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Order–disorder transition in triethylenediamine: A Raman scattering study
Journal of Molecular Structure 789 (2006) 195–199 www.elsevier.com/locate/molstruc
Order–disorder transition in triethylenediamine: A Raman scattering study Rekha Rao *, T. Sakuntala, S.K. Deb Synchrotron Radiation Section, Bhabha Atomic Research Center, Mumbai 400085, India Received 30 November 2005; received in revised form 28 December 2005; accepted 30 December 2005 Available online 29 March 2006
Abstract Order–disorder transition in triethylenediamine has been investigated by Raman spectroscopy. Large increase in linewidth accompanied by discontinuous decrease in the mode frequencies are observed across the transition to the disordered cubic phase at 351 K. Except for a few modes, the magnitude of discontinuity in frequency is much less compared to that expected for the given volume change. Most of the doubly degenerate modes show abrupt increase in linewidth at the transition temperature, which is understood to be due to dynamic disorder in the cubic phase. q 2006 Elsevier B.V. All rights reserved. Keywords: Raman Spectroscopy; Order–disorder transformations; Molecular solids
1. Introduction Molecular crystals consisting of highly symmetric globular molecules are ideal systems for understanding the packing in crystalline lattice, role of various non-bonded interactions, etc. At ambient conditions, many of these globular molecules are orientationally disordered and transform into an ordered low symmetry phase at lower temperatures. Physics of orientationally disordered crystals continues to be an interesting topic of basic research [1]. Attempts towards rigorous theoretical treatments of the phenomenon for a wide range of compounds have shown that there are a few important aspects, such as the role of translation–rotational coupling, existence of order parameter, symmetry considerations, etc., to be investigated in order to have complete understanding of the mechanism of transition to the ordered phase [1]. It is often observed that the underlying driving mechanism in the apparently similar systems, for example, in the case of C60 and C70, is quite different [2]. Similar to these carbon cages, a number of highly symmetric hydrocarbon-based molecular systems like methane [3], adamantane [4], bicyclooctane [5], cyclohexane [6], etc. exhibit order–disorder transitions. Related nitrogen-based systems, like hexamethylenetetramine (HMT) and triethylenediamine (TED), which are isoelectronic to adamantane and bicyclooctane (BCO), respectively, show a different behaviour. The transition temperature Tc increases with increase in * Corresponding author. Tel.: C91 22 25590190; fax: C91 22 25505151. E-mail address: [email protected] (R. Rao).
0022-2860/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2005.12.025
nitrogen atoms [7], i.e. of the systems BCO, quinuclidine and TED, BCO has the lowest Tc and TED has the highest, while HMT does not exhibit order–disorder transition up to melting [8]. There has been active research, both experimental as well as computational work, on the phase transition behaviour in molecular systems such as adamantane [9] and TED [7] as well as their derivatives [10,11]. Hydrogen-bonded monosalts of TED are known to exhibit transitions related to protondisordering and are considered to be ferroelectrics of potential technological importance [12]. Besides basic research interest, charcoal filters impregnated with TED are expected to be useful in nuclear reactors in the event of an accident owing to its ability to efficiently absorb noxious gases from air streams and radioiodine [13]. Triethylenediamine [N(CH2CH2)3N] exists in an ordered hexagonal structure at ambient conditions (space group: P63/m) with two molecules per unit cell [14]. Above 351 K, it exists in an orientationally disordered cubic phase (Fm3m); this transition was found to be associated with a large entropy as well as volume change [15–17]. Reynolds used Ising model to describe the behaviour [17] and reported that the configurational entropy could account for only about 40% of the measured change in entropy. Quasielastic neutron scattering studies [7] revealed that in the disordered phase, the molecules perform reorientational jumps between six equilibrium positions around the C3 axis together with a tumbling of the molecule from a [111] lattice direction to an equivalent position. Spectroscopic studies of order–disorder transition provide useful information on the extent of rotational–vibrational coupling, effect of disorder on phonon frequencies, and soft
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mode behaviour (if any) which are useful in modelling the transition [17]. Earlier Raman spectroscopic study by Sauvajol [18] reported the behaviour of external modes in the ordered phase over a temperature range of 110–330 K. In another Raman study, the activation energy associated with the reorientation process was estimated from the line shape analysis of the C–C symmetric stretching mode [19]. In the present work, we report the changes in the Raman spectrum of TED across the order–disorder transition. 2. Experimental details Raman spectra of unoriented crystal bits of TED are recorded in the temperature range 295–413 K from inside a capillary inserted in a high temperature cell. Temperature is controlled to an accuracy of better than G1 K using a Eurotherm temperature controller. The 532 nm laser line is used to excite the Raman spectrum and the power on the sample was 15 mW. Scattered light was analysed by a 0.9 m single monochromator [20] coupled with a super-notch filter and detected using a cooled CCD (Andor Technology). Resolution limited linewidth at 550 nm is measured to be about 2 cmK1 for an entrance slit opening of 50 mm. 3. Results At ambient conditions, the site symmetry of the TED molecule is C3h. Assignment of the Raman spectrum of TED in the ordered phase has been carried out by Sauvajol [21]. Owing to the centro-symmetric nature of the crystal, the Raman and the IR bands are mutually exclusive [22]. Raman spectrum of TED at ambient conditions agrees well with that reported earlier [21]. Raman bands arising due to C–H stretching motion appear in the region 2850–3000 cmK1. Most of the other internal modes of the molecule appear in the region 300– 1700 cmK1. Three Raman active lattice modes appear at frequencies less than 100 cmK1 [18]. In this work, we restrict to the study of internal modes at high temperatures. All the internal modes of TED were followed as a function of temperature. Figs. 1 and 2 show the evolution of Raman spectra at high temperature. At 351 K, there is an abrupt decrease in the frequencies of many of the internal modes accompanied by significant line broadening. The C–N stretching mode at 972 cmK1, which is of symmetry Ag, shows a discontinuous decrease in frequency (by 7 cmK1) at 351 K. Fig. 3 shows the temperature dependence of the mode frequencies. The mode at 1345 cmK1, identified as due to the CH2 twist [21], shows largest discontinuity across the transition. The mode at 800 cmK1 is not observed in the high temperature phase. Fig. 4 shows the variation of linewidth of some of the Raman bands across the transition. Most of the internal modes exhibit an abrupt increase in linewidth across the transition. It may be mentioned that in the earlier Raman studies also, rapid broadening of Ag and E1g lattice modes was observed prior to the transition [18]. This was attributed largely to the onset of disorder besides the cubic and quartic anharmonicity. In the present work also, large increase in the
Fig. 1. Raman spectra of some of the internal modes (NC3 deformation, C–N stretch and CH2 bending) of TED at various temperatures. Note the discontinuous decrease in mode frequency and increase in linewidth across the order–disorder transition above 351 K.
linewidth is noticed at the transition point. Further rise in temperature from 353 to 413 K (melting point: 433 K) does not produce significant increase in linewidth as compared to that across the transition.
4. Discussion 4.1. Temperature dependence of mode frequencies In the absence of any transition, varying the temperature produces a monotonic change in the vibrational spectrum. Across a phase transition, discontinuous changes in mode frequencies are sometimes observed which reflect the nature of changes in intermolecular interaction in different phases. For example, in the case of adamantane, across the order–disorder transition, molecules are oriented in such a way as to reduce certain non-bonded H/H repulsion [23], which is reflected in the phonon spectrum in the ordered phase [24]. Systems wherein the volume change across order–disorder transition is small, such as adamantane, C60 [24,25], spectral changes across the order–disorder transitions are mainly due to changes in crystal symmetry. In the present studies, not many new modes are observed in the ordered phase, except for the mode around 800 cmK1.
R. Rao et al. / Journal of Molecular Structure 789 (2006) 195–199
197
Fig. 2. (a, b) Raman spectra of the internal modes of TED across the transition.
This implies that the effect of correlation splitting is rather small. On the other hand, discontinuities are noted in the frequencies of several internal modes which may be partly due to large volume change across the transition. In the case of TED, as the volume change (z10.5%) is large [17], changes in the phonon spectrum arise due to volume change as well as altered intermolecular interaction. Table 1 summarizes the changes in the Raman modes of TED across the order–disorder transition. Effect of intermolecular interaction on phonon frequencies in the disordered phase can be obtained if the contribution arising from only the volume change may be quantified. An estimate of the discontinuity in mode frequency expected for a given volume change can be obtained from the knowledge of the compressibility and high pressure Raman measurements. Taking an average value of the bulk modulus and its derivative reported for several molecular solids [27], the pressure required for producing a volume change [17] of 10.5% is obtained from the Murnaghan equation of state to be 1.3 GPa. Taking the pressure dependence of the mode frequencies of the hexagonal phase of TED from the high pressure Raman measurements [28], expected changes in the mode frequencies over a pressure range of 1.3 GPa is given in Table 1 as Duhex. It is noted that most of the internal modes exhibit discontinuities much less than that expected for the given volume change. In particular, the modes at 579, 805 and 1061 cmK1 do not show any discontinuity across the transition implying that for these vibrational motions, effect of volume expansion is compensated by that due to increased intermolecular repulsion in
the disordered phase. While this holds for many of the modes, discontinuities observed in a few bands such as those at 972 (C–N stretching) and 599 cmK1 (C–N–C bending), both belonging to the symmetry Ag, and the two E1g modes at 1299 and 1458 cmK1 associated with the C–N stretch and NC3
Fig. 3. Temperature dependence of the frequencies of Raman bands in triethylenediamine.
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Fig. 4. Typical temperature dependence of the FWHM of the internal modes in triethylenediamine.
deformations, respectively, are found to be entirely due the volume change across the transition. 4.2. Temperature dependence of Raman linewidth As mentioned earlier, width of many of the internal modes changes significantly across the transition. A gradual increase
in linewidth may be expected due to increasing anharmonic contributions at higher temperature [29]. This contribution is obtained by fitting the observed variation to a linear equation in both the phases and is shown in Table 1. The other factor arises due to the coupling of different vibrations to the reorientational motion of the molecule. Table 1 also shows the fractional change in Raman linewidth across the transition with respect to
Table 1 Temperature dependence of the Raman frequencies and linewidth of the internal modes of TED in the ordered as well as disordered phases Symmetry
Mode assignment
E1g E2g E1g Ag Ag Ag E2g Ag E2g E1g
rNC3 [26] dasNC3 [26] dasNC3 [26] dsNC3 [26] CH2 rock C–C stretch nC–C [26] C–N stretch C–N stretch CH2 twist/C– N stretch CH2 scissor CH2 twist NC3 def C–H stretch C–H stretch C–H stretch C–H stretch C–H stretch
E1g Ag E1g E2g Ag E1g Ag E2g
Duhex (cmK1)
Du at Tc (cmK1)
T!Tc
TOTc
T!Tc
TOTc
336 430 579 599 800a 805 893 972 1061 1299
K6.4 K7.8 K4.8 K3.6 K5.5 K8.5 K7.4 K9.1 K7.9 K3.3
K1.5 K3.0 0 K2.2 – 0 0 K7.5 0 K4.4
3 2 3 3 1.9 4.5 2.8 4.4 4.3 2.1
3 1 6.5 6.8 – 1.0 – 3.5 2.5 1.6
0.84 0.62 0.6 0 – 0 0.95 0.72 0.77 0.86
1.1 2.0 1.1 1.1 1.9 0.2 3.0 2.1 3.1 2.0
4.5 5.0 3.8 1.1 – 0.2 – 3.6 8.8 8.4
1326b 1347b 1458 2876 2882a 2927 2941 2949
– – K5.7 K7.5 K12.4 K13.8 K11.4 K13.9
K3.7 K12 K3.3 K1.2 – K7.0 K5.0 0
4.8 4.0 4.9 2.8 5.75 2.8 5.5 K0.45
9.8 4.8 1.1 0.65 – 2.15 0.67 K1.4
– 0 0.93 0.3 – 0.6 0.65 2.03
0 7.1 3.5 1.6 0 3.6 1.0 3.0
– 7.1 8.3 3.5 – 0.8 6.3 1.0
Frequency (cmK1) at 295 K
du/dT (10K2 cmK1/K)
Ds/shex at Tc
ds/dT (10K2 cmK1/K)
Du and Ds are the discontinuities in frequency and width of the Raman modes, respectively. Assignments of Raman modes are taken from [21] unless specified. a Modes observed only in the ordered phase. b Raman modes for which high pressure data are not available.
R. Rao et al. / Journal of Molecular Structure 789 (2006) 195–199
the width in hexagonal phase at 351 K. It may be noted that most of the doubly degenerate modes show abrupt increase in linewidth at the transition temperature. Except for the C–N stretching at 972 cmK1, other Ag modes show relatively smaller changes in FWHM across the transition. In the light of the results of quasielastic neutron scattering [7] the abrupt increase in the linewidth of the internal modes is understood to be due to dynamic disorder in the cubic phase. Interestingly, the C–N–C bending mode of Ag symmetry at 599 cmK1 does not show any change in width across the transition indicating that this particular vibrational motion is least affected by the orientational disorder. The present behaviour may be compared with a few other typical globular molecular systems. In C70, no measurable discontinuity was found in either the mode frequencies or FWHM across the transition for any of the modes [30]. Changes observed in Raman linewidth in the present work are somewhat similar to that observed in C60, which was attributed to coupling of the phonons with the rotational motions of the molecules in the disordered phase [31]. It was argued that the coupling to more symmetric Ag modes was expected to be smaller [31] resulting in little change in linewidth across the transition. It may be mentioned that in TED, the ds/dT of many of the Ag modes before and after the transition are of similar magnitude while for the doubly degenerate modes, there is a considerable increase in ds/dT in the disordered phase. 5. Conclusion Order–disorder transition in TED has been investigated by Raman spectroscopy. Discontinuous changes are noted in many of the mode frequencies and linewidth of the internal modes at 351 K. However, except for a very few modes, the magnitude of discontinuity is much less compared to that expected for the given volume change suggesting that these vibrational motions are hindered by the molecular reorientations in the disordered phase. Only the CN-related modes (C–N stretching, C–N–C bending and the NC3 deformation modes) show discontinuities proportional to the volume change. Discontinuous changes are noted in the Raman linewidth of most of the internal modes suggesting a strong vibrational– rotational coupling in the disordered phase. A few bands of Ag
199
symmetry show little discontinuity suggesting that their coupling to the rotational motions is weak. References [1] R.M. Lynden-Bell, K.H. Michel, Rev. Mod. Phys. 66 (1994) 721. [2] A.K. Callebaut, K.H. Michel, Phys. Rev. B 52 (1995) 15279. [3] D. Fabre, M.M. Thiery, H. Vu, K. Kobashi, J. Chem. Phys. 71 (1979) 3081. [4] C.E. Nordman, D.L. Schmitkons, Acta Crystallogr. 18 (1965) 764. [5] W.K. Wong, E.F. Westrum, J. Phys. Chem. 74 (1970) 1303. [6] K.D. Wisotzki, A. Wurfinger, J. Phys. Chem. Solids 43 (1982) 13. [7] M. Bee, J.L. Sauvajol, A. Hedoux, J.P. Amourex, Mol. Phys. 55 (1985) 637. [8] S.S. Chang, E.F. Westrum, J. Phys. Chem. 64 (1960) 1547. [9] D.W. Greig, G.S. Pawley, Mol. Phys. 89 (1996) 677. [10] R. Fabrianskii, L. Firlej, B. Kuchta, J. Chem. Phys. 116 (2002) 10356; L.A. Fraczyk, Y. Huang, Spectrochim. Acta, Part A 57 (2001) 1061. [11] A. Katrusiak, M. Szafranski, Phys. Rev. Lett. 82 (1999) 576; M. Szafranski, A. Katrusiak, G.J. McIntyre, Phys. Rev. Lett. 89 (2002) 215507; M. Szafranski, J. Phys.: Condens. Matter 16 (2004) 6053. [12] A. Katrusiak, J. Mol. Struct. 552 (2000) 159. [13] J. Manusco, R.J. McEachern, J. Mol. Graph. Model. 15 (1997) 82. [14] J.K. Nimmo, B.W. Lucas, Acta Crystallogr., Sect. B 32 (1976) 348. [15] J.K. Nimmo, B.W. Lucas, Acta Crystallogr., Sect. B 32 (1976) 597. [16] J.C. Trowbridge, E.V. Westrum, J. Phys. Chem. 67 (1963) 2381. [17] P. Reynolds, Mol. Phys. 28 (1974) 633. [18] J.L. Sauvajol, J. Raman Spectrosc. 13 (1982) 270. [19] A.M. Amorim Da Costa, J. Mol. Struct. 141 (1986) 347. [20] A.P. Roy, S.K. Deb, M.A. Rekha, A.K. Sinha, Indian J. Pure Appl. Phys. 30 (1992) 724. [21] J.L. Sauvajol, J. Phys. C: Solid State Phys. 13 (1980) 1321. [22] G.J. Weiss, A.S. Parkes, E.R. Nixon, R.E. Hughes, J. Chem. Phys. 41 (1964) 3759. [23] R.M. Corn, V.L. Shannon, R.G. Snyder, H.L. Strauss, J. Chem. Phys. 81 (1984) 5231. [24] R. Rao, T. Sakuntala, S.K. Deb, A.P. Roy, V. Vijayakumar, B.K. Godwal, S.K. Sikka, J. Chem. Phys. 112 (2000) 6739. [25] M. Matus, H. Kuzmany, W. Kratschmer, Solid State Commun. 80 (1991) 839. [26] J.R. McDevitt, G.L. Humphrey, Spectrochim. Acta 32A (1974) 1021. [27] S.N. Vaidya, G.C. Kennedy, J. Chem. Phys. 55 (1971) 987. [28] R. Rao, T. Sakuntala, S.K. Deb, Solid State Phys. (India) 44 (2001) 41. [29] A.K. Sood, A.K. Arora, V. Umadevi, G. Venkataraman, Pramana 16 (1981) 1. [30] N. Chandrabhas, K. Jayaram, D.V.S. Muthu, A.K. Sood, Ram Seshadri, C.N.R. Rao, Phys. Rev. B 47 (1993) 10963. [31] P.H.M. van Loosdrecht, P.J.M. van Bentum, G. Meijer, Phys. Rev. Lett. 68 (1992) 1176.
Order–disorder transition in triethylenediamine: A Raman scattering study Rekha Rao *, T. Sakuntala, S.K. Deb Synchrotron Radiation Section, Bhabha Atomic Research Center, Mumbai 400085, India Received 30 November 2005; received in revised form 28 December 2005; accepted 30 December 2005 Available online 29 March 2006
Abstract Order–disorder transition in triethylenediamine has been investigated by Raman spectroscopy. Large increase in linewidth accompanied by discontinuous decrease in the mode frequencies are observed across the transition to the disordered cubic phase at 351 K. Except for a few modes, the magnitude of discontinuity in frequency is much less compared to that expected for the given volume change. Most of the doubly degenerate modes show abrupt increase in linewidth at the transition temperature, which is understood to be due to dynamic disorder in the cubic phase. q 2006 Elsevier B.V. All rights reserved. Keywords: Raman Spectroscopy; Order–disorder transformations; Molecular solids
1. Introduction Molecular crystals consisting of highly symmetric globular molecules are ideal systems for understanding the packing in crystalline lattice, role of various non-bonded interactions, etc. At ambient conditions, many of these globular molecules are orientationally disordered and transform into an ordered low symmetry phase at lower temperatures. Physics of orientationally disordered crystals continues to be an interesting topic of basic research [1]. Attempts towards rigorous theoretical treatments of the phenomenon for a wide range of compounds have shown that there are a few important aspects, such as the role of translation–rotational coupling, existence of order parameter, symmetry considerations, etc., to be investigated in order to have complete understanding of the mechanism of transition to the ordered phase [1]. It is often observed that the underlying driving mechanism in the apparently similar systems, for example, in the case of C60 and C70, is quite different [2]. Similar to these carbon cages, a number of highly symmetric hydrocarbon-based molecular systems like methane [3], adamantane [4], bicyclooctane [5], cyclohexane [6], etc. exhibit order–disorder transitions. Related nitrogen-based systems, like hexamethylenetetramine (HMT) and triethylenediamine (TED), which are isoelectronic to adamantane and bicyclooctane (BCO), respectively, show a different behaviour. The transition temperature Tc increases with increase in * Corresponding author. Tel.: C91 22 25590190; fax: C91 22 25505151. E-mail address: [email protected] (R. Rao).
0022-2860/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2005.12.025
nitrogen atoms [7], i.e. of the systems BCO, quinuclidine and TED, BCO has the lowest Tc and TED has the highest, while HMT does not exhibit order–disorder transition up to melting [8]. There has been active research, both experimental as well as computational work, on the phase transition behaviour in molecular systems such as adamantane [9] and TED [7] as well as their derivatives [10,11]. Hydrogen-bonded monosalts of TED are known to exhibit transitions related to protondisordering and are considered to be ferroelectrics of potential technological importance [12]. Besides basic research interest, charcoal filters impregnated with TED are expected to be useful in nuclear reactors in the event of an accident owing to its ability to efficiently absorb noxious gases from air streams and radioiodine [13]. Triethylenediamine [N(CH2CH2)3N] exists in an ordered hexagonal structure at ambient conditions (space group: P63/m) with two molecules per unit cell [14]. Above 351 K, it exists in an orientationally disordered cubic phase (Fm3m); this transition was found to be associated with a large entropy as well as volume change [15–17]. Reynolds used Ising model to describe the behaviour [17] and reported that the configurational entropy could account for only about 40% of the measured change in entropy. Quasielastic neutron scattering studies [7] revealed that in the disordered phase, the molecules perform reorientational jumps between six equilibrium positions around the C3 axis together with a tumbling of the molecule from a [111] lattice direction to an equivalent position. Spectroscopic studies of order–disorder transition provide useful information on the extent of rotational–vibrational coupling, effect of disorder on phonon frequencies, and soft
196
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mode behaviour (if any) which are useful in modelling the transition [17]. Earlier Raman spectroscopic study by Sauvajol [18] reported the behaviour of external modes in the ordered phase over a temperature range of 110–330 K. In another Raman study, the activation energy associated with the reorientation process was estimated from the line shape analysis of the C–C symmetric stretching mode [19]. In the present work, we report the changes in the Raman spectrum of TED across the order–disorder transition. 2. Experimental details Raman spectra of unoriented crystal bits of TED are recorded in the temperature range 295–413 K from inside a capillary inserted in a high temperature cell. Temperature is controlled to an accuracy of better than G1 K using a Eurotherm temperature controller. The 532 nm laser line is used to excite the Raman spectrum and the power on the sample was 15 mW. Scattered light was analysed by a 0.9 m single monochromator [20] coupled with a super-notch filter and detected using a cooled CCD (Andor Technology). Resolution limited linewidth at 550 nm is measured to be about 2 cmK1 for an entrance slit opening of 50 mm. 3. Results At ambient conditions, the site symmetry of the TED molecule is C3h. Assignment of the Raman spectrum of TED in the ordered phase has been carried out by Sauvajol [21]. Owing to the centro-symmetric nature of the crystal, the Raman and the IR bands are mutually exclusive [22]. Raman spectrum of TED at ambient conditions agrees well with that reported earlier [21]. Raman bands arising due to C–H stretching motion appear in the region 2850–3000 cmK1. Most of the other internal modes of the molecule appear in the region 300– 1700 cmK1. Three Raman active lattice modes appear at frequencies less than 100 cmK1 [18]. In this work, we restrict to the study of internal modes at high temperatures. All the internal modes of TED were followed as a function of temperature. Figs. 1 and 2 show the evolution of Raman spectra at high temperature. At 351 K, there is an abrupt decrease in the frequencies of many of the internal modes accompanied by significant line broadening. The C–N stretching mode at 972 cmK1, which is of symmetry Ag, shows a discontinuous decrease in frequency (by 7 cmK1) at 351 K. Fig. 3 shows the temperature dependence of the mode frequencies. The mode at 1345 cmK1, identified as due to the CH2 twist [21], shows largest discontinuity across the transition. The mode at 800 cmK1 is not observed in the high temperature phase. Fig. 4 shows the variation of linewidth of some of the Raman bands across the transition. Most of the internal modes exhibit an abrupt increase in linewidth across the transition. It may be mentioned that in the earlier Raman studies also, rapid broadening of Ag and E1g lattice modes was observed prior to the transition [18]. This was attributed largely to the onset of disorder besides the cubic and quartic anharmonicity. In the present work also, large increase in the
Fig. 1. Raman spectra of some of the internal modes (NC3 deformation, C–N stretch and CH2 bending) of TED at various temperatures. Note the discontinuous decrease in mode frequency and increase in linewidth across the order–disorder transition above 351 K.
linewidth is noticed at the transition point. Further rise in temperature from 353 to 413 K (melting point: 433 K) does not produce significant increase in linewidth as compared to that across the transition.
4. Discussion 4.1. Temperature dependence of mode frequencies In the absence of any transition, varying the temperature produces a monotonic change in the vibrational spectrum. Across a phase transition, discontinuous changes in mode frequencies are sometimes observed which reflect the nature of changes in intermolecular interaction in different phases. For example, in the case of adamantane, across the order–disorder transition, molecules are oriented in such a way as to reduce certain non-bonded H/H repulsion [23], which is reflected in the phonon spectrum in the ordered phase [24]. Systems wherein the volume change across order–disorder transition is small, such as adamantane, C60 [24,25], spectral changes across the order–disorder transitions are mainly due to changes in crystal symmetry. In the present studies, not many new modes are observed in the ordered phase, except for the mode around 800 cmK1.
R. Rao et al. / Journal of Molecular Structure 789 (2006) 195–199
197
Fig. 2. (a, b) Raman spectra of the internal modes of TED across the transition.
This implies that the effect of correlation splitting is rather small. On the other hand, discontinuities are noted in the frequencies of several internal modes which may be partly due to large volume change across the transition. In the case of TED, as the volume change (z10.5%) is large [17], changes in the phonon spectrum arise due to volume change as well as altered intermolecular interaction. Table 1 summarizes the changes in the Raman modes of TED across the order–disorder transition. Effect of intermolecular interaction on phonon frequencies in the disordered phase can be obtained if the contribution arising from only the volume change may be quantified. An estimate of the discontinuity in mode frequency expected for a given volume change can be obtained from the knowledge of the compressibility and high pressure Raman measurements. Taking an average value of the bulk modulus and its derivative reported for several molecular solids [27], the pressure required for producing a volume change [17] of 10.5% is obtained from the Murnaghan equation of state to be 1.3 GPa. Taking the pressure dependence of the mode frequencies of the hexagonal phase of TED from the high pressure Raman measurements [28], expected changes in the mode frequencies over a pressure range of 1.3 GPa is given in Table 1 as Duhex. It is noted that most of the internal modes exhibit discontinuities much less than that expected for the given volume change. In particular, the modes at 579, 805 and 1061 cmK1 do not show any discontinuity across the transition implying that for these vibrational motions, effect of volume expansion is compensated by that due to increased intermolecular repulsion in
the disordered phase. While this holds for many of the modes, discontinuities observed in a few bands such as those at 972 (C–N stretching) and 599 cmK1 (C–N–C bending), both belonging to the symmetry Ag, and the two E1g modes at 1299 and 1458 cmK1 associated with the C–N stretch and NC3
Fig. 3. Temperature dependence of the frequencies of Raman bands in triethylenediamine.
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Fig. 4. Typical temperature dependence of the FWHM of the internal modes in triethylenediamine.
deformations, respectively, are found to be entirely due the volume change across the transition. 4.2. Temperature dependence of Raman linewidth As mentioned earlier, width of many of the internal modes changes significantly across the transition. A gradual increase
in linewidth may be expected due to increasing anharmonic contributions at higher temperature [29]. This contribution is obtained by fitting the observed variation to a linear equation in both the phases and is shown in Table 1. The other factor arises due to the coupling of different vibrations to the reorientational motion of the molecule. Table 1 also shows the fractional change in Raman linewidth across the transition with respect to
Table 1 Temperature dependence of the Raman frequencies and linewidth of the internal modes of TED in the ordered as well as disordered phases Symmetry
Mode assignment
E1g E2g E1g Ag Ag Ag E2g Ag E2g E1g
rNC3 [26] dasNC3 [26] dasNC3 [26] dsNC3 [26] CH2 rock C–C stretch nC–C [26] C–N stretch C–N stretch CH2 twist/C– N stretch CH2 scissor CH2 twist NC3 def C–H stretch C–H stretch C–H stretch C–H stretch C–H stretch
E1g Ag E1g E2g Ag E1g Ag E2g
Duhex (cmK1)
Du at Tc (cmK1)
T!Tc
TOTc
T!Tc
TOTc
336 430 579 599 800a 805 893 972 1061 1299
K6.4 K7.8 K4.8 K3.6 K5.5 K8.5 K7.4 K9.1 K7.9 K3.3
K1.5 K3.0 0 K2.2 – 0 0 K7.5 0 K4.4
3 2 3 3 1.9 4.5 2.8 4.4 4.3 2.1
3 1 6.5 6.8 – 1.0 – 3.5 2.5 1.6
0.84 0.62 0.6 0 – 0 0.95 0.72 0.77 0.86
1.1 2.0 1.1 1.1 1.9 0.2 3.0 2.1 3.1 2.0
4.5 5.0 3.8 1.1 – 0.2 – 3.6 8.8 8.4
1326b 1347b 1458 2876 2882a 2927 2941 2949
– – K5.7 K7.5 K12.4 K13.8 K11.4 K13.9
K3.7 K12 K3.3 K1.2 – K7.0 K5.0 0
4.8 4.0 4.9 2.8 5.75 2.8 5.5 K0.45
9.8 4.8 1.1 0.65 – 2.15 0.67 K1.4
– 0 0.93 0.3 – 0.6 0.65 2.03
0 7.1 3.5 1.6 0 3.6 1.0 3.0
– 7.1 8.3 3.5 – 0.8 6.3 1.0
Frequency (cmK1) at 295 K
du/dT (10K2 cmK1/K)
Ds/shex at Tc
ds/dT (10K2 cmK1/K)
Du and Ds are the discontinuities in frequency and width of the Raman modes, respectively. Assignments of Raman modes are taken from [21] unless specified. a Modes observed only in the ordered phase. b Raman modes for which high pressure data are not available.
R. Rao et al. / Journal of Molecular Structure 789 (2006) 195–199
the width in hexagonal phase at 351 K. It may be noted that most of the doubly degenerate modes show abrupt increase in linewidth at the transition temperature. Except for the C–N stretching at 972 cmK1, other Ag modes show relatively smaller changes in FWHM across the transition. In the light of the results of quasielastic neutron scattering [7] the abrupt increase in the linewidth of the internal modes is understood to be due to dynamic disorder in the cubic phase. Interestingly, the C–N–C bending mode of Ag symmetry at 599 cmK1 does not show any change in width across the transition indicating that this particular vibrational motion is least affected by the orientational disorder. The present behaviour may be compared with a few other typical globular molecular systems. In C70, no measurable discontinuity was found in either the mode frequencies or FWHM across the transition for any of the modes [30]. Changes observed in Raman linewidth in the present work are somewhat similar to that observed in C60, which was attributed to coupling of the phonons with the rotational motions of the molecules in the disordered phase [31]. It was argued that the coupling to more symmetric Ag modes was expected to be smaller [31] resulting in little change in linewidth across the transition. It may be mentioned that in TED, the ds/dT of many of the Ag modes before and after the transition are of similar magnitude while for the doubly degenerate modes, there is a considerable increase in ds/dT in the disordered phase. 5. Conclusion Order–disorder transition in TED has been investigated by Raman spectroscopy. Discontinuous changes are noted in many of the mode frequencies and linewidth of the internal modes at 351 K. However, except for a very few modes, the magnitude of discontinuity is much less compared to that expected for the given volume change suggesting that these vibrational motions are hindered by the molecular reorientations in the disordered phase. Only the CN-related modes (C–N stretching, C–N–C bending and the NC3 deformation modes) show discontinuities proportional to the volume change. Discontinuous changes are noted in the Raman linewidth of most of the internal modes suggesting a strong vibrational– rotational coupling in the disordered phase. A few bands of Ag
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symmetry show little discontinuity suggesting that their coupling to the rotational motions is weak. References [1] R.M. Lynden-Bell, K.H. Michel, Rev. Mod. Phys. 66 (1994) 721. [2] A.K. Callebaut, K.H. Michel, Phys. Rev. B 52 (1995) 15279. [3] D. Fabre, M.M. Thiery, H. Vu, K. Kobashi, J. Chem. Phys. 71 (1979) 3081. [4] C.E. Nordman, D.L. Schmitkons, Acta Crystallogr. 18 (1965) 764. [5] W.K. Wong, E.F. Westrum, J. Phys. Chem. 74 (1970) 1303. [6] K.D. Wisotzki, A. Wurfinger, J. Phys. Chem. Solids 43 (1982) 13. [7] M. Bee, J.L. Sauvajol, A. Hedoux, J.P. Amourex, Mol. Phys. 55 (1985) 637. [8] S.S. Chang, E.F. Westrum, J. Phys. Chem. 64 (1960) 1547. [9] D.W. Greig, G.S. Pawley, Mol. Phys. 89 (1996) 677. [10] R. Fabrianskii, L. Firlej, B. Kuchta, J. Chem. Phys. 116 (2002) 10356; L.A. Fraczyk, Y. Huang, Spectrochim. Acta, Part A 57 (2001) 1061. [11] A. Katrusiak, M. Szafranski, Phys. Rev. Lett. 82 (1999) 576; M. Szafranski, A. Katrusiak, G.J. McIntyre, Phys. Rev. Lett. 89 (2002) 215507; M. Szafranski, J. Phys.: Condens. Matter 16 (2004) 6053. [12] A. Katrusiak, J. Mol. Struct. 552 (2000) 159. [13] J. Manusco, R.J. McEachern, J. Mol. Graph. Model. 15 (1997) 82. [14] J.K. Nimmo, B.W. Lucas, Acta Crystallogr., Sect. B 32 (1976) 348. [15] J.K. Nimmo, B.W. Lucas, Acta Crystallogr., Sect. B 32 (1976) 597. [16] J.C. Trowbridge, E.V. Westrum, J. Phys. Chem. 67 (1963) 2381. [17] P. Reynolds, Mol. Phys. 28 (1974) 633. [18] J.L. Sauvajol, J. Raman Spectrosc. 13 (1982) 270. [19] A.M. Amorim Da Costa, J. Mol. Struct. 141 (1986) 347. [20] A.P. Roy, S.K. Deb, M.A. Rekha, A.K. Sinha, Indian J. Pure Appl. Phys. 30 (1992) 724. [21] J.L. Sauvajol, J. Phys. C: Solid State Phys. 13 (1980) 1321. [22] G.J. Weiss, A.S. Parkes, E.R. Nixon, R.E. Hughes, J. Chem. Phys. 41 (1964) 3759. [23] R.M. Corn, V.L. Shannon, R.G. Snyder, H.L. Strauss, J. Chem. Phys. 81 (1984) 5231. [24] R. Rao, T. Sakuntala, S.K. Deb, A.P. Roy, V. Vijayakumar, B.K. Godwal, S.K. Sikka, J. Chem. Phys. 112 (2000) 6739. [25] M. Matus, H. Kuzmany, W. Kratschmer, Solid State Commun. 80 (1991) 839. [26] J.R. McDevitt, G.L. Humphrey, Spectrochim. Acta 32A (1974) 1021. [27] S.N. Vaidya, G.C. Kennedy, J. Chem. Phys. 55 (1971) 987. [28] R. Rao, T. Sakuntala, S.K. Deb, Solid State Phys. (India) 44 (2001) 41. [29] A.K. Sood, A.K. Arora, V. Umadevi, G. Venkataraman, Pramana 16 (1981) 1. [30] N. Chandrabhas, K. Jayaram, D.V.S. Muthu, A.K. Sood, Ram Seshadri, C.N.R. Rao, Phys. Rev. B 47 (1993) 10963. [31] P.H.M. van Loosdrecht, P.J.M. van Bentum, G. Meijer, Phys. Rev. Lett. 68 (1992) 1176.