Influence of an External Shear Stress on the Domain Structure in Incommensurate Phase II of Biphenyl

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Structure in Incommensurate Phase II of Biphenyl

A. Veron, J. Emery, M. Spiesser

To cite this version:

A. Veron, J. Emery, M. Spiesser. Influence of an External Shear Stress on the Domain Structure in Incommensurate Phase II of Biphenyl. Journal de Physique I, EDP Sciences, 1996, 6 (2), pp.277-286.

�10.1051/jp1:1996148�. �jpa-00247184�

J.

Phys.

I France 6

(1996)

277-286 _FEBRUARY 1996, PAGE 277

Influence of

_an

External Shear Stress

_on

the Domain Structure

in Incommensurate Phase II of Biphenyl

A. Vero~l

(~,*),

^J.

Emery (~)

a~ld M.

Spiesser (~)

(~) Laboratoire de

physique

de l'état

Condensé(" ),

Université du Maine-Avenue O. Messiaen, 72017 Le Mans Cedex France

(~ Laboratoire de

Physique

Cristalline-Institut des Matériaux de Nantes 2, _rue de la Houssinière, 44072 Nantes Cedex 03, France

(Received

29 June 1995, received in final form 25

September

1995 and

accepted

3 November

1995)

PACS.61.72.-y

Defects _in

crystals

PACS.64.70.Kb Sohd-solid transitions

PACS.64.70.Rh Commensurate-incommensurate transitions

Abstract. The incommensurate

phase

II of

biphenyl

is _a bi-domain _one. The

naphthalene

paramagnetic

molecular

probes

used in this

experiment permit

the differentiation of these two domains: each Electron

Paramagnetic

Resonance fine of the

high

temperature

phase

of

biphenyl

gives use to two incommensurate fines _in the phase II. But

by applying

_a relevant shear stress,

one favours _one

domain;

^{this behaviour} _is observed _on the E-P-R- spectra ^{which exhibit}

only

_one

incommensurate hne. These results

complete

the _ones obtained about the domain structure of

phase

II of

biphenyl.

Résumé. La

phase

incommensurable II du

biphényle

est composée de deux domaines. La sonde

paramagnétique

moléculaire de

naphtalène

utilisée dans cette

expérience

de résonance _pa-

ramagnétique électronique

permet de différentier les deux domaines. Ainsi

chaque

raie R-P-E- du

naphtalène

de la

phase

haute température du

biphényle

donne _en

phase

II deux _{raies incommen-} surables. Mais _en

appliquant

_une contrainte de cisaillement

judicieusement

choisie _on favorise _un

domaine;

_{ceci se} voit _sur le spectre R-P-E-

qui

_ne

présente

alors

qu'une

seule raie incommensu- rable

correspondant

_au domaine

pnhvégié.

Ces résultats

complètent

_ceux obtenus

précédemment

sur la structure _en domaines de la

phase

II du

biphényle.

1. Introduction

When the

biphenyl

molecular

crystal

with the chemical formula

Ci2Hio (Fig. l)

_is cooled from the

high

temperature

phase (phase I)

it exhibits _two structural

phase

transitions

iii

_a second order _one at

Ti

_" 40 K and _a first order _one at

Tu

_" 17 K. These

phase

transitions _were

extensively

studied in the deuterated and

hydrogenated compounds:

electronic

absorption

and emission in pure

biphenyl-dio Î2j,

neutron

scattering il,3-6], X.ray I?i,

^Brillouin

scattering [8,9],

(*)

Author for correspondence

(e-mail: veron@iota.univ-lemans.fr)

(**)

U-R-A- CNRS N°807

©

Les

Éditions

_de

Physique

1996

c~

fl b

a

Fig.

1. The

high

temperature structure of

biphenyl

_a

= 8.12

À,

b

= 5.63

À,

_c

= 9.51

À, fl

= 95.1°.

Raman

scattering [loi,

Nuclear

l/Iagnetic

Resonance

IN.M.R. Ill,12],

Electron

Paramagnetic

Resonance

[13-17].

ivhile the

biphenyl

molecules _are

planar

in the

high

temperature

phase.

these

phase

transitions _ai-e characterized

by

_a twist of the two

phenyl

_rings around their molecular _axis. The

amplitude

of the twist is modulated

through

_space with _{a wa,~e} vector k in _a

general

direction m the first iiicommensurate

phase (phase II).

The star of k has four

arms inside the

phase

I Brillouin _zone:

+ q~i "

(ôaa* ôcc~

₊

(~

~j b~; _+q~2

"

(ôaa' ôcc*

+

(~

^{~~ b~}

^il

2 2

In the second incommensurate

phase (phase III)

the _wave vector modulation is

along

the b

axis:

qs =

l~ j

^~~ _{b* 121}

aiid the order parameter ^dimension

changes

from _n

= 4 in the first incommensurate

phase

to _n

= 2 in the second _one. For _a

long

time the _main

question

was as follow: is the

phase

II _a

2q

mono-doiuain

phase

or is it a

lq

bi-domain one? These two structures stand for two diiferent incommensurate

phases

named

quilt-like phase

_or

stripe-like phase respectively.

In tl~e

quilt-hke phase ii-e- 2q mono-domain)

tl~e

configuration

of

displacement

fields would be

a

superposition

of t,vo modulation waves, witl~

amplitudes Ai

and

A2,

_one

propagating along

q~i and t.he second

along

_q~2. In tl~e

stripe-like phase Ii.e. lq bi-demain)

tl~e modulation

propagates along

_one direction

only,

eitl~er _{q~i or} q~2. Botl~ directions _are

equivalent, being

related

by

tl~e

application

of the

symmetry operations

^{lest in tl~e} incommensurate

phase

and define tl~e two structures: tl~e two structures are characterized

by (Ai # 0, A2

_"

0)

for _one

domain and

(Ai

"

0, A2 # 0)

for tl~e otl~er _one. Neutron

scattering

and Raman

scattering

results

[3,4, loi

bave shown tl~at tl~e

system

is bi-domain. N-M-R spectra

[12]

are

typical

of _a

lq

structure and Electronic

Paramagnetic

Resonance

(E.P.R.) [15,16]

results also showed the two domain structures.

Tl~erefore,

_we conclude tl~at tl~e

phase

II of

bipl~enyl

has _a

lq

^bi-domain

structure. Tl~ese results also agree with tl~eoretical

investigations [18-20].

In _{a previous}

study

_{[16] we} ha,~e shown the

signature

^{of the} two domains _on the E-P-R-

spectra.

^To

complete

this

study,

_we have

investigated

tl~e influence of

a shear stress _on the

N°2 INFLUENCE OF SHEAR STRESS ON BIPHENYL 279

demain structure. In Section 2 _we review the

previous

Electron

Paramagnetic

Resonance

(E.P.R.)

results in incommensurate

phase II;

this

part

is

mainly

devoted to the manifestation of the demain structure _on the E-P-R-

spectrum

^{and the} characteristic features of the E-P-R-

probe.

In Section 3 _we review Landau

theory

of

biphenyl

and determine the _stresses that break the

symmetry

^{and will faveur} one

particular

demain. Then _we describe the

experimental procedure

and _we present ^the

experimental

result. Some

particular

attention is devoted to the

experimental set-up

^used to

apply

_a stress inside the E-P-R-

cavity,

_on a

crystal

that is studied

in a

photo-excited

_state. A

comparison

of the results under stress and without _stress concludes this part.

2. Observation of Donlain Structure in Inconlnlensurate Phase II of

Byphenyl

2.1. EXPERIMENTAL PROCEDURE _AND PROPERTIES _OF THE E-P-R- PROBE

[là,16j

In order to

perform

_an E-P-R-

experiment

on a molecular

crystal,

_we include _a

paramagnetic probe

in the _pure

biphenyl (as

it _was clone in the

pioneenng

work of Hutchison et ai.

[21]).

Naphthalene-d8

molecules _,vere substituted for the

biphenyl

_ones with _a concentration

equal

to 0.5$l. The

products, biphenyl-hic

and

naphthalene-ds,

_were

purchased

from Aldrich _company and _were

purified

before use.The

biphenyl crystal

was grown

by lowering

trie melt

through

a

temperature

gradient (Bridgman method).

Although

the

ground

state of

naphthalene-d8

is _net

paramagnetic,

the excited

triplet

state is and it _can be

populated by photo-excitation.

Some studies

[22]

^{have shown that the lowest}

triplet

state

responsible

for the

paramagnetism

_is also _a

phosphorescent

state eut of the exciton band of the

biphenyl crystal,

with _a

sufliciently long

lifetime for E-P-R- measurement. In the

single biphenyl crystal,

this state is reached

by irradiating

the

naphthalene-d8

with _a

high

pressure mercury arc

lamp.

The

experimental _set-up

_{was as} de8cribed

previously [là,16].

The E-P-R-

experiments

_were

performed

_{on a} X-band spectrometer

equipped

with _a

cryostat.

The

crystal

_~vas cooled clown

by

helium _gas

flowing

in the dewar within the

cavity.

^The temperature is measured

by

_a

thermo-couple placed

in the gas flow under the

crystal. Althougl~,

an exact

reading

of tl~e absolute

temperature

^{of tl~e}

crystal

coula not be obtained witl~ tl~is

system,

tl~e temperature ^coula nevertheless be obtained

by using

tl~e

splitting

bet~v.een lines.

Tl~us _we obtain _a temperature measurement at about +0.1K.

Tl~e features of tl~e E-P-R-

spectra

of tl~e

probe

_are

reported

elsewl~ere

[là,16]

and

tl~ey

can be summarized _as follows. In tl~e

pl~oto-excited state,

tl~e

napl~tl~alene

has _a S

= 1

spin.

For any direction of the static

magnetic field,

two systems of three

peaks

eacl~ _are

observed;

tl~ey

_are associated witl~ tl~e two

magnetic inequivalent napl~tl~alene probes

in tl~e unit cell.

Tl~ree lines for eacl~ molecule _are

typical

for _a S

=

spin:

tl~e

Am~

= 2 transition in _la~&~ field and tl~e two

Am~

= transitions in

l~igh

^field. Wl~en tl~e

magnetic

field is in tl~e

symmetry plane la, c),

both molecules _are

magnetically equivalent giving

use to a

spectrum

^with

only

three lines. The

anisotropy

_curves which _give the line

positions

_{as a} function of the direction of the static

magnetic

field in the three

crystallographic planes,

enable _us to define the spin

Hamiltonian parameters in the

high

temperature

phase (or

normal

phase):

7io

"

flS§Bo

+

B(O(

₊

B(O(

with

B)

= 340 _x

10~~ cm~~

and

El

= -150 x

10~~ cm~~ (3)

The

§

tensor is

isotropic

with the free electron value

equal

to 2.0023. This Hamiltonian

has the

symmetry

of the

naphthalene

molecule and the directions of the _{axes are}

nearly

the

same as the _ones of the

biphenyl

molecules

[15,16]:

_{as a} result the

naphthalene

molecular

probe

tends to

align

itself with the _same orientation _as the

biphenyl

_one. The

symmetry

42w

1 _3s6K

2370 2405 2440

Magnct<cfroid (Gauss)

2380 2410 2440

Magncl<cficld (Gauss)

Fig.

2. Evidence of the

phase

transitions _on the E-P-R- spectra

(first

derivative

absorption).

The

magnetic

field is in the

(a, b) plane

with

(a, H)

= 37°.

of the

spin

Hamiltonian is the _{same as} that of the molecular

probe

but _not the _{same as} that of the site: the

crystalline

field is

weak,

_as

expected

for _a molecular

crystal,

and the

phase

transition will be _seen

through

the

geometrical

deformation and

for

disorientation of the molecular

probe [15,16].

For the

present system,

^the E-P-R-

probe

is sensitive to the two

phase

transitions for all directions of the

magnetic

field.

2.2. DOMAIN STRUCTURE. In incommensurate

phase,

where the translational Îattice _pe-

riodicity

is

lost,

there is _an

essentially

infinite number of

non-equivalent paramagnetic

sites which contribute _to the

magnetic

_resonance

spectrum.

^A

quasi-continuous

distribution of local E-P-R- litre is

expected

for the

paramagnetic absorption.

This

absorption

is marked

by

disconti-

nuities

(named singularities)

at its extremities

[23].

^In our

experiments

we use the derivative of the

absorption.

A

typical

E-P-R- spectrum, obtained in _an X bond

experiment [16]

^{is sketched}

in

Figure

2. Near 40 K the normal

phase

line

sphts

into two

singularities.

Then two other

singularities

_appear and _remain clown _to 20 K. Between 20 K and 15 K _a second

phase

tran- sition _anses and the

spectrum

^becomes more

simple

with

only

two

singularities

^{in the low}

temperature

phase (below

15

K).

In _a

previous

paper [16] ^it was

established, by using

_symme-

try considerations,

that the four

singularity

spectra are due _to the

superposition

of two

types

of domains.

Therefore,

E-P-R- spectra account for the two

phase

transitions at

Ti

" 40 K and

TII

" 17 K.

In

phase

^II

(between

40 K and 20

K)

the E-P-R-

probe

exhibits

peculiar

behaviour

[15,16j:

First,

the

analysis

of the _spin Hamiltonian

parameters

^{shows that the E-P-R-}

probe

rotates around _a direction that is

perpendicular

to its

long

_axis. The rotations of the molecules _in the _two domains have the _same

amplitude Ii.e.

^the maximum value of the modulated rotation

angle),

but their _{axes are} not

equivalent (they

do not

correspond

to each other

by

_a

symmetry operation

lost at the

phase transition).

This behaviour makes the _two domains

geometrically inequivalent,

and thus

they

_can be observed

separately.

Secondly,

_eveii

though

^the modulation is _a

plane

_{wave one,} the

naphthalene probe

molecule

N°2 INFLUENCE OF SHEAR STRESS ON BIPHENYL 281

/ ~

~ /

Sitea siteb S<tca s,teb

d,Splacement

U U U U

~~~ _°

b ~ °

dama<n 1 dama<n2

symmet~plane

Fig.

3.

Explanation

of the two 1q spectrum

superposition.

Demain effects and

displacement

fields:

the symmetry

plane exchanges

domains 1 and 2 but aise the

displacement

fields Ua and Ub between the molecules. Molecules with the _same orientation have E-P-R- _resonance at the _same value of the

magnetic

field.

Therefore,

molecule _a in demain 1

(respectively b)

and the molecule b transformed

(respectively

_a

transformed)

have the _same orientation but with various

displacement

fields

(after [16]).

exhibit8 _a "soliton

regime" [24, 25],

_as is sketched in

Figure 2,

where _{we can see} that the

splitting

near the

high temperature phase

line and the

edge singularities

are not

symmetrical.

This behaviour

persists

in

phase

III but the harmonics of the modulation _up to the third

order)

coula be observed

iii.

To understand

why

the diiferent domains _can be observed

separately

,

it must be noted that the

naphthalene

molecules have two

possible

orientations in the

high temperature phase.

Let

us call the two chains _a and

b,

and _assume that the two molecular

probes

in the unit cell _move

according

to two diiferent

displacement

fields

(for example

the

displacement

field

U~

in site _a and the

displacement

field

Ub

_in site b in the first

domain).

Such eifects _are

certainly

due to the

particular

behaviour of the E-P-R-

probes

which favours _some

phases

of the modulation.

By

virtue of the

application

of the

symmetry operation

lost at the

phase transition,

we obtain the second domain from the first _one. This

sgInlnetrg operation

is

specijic

ta the

ezchange of

sites _a and b. Thus the

displacement

field

U~

in site a of domaiii 1 lies _in site b of domain

2,

trie _same goes for trie

displacement

field

Ub

which lies in site a of domain 2

(Fig. 3).

In the

high temperature phase,

the "a" sites of the _two domains _are

equivalent,

thus _a

single

hne _is observed.

By

contrast, ⁱⁿ

phase

II two diiferent

displacement

fields

U~

and

Ub

_are

experienced

at these

sites,

which lead to two diiferent

sphttings

around the _same

high

temperature line

position.

This result

explains

the appearance of four

singularities

_in

phase

II.

An

experiment

under uniaxial _{stress can} favour _one domain _over the other and lead to _a

simplet

E-P-R- spectrum.

3. Influence of _an External Stress

3.1. LANDAU THEORY

[26].

In this

part,

_using Landau

theory,

_we

analyze

the role of strain and determine the

relationship

between it and

specific types

^of domains.

Given the

coupling

^{between the} strains and the order

parameter components,

^the

Ginzburg-

Landau free _energy reads

[5j:

FIT)

=

FolT)

₊

alT Ti)lloqs~

_l~ +

loqs~

l~) + 41U

U)lloqs~

_{l~ +}

loqs~

_l~)

8~(Qqs~ Î~ÎQqs2

_{Î~ +}

2(giei

_{+ §2e2 + 93e3} +

§5e5)(Îoqsi

_Î~ ~ ÎQqs2 Î~)

+21g4e4

+

gôeôl(loqsi

_l~

loqs~ l~l

+

_,j~ ~j _{C~jeiej (41}

1

where [Qq~~[ and [Qq~~[ ai-e the

amplitudes

of the four-dimensional order

parameter

^and

e~(i

₌ 1.

2,3,4, 5, 6)

the strain

components

in the abbreviated notation (e~ = em for1= 1,

2, 3;

~~

~~~~'

~~

~~~~'

~~ ~~~~ ~~~~ ~°~

ÎÎÎÎ

^~

ÎÎÎÎ °'~ ~'~'~~'

The

principal

axes ~i, x2, ~3 of the strain tensor are defined with the _x2 axis

along

b vector, trie other axis _{are in} the

la, c) plane.

The

Qqs,

are the order

parameter components;

the _{e~ are} the strain

components

that become

non-zero at the

phase

transition

(in phase

I the _{e~ are} all

equal

to

zero) [5j.

The last term in the free _energy

represents

^{the elastic} energy

having

the

symmetry

^{of the}

high temperature phase. Consequently

this term coula

split

into two

parts,

trie first

containing

the strain

components

_{ei, e2, e3, e5} and the

second,

the strain

components

e4, eô.

By making

the

following changes

of variable:

Qq~

=

~~

e~#> _{i =}

1,2

and

Ai

#

Pcos6,

~

/

A2

" P sin 6 the free _{energy can} be rewritten:

FIT)

=

FolT)

+

)P~

⁺

^~t

⁺

(13

^{+ Cos}

4Ùlj

^P~

+(91ei

_{+ 92e2 + 93e3 +}

95es)p~

+

(g4e4

+

g8e6)p~

_Cos 26 ₊

~ _c~jeiej

_I.s

i,J

Minimizing

this free _energy leads to the

follo,ving

results:

in the

2q

structure, and without any extemal stress, ^the

amplitudes Ai

and

A2

of the two modulations _are

equal,

and the

spoiitaneous

stratus e4 and _{eô are}

equal

to zero; the

average

symmetry

^is monoclinic _as in

phase

I.

in the _case of _a

lq

structure,vith

domains, A2

# 0 _or

Ai

" 0

corresponding

to 6

= 0

or 9

=

~/2,

_e4 and _{eô are non zero}

(they

_are

proportional

to

(A( A())

the average

symmetry

is no~v triclinic.

Since the

lq

structure has been

suggested

or demonstrated

by

_previous results

[3,4,10,12, 16,18-20j,

it will be the

only

case considered below. Under an external stress, the

equihbrium

equations

are:

ôF

j ₌ 2 3

4, 5,

6

1

^~~ ' '

ôF

j)

~

j

^{= °}

(6)

where the _{a~ are} the stress

components.

These

equatioiis

give e~ =

r[

+

r~p~

for

=

1,2,3,5

^{in which}

r[

and

r~

_are functions

independent

of 9 and _e4

=

'f(

_{+ ~y4P~}

cos2b,

_eô

=

'f(

+ ~yôP~ cos29. The order

parameter amplitude

_is written as folloIn.s:

2 ~' _~

~(§4'11

~

§6'Î~)

COS ~~

~

(~j

(4t1'

+

~(3

+ cos

46)

₊

4(g4'f4

+

gô'fô)

cos~

26)

N°2 INFLUENCE OF SHEAR STRESS ON BIPHENYL 283

with

1

~Î66°4 ~Î46°6 ~Î44°6 ~Î46°4

'~~ ~Î66~Î44 ~ÎÎ6 ^'~~ ~Î66~Î44

~ÎÎ6

~Î4Ù~6 ~ÎôÙ~4 ~Î4Ù~4 ~Î44~Ù

'~~ ~Î66~Î44 ~ÎÎ6 ^'~~ ~Î66~Î44 _~ÎÎG ^~~~

The ~y[

being dependent

_on extemal stress parameters, ^the

amplitude

_p of the order parameter varies from _one domain to another. The free _energy is _now

given by:

FIT)

=

TO

+

àp~

+ p~ +

p~ (ù

^{+ ~}

⁽³

⁺ cos

4b))

⁺

^(g4'f4

⁺ gô'fô

)P~ cos~

^2b 4

+(g4~/(

+

gô'f~)P~

+ cos 29 ₊

Kola)

+

f(2(a)p~

_cos 29 ₊

1(4P~ cos~

²⁹

(9)

with the definition:

~j _C~j

e~ej =

Ko (a

+

1(2 (a)

_{p~ cos} 29 ₊

K4P~ cos~

29 2

?J

Ko

and

K2

_can be _{seen to}

depend

_upon the extemal stresse8.

Therefore _a relevant stress, ^1-e- one

containing

at least _{a4 or où, can} diiferentiate the two domains. It is worth

noting

that the _a~ with

=

1, 2,3,

5 does not break the symmetry nor

does _it

modify

the

equilibrium

state.

They only

renormalize the various coefficients _in the free energy whereas _a4 and _où break the

high

temperature

phase symmetry

and will favour _one of the _two domains.

3.2. EXPERIMENTAL PROCEDURE TO APPLY _THE SHEAR STRESS ÎNSIDE _THE E-P-R- CAV-

iTY. Let _us recall that the

sample

is set at the bottom of _a

quartz

^switch

(used

_{as a wave}

guide)

with _an

altuglass

_cap. To

perform experiments

under stress inside the E.P.R.

cavity,

_we

use the contraction

properties

^of the cap. The

altuglass

_cap is

replaced by

another _one built with

Teflon,

since the contraction of the latter is _moi-e

significant

than of the former when the

temperature

^{is lowered. The} _a4 " a23 and _où

" a21 are shear stre8ses which _are

generated

by

the contraction of the

cyhndrical

_{cap as} described _as follows: the

crystal,

inside the _cap,

is a

parallelepiped;

the

(a, b)

face is horizontal and the

il10)

face _is

parallel

to the _{cap axis.}

The contraction is transmitted to trie two

opposites

^faces

(l10)

of the

crystal through

two

semi-cylindrical altuglass halas,

whose curved faces _{are in} contact with trie interior face of trie Teflon _cap and the

plane

faces _are in contact with the

(l10)

faces of trie

crystal. Thus, by applying

_a

compressional

and uniaxial stress

perpendicular

to the

(l10) face,

_we obtain _a shear

stress où " a21 with _a maximum value. This device does not

permit

_us to monitor trie _stress

intensity

and makes the

experiment diflicult;

the

opposite

^faces on which the stress is

applied

must be flat. But

given

that the E-P-R- experiment is

performed

in _an

optically

excited state

(obtained by irradiating

the

sample

inside the

cavity through

_a quartz

cap),

this _is the

only possibility.

3.3. EXPERIMENTAL RESULTS. In

Figure

4 _we

present

_a

particular

E-P-R- line measured

at diiferent

temperatures:

under stre8ses in

Figures

4a and

4b,

and without any extemal stress in

Figures

4c and 4d.

The _main features of the spectra ^without any ^stress can be summarized _a8 follow8. At the first

phase

transition

(from phase

I to

phase II)

the E-P-R- line

splits

in two

singularities.

As the temperature is lowered the

spectrum

^evolves

rapidly, showing

_a succession of three

singularities,

_seen in

Figure

4c. However _we remark that the low field

singularity (marked by

c)

T=45K T=40K

~ g

m

~

~ ~

3910 3950 3990 3910 3950 399o

Maguetic field (Gauss) Magneticfielcl (Gauss)

b) d)

~ g

m

~

3910 3950 3990 3910 3950 3990

Magnetic field (Gauss) Magnetic field (Gauss)

Fig.

4. Behaviour of fine

in the

(a,b) plane:

under stresses

a)

and

b),

without stress

c)

and

d). a)

The spectra in

phase

II exhibit

oniy

two

singularities. b)

During the second transition, the spectra move from

a two

singularities

system to another _one. The

singularity (indicated by

_an

arrow)

remained in

phase III,

_{appears m} this _range of temperature.

c)

The spectra exhibit

early

_in phase II four

singularities. Indeed,

the low field

singularity

is broaden. The

singularity (indicated by

_an

arrow)

remained in

phase

III is

already

present.

d)

In

phase

III the spectra exhibit two

singularities

_{as m 16}).

We note _a

change

_in the

splitting

between

(b)

and

(d).

the

symbol Î)

_is broaden because it is itself the

superposition

of two

singularities,

_{as cari} be observed in

Figure

2 where four

singularities

_are

clearly separated. During

the second

phase

transition

(sho~vn

in

Fig. 4d)

two

singularities disappear:

^the _{one near} ^3950G and the other

partially overlapping

with the low field

singularity land

marked

by

the

symbol Î).

Indeed,

this hne _{narrows proving} the

phase

transition. Phase III is characterized

by

_a

spectrum

^with two

singularities. Finally

_we remark that the

high

field

singularity (indicated

N°2 INFLUENCE OF SHEAR STRESS ON BIPHENYL 285

by

_{an arrow} in

Fig. 4d)

that

persists

in

phase

III is the _one which _appears first in

phase

II

(see

_arrow in

Fig. 4c).

Under _an

applied

stress the

spectra (Fig.

4a and

4b)

_are

simplified.

In

phase

II

(Fig. 4a),

as in

phase

III

(Fig. 4b), they

^exhibit

only

two

singularities.

Four

singularities

_appear in trie temperature range where the two

phases

coexist. The two

singularities

that appear last _are the _ones that

persist

ⁱⁿ

phase III, and,

in

particular,

the

high

^field

singularity

indicated

by

_an

arrow in

Figure

4b.

During

the

phase

transition from

phase

II to

phase

III _{we move} from _a

two

singularity system

to another _one and the

splitting

between

singularities

shows _{a gap iii} the two

phases.

We _can also remark tl~at the

splitting

between

singularities

is smaller with

stress tl~an witl~out.

Altl~ougl~

we observe tl~e two transitions in tl~e stressed

sample,

it is trot

possible

to determine tl~e eifect of tl~e stress _on tl~e

phase

transition temperature for _{two reasons:}

Witl~ _our

experimental

device _we do not bave _access to tl~e absolute

temperature

According

to

equation (7),

tl~e

splitting

between tl~e

singularities

is not

comparable

be-

tween the two

experiments (more important

in the

sample

without stress than in the

stressed

one).

So the

sample

itself cannot be used to recalibrate trie temperature be- tween tl~e two

types

of

experiments.

In tl~e stressed

sample experiment (Figs.

4a and

4b)

tl~e

spectrum

is that which is

generally

observed

during

tl~e first order

phase

transition:

single spectrum

in

phase

II and in

phase III,

and _a

superposition

of two

spectra

^{in tl~e}

vicinity

of tl~e

phase

transition

TII

" 17 Ii. We do net

observe _any

persistence

of _one

phase

in the other. SO _we think that the

higl~

^field

singularity,

wl~ich is

present

in the two

phases

when the

sample

is net

stressed,

cannot be attributed _to the

persistence

^of one

phase

_in tl~e otl~er.

Tl~e _two domains _can be differentiated because tl~e rotations of tl~e molecules in eacl~ of them _are net

equivalent (tl~eir

rotation _axes do net

correspond

to each other

by

the

symmetry operation

wl~ich is lest at tl~e

phase

transition

[15,16j).

Moreover tl~e

napl~tl~alene

molecular

probe

does not account for tl~e

plane

_wave modulation. Tl~is

particular

bel~aviour of trie

napl~tl~alene

molecules _can also

suggest

a

possible

location of tl~e

guest

molecule witl~in tl~e domain boundaries. Tl~is last

suggestion

is

supported by

the behaviour of the

hydrogenated

_or

deuterated

pl~enanthrene probes [24,27j:

the incommensurate distributions associated ~&~itl~ the two domains _are confused

(sample

without

stress),

and _account for _a

plane

_wave modulation.

Certainly

the _sizes of tl~e molecular

probes play

_an important ^role.

4. Conclusion

In

previous

_papers

[15,16j

we have

developed

tl~e

study

ofthe incommensurate

phase

of

bipl~enyl by

E-P-R-in _a

pl~oto-excited

_state of _a

napl~tl~alene probe. Analyzing

tl~e

experimental results,

we conclude tl~at _a

superposition

oftwo incommensurate distributions arises from eacl~ domain.

In tl~is paper we bave

determined,

_using Landau

tl~eory,

tl~e relevant stress

allowing

tl~e diiferentiation between domains.

Moreover,

_we bave

designed

_a

particular

dewce to

apply

_a

sl~ear stress on tl~e

sample

inside tl~e

cavity.

It is

important

to

empl~asize

tl~at tl~e

application

^of

a stress to such _a molecular

system

is diflicult.

Indeed,

several

samples

_were broken

during

the

experiment

because of _strains.

Moreover,

_even when this

expenment

is

correctly performed, by heating

the

crystal

from the low temperature

phase,

_some strains remain and broke the

crystal.

The

experimental spectra

obtained under stresses, are

typical

of _a

single

modulated

displacement

field.

They

demonstrate tl~at _we bave

successfully

favoured _one domain _oi~er the otl~er _in

phase

II and confirm the previous result

[16].

^In

particular they clearly

show tl~e

existence of _t,vo

displacement

fields associated witl~ tl~e two chains of tl~e

naphthalene probe.

However,

witl~ tl~is

particular

device _we cannot

analyze

tl~e E-P-R- spectra ^{in all tl~e}

planes

_nor

can we determine tl~e

spin

Hamiltonian

parameters

^eitl~er.

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H.,

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J-L-,

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J.,

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H.,

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