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A Raman signature of the
incommensurate-commensurate phase transition (lock-in) in a crystalline monomer diacetylene : pTS
M. Bertault, M. Krauzman, M. Le Postollec, R.M. Pick, M. Schott
To cite this version:
M. Bertault, M. Krauzman, M. Le Postollec, R.M. Pick, M. Schott. A Raman signature of the incommensurate-commensurate phase transition (lock-in) in a crystalline monomer diacetylene : pTS.
Journal de Physique, 1982, 43 (5), pp.755-759. �10.1051/jphys:01982004305075500�. �jpa-00209447�
A Raman signature of the incommensurate-commensurate phase transition (lock-in) in a crystalline monomer diacetylene : pTS
M. Bertault (*), M. Krauzman (**), M. Le Postollec (**), R. M. Pick (**) and M. Schott (*)
(*) GPS de l’ENS (***), Université Paris VII, Tour 23, 2 Place Jussieu, 75251 Paris Cedex 05, France (**) D.R.P. (***), Université P. et M. Curie, 4 Place Jussieu, 75231 Paris Cedex 05, France
(Reçu le 10 septembre 1981, accepté le 15 janvier 1982)
Résumé. 2014 Nous avons mesuré, en fonction de la température, les spectres Raman polarisés de basse fréquence
d’un cristal de pTS monomère. Nous observons deux modes associés à la phase incommensurable (qui existe entre Ti ~ 200 K et T1 ~ 155 K) et aux transitions de phase correspondantes. Le mode mou (ampliton) est détecté à
toute température en dessous de Ti - 15 K, en accord avec un caractère displacif de la distorsion dans ce domaine de température. Un mode à 13 cm-1 n’existe que dans la phase incommensurable. Nous proposons un mécanisme pour expliquer la détection de ce mode dans cette seule phase et montrons que nos résultats sont en accord avec les données neutroniques et I.R.
Abstract 2014 The low frequency polarized Raman spectra of monomer pTS crystals have been studied as a function
of temperature. We observe two features associated with the incommensurate phase, which exists between
Ti ~ 200 K and T1 ~ 155 K, and the related phase transitions. A soft mode (ampliton) is detected at all tempera-
tures below Ti - 15 K and corresponds to a displacive behaviour in this temperature range. A line at 13 cm-1 is present only in the incommensurate phase. A possible mechanism for the detection of that line in this sole phase
is discussed and shown to be in complete agreement with the neutron and I.R. data.
Classification
Physics Abstracts
64. 70K - 78. 30
1. Introduction. - The diacetylenes are a large family of molecules with general chemical formula
R-C -= C-C --_ C-R’, where R, R’ may be identical or
different substituents. They form typical molecular crystals; many of them polymerize in the solid state, and this is almost the only possibility for obtaining large polymer single crystals [1]. A well-investigated example is pTS, in which R and R’ are CH3-C6H4- -S03-CH2. Another, more recently discovered [2], interesting property of monomer pTS crystals is the
occurrence of an incommensurately modulated phase,
between about 155 and 200 K, which motivated the present Raman investigation. For the first time, a feature is found in the Raman spectrum, present only
in the incommensurate phase and disappearing rapidly, but not abruptly, at the lower end of the
corresponding temperature range.
Monomer and polymer pTS form a continuous
series of solid solutions, and the incommensurate
phase also exists in mixed crystals up to at least 10 % polymer content [3]. In this paper, only pure monomer
pTS is studied. Its high temperature phase I (Fig. 1) is
P21/C(C2’h) with Z = 2, above Ti - 200 K [4]; 3 the
low temperature phase III below T, - 155 K, again P21/c but with Z = 4, is related to phase I by doubling
of the unit cell along a ; the diacetylene molecules are
distorted in alternate ways, and the cell then contains
two families of molecules with slightly different geome- tries and environments [4, 5] ; the superlattice Bragg peaks, at (h + JL k,1) in phase I indexation, are gene-
rally weak.
Between T; and T,, pairs of satellite diffraction peaks
appear at (h + 2, k ± 6, 1), that is, phase II is incom-
mensurately modulated with a vector q = 2 a* + 6(T) b*. From Ti to a few degrees above T,, the
satellite intensity varies as (T ; - 7)20 with P = 0.43
and Ti = 199.2 K [3b], and 6 decreases smoothly from
about 0.06 at Ti [2, 3]. In the immediate vicinity of T,, there is a narrow temperature range in which
Fig. 1. - Structure of the three phases of crystalline mono-
mer pTS.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004305075500
756
superstructure Bragg peaks and broader satellites
coexist, before the incommensurate modulation locks
completely into the low temperature superstructure.
The lock-in transition is first order, as shown also by
the occurrence of a weak hysteresis on the value of 6 up to T, + 20 K at least [3b]. The origin of the incom- mensurate phase in pTS is far from being completely
understood.
2. Experiments. - pTS was prepared according to [6] and purified by several recrystallizations in CH2C’2-CH30H mixtures, to yield a white odorless
powder free from polymer and residual Tosyl Chloride.
Single crystals were obtained from this powder by
slow recrystallization from acetone solution at 4 OC
under a flow of pure N2 gas. Their polymer content,
from absorption spectra, was 5 x 10- 3 in weight.
Polarized Raman spectra were taken using the
6 471 A line of a Kr+ laser (spectra Physics 165), since poly-pTS chains in pTS monomer absorb in the A+
lines region. It was checked that resonance effects on poly-pTS were absent in the region of interest, by running a 7 525 A spectrum which showed relative Raman intensities identical to those obtained with 6 471 A excitation. In order to avoid hysteresis effects,
all Raman spectra were taken by increasing the tempe-
rature.
Fig. 2. - Satellite data from coherent elastic scattering.
Open circles : measured values of 6 in units of b* (the uncer- tainty is about the size of the ’dots). The dashed line is a
guide to the eye. Solid line : satellite intensity, from [(199.2 - T)O- 86] ; dashed parts are extrapolations in regions where there is scattered intensity from other origin, interfering with the measurements : crosses are typical
measured intensities near T,. The solid vertical bars are satellite widths when they are larger than the instrument
linewidth of 7 x 10- 3 b* also indicated.
3. Results. - Only the low frequency range,
co 50 cm-’, will be considered here. There are
already several optical phonon branches in this range, also found by inelastic neutron scattering [7] or far
I.R. spectroscopy [8].
Fig. 3. - Raman spectra of the soft mode (arrow) in the b(ac)a geometry (left) and in the b(cc)a geometry (right).
Two features are clearly associated with the incom- mensurate phase and the related transitions :
1) A line present in phases II and III, which softens
as T -+ T; from below.
2) A line present in phase II only, which is then the
Raman signature of the incommensurate structure in
pTS.
3 .1 THE « SOFT-MODE ». - Figure 3 shows spectra taken at various temperatures in the b(ac)a and b(cc)a geometries, where A. modes in phase I factor group
representation should appear. The arrows indicate a
mode present at least between 9 K and 184 K
(T; - 15 K), the highest temperature at which it appears already underdamped. This mode clearly
softens as T -+ T; but the presence of other strong modes to which it is probably coupled prevents the study of its frequency and intensity. The existence of such an Ag soft mode, corresponding in phase I to a
Raman inactive soft phonon at q = i a* ± b(T)b*
is predicted for displacive transitions [9, 10]. This
Fig. 4. - Typical low frequency Raman spectrum of phase II in the c(bb)a geometry. T = 171 K. The arrows
indicate the 13 cm - 1 mode studied in this paper.
Fig. 5. - Temperature dependence of the 13 cm-’ mode.
c(bb)a polarization. Curves a) to e) are for T = 156.6 K;
159 K, 159.6 K; 160.1 K; 161 K. Note the rapid variation
near T i. Curves f) to i) are for T = 168.3 K; 173 K; 179.9 K;
188.1K;211K.
indicates that the displacive character of the transition is dominant at least below T; - 15 K. On
the other hand, the structural analysis of phase I at Ti + 20 K does not allow to decide in favour of a
displacive transition [4] and no soft mode has been observed up to now in phase I by neutron inelastic scattering [7].
3.2 THE MODE CHARACTERISTIC OF THE INCOM- MENSURATE PHASE. - Figure 4 shows a c(bb)a spec- trum taken at 171 K, where a small peak is seen at
13 cm-1. Figure 5 shows this peak (in the Stokes spectrum) at several temperatures between T, and T;.
Identical spectra are obtained on all the crystals
studied. This line could not be detected in the other Ag geometries. It is totally absent in phases I and III.
There is no detectable frequency shift with T between T; and TI, and its intensity varies as shown on figure 6 :
it rises slowly when T decreases from Ti, then drops quickly within a few degrees above T,, so that, from
Raman data, it is possible to determine T, to an
accuracy of less than a few degrees.
4. Theory. - In this section, we show how such a
Raman feature, specifically related to the incommen- surate phase and having all the properties reported above, can be obtained theoretically. Detailed compa- rison to experiment is given in section 5.
The Raman polarizability can be written as the
sum of polarizabilities produced respectively by one,
two or three-phonon processes :
where the successive terms are :
where u(q, j, t) is the displacement produced by the phonon from branch j, with wave vector q and fre- quency 0153(q, j). The R£° factor is the rxf3 (= bb in our case) component of the Raman tensor relative to an
nth order scattering process between one photon and
n phonons. The Kronecker symbol A accounts for
momentum conservation. G is a reciprocal lattice
vector.
In the Landau theory of a displacive transition, one
can consider phases II and III as equivalent to phase I
distorted by a static phonon, with frequency co(qo) = 0, wave vector qo = a*/2 + bb* (with 03B4 = 0
in phase III) and amplitude ’1(qo). In these phases, as
the static distortion n(Qo) becomes large with respect
to a mean phonon amplitude, the above multiphonon scattering mechanisms transform into first order
758
Raman processes where all but one phonons contained
in equations (1) to (3) are taken as ’1(Qo), the remaining
one having a non zero frequency wl ( = 13 cm-1 in
our case); equations (1)-(3) yield :
where the af3 superscripts and the branch indices have been omitted for the sake of clarity. u labels the amplitude of the phonon observed at wl = 13 cm-’.
Each term of equations (4)-(6) represents an inde- pendent scattering mechanism. We shall use the known Raman properties of mode Wt (observed only in phase II with Ag symmetry) to discuss the relevance of these possible mechanisms to the present case and find that only (5) and the first term of (6) are possible
candidates.
Equation (4) would contribute in the same way in
phases I, II, III and cannot account for the observed
phenomenon. Similarly, the contribution of the last term of equation (6) is not affected by the lock-in
transition as 17(qo) 17( - qo) = 11 17(qo) 112 belongs to
the invariant representation of the crystal group for any qo. The absence of WI in phase III shows that this
term is not the scattering mechanism we are looking
for.
The symmetry analysis of the remaining terms containing R2 and R3 in equations (5) and (6) follows closely the method of references [9] and [10] where the activity Qf a non zone centre phonon in incommensu- rate phases is considered :
a) In equation (5), q(qo) and u(qo, t) transform as
some representation of the group of qo. In phase II,
where qo = a*/2 + bb*, the group of qo is isomor-
phous to C2 and contains two one-dimensional
representations [11]. In phase III, the group of qo = a*/2 is isomorphous to the phase I crystal
factor group, C2h, and contains four one-dimensional
representations. As WI is seen only in a diagonal geo-
metry (a = f3 = b), equation (5) leads to Raman activity in phase II only if 17(qo) and u(qo) belong to the
same representation [10] of qo = a*/2 + bb*. This
common representation induces two representations
of the group of qo = a*/2. As the WI feature is not seen in phase III, it means that R2(qo) must be equal
to zero in this phase. Using the methods of [10, Appendix A], one sees that this is possible if and only
if q(qo) and u(qo) do not belong to the same repre- sentation of the group of qo = a*/2. As they belong
a* , a*
to the same representation for qo
= 2013
+ bb*,17 T
must transform as the representation with opposite parity to that of u(a*/2). Then R2 [which transforms
as the direct product q(a*/2) u(a*/2)] belongs to the Au representation of C2b.
As bb* transforms as the same representation of C2h, by expanding R2(qo) in the vicinity of a*/2, one
sees that OR210q,, belongs to the unity representation
of the group of a*/2 so that
with
The substitution of (7) into (5) gives :
Assuming that r2 does not vary in the narrow tempera-
ture range of observation (8) leads to a Raman inten- sity :
where n(T) is the Bose-Einstein population factor.
The temperature dependence of (9) has been written explicitly and will be examined in section 5.
b) The first term of equation (6) may be analysed
in the same way, as equation (5) if we consider 172(qo)
on the one hand, and u(- 2 qo, t) on the other hand.
The analysis is even simpler because 172(qo) always belongs to the unity representation of the group of 2 bb*, for any value of 6. Including 6 = 0 hence u( - 2 qo, t) belongs to the unity representation of
2 6b* for 6 :A 0, and transforms as the Au represen-
tation of the C2h point group for 6 = 0 (cf. section 5 below). As a consequence in phase II :
and the intensity obtained from the first terms of (6) is :
Before closing this section, it is worth noting that
the whole discussion is only based on series expansion
and symmetry considerations. Its conclusions would not be different, should the transitions be of the order-disorder type. We preferred the above discussion
since the observation of the soft mode points towards displacive behaviour in the temperature range of interest.
5. Discussion. - As the intensity of the satellite
measured by neutron diffraction (Fig. 2) is propor- tional to q’(T), [9] and [11] provide a quantitative way of cross checking Raman and neutron data. The
13 cm-1 Raman peak integrated intensity, divided by [n(T) + 1], is displayed (crosses) on figure 6. It may be
compared to the neutron determination of
12(T) = K2 n2(T) bl(T) (full circles) and 13(T) = K3 q4 (T) 62 (T) (open circles) where K2 and K3 are arbitrary scaling factors and t¡2(T) has been approxi-
mated by the integrated area of the satellite. Good agreement is obtained using 13 only.
Fig. 6. - Comparison of the Raman data (dots) (inte- grated Raman intensities divided by (n + 1 )), to the neutron
determination of I2 = K 2 n2 a 2 (crosses) and I3 = K3 ?,16 2 (open circles).
The phenomenological theory of section 4, applied
to the first term of (6) alone, thus explains :
1) The detection of the peak around 13 em - 1 in phase II only.
2) The temperature dependence of its intensity
which allows for an optical detection of the lock-in transition.
Furthermore, as 6 is always a small quantity, co 1 (qo)
has no reason to appreciably vary with T in phase II,
which is in fact the case.
We can finally note that for the same reason, WI (qo)
is certainly close to WI (q = 0). The symmetry analysis
of section 4 has shown that this mode is k, then I.R.
active in all three phases. This is in fact the case [8].
Furthermore, recent neutron inelastic scattering expe- riments performed on deuterated monomer pTS
above T; confirm the existence of phonons at the zone
centre in the vicinity of this frequency [7] (1). The pro-
posed explanation of the effect seems thus totally
consistent.
Let us finally note that the above-described mecha- nism is quite general and could in principle be effective for other modes of pTS, or, with some minor modifica- tions, to other incommensurate systems. It is not clear why only one mode of pTS has revealed it
(1) Since the contribution of IZ(T) turns out to be negli- gible, no phonon is needed at 13 cm-’ elsewhere in the BZ in particular at qo = a*/2.
References
[1] For recent reviews, see for instance :
a) BAUGHMAN, R. H., in Contemporary topics in polymer science, Pierce, E. M. and Schaerfgen, J. R., eds, (Plenum Press) 1977, Vol. 2, p. 205.
b) WEGNER, G., in Molecular Metals, Hatfield, E. E., ed., (Plenum Press) 1979, p. 220.
[2] ROBIN, P., POUGET, J. P., COMES, R. and MORADPOUR, A., Chem. Phys. Lett. 71 (1980) 217.
[3] a) PATILLON, J. N., ROBIN, P., ALBOUY, P. A., POUGET, J. P. and COMES, R., Mol. Cryst. Liq. Cryst. 76 (1981) 297.
b) AIME, J. P., BERTAULT, M., LEFEBVRE, J. and SCHOTT, M., in preparation.
[4] AIME, J. P. LEFEBVRE, J., BERTAULT, M., SCHOTT, M.
and WILLIAMS, J. O., J. Physique 43 (1982) 307.
[5] ENKELMANN, V., LEYRER, R. J. and WEGNER, G., Makromol. Chem. 180 (1979) 1787.
[6] WEGNER, G., Z. Naturforsch. (b) 24 (1969) 824.
[7] AIME, J. P., LEFEBVRE, J., POUGET, J. P. and SCHOTT, M., unpublished results.
[8] BLOOR, D. and KENNEDY, R. J., Chem. Phys. 47 (1980) 1.
[9] DVORAK, V. and PETZELT, J., J. Phys. C 11 (1978)
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[11] KOVALEV, O. V., Irreducible representations of space groups (Gordon Breach) 1965.
