Preliminary X-ray study of the ordering phase transitions in the inclusion compound TANO-hexadecane

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Preliminary X-ray study of the ordering phase

transitions in the inclusion compound

TANO-hexadecane

P.-A. Albouy, J. Lajzerowicz, M. Le Bars-Combe

To cite this version:

Preliminary X-ray study

of the

_{ordering phase}

transitions in

the inclusion

_compound

TANO-hexadecane

P.-A.

_Albouy

_(1),

J.

_Lajzerowicz

₍₂₎

and M. Le Bars-Combe

₍₂₎

(1)

Laboratoire de

_Physique

des _Solides, Bât. 510, Université Paris-Sud, 91405

_Orsay,

France

(2)

Laboratoire de

_{Spectrométrie Physique,}

Université

_scientifique

et médicale de Grenoble,

B.P. 68, 38402 Saint-Martin

d’Hères,

France

(Reçu

le 2 novembre 1989, révisé le 8

février

1990,

accepté

le 12

_{février 1990)}

Résumé. 2014 Le radical

nitroxyde (2,

2, 6,

5-tétraméthyl

4-oxo

_{1-piperidyl) oxyde}

ou TANO

(C9H16NO2)

forme avec des molécules linéaires, dont les alcanes, de nombreux

composés

d’inclusion à canaux. A

_température

ambiante, les alcanes et les molécules de TANO

_présentent

d’importants

désordres. Nous

_présentons

une étude

_{préliminaire,}

par diffraction X, de l’évolution de ces désordres en fonction de la

_{température,}

pour le

composé

TANO-hexadécane. Deux transitions de mise en

ordre, complexes,

sont observées à 171 K et 137 K ; une

_période

d’environ

100 Å

apparaît

à basses

_{températures.}

Des

_comparaisons

avec le

_composé

_déjà

étudié

TANO-heptane,

sont faites.

Abstract. 2014 The nitroxide radical:

(tetramethyl-2,2,6,6

oxo-4

_{piperidyl-1) oxyle-}

or TANO

(C9H16NO2)

can form numerous channel inclusion

_compounds

with linear molecules

including

alkanes. At room _temperature both alkanes and TANO molecules exhibit

_important

disorders.

We _present a

_{preliminary X-ray study}

of the evolution of these disorders as a function of

temperature for the inclusion

_compound

TANO-hexadecane

₍₂₄

_C9H16NO2,

1

_C16H34).

It has two

complex ordering phase

transitions at 171 K and 137 K ; the lower temperature

phase

has a

superperiod

of about 100

Å.

A

_comparison

with the well-studied

_TANO-heptane

_compound

is made.

61.50K - 61.65K - 64.70K

1. Introduction.

The TANO molecule is a stable nitroxide radical

_represented

in

_figure

la. This chiral

molecule has enantiomeric forms shown in

_figure

1 b and labelled

_A

and

_{B [1].}

It forms

inclusion

_compounds

with linear n-alkanes

_{CnH2 n + 2}

for n

_ranging

from 7 to 44 at least

[1].

The inclusion

_represents

less than 5 % in

_weight.

At room

_temperature,

all these

_compounds

are monoclinic

_(C2/c,

24 TANO per

cell)

and their lattice constants differ

_by

less than 1 %

(typically

a = 36.0

Â,

b = 5.95

Á,

c =

35.5 Â

and

_{f3 =}

120°).

The

similarity

of these

parameters and of the

_X-ray

_patterns

_strongly

_suggests

a similar

_organization

in the whole sequence.

Structure determinations have been carried out

_only

for the

_{TANO-heptane compound}

(abreviated

as

_{TANO-C7) [la].}

A

_projection

of the structure of the

_high

_temperature

structure on the

_(a,

_{c ) plane}

is

_represented

in

_tigure

2. Disordered included chains are

Fig.

1. -

a)

TANO molecule.

_b)

The two enantiomeric forms of the TANO.

_Methyl

_groups are

omitted for the sake of

_simplicity.

Fig.

2. -

(a, c )

projection

of the TANO-C7 structure. The

_heptane

chains are

_{running along}

the monoclinic b axis and centered on the screw axis

_(from

Ref.

_[1]).

_Light

and

_heavy

lines

_correspond

to

the two

_{configurations}

A and B of the TANO molecule.

embedded in four

_channels,

18 Â

distant,

parallel

to b. Each TANO molecule

_presents

a

statistical disorder between the A

_{and B}

forms. It is

_thought

that the

_flipping

between these

two, forms is connected to the orientational and translational motions of the

_heptane

molecules

_along

the channels.

_{Upon cooling}

down a first-order

_phase

transition occurs at

195 K. At lower

_temperatures

structural order sets _up.

_Preliminary

incoherent

_quasielastic

neutron

_scattering

_experiments

that we have

performed

at the

_{Laue-Langevin}

Institut have

confirmed the

_dynamic

character of both alkane and TANO molecules disorders at room

temperature.

These studies are in progress.

A

_systematic

calorimetric

_study

was carried out

_by

two of us for TANO-n-alkanes with

n

_ranging

from 7 to 16

_{[1b] .}

Results are shown in

_figure

3. It shows that :

i)

only

one

phase

transition is observed for n 11

(n being

the number of carbon atoms in the alkane

_{chain) ;}

ii)

for n >

_11,

two distinct

_phase

transitions are seen. The first one has

_pratically

no

Fig.

3. - Plot of the

temperatures of transitions obtained

_by

D.S.C. as a function of the number of

carbon atoms of the included alkane

(from

Ref.

[1]).

(A ) increasing

temperature and

_{(V) decreasing}

temperature.

related to the

_phase

transition observed in the short chain

_{compounds (n}

11 )

as shown

by

the

_continuity

of the transition

temperatures.

In the

_present

work we

began

to

_investigate

the TANO-C16

_compound

which

_distinctly

presents

the two

_phase

transitions at about 165 K and 125

_{K ;}

_owing

to the

_complexity

of the results we decided to

_study

the TANO-C7 transition more

_carefully.

In _{this paper after} an

X-ray

experiment

description

we shall describe TANO-C7 and then TANO-C16

_ordering

phase

transitions.

Other inclusion

_compounds,

urea-alkanes,

have been

_widely

studied ;

they

have intricàte

phase

transitions and show similarities with TANO-alkanes

_{[2] ;}

nevertheless their ratio of inclusion is about 27 % in

_weight

and the channels are

8 Â

distant.

2.

_{Experimental.}

TANO-C7 and TANO-C16

_crystals

_{have been grown}

_by

slow

_cooling

of a solution of TANO

in

heptane

and hexadecane

_{(50 ° C}

to room

_temperature

in

_steps

of 1

_{° C/day). They}

_appear as

orange needles of

typical

size 8 x 0.5 x 0.5

mm 3.

Due to the

_{pseudo-hexagonal}

symmetry

of the

_crystal,

these needles are

_always

bundles of six

_{single crystals sharing}

their

(a, b )

and

(b, c )

faces.

_They

can be

_separated

with a razor blade. As the

_{crystals slowly}

sublimate at room

_temperature,

_they

must be handled either in a

_{capillary glass}

or

_{rapidly brought}

below room

_temperature.

Three

_X-ray

set-ups

were used for this

_{study. They}

were all

_equipped

with

_doubly

bent

graphite

monochromators

_isolating

the Ka radiation from a _{copper anode.}

_Photographs

and

intensity

measurements were

_performed

with a 3-circle

_goniometer

in the normal

beam-lifting

detector

_geometry

_equipped

with a home-made linear detector. A

_temperature

_{range from}

20 K to 400 K can be

_explored

with an absolute _accuracy of ± 0.2 K and a

stability

of 0.01 K.

The

_sample

is _{held in gazeous helium. Numerous oscillation}

_photographs

have been taken at

different

temperatures

with this

_apparatus.

In all cases the

_sample

was oscillated around its

monoclinic axis b

_during

the exposure

(amplitude

of oscillation : ±

5°,

b axis

vertical).

Quantitative

measurements of lattice constants and reflection

_positions

were obtained on a

operating

between 10 K and 300 K.

_{Complementary}

results were obtained with a low

temperature

Weissenberg

camera

_operating

between 10 K and 300 K. In these two

_apparatus

the

_sample

is under vacuum and has to be held in a sealed

glass capillary.

All these

_set-ups

are

equipped

with helium

_closed-cycle

_{cryogenerators}

_[3].

The resolution of these

_apparatus

is

_typically

0.01

 -1.

3. TANO-C7.

Let us

_briefly

remind the most

_important

features of the TANO-C7

_phase

transition. At room

temperature

two TANO molecules - A and B enantiomeric forms- are found on each site

Fig.

4.

_{- a)}

X ray pattern of a TANO-C7

_{single crystal}

at 297.4 K. The monoclinic axis is vertical and the

_crystal

was oscillated

_during

the

_exposure

(oscillation: ±5B ACux

= 1.54

Á,

45 kV-25 mA,

with occupancy factors around 70 % A or vice versa.

_Heptane

chains are disordered inside the

channels. Below the

_lock-in

transition the cell

_{parameters a}

and b become b’ = 2 b and a’ =

_al2

with the _{space groupe Pc and still 24 TANO per} cell. The

_{stoichiometry}

of the

complex

is 12

TANO,

1

_heptane.

Simultaneous structural modifications occur :

-

Heptane

chains are ordered.

- Very large

molecular shifts of TANO molecules occur

_parallel

to the b axis.

_Along

the TANO files

_parallel

to b A and B conformations alternate

_(the

cell

_parameter

is now

b’ -

_{2 b).}

- TANO molecules

These

_phenomena

are illustrated in the

_{following photographs. They}

have been taken in the conditions described in

_paragraph

_2,

the

temperature

being

decreased.

Figure

4a,

297.4 K :

One observes :

i)

First

_Bragg

_spots

_{arrays due} to the diffraction

_by

the TANO host lattice with a

periodicity b

=

5.95 Â

(see

k index _on the

photograph).

ii) Secondly

we can see diffuse lines

_{perpendicular}

to the b axis

_{(see arrows). They}

are

equally

spaced

and

_correspond

at the

_precision

of the

_photograph

to a

periodicity

of

2 b = 11.9

Â.

No zeroth order line is

present.

These lines are observed whatever the rotation

of the

_crystal

around b.

_{They correspond}

thus in the

_reciprocal

space to the intersection of diffuse

_{planes perpendicular}

to the b* axis with the Ewald

_sphere.

Such

_planes

are

_typical

of

the diffraction

_by

uncorrelated linear chains

_[4].

The

_length

of an alkane

_{CnH2 n + 2}

is

approximately

given by

the formula L = 1.272

(n - 1)

₊ 3.6

Â.

For

heptane

one obtains

L =

11.23 Â

_{which compares well with 2 b. The diffuse lines}

correspond

thus to the

diffraction

_by

the

_heptane

chains embedded in the TANO matrix and

_{running along}

the

monoclinic axis b. The absence of zeroth order diffuse is characteristic of a translational

disorder

_polarized

in the chain direction : the

_projection

of the structure on a

_plane

perpendicular

to the alkane chains

presents

no disorder.

At the

_precision

of our measurement the width of the diffuse lines is resolution limited.

Long-range

order is thus

_preserved

in the channel direction over a few hundred of

Â

at least.

Figure

4b,

201.1 K :

The diffuse lines are now

_broadly

modulated,

_indicating

the

development

of interchain

correlations

(see

arrows).

Figure

4c,

191.4 K :

Additional

Bragg

reflections have

_{appeared :}

i)

First on the

_Bragg

arrays of index k = ± 1

_{(the apparition}

of reflections on the arrays

k = 0 and k = ± 2 is

only

due to _a

significant

increase of the

crystal mosaicity

at the

transition).

ii) Secondly

on the diffuse lines. The

_{high intensity}

of these last

_Bragg

reflections

implies

a

contribution of both alkane and TANO molecules

_[1]

_]

_{(see arrows).}

A

_study

was then made with

_increasing

_temperature

in order to

_explain

different facts

observed in

_{preliminary experiments [1b] :}

- The DSC

signal

obtained on

warming-up

_presents

an

_unexplained

shoulder at ca. 20 K under the endothermic

_peak.

- On

cooling

down the

_Bragg

reflections intensities and the cell

parameters present

a

jump

at the

_phase

transition

_{(first-order phase transition).}

_Upon

_warming-up

_they

continu-ously

return to their

_high

_temperature

value. This evolution takes

_place

in an interval of

ca. 20 K

[ 1 b].

Figure

4d,

220.8 K :

After

_warming-up,

intense diffuse lines have

_reappeared

at k = ± 0.5. It _means that the

heptane

chains have recovered an

_important

disorder. Furthermore

Bragg

reflections at

k = ±

_{(2 n}

+

_{1 )/2}

have

_split

into two

_Bragg

reflections of index k = ±

_{(2 n}

+

_{1 )/2 ±}

_1/16

(see arrows).

The shoulder observed on the DSC

_signal

can be thus correlated with the

reflection

_developing

on the

Bragg

array of index k = 0.5. We observe an

_{intensity jump}

at

7c

= 193

K,

characteristic of a first-order transition.

_Upon

warming-up,

the

splitting

of the

Bragg

reflection into two

_components

of index k

_{=1/2 ±1/16}

_appears at 203 K. Above this

temperature,

we have

_plotted

the sum of the

intensity

of both

_components.

The

hysteresis

amplitude

is about 35 K.

Fig.

5. - TANO-C7 :

temperature

dependence

of the

intensity

of a

_Bragg

_reflection

of index

k = 0.5.

4. TANO-C16.

4.1 PHOTOGRAPHIC STUDY. - The

photographic study

was

_performed

under the same

experimental

conditions as for TANO-C7

_(monoclinic

axis b

_vertical).

Figure

6a,

270.2 K :

As for the

_TANO-C7,

one observes :

i)

First horizontal

_Bragg

_spots

arrays

corresponding

to the diffraction

_by

the TANO lattice

with a

_{periodicity along}

b of b = 5.945

À

(see

below the

precise

determination of the lattice

parameters). They

are indicated

_by

a k index on the

_photograph.,

ii) Secondly

diffuse lines due to the disordered hexadecane chains

(no

zeroth-order

_line).

They

are indicated

_by

a « - » on the

_photograph.

These lines

_correspond

to a

_periodicity

4 b = 23.8

À

which is similar to the hexadecane

length

L = 22.7

Á.

The

Bragg

reflections

present on the diffuse lines at

_{b * /2}

_correspond

to

_{a À / 2}

contamination. The

_homogeneity

of the

_intensity

of the diffuse lines

reflects,

on the one

_hand,

the absence of interchain

correlations

and,

on the other

hand,

the featureless molecular structure factor of linear

hexadecane molecules. As for the

_TANO-C7,

the absence of zeroth-order line means that the

iii)

The third feature that can be observed on the

_photograph

consists of broad modulations

of the

_{background (see arrows).}

Figure

6b,

176 K :

Bragg

spot

arrays remain

unchanged.

i) Sharp

modulations of

_intensity

have

_appeared

on some diffuse lines

_{(see symbols}

« >

_»).

It reflects the

_development

of interchain correlations.

ii)

Furthermore some

_segments

of diffuse lines are visible at

_higher

k index. This

corresponds

to the reduction of the

_longitudinal

thermal

_agitation

of the molecules

_along

the channels

_(diffuse

lines indicated

_by

« -

_»).

Fig.

6. -

a)

X _{ray pattern} of a TANO-C16

single

crystal

taken at 270.2 K.

_{b) TANO-C16 :}

T = 176 K.

c)

TANO-C16 : T = 161.6 K.

d)

TANO-C16 : T = 151.5 K.

e)

TANO-C16 : T = 123.1 K.

iii)

Thirdly,

the broad modulations of the

_background

observed in

_figure

4a are

_sharper

(see arrows). They

are observed in the b* direction at k =

(2 n

₊

1 )/2

±

_1/8

in b* units. These

last precursor

phenomena

have an

_aspect

_very different from that of the diffuse lines. In

particular they

are much broader

_along

b*,

_reflecting

a smaller correlation

_{length along}

b.

Secondly,

their

_intensity

_repartition

_{in space}

_suggests

the influence of a

_{strongly varying}

structure factor. It is thus

_tempting

to attribute them to the TANO molécules.

Figure

6c,

161.6 K :

New

_Bragg

reflections are now

clearly

visible :

i)

On the diffuse

_lines,

which means that the hexadecane chains are now ordered on a 3D

lattice of

_periodicity

4b in the chain direction

_(see

line indexation on the left side of the

ii)

In

_place

of the

_background

modulations at

_{k = (2 n + 1 ) b * /2 ± b * /8}

_(see

line

indexation on the

right

side of the

photograph).

These reflections have an

higher intensity

than the reflections

_{corresponding}

to the diffuse lines

_(that

is,

to the hexadecane

_lattice)

and

can be

_interpreted

as a response of the TANO lattice to the

_ordering

of the hexadecane

molecules

_(see

also

_above).

The

_periodicity

common to both lattices is thus 8b in the chain direction.

As for the TANO-C7

_compound

the

_ordering

of the hexadecane sublattice is

_probably

accompanied by

the lock-in of the TANO molecules in a

_given

_A

or B

position.

In this case one could observe an _occupancy wave

_{(A, B )}

with a

_{wave-vector qy}

=

b * /2 :t b * / 8.

The

absence of modification of the main

_Bragg

reflections shows that the structural modifications

of the TANO matrix

_accompanying

this

_phase

transition

_{(temperature Tl -}

171

_K)

are

Figure

6d,

151.5 K :

Weak additional

_Bragg

reflections can now be seen at nb * ± b *

_/8

_{(see arrows).}

The

_crystal

periodicity

in the chain direction remains 8 b.

Figure

6e,

123.1 K :

The

_X-ray

_pattern

is

_highly

modified :

i)

We can see first that additional

_Bragg

reflections have

_appeared

on the

_Bragg

_arrays

k = ± 1.

_Bragg

_spot

_arrays of index k = 0 and k = ± 2 remain

_unchanged.

ii)

Some

_Bragg

reflections have

appeared

at

_positions

that

_correspond

to a

_periodicity

16b

at the

_precision

of the measurement

_{(see arrows).}

We shall call this

_{phase : phase}

2. On the

whole,

the

_crystal

appears

highly

stressed as shown

_by

the _many

_{badly shaped}

_Bragg

reflections and the diffuse streaks

_{(second phase}

_transition,

_temperature

_T2

= 137

K).

One

can also observe that the diffuse lines at k = _{± n}

/4

remain

_present.

They

were observed down to the lowest

_temperature

reached

_during

this

_{cycle :}

20 K.

The

_following

two

_photographs

were taken

_during

the

_rewarming

_part

of the

_{cycle :}

Figure

6f ;

216 K:

This

_photograph

has been taken above the transition

_temperature

_Tl.

Two facts can be

noted :

i)

First the almost

_{complete disparition}

of the

_Bragg

reflections on the diffuse lines. It means that the hexadecane chains have recovered an

_important

disorder.

ii)

The additional

_Bragg

reflections of index k = _± 1 and the

Bragg

reflections at

k = ±

_{(2 n}

+ 1

_{)/2 ± 1/16}

characteristic of

_phase

2 remain

_clearly

visible

_(see

_arrows).

This

X-ray

pattern

strongly

recalls that of

_figure

4d.

These observations

_suggest

the

_{following interpretation :}

below

_T2,

_phases

1 and 2 coexist.

Upon warming-up

the domains of

_phase

1 retum to the

_high

temperature

phase

at

Tl

(no hysteresis)

and

_only

the domains of

_phase

2 remain. This

_hypothesis

is

_{supported by}

the DSC results of

_figure

3 which show two

_phase

transitions in the TANO-C16 upon

warming-up.

Furthermore the

_amplitude

of the endothermic

_peak

_{corresponding}

to the

_phase

transition 1

_depends

on the time

_spent

_by

the

_sample

under

_T2

but does never

completely

Figure 6g,

225.8 K :

All the additional features have

_disappeared

and we obtain the same diffraction

_pattern

as

in

_figure

6a.

_Differently

from

_TANO-C7,

TANO-C16

_crystals

sustain a

_temperature

cycle

without deterioration.

The

_precision

of the

_photographic

data is not

_{high enough}

to indicate if the hexadecane

sublattice becomes incommensurate with the TANO lattice at some

_temperature.

Some

_quantitative

results have been obtained

_concerning

first the

_{crystallographic}

data of the different

phases

and

_secondly

the

_temperature

_dependence

_{of the precursor}

_phenomena

and the

_Bragg

reflections associated.

4.2 TEMPERATURE DEPENDENCE OF THE BASIC CELL LATTICE PARAMETERS. - In

_figure

_7,

we have

_plotted

the

temperature

dependence

of the lattice

parameters

as defined in the

_high

temperature

phase (space

group

C2/c).

At room

_temperature

_{(293 K),}

we have the

_following

crystallographic

data :

On

_cooling

down to 80

_K,

all the

parameters

regularly

decrease without

_apparent

accident at

the

_phase

transition

_{temperatures.}

Fig.

7. - TANO-C16 :

temperature

dependence

of the lattice constants as defined in the

_high

integer position.

Due to their

weakness,

only partial

measurements have been

_performed

yet.

i)

On the hexadecane

sublattice,

for k =

1/4, only

h odd reflections were observed

(55

observable

_reflections)

and for k =

1/2, only

h even reflections were observed

(58

observable

reflections).

This is

_compatible

with a hexadecane sublattice of space group

C2/c

and

monoclinic

_parameter

4 b

_(a

and c

unchanged).

ii)

The

_Bragg

arrays of index k =

1/2

₊

1/8

and

1/2 - 1/8 correspond

to an index

h odd and even

_{respectively.}

4.3.2 Second transition. -

Weissenberg

X-ray

patterns

of the

planes (h,

0,

l )

and

(h, 1,

f )

have been taken at different

temperature.

i)

Above 137

_K,

one observes the extinction rules characteristic of the

C2/c

space group :

(h, f )

even on

(h,

_0,

f )

_plane

and h odd on

(h,

1, e)

plane.

No difference is observed

between

_photographs

taken above and below the first transition.

ii) Photographs

taken below 137 K

_(at

_{112 K)}

reveal that :

₁₎

the

_plane

_{(h, 0, l )}

is

unchanged, 2)

the restriction h odd is

_dropped

in the

_{plane (h,}

_{1, l ).}

As there is no

monoclinic space group

satisfying

these

conditions,

we can _{propose the}

_following

explanation

based upon the coexistence of

phases

1 and 2 below

_T2

= 137 K

(see above) :

i)

Phase 1

_{( Tl}

= 171

K) keeps

the space group

C2/c.

ii)

The space group of

phase

2 satisfies the extinction rules

(h,

f )

even on

_(h,

_0,

f )

and

h even on the

(h, 1,

f )

plane.

This space group could be Pc as found in the TANO-C7

compound

with a

_{parameter a’ equal}

to

_a/2.

Due to movements of the

_crystal

in the

_glass

capillary,

it was not

_possible

to

_reach

a lower

temperature.

4.4 TEMPERATURE DEPENDENCE OF THE TRANSITION PARAMETERS.

4.4.1 First transition. - We have

seen that at the transition

temperature,

we have

simultaneously

the

_apparition

of

_Bragg

reflections of index k =

n /4

(diffuse lines)

and

k =

(2 n + 1 )/2 ± 1 /8.

The latter reflections are more intense and were used for the

_study

of the

phase

transition. The evolution of the

_profile

of a _precursor

_{peak (index k}

=

13/8)

was

measured

_{perpendicularly}

to the b axis with a linear detector. The deconvolution

_proceeded

as shown in reference

_[5]

_{assuming Voigt profiles}

for’thé

_{peak shape}

and the resolution.

Almost Lorentzian

_profiles

were found for the deconvoluted curves.

The extension of the interchain correlations in the

_{(a, c ) plane}

is characterized

_by

a

correlation

_length

_e,

_assuming

an

_{in-plane isotropy.}

In the context of

_phase

_transitions,

the Ornstein-Zernike correlation function is very often used

[6].

It leads to a Lorentzian

_intensity

profile :

If _q, is the wave-vector

_{corresponding}

to the

_{Bragg reflection,}

the

_intensity

scattered

at q

= qc

+ 8 q

can be written in the form :

_{I (q )}

= I (qc) / (1

+ e2

6 q2) .

The half width at half maximum

_{& q 1/2}

is thus related

_to

_by

_{& q 1/2}

=

1 / .

This

quantity

is

plotted

in

figure

8a. The

correlation

_{length e}

is about 23

Å at

198 K and

_diverges

at about 170 K. In a mean field

approximation,

we

have -1 oc

(T -

Tc)1/2

and hence

_8q1/2

oc

_{( T -}

Tc)1/2,

where

_Tc

is the

transition

temperature

[6].

We see that below about 190

_K,

this law is well

_{obeyed, leading}

to a

_Tc

of 170 K. In

_figure

8b we have

_plotted

the ratio

_{(temperature)/(intensity}

at

qc)

as a function of the

_temperature.

This

_quantity

is

_proportional

to

_{( T - Tc)}

in a mean field

theory,

which is well observed below 180 K.

Fig.

8.

- a)

TANO-C16 : temperature

dependence

of the half width at half the maximum

_intensity

of a precursor

phenomenon

of index k =

13/8.

The solid line

corresponds

_{to a} mean-field fit.

b)

TANO-C16 : temperature

dependence

of the ratio

_{(temperature)/(intensity}

at the

_maximum)

of the same

precursor. The solid line

corresponds

to a mean field fit.

Fig.

9. - TANO-C16 :

temperature

dependence

of the

_intensity

of the

_Bragg

reflection

corresponding

the precursor

phenomenon

of the

_figure

8.

7c

=

Tl -

171 K. As

long

_as the second transition is not reached

(T >.

137

K),

this transition

is

_perfectly

reversible and did not show any measurable

hysteresis by X-ray

measurements.

4.4.2 Second transition. - Measurements have been

performed

on a

_Bragg

reflection

Fig.

10. - TANO-C16 :

temperature

dependence

of the

intensity

of

_Bragg

reflection of indices k = 1 and h even.

transition,

although

calorimetric data

_suggest

a first-order transition. This could be due to some

_{inhomogeneity}

in the

_crystal

and related to the fact that the two

_phases

cohabit in some

temperature

range

(see

above).

5. Conclusion.

This

_preliminary

_X-ray

_study

has shown a different behaviour with the

_temperature

of the

long-chain compound (TANO-C16)

and short-chain

_{compound (TANO-C7).}

The

_complexity

of the observed

_phenomena

reflects the existence and the

_competition

of three different interactions at least :

_host-guest,

host-host and

_guest-guest

within the same channel. The

interaction

_guest-guest

from

_neighbouring

channels was shown to be very weak in urea-alkane

compounds [7].

In both

_compounds

the alkane chains are uncorrelated at room

_temperature

but remain commensurate with the TANO lattice

_(periodicity

2 b for TANO-C7 and 4 b for

_TANO-C16).

In the TANO-C16 the

_ordering

of the alkane chains

_{proceeds through}

a

second order

_phase

transition

_(periodicity

4 b in chain

direction,

T1 =

171

_K).

The transition is

_{accompanied by}

a modulation of the TANO lattice. This modulation

could

be an

occupation

wave between the A and B

configurations

of the TANO

molecuies

of

period

8 b. This transition is

_perfectly

reversible. A first-order

_phase

transition takes

_place

at a lower

temperature

( T2

= 137

K).

It is characterized

by

the

apparition

of a

_periodicity

16 b and a

change

of the space group of the TANO average lattice. This last transition exhibits a

_large

.

hysteresis

of 87 K.

Thereby

for T >

_Tl

the

_{only periodicity}

16 b is observed up to 224 K with

increasing

temperature.

In the TANO-C7

_only

one first-order

_phase

transition exists with

decreasing

temperature

(Tc

= 193

K).

It

corresponds simultaneously

to the

ordering

of the

heptane

chains and to a

change

of the TANO

lattice, contrary

to the TANO-C16 for which these two modifications

occur at two different

temperatures.

This transition has an

_hysteresis

of 35 K and should be

related to some extent to the second transition observed in the TANO-C16. This is shown

_by

the

_following

facts :

ii)

The fact that very similar

X-ray

patterns

are observed above 210

_K,

characterized

_by

a

modulation of the TANO lattice of

wave-component

qb =

b */2

±

_{b */ 16 (at}

the

_precision

of the

measure).

Much work has to be devoted to structure determination in the TANO-C16

phase

1 and

phase

2. It should be also

_important

to check

_precisely

the

_{commensurability}

of the hexadecane chains with the TANO lattice in

temperature.

The

_question

which remains open is the choice of TANO-C7

(heptane

length L ~ 2 b)

and TANO-C16

(hexadecane

length

L = 4

b)

as

_{representative examples}

of short and

_long

chain inclusion

_compounds.

For

instance will the 16 b

_periodicity

observed in both cases be found with octane

₍₃

L =

7 b )

and

tetradecane

₍₂

L =

7 b ) ?

Acknowledgments.

The authors want to thank G. Commandeur for chemical

synthesis

and

_{crystal growth.}

References

[1] a)

LE BARS-COMBE M. and LAJZEROWICZ J., Acta

_Cryst.

B 43

₍₁₉₈₇₎

386.

b)

LE BARS-COMBE M. and LAJZEROWICZ _J., Acta

_Cryst.

B 43

₍₁₉₈₇₎

393.

[2]

FORST R., JAGODZINSKI H., BOYSEN H. and FREY _F., Acta _Cryst. B 43

₍₁₉₈₇₎

187.

[3]

ALBOUY P.-A., Thesis,

Orsay (1988).

[4]

VAINSHTEIN B. K. in « Diffraction of

X-rays

by

Chain Molecules », Amsterdam, London

_(Elsevier,

New

_York)

1960.

[5]

LANGFORD J. I., J.

_{Appl. Crystallograph.}

11

₍₁₉₇₈₎

10.

[6]

DORNER B. and COMÈS R. in «

_Dynamics

of Solids and

_{Liquids by}

Neutron

_Scattering

_»,

Topics

in

Current

Physics (Springer Verlag, 1977),

p. 127-192.

[7]

FORST R., BOYSEN H., FREY F., JAGODZINSKI H. and ZEYEN _C., J.

_Phys.

Chem. Sol. 47

₍₁₉₈₆₎