence of the frequency (wavenumber) of Raman modes involving the pressureinduced phase transition using the molecular field theory and also by analyzing their linewidths through the PS and EF models, the mechanism of order-disorder transition in MHyMn can be
G0 (cm1) 7.35 8.91 11.31 12.96 32.67 39.97
A0 (cm1) 1.12 3.10 1.227 4.064 3.438 15.589
Temperature Interval (K) 230.0 < T < 310.8 318.3 < T < 399.1 229.1 < T < 310.1 319.2 < T < 400 229.1 < T < 309.9 320.1 < T < 399.1
explained. 4. Conclusions Raman and IR frequencies of some modes involving phase transitions were calculated at various temperatures in MHyMn by the molecular field theory using the observed data. Raman and IR frequency was assumed as an order parameter which was fitted to the observed wavenumber of those modes studied in this compound. Damping constant from the pseudospin-phonon coupling model (PS) was also fitted to the observed FWHM of those Raman and IR modes below and above the transition temperature (Tc ¼ 220 K) for MHyMn. We found that molecular field theory and the PS model are satisfactory to explain the observed behaviour of the wavenumber and FWHM, respectively, close to the phase transitions in MHyMn. References [1] A.P. Ramirez, J. Phys. Condens. Matter 9 (1997) 8171. [2] K.M. Rabe, C.H. Ahn, J.M. Triscone, Physics of Ferroelectrics: a Modern Perspective, Springer-Verlag, Berlin, Heidelberg, 2007. [3] M. Maczka, A. Gagor, M. Ptak, W. Paraguassu, T.A. da Silva, A. Sieradzki, A. Pikul, Chem. Mater. 29 (2017) 2264. [4] P. Jain, V. Ramachandran, R.J. Clark, H.D. Zhou, B.H. Toby, N.S. Dalal, H.W. Kroto, A.K. Cheetham, J. Am. Chem. Soc. 131 (2009) 13625. [5] M. Sanchez- Anjujar, S. Presedo, S. Yanez-Vilar, S. Castro-Garcia, J. Shamir, M.A. Senaris-Rodriguez, Inorg. Chem. 49 (2010) 1510. [6] W. Wang, L.Q. Yan, J.Z. Cong, Y.L. Zhao, F. Wang, S.P. Shen, T. Zhou, D. Zhang, S.G. Wang, X.F. Han, Y. Sun, Sci. Rep. 3 (2013) 2024. [7] M. Maczka, A. Gagor, B. Macalik, A. Pikul, M. Ptuk, J. Hanuza, Inorg. Chem. 53 (2014) 457. [8] M. Kosa, D.T. Major, Cryst. Eng. Commun. 17 (2015) 295. [9] P. Jain, A. Stroppa, D. Nabok, A. Marino, A. Rubano, D. Paparo, M. Matsubara, H. Nakotte, M. Fiebig, S. Picozzi, E.S. Choi, A.K. Cheetham, C. Draxl, N.S. Dalal, V.S. Zapf, NPJ. Quantum Mater. 1 (2016) 16012. [10] H.D. Duncan, M.T. Dove, D.A. Keen, A.E. Phillips, Dalton Trans. 45 (2016) 4380. [11] R. Brout, PhaseTransitions, Chapter 2, Benjamin, New York, USA, 1965. [12] M. Matsushita, J. Chem. Phys. 65 (1976) 23. [13] G. Lahajnar, R. Blinc, S. Zumer, Phys. Condens. Matter 18 (1974) 301. [14] G. Schaack, V. Winterfeldt, Ferroelectrics 15 (1977) 35. [15] I. Laulicht, N. Luknar, Chem. Phys. Lett. 47 (1977) 237. [16] I. Laulitch, J. Phys. Chem. Solid. 39 (1978) 901. [17] H. Yurtseven, H. Karacali, Spectrochim. Acta 65 (2006) 421. [18] H. Yurtseven, E. Kilit Dogan, Polyhedron 154 (2018) 132. [19] K. Szymborska-Malek, M. Trzebiatowska-Gusowska, M. Maczka, A. Gagor, Spectrochim. Acta 159 (2016) 35. [20] H. Yurtseven, A. Aslan, Ferroelectrics 526 (2018) 9. [21] M. Maczka, K. Pasinska, M. Ptak, W. Paraguassu, T. Almeida da Silva, A. Sieradzki, A. Pikul, Phys. Chem. Chem. Phys. 18 (2016) 31653.