X-ray evidence for incommensurate phases in crystalline thiophene. An effect of the pseudo-pentagonal molecular symmetry ?

HAL Id: jpa-00210185

https://hal.archives-ouvertes.fr/jpa-00210185

Submitted on 1 Jan 1986

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

X-ray evidence for incommensurate phases in crystalline thiophene. An effect of the pseudo-pentagonal molecular

symmetry ?

D. André, H. Szwarc

To cite this version:

D. André, H. Szwarc. X-ray evidence for incommensurate phases in crystalline thiophene. An ef- fect of the pseudo-pentagonal molecular symmetry ?. Journal de Physique, 1986, 47 (1), pp.61-70.

�10.1051/jphys:0198600470106100�. �jpa-00210185�

61

X-ray evidence for incommensurate phases ⁱⁿ crystalline thiophene.

An effect of the pseudo-pentagonal ^molecular symmetry ?

D. André (*) ^{and H. Szwarc} (**)

(*) Laboratoire de Physico-Chimie Structurale, Université de Paris-Val de Marne, ^{94010 Créteil} Cedex, ^France (**) Laboratoire de Chimie Physique des Matériaux Amorphes (+), Université de Paris-Sud, ⁹¹⁴⁰⁵ Orsay, ^France (Reçu ^{le 24 mai 1985,} accepté ^{le 23} septembre 1985)

Résumé.

Cette nouvelle étude par diffraction des rayons X de la séquence ^des phases métastables du thiophène

de 98 à 218 K montre que les phases ^II (ou II’), II1 et II2 correspondent ^{à des} surstructures du réseau orthorhom-

bique ^{de la} phase I ; celui-ci constitue une structure géométrique ^{commune avec} laquelle celles des 3 phases pré-

cédentes ne sont pas commensurables. L’existence de ces 3 phases incommensurables pourrait bien être la consé- quence de la symetrie quasi-pentagonale de la molécule de thiophène.

Abstract

A new X-ray investigation ^{from 98 to 218 K on} the sequence of metastable phases ^of crystalline thiophene shows that phases ^II (or II’), II1 ^and II2 correspond ^to superstructures ^{of the} orthorhombic lattice of phase ^{I which} constitutes a common geometrical frame with which they ^{are not} commensurable. The emergence of these incommensurate phases ^{is believed to be related to the} quasi-5-fold symmetry ^{of the} thiophene ^molecule.

J. Physique ⁴⁷ (1986) ^{61-70 JANVIER} 1986,

Classification

Physics ^Abstracts

61.10

61.50K - 61.65

Radiocrystallographic ^{data on} crystalline thiophene, C4H4S (1), ^{which could not} be understood in terms of the results of previous ^work [1, 2] ^{led to a new} experi-

mental investigation ^{of the} thermodynamic ^and

structural properties ^{of this} compound. Calorimetric

measurements revealed the existence of two series of crystalline phases [3, 4] and the thermal treat- ments to get ^{them. The two} phase sequences and the

corresponding phase transition temperatures ^are recorded on table I, ^which also shows that each phase

sequence contains a low temperature glassy crystalline phase [5] (Vg ^and II2g respectively). According ^to X-ray ^data [6], the best molecular packing ^for phase ^I

is obtained with space group Cmca with 20 equipro-

bable molecular orientations. At 183 K, the unit cell parameters ^{are :}

with Z

4 molecules _per unit cell.

Phase III (mistakenly ^{called II in Ref.} [6]) ^{is best}

described by the space group Pnma with 10 molecular orientations. Single crystals of metastable phase ^II’

(instead ^{of I’ in Ref.} [6]) ^{were easily obtained by cooling} single crystals ^of phase ^{I. At 163} K, the unit cell of

phase ^II’ could be derived from that of phase ^I by multiplying ^the parameter ^b by ^{2 and the} parameter ^c

by ^{20, i.e. :}

Such a factor for a crystalline superstructure ^{is rather} unusual. It was thought that, ^{in some} way, it was

linked to the 20 molecular orientations which are

equiprobable ^{at each site of} phase ^{I and} that this link would give ^{some clue in} understanding ^{the rela-} tionships ^between phases ^{I and II} (or II’).

Unfortunately, ^these single crystals spontaneously

shattered after a few hours (because phase ^II’ usually recrystallizes ^into phase ^III within the 150-165 K temperature range), ^{so that it was not} possible ^to get ^a complete X-ray collection. Accordingly, the purpose of the present ^{work was to} get ^{such a} collection and to

try and record as much information as possible ^about

the metastable phase sequence.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198600470106100

Table I.

Phase transitions in the two phase sequences of crystalline thiophene according ^to reference [5]. ^These

data correspond ^to thoroughly purified thiophene. ^Phases Vg ^and II2g ^{are glassy} crystalline. ^{The arrow indicates}

the irreversible transformation II’-to-III that occurs from the metastable _sequence to the stable one.

1. ExperimentaL

Thiophene ^was purchased from Merck (Spectroscopic Grade) and used without further purification. ^Two samples ^{were used} Crystal ^{1 was} prepared ^with product ^{taken from the same} bottle that was used in references [3], [4] ^and [6]. Crystal ^{2 was made with} thiophene taken from ^{a more} recently purchased

bottle.

Both samples ^were processed according ^{to the same} procedure. ^{A 0.3 mm} diameter Lindemann capillary

was filled with liquid thiophene and sealed at both ends. Afterwards, ^{it was fastened onto the} goniometer

head of a Syntex P21 four-circle diffractometer which

was equipped ^{with a} copper X-ray ^{tube and a} graphite monochromator (CuKa ^{= 1.5418} A). ^The temperature

was then lowered to about 10 K below melting using low-temperature equipment in which the cooling agent

was gaseous nitrogen [7]. Then, ^a cylindrical single crystal ^{about 0.8 mm} long ^was grown in ^situ by ^zone melting ^as previously ^described [8].

To prevent ^{stresses from} developing, ^the cooling ^or heating ^{rates were} kept low, ^{about 0.01 K. s-1. The}

uncertainties ^on the temperature ^{values are believed}

to be about 2 K.

2. Results.

The single crystals ^were studied in the 98 to 218 K

temperature range. Contrarily ^{to what was observed}

in reference [6], ^no alteration of the crystals ^occurred

at the different phase transitions which have been encountered either on cooling ^{or on} heating. ^The persistence ^{of the} metastable phase sequence is ^to be related to the influence of impurities (probably ^water

in the present case) which have been shown [5, 9] ^to prevent phase ^{III from} crystallizing.

The presence of impurities ^also explains ^{the diffe-}

rences between the phase transition temperatures which are recorded in table I (and which refer to

thoroughly purified thiophene) and those which have been determined in the present work and which will be given ^below.

In what follows, ^the chronological ^{order for the} temperatures ^{of the} measurements will be mentioned to point ^{out the fair} reproducibility of the different results for ^a given sample. Therefore, these results seem to be independent of thermal treatment.

2.1 CHARACTERIZATION ^{OF THE} D,IFFERENT ^METASTABLE

PHASES.

The results described in reference [3]

indicate the temperature domains of existence of the different metastable phases ^of crystalline thiophene

of equivalent purity. Therefore rotation photographs

were taken at 160, 128 and 103 K, ^where phase ^II’

(that ^is phase ^{II in its} metastability range), II1 ^and 112, respectively, ^were expected ^{to exist.}

A 160 K, ⁱⁿ phase II’, ^all Bragg reflexions of ortho- rhombic phase ^{I are} still observed. As already ^noted

some years ago [6], ^new superstructure ^reflexions appear, with intensities that are only ^{one order of} magnitude lower than those of the reflexions of the

original orthorhombic sublattice. An X-ray ^collection

has been made _up to 2 0 ⁼ 500 with crystal ^{1. A list}

of the observed reflexions I > 5 u(I) ^is given ⁱⁿ

table II. From the examination of rotation photo- graphs, together with the calculation of indices from the orientation matrix and the analysis ^{of the} diffraction pattern, ^{it can} be concluded that parameter a ^remains

unchanged (neglecting ^thermal contraction). ^{The exis-}

tence of some new weak reflexions in the diffraction pattern ^could suggest ^that parameter ^{b is to be multi-} plied by 2, ^{as we will assume in the} following.

To get integer indices for I (that is, along c) ^several multiplying ^{factors were tried.} Although the results with 3 and its multiples ^{are fair} enough, ^{it can be seen}

on table III that the best results for all reflexions are

obtained for 20. In what follows, 20 will be used as the

multiplying factor for c.

At 128 K, ⁱⁿ phase II,, the rotation photograph

reveals new Bragg reflexions with noticeable intensities.

They ^{are of two kinds : some of them} correspond ^to

reflexions which ^can be quite fairly indexed in the orthorhombic sublattice but which were forbidden in a

C-centred lattice such ^as Cmca. The other emerging

reflexions are of the same kind as those which appeared

in phase ^II’. Table IV records the reflexions we deter-

63

Table II.

Observed structure factors (I > 5 a(I))

corrected for Loren tz-polarization for the metastable

crystalline phase ^II’ of thiophene ^at 160 K. Bold type

corresponds ^to reflexions of the orthorhombic sublattice.

We have pointed ^{out the} reflexions ^with structure factors higher ^{than 100} by underliping ^them. Multiplications of ^the original ^b by ^{2 and c} by 20 have been taken into account.

mined for both types. ^An examination of the data recorded at 160 K in crystal ¹ shows that the above reflexions ^are non-observed or very weak in phase ^II’.

They ^are truly characteristic of phase Ill. ^{At 103 K,}

no new Bragg reflexion is revealed by ^rotation photo- graphs.

It is to be stressed that ^we performed quantitative

studies only ^{on the « new »} Bragg reflexions ^{that the} rotation photographs revealed in each phase. ^No systematic ^{search for new} reflexions has been carried out in the present ^work because the 4-circle diffracto- meter is not the pertinent apparatus with which to do

so. This explains why ^a thorough description ^{of the} reciprocal space will not be given ^here.

2.2 PHASE TRANSITIONS AS REVEALED BY THE EVOLU- TIONS OF THE INTENSITIES OF BRAGG REFLEXIONS AS A FUNCTION OF TEMPERATURE.

The rotation photo- graph ^of crystal ^{1 at 160 K} showed that the new

superstructure Bragg reflexions of phase ^{II’ were}

almost as intense as those of the orthorhombic sublattice. We found it rather intringuing ^{and we}

decided to study the evolution of the intensities of

some of the ^{« new »} reflexions ^as a function of tem-

perature.

In the case of crystal 2, ^the integrated intensities

(uncorrected ^for Lorentz-polarization) of 9 super- structure reflexions were determined in the 98 to 170 K temperature range and are recorded in table V.

The behaviours of these intensities with tempera-

rature are even more obvious on figure ^1, which

represents the reflexions (3 ⁴ 7,14 33) ^and (1 4 20, ² 0 13) ^which emerge in phase ^{II and} Ill, respectively.

Starting ^{from 98} K, all intensities decrease as T increases. At about 109 K, ^most of the curves 3 ⁼ f(T)

exhibit a kink the more conspicuous of which lies on the 3 4 7 intensity ^curve.

Table III.

Calculated 1-values, Ical’ corresponding ^to superstructure reflexions ⁱⁿ phase ^II’ of thiophene ^{at 160 K}

for different multiplying factors of ^the parameter c ; dl/l = B (/calc

/)/1B.

Table IV.

Crystalline thiophene : Bragg reflexions

which were observed ⁱⁿ phase III ^{and which do not exist}

in phase ^II’. The values between parentheses correspond

to the indexation with respect ^to the lattice of phase ^I

and would be forbidden ^{in C-centred space} group Cmca.

Heating further, the intensities continue ^{to decrease,}

but the behaviour of curves 3(1 4 20) and 8(2 0 13) ^is

most surprising : ^the intensities decrease almost

linearly ^{with T and the} corresponding straight ^lines

encounter the T ^{axis at 136 K. Table} V shows ^that

reflexions 1420,2013 and also 0 2 40 are non-

observable at 136 K. At this temperature, ^{a noticeable} kink can be observed ^{on curve} 3(3 ⁴ 7). ^{These obser-}

vations _prove that 136 K is the temperature ^{at which} phase transition II1-to-II’ ^takes place.

As temperature ^{increases further,} 3(347) ^and J(1 4 33) ^decrease according ^to a T - ¹⁷¹ K I’ law,

with a roughly equal ^{to 0.5} (Fig. 1). ^{No careful} intensity

measurements were performed ^at temperatures higher

than 170 K on crystal ^2. However, ^{it was} checked that the above reflexions were not observable at 172 K in crystal ^1. Furthermore, ^a very conspicuous ^kink

could be observed near 171 K on almost _every intensity

versus temperature ^curve corresponding ^{to the} Bragg

reflexions of the everlasting orthorhombic lattice.

Therefore, ^{it can be concluded} that transition II-to-I takes place ^{at 171 K in our} experimental conditions.

The relationships 3 ⁼ f(T) ^near the transitions at 136 and 171 K are very approximate. ^{It will therefore be}

necessary ^to perform ^{a detailed} study using ^{an accurate} temperature control. Neutron measurements seem more fitted to this purpose with respect ^{to the} tempe-

rature control, ^{but the} intensity measurement accuracy could be found to be wanting.

Fig.1.

Metastable phase sequence of crystalline thiophene.

Variations of the intensities (uncorrected for Lorentz-

polarization) ^{of some} superstructure Bragg reflexions as a

function of temperature :

The vertical straight ^lines correspond ^{to the} phase ^transition temperatures (109, 136 and 171 K).

We have seen that _every Bragg ^reflexion disappea-

rance is accompanied by ^some kink in the J(T) ^curves corresponding ^{to the} remaining reflexions. The changes

in the J(T) slopes ^{at 109 K} could indicate the emer-

gence of some new superstructure Bragg ^reflexions accompanying ^a redistribution of X-ray ^scattered

energy ^{at a new} phase transition. It can be conjectured that, similarly ^{to what} happens ^{at the} phase transitions at 171 and 136 K, the intensities of the new reflexions would start at zero at 109 K and _grow ^as temperature is lowered The rotation photograph ^{at 103 K failed}

to detect them, possibly ^{because these new reflexions}

had not benefitted from a temperature ^interval large enough (6 K) ^to grow ^to measurable sizes.

The value of 109 K corresponds ^to temperatures ^at which a phase transition has already been observed in thiophene ^of comparable purity [4], ^{i.e. about 100}

to 117 K depending ^{on the} sample ^{and the} experi-

mental method This represents ^an important ^diffe-

rence with the temperature ^{that is} reported ^{in table I}

for the phase transition 112-to-II, ^{in a} thoroughly purified thiophene sample. ^{But the} temperature ^sensi- tivity of the transition is demonstrated by ^{the fact that}

accurate heat capacity measurements failed to detect it in a thiophene sample containing ^{1.83 mol} per ^cent benzene [10]. Therefore, ^{we will} tentatively assign ^the

kinks which exist at 109 K on the curves of figure ^{1 to}

65

Table V.

Metastable phase sequence of crystalline thiophene : intensities of some superstructure Bragg reflexions

as a function of temperature. (The experimental chronological order for ^the temperatures ^has been followed.)

the phase transition 112-to-Il,. Nevertheless, ^{we shall}

have to check that our lower temperature phase ^is really phase II2 by performing ^{X-ray or neutron}

measurements on purified thiophene. Moreover, ^these experiments ^{will have to} be carried out at temperatures much lowek than that of the transition 112-to-11, ^so

that the possible ^new Bragg reflexions would have grown enough ^to be observable.

To sum up this paragraph, superstructure Bragg reflexions _appear at 171 K and their intensities increase while cooling through phases II, II’, III ^and ,12. ^{At 136} K, ^other superstructure reflexions _emerge, which in turn have intensities which increase through phases 11 ^and 112. ^{It is} thought ^{that new} superstructure reflexions _appear at 109 K and their intensities increase on cooling. During ^{all these} transformations and evolution, ^the orthorhombic lattice of phase ^I

continues to exist as a frame within which structural

complexity ^increases.

2. 3 EVOLUTION OF THE UNIT CELL PARAMETERS AND VOLUMES AS A FUNCTION OF TEMPERATURE.

Advan- tage ^was taken of the persistence of the orthorhombic sublattice to compare the dimensional properties ^of

the crystalline ^unit cell of all the phases.

The evolution of this sublattice has been followed as a function of temperature through ^all phases, using ^sets

of Bragg reflexions which ^were initially observed in

phase I (6 reflexions with ^{18° 20 31° for crystal 1 :}

002, 112,112,111,111 ^and 200; ^{7 Friedel} pairs ^with

51° 2 0 81° for crystal ^{2 :} 004, 331, 422, 204, 600,

240 and 044). ^The parameters of ^the orthorhombic

crystalline ^{cell were} first determined using ^{a routine of}

the Syntex ^Nicolet P21 diffractometer [11]. ^{For each} temperature, ^the angles ^a, fl, y of the unit cell remain

equal ^to 900 with the same accuracy ^as in phase ^I.

Therefore, ⁱⁿ the refinement process, the cell ^was

initially considered as orthorhombic and the values of the crystalline parameters a, b, ^c and V have been calculated by ^{means of the} programme PARAM of the

X-ray ⁷² system [12] (2).

The agreement between the values we determined for the two crystals ^is quite good. Figures ^{2 and 3 show}

the variations of the parameters corresponding ^to crystal ^2.

The behaviour of parameter ^{b is} quite remarkable.

(1) ^{The cell} parameter values may be obtained from the

authors on request

Fig. ^2.

Metastable phase sequence of crystalline thiophene.

Variations of the parameters a, b ^{and c} of the unit cell of the orthorhombic sublattice with temperature.

It seems to freeze when approaching ^the phase ^transi-

tions I-to-II, II’ -to-II1, ^and IIl-to-II2 ^on cooling.

Furthermore, ^the corresponding expansion coefficient is negative from 170 K downwards. The other _crys- talline parameters (a, ^{c and} Y) ^{behave in a usual} way with positive expansion coefficients (the larger ^one corresponds ^to c) ^and slight discontinuities at the different phase transitions. This can be roughly

related to what is known about the molecular packing

of phase ^I [6]. Figure ⁴ shows that direction b corres-

ponds ^to closely packed parallel thiophene ^molecules,

whereas direction c corresponds ^{to a looser} packing

in the herringbone-patterned crystallographic ^struc-

ture of this phase. ^This packing ^will undoubtedly

constitute an important ^{clue in} describing ^{the mecha-}

nisms of the phase transitions at 171, 136 and 109 K which are not yet understood.

2.4 EVOLUTION OF THE hkl INDICES OF THE SUPERSTRUC- TURE BRAGG REFLEXIONS WITH TEMPERATURE : INCOM- MENSURABILITY OF, THE ^« SUPERSTRUCTURE LATTICES »

Fig. ^3.

Metastable phase ^sequence of crystalline thiophene.

Variation of the volume V of the unit cell of the orthorhombic sublattice as a function of temperature.

Fig. ^4. - Thiophene phase ^{I at 183 K} (from ^Ref. [6]) : projections ^{of the mean molecular} planes ^{on the} (1 0 0) plane. ^{Full lines} correspond ^{to molecules at x}

^{0.0 and} dotted lines to molecules at x

0.5.

WITH RESPECT TO THE ORTHORHOMBIC SUBLATTICE.

The values of parameter ^{c at} temperatures ^{lower than} 170 K seemed surprisingly large (about 140 A) ^{and it}

was decided to put them under closer scrutiny ^{to detect}

the possible evolutions of the positions of the super- structure Bragg reflexions in the reciprocal space. At every temperature, ^the angular ^values corresponding

to each reflexion were refined and their indices were

calculated using ^the orientation matrix which defines the orthorhombic sublattice. In table VI, ^{the values} of h, k ^{and I} for the reflexion 347 are reported ^This particular reflexion has been chosen because the values of the 3 indices are of the same order of magnitude ^so

that their variations can be easily compared.

It gives ^{a fair} example of what is observed for all reflexions. In all _cases, the indices h and k remain constant in the whole temperature range. The diffe-

rence between their lowest value and the highest ^one

never exceeds 0.01 and one of their extremum values is

always ^an integer.

On the contrary, the values of I exhibit a slight ^but

67

Table VI.

Metastable phase sequence of crystalline thiophene : ^variation with temperature of ^the indices I I of different Bragg reflexions for crystal ^2. The values of I I that would have resulted from ^the multiplication of ^the corresponding parameter of the orthorhombic sublattice by ^{3 have been} tabulated for ^some reflexions for comparison.

(The chronological ^order for ^the temperatures of ^the measurements is 163, 170, 165, 160, 154, 148, 143, 138, 133, 128,123,118,113,108,103 ^{and 98} K.)

systematic shift for all reflexions when temperature varies. Tables VI and VII show the evolutions of the values of lwith temperature for different superstructure reflexions together with reflexions of the orthorhombic sublattice for crystals ^{2 and} 1, respectively. ^The repro-

ducibility between the data for both crystals ^{is not} perfect. ^{There are} differences in the values of 1 at a given

temperature and 1 does not seem to change ^{at all in} crystal ^{2 at} temperatures lower than 136 K (that ^{is the} II1-to-II’ phase transition temperature). ^However,

the overall trend is analogous ^{in both cases. For} instance, ^for both crystals I I increases when T increases for 1 ⁼ 33, while it decreases with increasing

T for / ⁼ 7, ^{27 and 47.} Simultaneously, ¹ values for the

Table VII.

Metastable phase sequence of crystalline thiophene : ^{variation with} temperature of the indices 1

of different Bragg reflexions for crystal ^1. (The ^chrono- logical order for ^the temperatures of ^the measurements

is:160,164,168,170,158,153,148,143,138,133,128, 123,118,113,108 ^{and 162} K.)

(*) ^{After a 30-hours} stay ^{at this} temperature.

orthorhombic sublattice hardly change. This is illus- trated on figure ⁵ where the evolution of 111 for different reflexions are represented.

Another _way to point ^{out the} differences between the orthorhombic sublattice (A) and the sublattice defined

by ^the superstructure Bragg reflexions (B) ^{is shown}

on table VIII. This table reports the values of the parameters ^{of the} crystalline unit cell for crystal ^{2 at}

168 K as calculated by ^means of the diffractometer routine method using reflexions of sublattices A and B, respectively. ^{Even when} the calculated uncertainties

are always greater ^with sublattice B, ^the agreement ^for parameters a, b, ^{c and Y is} good. ^{But, while} right angles

are calculated from sublattice A, angle fl ^{as calculated}

from sublattice B differs significantly ^{from 900.}

All these results clearly ^{show that} sublattice B is not commensurable with the original orthorhombic sublat- tice for phases 11(11’), III ^and 112, ^so that these 3 phases

Fig. ^5.

Metastable phase sequence of crystalline ^thio- phene. ^{Variation of} index III ^{as a} function of temperature for some Bragg reflexions :

* Crystal 1 : Reflexions 1 4 27 and 1 2 20;

40 Crystal 2 : Reflexions 1 4 27 and 3 6 20.

are to be considered as incommensurate. As pointed

out by ^{one of the referees, the} incommensurability may be characterized by ^{a wave vector} q ⁼ bc* with 6 - 7/20. 6 varie from 0.33 to 0.36 when temperature decreases and the positions ^{of the} supplementary

intense reflexions can be described by ^vectors GBragg - ^q

for 1 ⁼ 33 and GBragg ^{+ q for 1 = 7,27 and 47.}

3. Discussion and conclusions.

The lattices of the metastable phases ^of thiophene, II(II’), II1 ^and 112 correspond ^to superstructures ^{of the} orthorhombic lattice of phase ^I which constitutes a common geometrical ^{frame down to} the lowest temperature. ^On cooling, ^the complexity ^{of these} superstructures increases each time a phase ^transition

is encountered, ^{as witnessed} by ^the emergence of new

Bragg reflexions. Nevertheless the ^mean geometrical

characteristics of the superstructure ^which emerges in phase ^{II are retained.}

The most remarkable feature is that the superstruc-

Table VIII.

Crystalline thiophene. Phase II’. Unit cell parameters ^{at 168 K as} calculated by ^means of the Syntex P21 diffractometer ^{routine method :} A) Using Bragg reflexions of the orthorhombic sublattice (7 ^Friedel pairs : 004, 331, 422, 204, 600, 240, ^{044) ; B)} Using ^Bragg reflexions of ^the superstructure ^lattice (7 Friedel pairs : ¹⁴ 33,

14 27, 2 2 53, 2 2 47, 3 0 47, 3 4 7, 4 2 27).

69

ture lattices are not commensurable with the ortho- rhombic sublattice from the temperature ^of the I-to-II

phase transition downwards.

Incommensurate phases ^{are known to be} very sensitive to impurities [13] ^{and this} probably explains

the differences we have already pointed ^{out in the}

detailed behaviours of the index I in crystals ^{1 and} 2, respectively. ^{It could also} explain ^the formidable shift of the 112-to-III transition temperature (almost ^{20 K}

between thoroughly purified thiophene ^{and the} present

samples).

Heat capacity measurements have failed to detect any phase transition between 13 and 90 K, _except ^a glass transition at about 37 K [5]. One nay wonder whether this glass transition corresponds ^{to the} supercooling ^of phase II2 ^while avoiding ^some

incommensurate-commensurate phase transition lying

between 37 and 90 K.

One important feature does not fit in with the usual characteristics of the hitherto known incommensurate solids. The intensities of some superstructure ^reflexions increase in such a way ^{as to} become some of the strongest ^{ones of the} diffraction pattern ^{and are far too} strong ^to represent harmonics related to some struc- tural modulation. So, important modifications in the scattered intensities undoubtedly correspond ^to

noticeable changes ^{in the mean} electronic densities in the different metastable phases. ^One may speculate

on the part played by orientational disorder : phase ^{I is}

known to be plastic ^{with some} complex dynamic

disorder [6]. ^Nuclear magnetic ^{resonance data} [14]

show that this disorder continues to exist in the metastable phases ^when temperature decreases and that the frequency of the molecular reorientation is still much higher ^{than 104 Hz at 85 K in} phase II2. ^This

suggests that the molecular orientations undergo ^some complex progressive rearrangements leading ^{to stacks}

of molecules the reorientations of which would be correlated along the c-direction.

The length ^{of axis c} should be related to the sizes of

these possible stacks, ^{but this} very length gives ^{rise to}

some ambiguity. ^{We have seen} that it is _necessary to

multiply ^the length ^of parameter ^{c of the} orthorhombic sublattice, ^as derived from phase I, by ^{20 to} get ^near integers for the values of the c indices of all Bragg

reflexions in phases 11(11’), III ^and II2. ^{The agreement}

is almost perfect ^{at 160 K,} but table VI shows that

multiplying ^c by ³ (or multiples ^of 3) gives results that

are closer and closer to integers ^{as the} transition II-to-I is approached

We have already ^shown [6] that the 20 equiprobable

molecular positions ^{at each} crystalline ^{site of} phase ^I

can be roughly distributed between 6 groups. On the other hand, ^{Sanford an} Boyd [9] ^and Gavezzotti and Simonetta [15] ^have calculated independently ^{a 6-well}

distribution for the thiophene ^molecule using

Abrahams and Lipscomb’s 4-position description [2]

for phase ^{I as a} starting point. Finally, ^mechanical

simulations performed by Branka and Wojciechowski [16] ^{for a} system ^{of hard} cyclic pentamers ^{reveal a} rotational 2D-phase ⁱⁿ which the mean molecular symmetry ^{is a 6-fold one.}

It can be conjectured ^{that such a 5-6} duality ^corres- ponds ^{to the manner} in which the crystalline ^structure

may accomodate itself ^to the quasi ^five-fold symmetry of the reorientating thiophene ^{molecule. It could be} thought ^{that this} duality ^{is the} origin of the incommen-

surability ^{when a} decrease in temperature ^{leads to a} partial ordering of molecular reorientations.

Close similarities can be found between the two sequences of phases ^of thiophene : their heat capacity

behaviours are very similar [5] ^{and fast} reorientational motions (with frequencies higher ^{than 104} Hz) persist

down to 85 K in both _sequences [4]. ^{Thus we} expect ^to find similar structural results in the stable _sequence as we have done so in the metastable one. If this were

the _case, it would emphasize ^the part ^{that we believe} the pseudo-pentagonal ^molecular symmetry plays ⁱⁿ

the emergence of incommensurate phases and/or glassy crystalline ^states [3].

References

[1] WADDINGTON, G., KNOWLTON, ^J. W., SCOTT, ^D. W., OLIVER, ^G. D., TODD, ^S. S., HUBBARD, ^W. N., SMITH, J. C. and HUFFMAN, ^H. M., J. Am. Chem.

Soc. 71 (1949) ^797.

[2] ABRAHAMS, S. C. and LIPSCOMB, ^W. N., ^Acta Crystal- logr. ⁵ (1952) ^93.

[3] ANDRÉ, D., DWORKIN, A., FIGUIÈRE, P., FUCHS, ^{A. H.}

and SZWARC, H., ^C.R. Hebd. Séan. Acad. Sci.

Paris, Ser. II 295 (1982) ^145.

[4] ANDRÉ, D., DWORKIN, A., FIGUIÈRE, P., FUCHS, ^{A. H.}

and SZWARC, H., J. Phys. Chem. Solids 46 (1985)

505.

[5] FIGUIÈRE, P., SZWARC, H., OGUNI, ^{M. and} SUGA, H.,

J. Physique ^{Lett. 45} (1984) L-1167; ^{J. Chem.}

Thermodynamics ¹⁷ (1985) ^949.

[6] ANDRÉ, D., FIGUIÈRE, P., FOURME, R., GHELFENSTEIN, M., LABARRE, ^{D. and} SZWARC, H., ^J. Phys. ^Chem.

Solids 45 (1984) ^299.

[7] RENAUD, ^{M. and} FOURME, R., ^Acta Crystallogr. ²² (1967) 695.

[8] ^{RENAUD, M. and} FOURME, R., Bull. Soc. Fr. Mineral.

Cristallogr. ⁸⁹ (1966) ^243.

[9] SANFORD, ^{W. E. and} BOYD, ^R. K., Can. J. Chem. 54

(1976) ^2773.

[10] ^SUGA, H., ^Private communication.

[11] ^{SPARKS, R. A., in} Crystallographic Computing ^Tech- niques, ed. R. F. Ahmed, Munksgaard, Copen- hagen (1976), p. 452-467.

[12] STEWART, ^J. M., KUNDELL, ^{F. A. and} BALDWIN, ^J. C., The X-ray system, University ^of Maryland, ^Col- lege Park, Maryland (1972).

[13] DENOYER, ^{F. and} ANDRÉ, G., unpublished ^{results on}

thiourea.

[14] ^FRIED, F., Thèse, Nice A. O. CNRS 9740 (1974);

some of the N.M.R. data have been reproduced ⁱⁿ

reference [4] ^{with the} permission of Dr. Fried.

[15] GAVEZZOTTI, ^{A. and} SIMONETTA, M., ^Acta Crystallogr.

A 31 (1975) ^645.

[16] BRANKA, ^{A. C. and} WOJCIECHOWSKI, ^K. W., Phys. ^Lett.

101A (1984) ^349.