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Domain structure in biphenyl incommensurate phase II observed by electron paramagnetic resonance
A. Véron, J. Emery, M. Spiesser
To cite this version:
A. Véron, J. Emery, M. Spiesser. Domain structure in biphenyl incommensurate phase II observed by electron paramagnetic resonance. Journal de Physique I, EDP Sciences, 1994, 4 (11), pp.1705-1723.
�10.1051/jp1:1994216�. �jpa-00247026�
J. Ph_vs, l Fiaiic.e 4 (1994) 1705-f723 NOVEMBER 1994~ PAGE f705
Cla~sification Pfiv.çi<.ç Ah;ficJii.,
6f.70 64.70K 64.70R
Domain structure in biphenyl incommensurate phase II observed by electron paramagnetic resonance
A. Véron j'), J. Emery j') and M. Spiesser (~)
(') Equipe de Phy~ique de Etat Condensé (*), Univer;ité du Maine, Boulevard O. Messiaen, 7?017 Le Mans Cedex. France
fi Laboratoire de Phy~ique Cri~taliine, ln,titut des Matériaux de Nante~. ? Rue de fa Hou~,inière.
44072 Nante~ Cedex n3. France
(Reieii'ed ~5 Maic.fi 1994. iei,içed ~7.lwie 1994, a<.cepied 27.luJi' 1994)
Résumé. La structure en domaines de la phase II du biphényle est mise en évidence par les investigations dans [es état~ photo-excités de~ mofécule~ de naphtaléne deutéré, utilisée; comme sondes de Résonance Paramagnétique Electronique, ~e substituant de manière diluée dans le
mono-camai de biphényle. Ceci confirme que cette phase est lq hi-domaine. L'analyse des spectre~ obtenu~ dans de~ expérience~ en bande X j9.5 GHz) en relation avec le~ propriétés de l'hamiltonien de spin permet de montrer que la wnde moléculaire tourne autour d'une direction
perpendiculaire à son grand axe alors que la molécule de biphényle subit un mouvement de tu.i~t
autour de cet axe. Les résultats montrent que ces sondoe rendent compte d'un régime qui est
comme un régime « mufti-salirons
>, alors que la modulation est plane dans le cristal pur. Le~ deux
molécule~ sondes de la cellule élémentaire haute température ne subi~sent pas les mêmes champs de déplacements dan~ la phase incommensurable et en conséquence le~ deux domaines peuvent être distingués. Les paramètres de l'hamiltonien de spin qui caractérisent les sonde~ R-P- E. ont été
déterminé~ dans la phase II du biphényle.
Abstract. The demain ~tructure in incommensurate phase Il of ~ingle biphenyl crystal has been
observed by investigation~ of the optically excited states of the Electronic Paramagnetic Resonance (E.P.R.) deuterated naphthalene molecular probes which ~ubstitute biphenyl molecules.
Ouf results confirm that this phase is a fq bi-demain one. The analysis of the spectra obtained in X band (9.5 GHz) experiments, in relation with the spin Hamiltonian parameter properties permits us to show that the E-P-R- probe rotates around a direction perpendicular to its long a~is while the
biphenyl molecule undergoe~ a twi~t movement around this axis. They aise account for a regime
which is like a
« mufti-wliton
» regime while the modulation is
a plane wave one in the pure single cry~tal. The two molecules of the high temperature cell do net exactly experience the same
displacement field in the incommensurate phase and consequently the two domains can b~
di~tinguished. The spin Hamiltonian parameteà which charactenze the E-P-R- probes have been determined in the incommensurate phase II of biphenyl.
(~) U-R-A- N° 807.
1706 JOURNAL DE PHYSIQUE I N°
1. Introduction.
Molecular crystals are generally charactenzed by a weak intermolecular potential compared with the intramolecular potential. Nevertheless when the~e two interactions become compar- able, interesting phenomena appear [Ii. The biphenyl molecular crystal, with chemical formula Cj~Hj~~ exhibits such a behaviour [2-4]. At room temperature the symmetry of the biphenyl molecular crystal is P21la (Fig. ) in this phase (called phase I) the molecules are planar (in average). When the temperature is lowered, this system exhibits two structw.al
phase transitions.
r~
b
a
Fig. The high temperature structure of biphenyl a 8.12 À. h 5.63 À,
< 9.51 À, p 95,1
from Ii
At T~ =
40 K a second order phase transition occurs, the crystal becomes incommensurate.
This phase (named phase II) is complex. The order parameter has four components (n
= 4) [3, 4] and is a~sociated with the twist of the phenyl rings around the molecular axis.
The modulation wave vector componènts are
± q,j = (ô~ a* ô~ c*) + ~~ ~~~
b* il)
± q,~ = (ô~ a* à, c*) + ~~ ~~~
b*
After a first-order phase transition which occurs at T~~ =
17 K down to 4? K the crystal
remains in a second incommensurate phase (named phase III) with the modulation wave
vector
à/,
± q, #
~
b* (2)
These phase transitions were extensively studied indifferently in the deuterated or
hydrogenated compounds by electronic absorption and emission in pure biphenyl-djo [5],
neutron scattenng[3, 4], Brillouin scattering[6, 7] and Raman scattenng[8, 9]. Local
N° II DOMAIN STRUCTURE IN PHASE Il OF BIPHENYL 1707
investigations, such as R. M.N. [10~ Ii and Electronic Paramagnetic Resonance (E. P-R- [12~
13]~ were also performed. Nevertheless the first investigations by (E.P.R.) were interpreted
without any reference to their incommensurate characteristics. On another hand in refer-
ence [14] the authors give a partial description of the complex phenomena.
The major problem in phase II concern~ the n
=
4 dimension of the order parameter there
are two pos~ibilities for the modulated structure
a superposition of the two displacement l'ields with the wave vector~ ±q,j and
± q,~ (2q system)~ and
a domain structure corresponding to displacements with the wave vectors ±q,j or
± q,~ (lq system).
A theoretical analysis of the 4 vibrational soft modes [15, 16] associated with the
n =
4 component~ of the order parameter, allows u~ to differentiate the two cases. In the ?q sy;tem, the phason mode (mode without gap) is doubly degenerate while the other two modes (with gap) are not. In the lq bi-domain case it 1; one of the two modes with gap which is
degenerate [15]. The neutron ~cattering experiments then suggested that the system is bi-
domain. The Raman scattering experimental results under pressure agree with these
results I?i and Nuclear Magnetic Resonance spectra are typical ones of a lq structure [1Ii All these experimental results are supported by theoretical analyses Il 8-20] which conclude to a domain ~tructure.
In this paper we present an analysis of the E-P-R- spectra obtained in a photo-excited
electronic triplet state of molecules of naphthalene-d~ (deuterated molecules) which hâve been dilutely substituted for the molecules in the host biphenyl-hjo Thi~ sub~titution modifies one half of the cell and will have several effects on the incommensurate pha~e properties. This paper, devoted to the analysis of these modifications~ will tackle the following points
lq or 2q problem
domain observations, and
E-P-R- probe behaviour in the incommensurate states.
This paper is organized as follows. In section 2 we give the experimental procedure the results in the high temperature phase are rapidly given to recall the general behaviour of the
naphthalene E-P-R- probe: competition between the molecular symmetry and the site
~ymmetry in the determination of the spin Hamiltonian, orientation of the probe in the biphenyl
host crystal. Spectrum general features in the incommensurate phases obtained in the experiments in low- magnetic field (zero-field~ with the frequency near 4 GHz) and in X band (field at about 3 500 G and frequency near 9.5 GHz) will be given in section 3. This section is
concluded with the lq bi-domain structure in phase II. The domain structure effects on the E-P-R- spectra are descnbed in section 4 in which the analysis of the spin hamiltonian
parameters permits us to conclude with the evidence of domains in the incommensurate
phase II. Theoretical spectrum reconsruction which allows us to determine the spin Hamilto-
nian parameters in the incommensurate phase will be given in section 5.
2. Experimental procedure and probe properties.
2.1 EXPERIMENTAL PROCEDURE. TO perform an E-P-R- expenment on diamagnetic
biphenyl we hâve to include some probes in the pure biphenyl. The deuterated naphthalene- djo molecules substitute the biphenyl with a concentration equal to 0.5 fil. The biphenyl
cry~tal was grown by lowering the melt through a temperature gradient (Bridgman method).
The products~ biphenyl-hjo and naphthalene-d~, were purcha~ed from Aldnch company and
were purified before u~e. It is worth noting that the length of naphtalene along its long a~is is
less than that of biphenyl.
1708 JOURNAL DE PHYSIQUE I N° Il
E-P-R- measurements were performed on a X-band spectrometer (9.5 GHz equipped with a
cryostat. The crystal is cooled down by helium gas flowing in a dewar within the cavity. The
precise temperature of the sample may differ because of the temperature gradient of the flow.
The exact conditions of the current flow may vary from one experiment to another. But in one experiment the conditions are held constant~ and in the whole set of experiments the
temperature is recalibrated by using the sample itself (the splitting between edge singularities is
an exact measure of the temperature). This system permits a temperature measurement at about
±0.1K but we are non able to evaluate an absolute temperature and then to observe a
modification of the phase transition temperature due to the naphthalene E-P-R- molecular probe.
The ground state of naphthalene-dx is not paramagnetic. Thus we must work in an excited triplet state. Some studies [12] have shown that the lowest triplet state responsible for the
paramagnetism is also a phosphorescent one : the molecule is optically e~cited in a higher singlet state before it faits into the phosphorescent state. The decay time measured from the E-P-R- signal is about 17s in agreement with that obtained from the phosphorescence omission.
This state is reached in the single biphenyl crystal by irradiating the naphthalene-dx with a high
pressure mercury arc lamp. The light is focused with a quartz lens and a mirror at the top of a
quartz switch in the cavity with an altuglass hood. The lamp output was filtered by a 5 cm path length of solution containing a COS04 and NiSOj mixture which avoids heating the cryual with irrelevant radiations.
2.2 EXPERIN4ENTAL RESULTS IN THE NORMAL OR HIGH TEMPERATURE PHASE. Two sy~lems
of peaks are found which are associated with the two inequivalent naphthalene molecules in the cell. Three fines for each molecule are typical for a S
= spin the ~~, = 2 transition in low
field and the two A~, = transitions in high field [2 Ii The anisotropy curves which give the fine positions i,eisus the orientation of the magnetic field in the three crystallographic planes,
allow us to define the spin Hamiltonian parameters :
,,, ~
,1Cu =
bS#Bjj + jj BÎ' OI' (3)
In
its main value equal to that of the free electron g = 2.0023. the crystal field
arameters are :
BÎ =
(The B] arameters are related to b(1'
ones
: 87 = ~
" 3 -
pin
rientations in the crystal oeil These orientations correspond to the
molecular axis directions.
These results mean that the E-P-R- naphthalene
probe, when it is
substituted
biphenyl molecules, takes nearly the same orientation. The analysis of esults in
the high temperature phase [21] permits us to determine the origin of the
principalontribution cames from the spin-spin which depends on the eometry of
the molecule and no ontribution of the crystalline field was bserved. Coiiseqiientli' the
iaiisitions u.ould be
obseii,ed
thiou,qh efoiniation and/oi disoiientafion of
molecular probe ndl~ced by a chan,qe in the O.ystal
field.
phase III.
N° II DOMAIN STRUCTURE IN PHASE II OF BIPHENYL 1709
V
X
Fig. 2. Spin Hamiltonian molecular a~e~ of naphthalene E-P-R- probe.
Table I. Orientation of the spin Hamiltonian a-tes &~, @~ and of the biphenyl moleculai
a-tes (&~, @~) in trie Ciystal fi.aune (a, h, c* ).
~H ~H ~M ~~
O-1 18.2° 7.1° 17.~° 4.6°
A~is
Oj, 93.6° 63.2° 100.7° 57.7°
Axis
O= 108.1° 38.0° 103.1° 35.4°
Axis
3. Experimental results.
3.1 EXPERIMENTAL RESULTS IN INCOMMENSURATE PHASE. In order to ob~erve the pha;e
transitions in biphenyl~ Cullick and Gerkin [12, 13] performed an E-P-R- low field (or zero
field) experiment on an excited state of naphthalene and phenanthrene probes. At atmo~pheric pressure the phase transitions occur at 40 K and 17 K. At 40 K the E-P-R- fine split~ into two
singularities then two other ~ingularitie~ appear. Let us notice that the four edge ~ingularitie~
are the characteri~tics of the E. P-R- ~pectrum in phase Il. At 17 K a ~econd transition occur~
marked by the disappearance of two singularities and the position~ of the two remaining are
weakly modified in an intermediate position.
A typical spectrum, obtamed in our X-band experiments and sketched in figure 3~ exhibits a similar behaviour. In phase II we observe three of four singularities in ail orientations of the
~tatic magnetic fields in which the splitting i~ sufficient to di;criminate the dit'ferent
singularitie~ (becau~e the fine width i~ forger in X band thon in zero field, the re~olution i~
better in the latter case). The main characteri~tic in phase II, apart from the four singularitie~.
is the dissymmetry between them (Fig. 3). The number of ~ingularities (4) ii al~o an important charactenstic of this phase because it i~ independent of the orientation and it has been al~o observed in « zero field
» experiment by Cullick and Gerkin [1?~ 31 u,hile trie.ipecfi.a ai-e trot
sensitii'e to the ~ianie paianieteis as we wi Il see below. Thi~ seems to be in contradiction with
17J0 JOURNAL DE PHYSIQUE I N° II
a) b)
=42.5K
=20K
5 /
§ j
< é
1 =34
2370 2405 2440
MagnetJc field (Gauss)
2380 2410 2440
Magnetic field (Gauss)
Fig. 3. Evidence of the phase transitions on the E-P-R- spectra (first denvat(ve absorptions). The magnenc field is in the (a, b) plane with la, H ~7°.
the general behaviour [19, ?0] of the first-order and second-order contributions oui of phase in
the development of àH(d (~ee Eq. (8)) which would be orientation dependent.
In the vicinity of 17 K an evolution of the X band spectrum occurs two singulanties
decrease and simultaneously the other two increase in the same proportion (total intensities
before and after are equal) During this transition the positions are weakly modified at
intermediate values.
An intermediate ~pectrum can be reconstructed as the ~uperposition ofa spectrum of phase II and the spectrum of phaselll (Fig.4) with a proportion which is temperature dependent (Fig. 5). This result accounts for the pha~e coexistence characteri~tic of a fir~t-order transition
which has been observed by neutron scattering [l~ 3].
3.2 MAGNETIC RESONANCE LINE SHAPE IN INCOMMENSURATE PHASE [22]. In a commensur-
ate system the spectrum ha~ a reduced number of fines because only a few paramagnetic sites are non equivalent. Reversibly, in an incommensurate system where the translation lattice
periodicity i~ lost~ there is an e,~entially infinite number of non equivalent paramagnetic sites
which contribute to the magnetic resonance spectra. Thus the resonance fine ~hape is
characteristic of the local nature of the incommensurate modulation. In a structural phase
transition the atomic displacements from their high temperature positions i~ given by the
displacement field
U(r ~ COS ~b ir + '
ù 5
~~~ ~ s~.
where A is the amplitude of the order parameter~ # jr
=
k r i~ the local phase in the plane
wave limit with k the incommensurate wave vector. The fine positions can be expanded in
N° Il DOMAIN STRUCTURE IN PHASE II OF BIPHENYL I?I1
E~penmental Built
=17.0K
~ /
fi 1
~
T= K
K
=15.1 K
4030 4080 4130
Magnetlc field (Gauss)
Fig. 4. Evidence of the pha;e coexistence : the different ~pectra are built as a weighted sum of the two
experimental spectra the first obtained at 19 K (pha~e Il) and the ~econd obtained at 15 K (phase Ill la, b plane with (a, H
= 30°.
powers of the amplitude of the displacement field u
H=Ho+aju+~a~ii~+. (6)
2
where Ho is the fine position in the high temperature phase. By inserting (1) into (?) we find the local fine splitting
àH(#)=H(#)-H~=hjcos# +h~(1+cos2#).
By taking the non-local contributions mto account [23] we obtain a more general form of the local field splittmg
AH (#
= hi cas (# # + h~ + hi cas 2 (# #11. (7)
In a first step the spectra are reconstructed as a sum of local fines [22] :
1(H) = j~~P(4 if ~~~~~ ~' ~~~
1712 jOURNAL DE PHYSIQUE I N° Il
ÎÙÙ . . . .
n
@~
.
~Î
o
$ 0
12
ig.
here idth.
The pectruni
AH omain by a ontinuous bacl~groundj at efined by :
ô3Hl~i~) ~ éd
Such spectra in
iphenyl are displayed in
figure 3. We can see
are net symmetrical, le-,
that
some phases are privileged. In a
analysed
ith i;tribution
~ ~~ ~ ~ j 2 ~~Pl~b ~ ~b(ÎJ
~~~
.ç + cas- ~
where p is an integer which the
periodicity
in
the locLing phase.
In thetwo «
air) = j
os
~b
j
A~
cos
ith ~i~ j
=
to
trie econd order takes the form [24]
H(~bj, ~i~~) = hjj Idi - j~b~ - ~bjj~) +
+
li~~ cas j cas + h,, sin ~i~
(loi
In this case the
~pectra
are econstructed as above, by summing the local
2W 2« H-H(#j, ~i~~)1
1(Hi -
l~ d~b l~ ~b,P(~b ~~~, ~~i ~iI)
N° II DOMAIN STRUCTURE IN PHASE II OF BIPHENYL 1713
The spectrum is characterised by singularities located at positions given by
ôàH(~i~j,~i~z)~~ ~~~ ~~~~~"~~~=0.
ô~i~j ~~2
3.3 Is PHASE II A 2q STRUCTURE PHASE ? We have tried to fit an experimental Îine with a 2q
line with (1 1j (Fig. 6). Firstly we remark that it is always possible to account for the singularity positions if the number of parameters is known. Secondly it is necessary to introduce a phase probability distribution to fit the intensifies of singularities correctly.
°° Experimental
-Theoretical
o@d
4225 4275 4325
Magnetic field iGauss)
Fig. 6. Expenmental fine observed in the la, hi plane with la, Hi 15°, simulated with a 2q fine
the parameters are hi 21.5 G, iij~ 8.5 G, h~~ 4 G. ~j 0.4 rad, ~~ rad jsee Eq. (10))
Positions and intensities are correctly fitted but fine shapes are not. If we compare a
simulation between a 2q spectrum (Fig. 6) with that obtained with the lq spectrum (Fig. 7a obtained with 8), we remark that they have the same number of singularities at the same
positions, but there is a fundamental difference m the singulanty shapes. It is certamly the most
exact argument to discriminate between a lq and a 2q spectrum. We deduce from this that the
experimental line is typical of a lq structure.
This E-P-R- result agrees with the N-M-R- [1ii, Raman [17], neutron diffraction [15, 16]
results and the conclusion of theoretical investigations [18-20]. The singulanty number observed on the E-P-R- spectra must be searched in the displacement field ongin (non-lineanty
line splitting) or in the domain effects.
4. Domain structure analysis.
In phase III (Fig. 3b-15K), the E-P-R- spectrum is very simple with only two dissymmetncal singularities corresponding to lq modulation without demain structure. The number of four
