HAL Id: jpa-00211023

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Structural determination of the lowest temperature modulated phase of

tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) : another investigation

Y. Bouveret, S. Megtert

To cite this version:

Y. Bouveret, S. Megtert. Structural determination of the lowest temperature modulated phase

of tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) : another investigation. Journal de

Physique, 1989, 50 (13), pp.1649-1671. �10.1051/jphys:0198900500130164900�. �jpa-00211023�

Structural determination of the lowest temperature ^modulated phase ^of tetrathiafulvalene-tetracyanoquinodimethane (TTF- TCNQ) : ^another investigation

Y. Bouveret and S.

Megtert

Laboratoire de

Physique

^des

Solides,

^Bât.

510,

^Centre

d’Orsay,

⁹¹⁴⁰⁵

Orsay,

^France

(Reçu

^{le 5}

juillet

1988, révisé le 24 mars 1989,

accepté

^{le 28 mars}

1989)

Résumé. ²⁰¹⁴ Cette étude structurale effectuée au moyen de rayons X ^est consacrée à la détermination

approfondie

^{de la structure de la}

phase

modulée basse

température (phase d’accrochage)

^à

pression

normale du conducteur

organique quasi-unidimensionnel

tétrathiofulva-

lene-tétracyanoquinodiméthane (TTF-TCNQ).

^Nous

procédons

à l’affinement d’un modèle de

déplacements

de molécules

semi-rigides.

Nous obtenons deux modes de distorsion

opposés

pour les chaînes TTF et TNCQ. Les molécules TTF ne

présentent

pas de déformations internes

appréciables

^et

glissent parallèlement

^{à leur}

plan

moléculaire moyen, alors que les molécules TCNQ subissent une

importante

distorsion intramoléculaire se traduisant par des

déplacements plus importants

^du

cycle quinonique perpendiculairement

^{à leur}

plan

moléculaire. De

plus,

^une

analyse

^de

symétrie

des modes de translation révèle deux modes de

polarisation

distincts dans les feuillets

parallèles

^du

plan (b, c)

regroupant des chaînes

TTF,

^{et un}

unique

^{mode de}

polarisation

dans tous les feuillets TCNQ. Nous déduisons de cette étude structurale le schéma des Ondes de Densité de

Charge (OCD)

^{dans la}

phase d’accrochage

ainsi que la nucléation de celle-ci

juste

avant la transition

d’accrochage

^du

premier

ordre pour la valeur

particulière

qa ⁼

3/10

^{a* de la}

composante transversale du vecteur d’onde de la modulation.

Abstract. ²⁰¹⁴ This

X-ray

structural

study

deals with an

improved

structural determination of the lowest temperature ²

kF

^modulated

phase

^at normal pressure

(locking phase)

^{of the}

quasi-one-

dimensional conductor

tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ).

The refine- ment of a

semi-rigid

^molecular

displacement

^{model is carried out. Two}

opposite

distortional modes are obtained for the TTF and TCNQ stacks. The TTF molecules do not exhibit any

significant

intramolecular deformations and slide upon their ^mean molecular

plane,

whereas the TCNQ molecules

undergo

^a

large out-of-plane

intramolecular distortion which involves a

substontial

displacement

^{of the}

quinoid ring perpendicularly

^{to the mean molecular}

plane.

Furthermore, ^an

analysis

^{of the} symmetry of the translational modes reveals two distinct

polarization

modes within the TTF sheets

parallel

^{to be}

(b, c) plane,

^and

only

^one within all the TCNQ sheets. The

Charge Density

^Wave

(CDW) ordering

^{in the}

locking phase

is deduced from this structural

study

and its nucleation

just

before the first-order

locking

transition is

suggested

^for

the

special value qa

⁼

3/10 a*

^{of the} transverse component of the modulation wave vector.

Classification

Physics

^Abstracts

61.65 ^- 64.70K ^- 71.30 ^- 63.20K

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500130164900

1. Introduction.

The

organic

one-dimensional conductor

Tetrathiafulvalene-Tetracyanoquinodimethene (TTF-TCNQ)

^{is known to be an}

interesting prototype

^of

Charge Density

^Wave

(CDW)

system. TTF-TCNQ undergoes

^at ambient pressure ^a succession of three structural and electronic

phase

transitions from a

high temperature

^metallic

phase

^{down to a low}

temperature insulating phase.

Each transition leads to an incommensurate modulated structure which can be characterized

by

the value of the

component

^{in the} a *-direction of the modulation wave vector

q (qa,

qb,

qc ) (with

qb ⁼ 0.295 b * _{and qc} ⁼

0) :

^at

TH

^{= 54 K the}

diffuse sheets condense into

sharp

satellite reflections with transverse qa

component equal

^to

a */2. At

TM

^{= 49}

K qa begins

^{to decrease}

continuously

^{with the}

temperature

^{until a value}

near to 0.3 a*. Then at

TL = 38 K qa jumps

^{and locks to the} commensurate value

a */4.

The first two transitions have found a

satisfactory phenomenological interpretation

^{in the}

framework of a two

independent

^chain

system [1].

^{In this context the} chain distortion

begins

to order at different

temperatures

^{for both}

types

^of chains. There is a

general agreement

^to associate the Peierls-like transition at

TH

^{with the}

^TCNQ

stacks and the

beginning

^{of the}

sliding

^motion

of qa

^at

TM

with the TTF stacks. The

partially

incommensurate-commensurate transition at

TL

^{is a} first order transition. Several theories have been

proposed

to account for the

pinning

transition at

TL [1-6].

The appearance of fourth order

umklapp

^{terms in the}

energy Landau

expansion

^is

expected

^{to be}

responsible

for the stabilization of the low

temperature

^modulated

phase

^of

^TTF-TCNQ [3].

^Such

approaches

^{lead to} chain distortion

configurations

^{that did not} find until now any

experimental

confirmation.

In addition the real nature of the lattice distortion is still undetermined.

Many

distortional modes have been

proposed

to account for the

physical properties

^{of this}

material, involving rigid

^molecule

displacements

^as translations

[7, 8]

^or librations

[5, 9]

^{or even internal}

deformations of the molecules

[10,11].

Although

^a very

large

^amount of structural work has been devoted to the most known of the one-dimensional conductor

TTF-TCNQ

in the

past decade,

the lattice

dynamics

^{is still}

almost unknown. The structure of the low

temperature

^modulated

phases

^was

only slightly

touched even if the available data were of first

importance

^{for the}

community [7, 8].

^{This state}

came from the fact that there was no

sample big enough

^to

perform

exhaustive inelastic

scattering

studies and because the weakness of the satellite intensities

(typically 10- 3-10- 4

of the main

Bragg reflections)

rendered X ray data collection time

prohibitive. Nowadays,

^new

intense

light

^{sources like}

rotating

^{anodes or}

synchrotron

^radiation facilities became

customary

and make almost

possible

^{what was} unrealistic before.

By

^{the time we were}

dealing

^{with the} refinement

procedure

^{of the low}

temperature

modulated

phase (T 38 K )

^of

^TTF-TCNQ, Coppens

^{et al.}

[12] published

^an

approach

^of

the structural determination of the same

phase using

^{a dataset obtained with the use of}

synchrotron light

^source.

They

^{reached a}

picture

^of the molecular

displacements

^associated

with the

periodic

lattice distortion

(PLD) using

^{a model of}

rigid

^{molecules as it was}

suggested

a

long

time ago after the

X-ray analysis

^{of the} one-dimensional

(1-D)

precursors

[13].

^{In this}

respect

their results are similar to the conclusions derived

by Yamaji

^{et al.}

[14]

^{in the}

isostructural

compound TSF-TCNQ :

^the

displacement pattern

^of the TTF molecules is the

same as the

herring

^bone

pattern

of the TSF molecules in

TSF-TCNQ.

Even if the onset of transition

temperatures

^is

quite

different between the two isostructural

compounds,

^{the 1-D}

precursors reveal the ^same kind of molecular

displacements.

^The

analysis by Coppens

^{et al.}

shows that the main molecular distortions involved in the PLD are

qualitatively

^conserved

from the

high temperature

1-D precursors down ^to the lowest three-dimensional modulated

phase

^of

^TTF-TCNQ.

^But this structural

study

^{does not take into account} the intramolecular distortional modes which have found some

experimental

^{evidences in I.R.}

experiments [15- 17].

The aim of this communication is to establish the structure of the molecular distortions associated with the 2

KF-PLD

in the third modulated

phase

^of

^TTF-TCNQ (Le.

^{T 38}

K) using

^a

simple

^model

containing

both intermolecular

displacement

modes and intramolecular distortion modes as

proposed by

^{Gutfreund et al.}

[10]

^{and Rice et al.}

[11].

^This

improved

structural determination allows us to

get

^{a more} realistic view of the lattice distortion and to

deepen

^our

understanding

^{of the}

coupling

mechanisms between the

conducting

electrons and the various distortional modes in such molecular

crystals.

^In

addition,

it will be shown that this structural information can

bring

very useful results about the electronic

aspect

^{of these} one-dimensional

system

instabilities.

In

part

^{2 we} shall describe the

experimental

conditions and

limitating

constraints. Part 3 will concern a

description

of the data

processing using Superspace

group formalism. The final refinement results of a

semi-rigid

^molecular

displacement

model will be shown in

part

^{4 after}

a short discussion about the determination of the superspace group of the modulated

crystal using

^the refinement of a

simpler displacive

^model.

Finally part

5 will deal with a

thorough analysis

^{of the} refinement results in terms of

displacive

^{modes and DCW}

ordering.

2.

Expérimental

conditions.

For this

study

^we have used a

single

^domain

^TTF-TCNQ crystal synthetized by Nigrey (Pennsylvania University) (0.725

^{x 0.875 x 0.125 mm3}

respectively along the a, b,

^{c direct}

axes).

^{A closed} circuit Helium

cryogenerator (Air Products)

^{was used to}

keep

^the

crystal

^{at a}

constant

temperature during

^{the whole}

experimental period.

^The

experiments

^{were carried}

out at 13 K in the third modulated

phase

^of

^TTF-TCNQ.

We

employed

^a

rotating

^anode

(12

^kW

Rigaku 200) ^generator

^{with a} copper anode. We took the

Ka wavelength

^radiation

(1.542 Á) using

^a double bent

pyrolitic graphite

monochromator.

The data collection was carried out on a « home made » 3 circle diffractometer

(R. Moret).

This diffractometer offers an w rotation for the

sample

around the vertical axis and two

rotations u,

^T for the detector. One rotation lies in the

equatorial plane

^{of the} diffractometer

( Q )

while the other

(r)

^{moves the} detector above this one.

We measured the reflection

integrated

intensities with a Nal

scintillator, using

^the

step by

step

^{scan in the}

reciprocal

space

( (h, ^k, 1 ) scan).

^For each reflection we took 21

steps along

^a

reciprocal segment

^{centered on} the considered reflection. Since it was known that the main

displacement polarizations

^were

along

^{the b and c direct axes}

(in

^fact

c *) [8],

^we

aligned

^the

crystal

^{with the}

b *,

^{c *}

reciprocal

^{axes in the}

equatorial plane

^of the diffractometer and we

chose the

step

^{size as}

8Q

^{= 0.005 b*. In that} way the measured

reciprocal

^{knot moved}

parallely

^{to the}

equatorial plane.

This method ensured us to be near the usual 8-20 scan

employed

^{with a} conventional diffractometer.

Owing

^to the fact that the range of ^{T was} restricted

to 1 T 1 20°,

^we considered the

spatial

resolution of the diffractometer as a constant. A Gaussian

profil

^{was fitted to each scan} from which we derived the gross

(1 )

^{and net}

(I N ) integrated

intensities as well as the

integrated background (B ).

^{Then the}

observed structure factor

Fobs is given by :

where

1,

p and a

represent

the Lorentz

factor,

^the

polarization

^{factor and the}

absorption

coefficient, respectively.

We measured 455 main reflections from the average ^structure and 1 008 first order

« 2

kF

satellites ^».

Among

^{these two}

^datasets, only

^a few reflections were related to one

another

by symmetry

^because of the diffractometer

geometry.

^{Thus we could not}

perform

^an

average of the reflection intensities over the

symmetry equivalent

reflections as it is

usually

done. We

rejected

^all reflections

suspected

^to be affected

by

instrumental errors and those

showing exaggerated misalignment.

We then retained 421 main reflections

(388

^with

I > 3 u

(I ))

^{and 621 « 2}

kF

satellites »

(437

^{with I} > 3 ^ff

(I )).

^The ratio between the average

Bragg

reflection structure factors and the average satellite’s ^structure factor was 37.

During

data collection we

regularly

^{checked 4 « reference »}

reflections ;

^{one main}

Bragg

reflection and three

typical

^satellite

reflections, namely :

The

experimental

^{scan of}

Qo, Q1, Q2

^and

Q3

^{at the}

beginning

^{of the}

experiment

^{are shown in}

figure

^{1. The}

Qo integrated intensity

showed fluctuations of about 5 to 10 % over

large periods (10 hours) revealing

fluctuations of the incident

X-ray

^{beam that we} attributed to vacuum

stability problems

within the

X-ray generator.

Figure

²

displays

^the

intensity

behaviour of the three reference satellites versus exposure time after correction of beam fluctuations. There is a continuous decrease of the

integrated intensity

^{with the}

running

^{time :}

0.53,

^{0.41 and 0.54 %} per irradiation hour for

Qi, Q2

^and

Q3

^satellite reflections

respectively.

This attenuation seems to be

nearly homogeneous

in the whole

investigated reciprocal

volume and does not

depend strongly

^{on the}

longitudinal (large k

^{index :}

Q2)

^or transversal

(large

^{1 index :}

Q3)

^nature of the satellite reflections. No

appreciable

^satellite

broadening

^{was observed}

contrarily

^{to what was mentioned}

by

^Forro

et al.

[18].

^{This is}

probably ’due

^{to the} diffractometer resolution.

Anyway,

the absence of

broadening

^{after 350 H of} irradiation time

clearly suggests

^that the Peierls distortion still exists over

large

^domains.

We also noticed after an unfortunate breakdown of the

cryogenerator

^{and a} consecutive

warm up ^{to room}

temperature

^some restoration of the satellite intensities of about 30 %. Such

an

annealing

^{like effect was}

already

observed in

(TMTSF)2CI04

^{and was}

interpreted

^as

constraint relaxations in the external volume

surrounding

^{a default}

[19].

^The

preceding

remarks show how irradiation effects are

important

^{and must be}

carefully

^followed

during

^the

data collection in order to be able to

apply

proper corrections ^to the observed intensities of a

full set of collected reflections because the irradiation time becomes a new

parameter.

^{For our} purpose ^{each 2}

kF-satellite intensity

^{was corrected for} incident beam fluctuation and was

renormalized with

respect

^{to the}

QI

reference satellite

intensity.

3. Refinement program.

The modulated structure refinements were

performed

^{with a least} squares

computer

program,

specially

^{devoted to the low}

temperature phase

^of

^TTF-TCNQ.

In this program

M w ( 1 Fol - ^{1 Fe 1 )2}

^was

minimized,

^where

Fo

^and

Fc

^{are the observed and} the calculated structure factor. We used the conventional

weighting

^{scheme w =}

1/o 2(F0).

^{The two}

agreement

^factors

were calculated at the last

stage

of refinement.

Fig.

^{1. -}

Typical experimental

^scans

^along

^the

reciprocal

b * direction

through

^{a weak}

principal

reflection

(a),

^the strongest satellite reflection

(b),

^a

longitudinal

satellite reflection

(large k index) (c)

and a transversal

(large

¹

index) (d)

satellite reflection.

Fig.

^{2. -}

Integrated intensity

^versus

X-ray

exposure time of the three reference satellite reflections

during

the first 100 hours of the data collection.

De Wolff

[20]

Janner and Janssen

[21]

showed that an incommensurate structure can be described in a

higher

dimensional space, in order ^{to recover} the lost translational invariance and the spacegroup

symmetry.

^{In the}

present

^{case the}

assignment

of the satellite reflections

requires

^two additional

integers

^{related to} the modulation wave vectors q, ⁼

(a */4,

²

kF, 0)

and q2 ⁼

(-

^a

* /4,

²

kF, 0 ) (with

²

kF =

^{0.295 b}

*),

^{in such a} way that the diffraction ^vector

Q

of the satellite reflection can be written as :

Where

h, k, l ,

m 1, m2 ^are

integers

^and

a *, b *,

^{c * are the}

reciprocal

^{basis vectors. Thus in}

the frame of the superspace group

formalism,

the incommensurate modulated

crystal

^{must be}

described in a five-dimensional superspace

[22].

^{The two} additional dimensions

correspond

^to

the so-called internal space and ^{act on} the

phase

of the modulation wave. This

approach

^leads

to a structure factor formula

[23]

^more suitable for

computation

purposes. We

employed

^this

formalism in our refinement program.

Practically

^{this means that the}

displacement

^{field can}

be

expressed

^{with a}

periodic

^{vectorial function of two variables}

(e.g. d (x + m, y + n ) = d (x, y )

^{with m, n}

integers).

^The

displacement d un

^{of the}

^pth

^{atom with}

^respect

^to its average

position ruo,

in the unit cell indexed

by

the lattice vector n takes the form :

Therefore

du

^{can be}

^expressed

ⁱⁿ the form of a discrete Fourier series.

Nevertheless,

because of the weakness of the second-order satellite

reflections,

^we restricted ourselves to the refinement of the two fundamental

components

^{related to} the modulation wave vectors qI ^and q2.

The size of the

experimental

dataset did not allow the refinement of a full atomic

displacement

^model

(156 parameters required

^at

least),

^{as it was done for}

DMM (TCNQ )2

[24].

^{Thus we}

adopted rigid body displacement

^models. We used the structure factor formalism

proposed by Petricek, Coppens

^{and Becker}

[25]

^{which is more suitable for}

molecular

displacements.

^{We had to} extend their

scattering

^{formalism to the case of a two-}

dimensional modulation. The

displacement

^vector

dp,i

^{of the}

^pth

^atom

belonging

^{to the}

rigid body assigned by i,

^can be written with the translational and the rotational

displacement components

^{of the}

rigid

block in the

general

^{form :}

where C and S

respectively

^{refer to} the cosine and to the sine

components

of the modulation.

The

subscript j = 1,

2 indexes the

components

associated with the modulation wave vectors qI and q2.

-

TCia/s( qj)

^are the translational

components

^{of the}

rigid

^{bodies i}

along

^{the three}

crystallographic

^{axes a, b and c}

(subscript a = 1, 2, 3),

^carried

by

^{the unit vectors}

ea.

-

RiBclS( qj)

^are the rotational

components along

the three inertial axes of the isolated molecule

L,

^M and N in order of

increasing

^moment of.inertia

(subscript /3 = 1, 2, 3) (Fig. 3).

These three axes are carried

by

^{the unit vectors}

nie,

^{and cross} each other at the

point

^located

by

^{the vector}

_rc.

Fig.

^{3. - Inertial axes of the TCNQ molecule}

(a)

and the TTF molecule

(b).

- gi

represents

^the

phase origin

^{of the}

rigid body displacements.

It has been chosen as the center of mass of the undistorded molecule

(TTF :

gp ⁼ rp ⁼

0, _{TCNQ : gQ}

⁼ rQ ⁼

a/2).

These

phase origins

^{coincide with the center of inversion} in the average structure. This choice leads to an easier

interpretation

^{of the}

symmetry properties

^{of the cosine} and the sine

components

of the modulation

(respectively

^even

(g)

^{and odd}

(u)

^with

respect

^{to the}

inversion).

^The

displacements

of the TTF and

TCNQ

molecules related to the above mentioned molecules

by

^the twofold-axis

(TTF

^at

(b

⁺

c )/2 ; ^TCNQ

^at

(a

^{+ b +}

c )/2)

^were

calculated

using

the superspace group

operators.

The atomic

scattering

^{factors were} taken from the International Tables for

X-ray crystallography [26].

^The

hydrogen

^{atoms were not} taken into account in the

present work,

because of their too small

weight

in the diffraction

pattern.

^We

performed

the refinement of the average ^structure from the 388 main reflections.

Although

^{we did not} notice any abnormal

displacements

^with

respect

^{to the}

positional parameters

of the average structure at 45 K determined

by

Schultz et al.

[27],

^{we obtained}

only

^a poor

agreement

^factor

(R =12 % ).

These results

might

^come from instrumental reasons

(truncated reflections,

^beam

intensity

fluctuations,

variation of diffractomer

resolution...).

^{Thus we}

adopted

the average ^structure

parameters

^of

TTF-TCNQ

^at 45 K of reference

[27].

^{We did not}

perform

any refinement of the thermal

parameters,

because of their too poor

reliability.

Bak and Janssen

[22]

have derived from observed

systematically

^extinct

reflections,

^{the two}

possible

five-dimensional superspace groups of the

« locking phase » according

^{to the}

presence ^{of the} inversion center in the modulated structure

P P2,/ C )

^{m m}

⁾

^{or not}

PP21m .

^{m In the}

first _case,

systematic

extinctions are

expected

^for satellite reflections

assigned by (h, ^{0, 1,} m, - m )

^{with l odd}

[22]. Although

^{we found} the presence of such reflections at the

reciprocal position Q

⁼

a */2

⁺

^{la *,}

^no noticeable

temperature dependence

^{of their}

intensity

was observed. We then attributed them to second order harmonic of diffraction of the main reflections

Q’ = a * + 2 lc *.

^{As we were left} with the indetermination of the superspace group of the lowest

temperature

^modulated

phase

^of

^TTF-TCNQ,

^we first dealt with a

rigid

molecular

displacement

^model

involving

^a small number of refinement

parameters,

^{and we} refined it in the two superspace groups in order ^to solve this

ambiguity.

^The

description

^{of the}

displacive

modulation in the frame of this

model, requires

²⁴

displacement parameters

(TiSa(qj) Rib (qj)

^{with i =}

TTF, TCNQ ;

^{a =} a,

b,

c ;

f3

⁼

L, M,

^N

and j = 1, 2)

^{for the}

superspace group

Pp21/C mm

_{m m} ^{and 48}

parameters

^of

displacement

for the superspace group

PP21 _(all

sine and cosine

components allowed).

^The refinement of this

displacive

model in the

m

first superspace group

corresponds

^to

Coppen’s

structural determination.

Then,

in the basis of this first structural

determination,

^we undertook the refinement of ^a

more realistic

displacive

^model

involving

intermolecular

displacements

and intramolecular deformations of both

types

of molecules.

4. Refinement results.

REFINEMENT OF THE RIGID MOLECULAR DISPLACEMENT MODEL IN THE SUPERSPACE GROUP

PP21/C.

^-The refinement of the modulated structure was carried out

using

^the 621 first-order

m m

satellite reflections. These results are summarized in tables 1 and II. There are

only

^few

differences with

respect

^to

Coppens’

^results

[12]

^{but with a}

higher

^R factor. However the small number of reflections retained

by Coppens (137)

^{should have}

certainly

contributed to an artificial

improvement

^{of their}

agreement

^factor.

The TTF and

TCNQ displacive

behaviours are almost similar to those determined

by Coppens

^and coworkers.

Nevertheless,

^{we obtained}

higher amplitudes

for the translations

(2-

fold for

TCNQ-1.3-fold

^for

TTF)

^and

inversely

^lower

amplitudes

for the librations. The TTF molecules move

along

^{a direction}

nearly parallel

^to the L-axis with a tilt

angle

^{of about 16°}

with

respect

^to the molecular

plane.

The translation

amplitudes change

from 0.018 to 0.036

 according

^{to the location of the stack}

along

the a-axis. The

TCNQ

molecules do not exhibit such a characteristic behaviour

except

^{for a} ql translation

component polarized perpendicu- larly

^to the molecular

plane (0.0075 Â)

^{and for a q2} translation

component polarized

^{in the}

direction of the a-axis.

Taking

^{into account the tilt}

angle

^{of TTF}

(24.5°)

^and

^TCNQ (34°)

^with

respect

^{to the}

stacking axis,

^these results confirm the

displacement polarizations

^{in the b and}

c* directions

previously

^observed

by

Comès et al.

[28]

^and

Kagoshima et

^al.

[29]

^from

structural studies.

The weak

amplitudes

of librations

only

involve small atomic

displacements (0.005 ^Â

^for

TTF,

^0.007

Â

for

TCNQ).

^{The libration of TTF} around the L-axis seems to be the most

important

rotational

component

ⁱⁿ accordance with

Coppens’

structural determination.

Hence,

^the refinement of the

rigid

^molecular

displacement

^model

disproves

^{a dominant mode}

of libron around L-axis

(Moravitz [9])

^or around the N-axis

(Weger

^{and Friedel}

[5]).

Table I. ^-

Agreement factors

^{R and}

Rp

^obtained

^for

successive

stage of

the structural

refinement of

^the

locking phase of TTF-TCNQ

^{at 13 K.}

(a)

⁴³⁷

first-order

^satellite

reflections.

(b)

⁶²¹

first-order

^satellite

reflections. (c) R= ¿ IFcal |/M ^{1 Fobs| . (d)}

^{wR =}

Table II.

- Refinement

^results

o f

^the

rigid

^molecular

displacement

model in the superspace group

pP21,/C

group

m m

REFINEMENT OF THE RIGID MOLECULAR DISPLACEMENT MODEL IN THE SUPERSPACE GROUP

pP21.

_m ^{The use} of the superspace group

pP21

_m ^{led to a}

slight improvement

^{of the}

agreement

factor

(see

^Tab.

1)

ⁱⁿ

spite

^{of the} twofold number of

parameters.

We obtained

large

translation

components along

^the a-axis for both

types

^{of chains}

(0.02 A

^for

^{TIF, 0.03 À}

^for

TCNQ) leading

^{to an}

important

modulation of the interatomic distances between the

neighbouring

^{stacks. For}

instance,

^{we found a} modulation

amplitude

of the shortest S-N bonds

nearly equal

^{to 0.05}

À.

These molecular

displacements

^{cannot be}

physically

^reliable

because of the shortness of these distances

(inferior

^{to the sum} of Van der Waals

radius).

^In

addition,

^the

majority

of structural studies did not reveal any

strong

distortional mode of the

chains

along

^the transverse a-direction. Therefore we decided to

adopt

^{for the}

following part

of this work the superspace group

pPZl/C.

^{At this}

^stage,

^{it can be}

^pointed

^{out that the}

R factors obtained with our 621 first-order satellite reflections is

appreciably larger

^{than the}

one calculated

by Coppens et

^{al. with 137 satellite} reflections. Such a number of reflections constitute a more selective test for the

reliability

^{of the}

displacive

^model.

Hence,

this may

mean that the

rigid

^molecular

displacement

model could not account

satisfactorily

for the real distortion mode of the molecule

chains,

^and

suggests

that the Peierls distortion involves

significant

intramolecular deformations.

SEMI-RIGID MOLECULAR DISPLACEMENT MODEL. - The

comparatively

more numerous

experimental

^{dataset we}

got,

^{enable us to refine an}

improved displacive

model. Now this

semi-rigid

^molecular

displacement

model takes into account some « low

frequency »

intramolecular distortion modes which appear ^at low

temperatures

in close connection with the onset of the Peierls distortion on both

types

^{of chains}

[15-17].

^This

displacive

model allows relative translations

(Tj(qj»

^{and rotations}

(Rs (qj))

^{of the two fulvalene}

^{rings FI}

^and

F2

^{assumed to be}

rigid

^unities

(Fig. 4b).

^We

split

^the

^TCNQ

molecule into three

rigid parts :

the two

cyanomethylene

groups

C (CN)2 NI

^and

N2,

^{and the}

quinoid ring ^Q (Fig. 4a).

^The

NI

group ^rotates around the carbon atom

C6. Analogous symmetry arguments

^{lead to} attribute 24

displacement parameters

^{to the fulvalene}

ring FI

^{and the}

C (CN)2

group

NI (all

cosine and sine

components allowed)

^{and 12}

parameters

^{to the}

rigid quinoid ring ^Q.

The

displacements

^of

F2

^and

N2

^were deduced from those of

FI

^and

NI applying

^the

pseudosymmetry operations

of the superspace group. This model has been

suggested by

^the

noticeable value taken

by

^the unauthorized

displacement parameters

^{in the}

rigid

^molecular

displacement

^{model and}

by

the static distortions of the TTF and

TCNQ

molecules observed in the average ^structure

by

Kistenmacher et al.

[30]

^{at room}

temperature.

Fig.

^{4. -}

Decomposition

^{of the TCNQ molecule}

(a)

and the TTF molecule

(a)

^{in the}

semi-rigid

molecular

displacement

^model.

REFINEMENT OF THE SEMI-RIGID MOLECULAR DISPLACEMENT MODEL IN THE SUPERSPACE GROUP

pP21/C.

_{m m}^- The refinement of this

displacive

model has been

performed using

^the

results obtained from the first model as

starting parameters.

^{The new} modulation

parameters

have been introduced

progressively

^{in order to} check their relative

importance

^{in the}

modulation wave.

Nevertheless,

the final results were found

independent

of the initial conditions and the refinement

path.

^A

good agreement

^{factor was obtained at the}

lastsstage

^of

refinement

(Tab. I)

^{if we refer to the intrinsic}

quality

^{of the}

experimental

dataset. The

improvement

of the R factors from 28 % to 12.6 %

unambiguously

shows that the

rigid

molecular

displacement

^model

gives only

^a

rough description

of the lowest

temperature

modulated

phase

^of

^TTF-TCNQ.

The refinement results are shown in table III.

Figure

^5a

Table III. ^-

Refinement

^results

of

^the

semi-rigid

^molecular

displacement

^{model in the}

superspace group

PP21/ C’

m m

represents

^the

projection

^{onto the}

(b, c * ) plane

^{of a} sheet of the TTF stacks

passing through

the

origin

^{and a sheet of the}

^TCNQ

^stacks

lying

^{at x =}

a /2.

^The

superposition

^{in the same cell}

of the whole

positions occupied by

^a

particular

^atom

belonging

^to the molecules of the same

stack

gives

^an

ellipsoidal trajectory

^{centered at} the average

position

^{of this atom.}

Figures

^5b

and 5c show the

projection

^{of such}

trajectories

upon the

(b, c*) plane

^{and the}

(a, c) plane

for the TTF and the

TCNQ

chains.

We did not notice any

significant

modification of the intermolecular

displacement

components

for TTF molecule

(TS, RC) (Tab. III).

^The

amplitude

of the intramolecular translational

components (TC)

^remained

^small,

^{whereas we obtained an} intramolecular

Fig.

^{5. -}

Representation

^{of the chain} distortion

according

^to the refinement results of the

semi-rigid

molecular

displacement

^{model :}

(a) projection along

the a-axis of the TTF sheet

lying

^{at x = 0 and the} TCNQ ^sheet

lying

^{at x = a/2}

(full

line : real

position

^{in the modulated structure} - dotted line : mean

position

in the average

structure) ; (b) (c)

^schematic

representation

of the full

positions occupied by

^the

atoms in the molecular chains

projected along

the a-axis

(b) (upper

and lower left sketches

correspond respectively

^to the TTF chains at x ⁼ 0 and x ⁼ _a, upper and lower

right

^sketches

correspond

^{to the} TCNQ chains at x ⁼ a/2 and x ⁼ 3

a/2)

and b-axis

(c) (from

^{left to}

right

^chains

lying

^at

x = - a, - a/2,

a/2, a).

^The

displacement amplitudes

^{have been}

multiplied by

^30.

b3u

rotational

component (Rt)

^{of the same order of}

magnitude

^{as the} libration around the M- axis

(RI). ^However,

these last

components

^involve

only

^{small atomic}

displacements (0.005 Â).

^{This means} that the TTF molecule

rigidity

^is

preserved

^{in the}

locking phase,

^{and a}

fortiori

^{in the}

higher temperature

^modulated

phases.

The TTF molecules slide upon their ^mean molecular

plane

^{in the direction of the}

L-axis,

and rotate

slightly

^around the L and M-axes

(Figs.

^{5a and}

5b).

^The

displacive

^scheme

occurring

^{in both}

types

^{of TTF sheets at x = 2 na and x =}

(2 n + 1 ) a

exhibits the same

translational behaviours as is was

pointed

^{out in the}

previous model,

^{and can be}

distinguished only by

the relative

amplitude

^{of their}

displacements (factor 2).

The torsion of both fulvalene

rings

^{around L-axis were found}

negligible.

^Thus the various IR active modes which have been

assigned

^to that torsional mode

by

^{Bates et al.}

[15]

^{should rather be} associated with the libration around the L-axis. In addition Bates et al.

[15]

have noticed the activation

(E//b )

^{of a} vibrational mode at 260

cm-1

which could be

assigned

^{to the} M-rotational

components (RM, RSM).

On the

contrary,

^{we obtained a} substantial modification of the

TCNQ

chain distortion mode. The

quinoid cycle

behaviour consists of a

large

translational

component along

^the

direction

perpendicular

^to the molecular

plane (TN Figs.

^{5a and}

5b)

^{with a}

significant

translational

component along

the a-axis

(Fig. 5c).

^The

cyanomethylene

groups

present

^the

same translational

components

^{but with lower}

amplitude (twofold)

^{and exhibit a}

large

rotational

activity

around the a-axis of

b2 g ^symmetry (Tcm :

rotation of

Ni

^and

N2

groups in ^the

same way ^as a M-libration

does)

^{and of}

b3u symmetry (Tsm :

rotation of

Ni

^and

N2

groups in

opposite way).

^The

partial

refinement of these

parameters

^alone

yields

^an

improvement

of the R factor of more than 10 % with

respect

^{to the R factor obtained with the}

rigid

^molecular

displacement

model. It may be ^seen that the translational

components

TN

^{of the}

cyanomethylene

groups combine with the rotational

components RM

^{in such a} way

as to

bring

^the

nitrogen

^{atoms closer to the mean molecular}

plane.

^{Such a}

configuration obviously

^{reduces the}

amplitude

of the modulation of the S-N interstack contacts between

neighbouring

^chains.

This

out-of-plane

distortion modes confirm the observation

by

Bozio and Pecile

[16]

^{of an}

antiresonance

dip

^{in the IR}

absorption spectrum

^of

TTF-TCNQ

^at low

temperatures,

^that

they assigned

^to the three

out-of-plane

distortional modes of

TCNQ

_{vso, v5l} and v52.

They

also agree with the

assignment [15]

^{of the two lowest}

frequency b3u out-of-plane

modes v53 and v54 which

represent

^{the most}

important part

^{of the} intramolecular distortion.

However our molecular distortion model did not

give

any evidence of the

totally symmetric

(ag)

^{modes Yq of}

^TCNQ

and P7 of TTF which appear

respectively

^{at the Peierls transition}

temperature TH

^and

TM according

^{to Bozio and Pecile}

[16].

Nevertheless this does not mean

that the

ag

^modes

play

^a minor role in

TTF-TCNQ,

^but

only

^{that our}

displacive

^{model does}

not allow a convenient

description

^{of the}

higher frequency _ag

^{mode. In}

particular,

^{it cannot}

account for the internal deformations of the

cyanomethylene

groups

(C -

^N

bending :

v9, vlo,

C (CN)2 scissoring :

v6, P8 and C - N

stretching : v6)

which exhibit IR activities under the transition

temperatures [17].

^{However the atomic}

displacement amplitudes

^induces

by

^these

_ag

^{modes are}

expected

^to be small because of

large

intramolecular interactions. We

attempted

^{to refine a more}

sophisticate displacement

^model

involving

individual

displace-

ments of the

nitrogen

^{atoms or the CN} groups

apart.

^{But we did not} obtain successful results

(aberrant displacements, stability problem...).

Thus in the framework of this

semi-rigid

^molecular

displacement

^{model the refinement}

results show that the

major part

^{of the} Peierls distortion consists of inter and intramolecular distortion modes which involve a

large

modification of the

spacing

distance between

neighbouring

molecules. Therefore the modulation of the intrastack transfer

integral

^{seems to}

represent

^{the most}

important coupling

mechanism of the low

frequency

vibration modes with the CDW.

5. Discussion.

ORIGIN OF THE DISPLACIVE BEHAVIOUR OF TTF ^AND

TCNQ

MOLECULES. - Such molecular motions are

expected

^{to be}

linearly coupled

^to the conduction electrons.

They change

^{to first}

order the intrastack transfer

integrals

^{that can} be related to the molecular

overlap

^between

the

neighbouring

molecules. Therefore the electron-vibration

coupling

^constants

sensitively depend

^{on the wave} function of the molecular orbital on both

types

of chains. It should be noticed that there is a

strong analogy

^{between the two}

opposite displacive

behaviours of the TTF molecules

(sliding

upon the molecular

plane

^{in the}

longest

^axis

direction)

^{and the}

^TCNQ

molecules

(displacements

^{of the}

quinoid ring perpendicular

^{to the mean molecular}

plane),

and the mean orientation of the nodal surfaces of the molecular orbitals involved in the

conducting

bands. The

highest occupied

^{molecular orbital} of TTF molecule has

bl " symmetry

and

presents

nodal surfaces that

spread

^{over the whole}

length

of the molecule

nearly

^{in the}

same way ^as the

polarization

^{vector of the}

displacement

^on the TTF chains

(Fig. 6b).

Inversely,

the lowest

unoccupied

^molecular orbital of

TCNQ

molecule has

b2 g ^symmetry

^and

presents

^nodal

planes perpendicular

^{to the}

long

axis of the molecule

(Fig. 6a).

Let us now turn to the

origin

of the intramolecular distortion of the

TCNQ

molecule. The

electron-phonon coupling

^{constants in the case of}

large planar

^{molecules are} also very sensitive to the

charge

distribution. Duke

[31]

^has

proposed

^a successful

microscopic interpretation

of the relative

strength

^{of the}

electron-phonon coupling

^{constants for the}

totally symmetric _ag

^modes of TTF and

TCNQ

based on the electronic structure informations and the normal mode coordinates. We can

easily generalize

^this

approach

^{to the}

out-of-plane

intramolecular vibration modes. Various electronic structure calculation

[32-34]

^{have been}

carried out for

TCNQ

molecule. There is a

general agreement

^{that the}

hydrogen

^{atom and the}

carbon atoms

C4

carry ^a small

part

of the additional

charge. Now, taking

^{into account the}

slipped overlap

^{of two}

adjacent

molecules within a chain

(Fig. 7),

^{it can} be noticed that the

nitrogen

^{atoms on one}

^TCNQ molecule, principally

^{face the}

hydrogen

^{atoms on the}

neighbouring

^molecule.

Therefore,

^the

displacement

^{of the}

cyanomethylene

groups perpen-

dicularly

^to the molecular

plane

^{does not lead to a}

significant change

of the intrastack transfer

integral.

^{On the}

contrary,

^the

major part

^{of the}

charge

distribution

spreads

^{on the}

quinoid ring

^{and the}

C3

^atoms

(Berlinsky

^{67 %}

[32],

^{Duke 84 %}

[31]).

^{Thus the}

quinoid ring displacements

^are

expected

^{to be more}

strongly coupled

^to the CDW than those of the

1 ^.

Fig. 6. Fig. 7.

Fig.

^{6. - Nodal surfaces}

(dashed line)

of the lowest

unoccupied b2 g

molecular orbital of TCNQ (a) ^anis the

highest occupied bl u

molecular orbital of TFF

(b)

^{in the}

plane lying

^at 1/4 of the _way between

adjacent

molecule in a TCNO ^stack.

Fig.

^{7. -}

Projection

^{of the two}

neighbouring

^TCNQ molecules in TTF-TCNQ

along

the normal to the

mean molecular

plane.