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Neutron diffraction study of the compressibility of TTF-TCNQ under hydrostatic pressure

D. Debray, R. Millet, D. Jérome, S. Barišić, L. Giral, J.M. Fabre

To cite this version:

D. Debray, R. Millet, D. Jérome, S. Barišić, L. Giral, et al.. Neutron diffraction study of the com-

pressibility of TTF-TCNQ under hydrostatic pressure. Journal de Physique Lettres, Edp sciences,

1977, 38 (12), pp.227-231. �10.1051/jphyslet:019770038012022700�. �jpa-00231365�

NEUTRON DIFFRACTION STUDY OF THE COMPRESSIBILITY

OF TTF-TCNQ UNDER HYDROSTATIC PRESSURE

D.

DEBRAY,

^{R. MILLET}

Laboratoire Léon-Brillouin et Service de

Physique

^{du Solide et} de Résonance

Magnétique, CEN-Saclay,

⁹¹¹⁹⁰

Gif-sur-Yvette,

^France

D.

JÉROME

Laboratoire de

Physique

^des

^Solides,

Université Paris-Sud, 91405

Orsay,

^France

S.

BARI0160I0106,

^{L. GIRAL}

Institute of

Physics

^{of the}

University,

⁴¹⁰⁰¹

Zagreb, Yugoslovia

and J. M. FABRE

Laboratoire de Chimie

Organique Structurale, USTL,

³⁴⁰⁶⁰

Montpellier,

^France

DPh-G/PSRM, CEN-Saclay,

^{B.P. n°}

2,

⁹¹¹⁹⁰

Gif-sur-Yvette,

^France

(Re_Cu

^{le 20 avril}

1977, accepte

^{le 18 mai}

1977)

Résumé. ^- Nous

présentons

^{des mesures de}

compressibilité

^de TTF-TCNQ deutéré par diffraction de neutrons sous hautes

pressions hydrostatiques jusqu’à ~

^{20 kbar à la} température ^ambiante.

Les valeurs observées sont

respectivement

^{suivant les axes a, b et c,}

ka

⁼ 2,7, kb ⁼ 4,7 ^et

kc

^{= 3,2 x 10-12}

cm2/dyne.

^{Ces résultats}

indiquent

l’existence d’une contribution

importante

^de type

électrostatique

(coulomb) à l’interaction interchaînes. Nous suggérons que la cohésion des cris- taux de TTF-TCNQ

provient

^de

l’empilement

^de

dipôles

moléculaires fluctuants.

Abstract. ^- The linear axial

compressibilities

^{of a} deuterated sample ^of TTF-TCNQ (tetra-

thiafulvalene-tetracyanoquinodimethane)

^{have been measured}

by

^{a neutron} diffraction

technique

under hydrostatic pressures up ^{to ~} 20 kbar at room temperature. The observed

compressibilities

along ^the

crystallographic

^{axes are,} respectively,

ka

⁼ 2.7,

kb

^{= 4.7 and}

kc

^{= 3.2 x 10-12}

cm2/dyne.

These results indicate a strong ^Coulomb type interchain interaction. It is

suggested

that the dominant part ^{of the} crystal cohesion results from a

stacking

^of

strongly

dynamically

polarized

^{TTF and} TCNQ

molecules

acting

^{as effective molecular} dipoles.

Classification

Physics ^Abstracts

61.12-62.20-72.15 N

1. Introduction. ^- The

organic charge-transfer

salt

TTF-TCNQ (tetrathiafulvalene-tetracyanoquino- dimethane)

has been the focus of considerable

experi-

mental and theoretical work in recent years because of its unusual

quasi-one

dimensional electronic transport

properties [1]

^{and its} sequence of Peierls and collective

phase

transitions at low

temperatures [2]. However, despite

^{all the recent} advances which have

substantially improved

^our

understanding

^{of this}

compound,

^the

fundamental

question

^of paramount

importance

^still

remains unanswered. This is the nature of the interac- tion between the molecular b-axis chains. As is well

known,

it is this interaction between the chains which suppresses the effect of ^1-D fluctuations and

brings

about a collective

phase

transition at a non-zero

temperature

^{in a real} system ^like

TTF-TCNQ [3].

Theoretical attempts ^to get ^even

qualitative

features of such a system

depend drastically

^{on the nature of the}

interactions considered in each model

[4].

^Unfortu-

’

nately,

^{we do not}

yet

^{have a clear}

understanding

^{of the}

nature of this interaction between the chains.

It is common

knowledge

that the elastic

properties,

in

particular

the elastic

moduli,

^are

intimately

^connect-

ed with the

binding

energy of ^a

crystal

^{and can,}

together

^{with their} pressure

derivatives, provide

valuable information about cohesive

energies

^and

interatomic forces. With this in

mind,

^{we undertook}

an

experimental

determination of the linear

axial

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019770038012022700

L-228 JOURNAL DE PHYSIQUE - ^LETTRES

compressibilities

^{of a} deuterated

sample

^{of TTF-}

TCNQ by

^neutron diffraction measurements under

hydrostatic

pressure. ^In this work we report the results of our

investigation.

2.

Experimental.

^{- The}

high-pressure

^cell

[5]

used for neutron diffraction measurements was

developed

^at the C.E.N.

Saclay

in collaboration with the

high-pressure

group of

Orsay.

^{It is a}

piston- cylinder

device and consists of a

supported high- density Al203 cylinder

^with tungsten ^carbide

pistons.

The device has three

symmetrically placed ^windows,

each

giving

^{an access to the}

sample

of 90° in the hori- zontal

plane

and 30° in the vertical

plane.

^The

poly- crystalline sample

is contained in a teflon cell filled with the

liquid

Fluorinert FC-75 as the _pressure

transmitting

medium. The pressure is monitored

by

^a

manganin

pressure gauge

directly placed

^{in the}

transmitting liquid

and calibrated

previously by

^refe-

rence to the NaCI _pressure scale. The pressure gene- rated is

purely hydrostatic

^{at least} up ^{to ~} 20 kbar at room

temperature.

^The geometry ^{of the}

high-pressure

cell is such that the incident neutrons ^see neither the

pistons

^{nor the} pressure gauge. Neutron diffraction patterns ^{were taken at room} temperature ^{in the} pres-

sure range 0-20 kbar

using

the conventional two-axis diffractometer H12 at the C.E.N.

Saclay.

This diffrac- tometer uses a

wavelength

^1.14

^A

and the flux at the

sample

^{is ~ 2 x}

^106.

^The

angular positions

^of

eight

individual

Bragg peaks

^{were followed as a function of}

pressure. The lattice constants a,

b,

c, and

P

^{of the}

monoclinic unit cell of the deuterated

TTF-TCNQ sample

^were determined

by

^a

least-square fitting

^{of the}

eight Bragg peak positions.

3. Results and discussion. - As an illustration of the

change

ⁱⁿ

angular positions brought

^about

by

^the

applied

pressure, ^we have shown in

figure

¹ the pres-

sure

dependence

^of

Bragg angles (2 0)

for the nuclear

Bragg peaks (112)

^and

(013).

Note that the

applied

pressure does ^{not cause} any

broadening

whatsoever of the

peaks, confirming

^its

hydrostatic

^nature.

Figure

²

shows the

percent compressive

^strain

(- (A///) 100) along

^{the three}

crystallographic

^axes. Note that the

experimental

^errors associated with the a-, b- and c-axial strains are,

respectively,

±

0.2,

± ^{0.2 and} + ^0.25

%.

^{We have not} shown them in the

figure

^to

maintain a clean appearance. In

general,

^the

angle P

also

changed

with pressure.

However,

this variation

was not

systematic

^{and was within our}

experimental

error of 0.3

%.

^We

have, therefore,

^{chosen to}

ignore

^it.

When

subjected

^to

hydrostatic

pressure, the stress

I

always

^{acts normal to the}

crystal

^face.

Hence,

^there

are no shear stresses.

Also,

^{if the}

crystallographic

^axes

are not deformed

orientationally (as

^{is true in our}

case),

there are no shear strains either. Under these cir- cumstances, Hooke’s law ^can be written as a set of three

equations, ^viz.,

^"

FIG.1. ^- Pressure dependence of the nuclear (112) (weak) ^and (013) (strong) Bragg angles ^{of a} deuterated sample ^of TTF-TCNQ ^at

room temperature. Solid lines are guides ^{to the} eye.

FIG. 2. ^- Compressive axial strains of a deuterated sample ^of TTF-TCNQ ^{as a} function of applied hydrostatic pressure ^{at room}

temperature. Solid ^{lines are} guides ^{to the} eye.

where

ka, kb and k~

^are,

respectively,

the linear axial

compressibilities (i.e. compressive

^strain per unit

pressure) and C’s

^are the elastic stiffness constants or

!

moduli of

elasticity.

Note that for symmetry reasons,

Cij

⁼

Cji ^{(i ~ 7).}

^{The linear}

compressibilities, k’s,

^can be obtained

directly

^from the initial

slopes

^{of the}

strain vs. pressure ^curves. We have used the data shown in

figure

^{2 to} obtain these values for

TTF-TCNQ

We note that the linear

compressibility, kb, along

the b axis is similar to that for a soft metal like sodium

(k

^{= 4.5 x}

^{10 - 12} cm2/dyne [6]).

The rather

surpris- ing

feature of our results is that the

compressibilities along

^{the a and c axes}

(i.e. perpendicular

^{to the chain}

axis)

^are about half of that

along

^{the b axis}

(chain axis)

and are clo~e to values for ionic solids like CsI

(k

^{= 2.4 x}

lO-12 cm2/dyne [6]).

^{The a- and c-axis}

compressibilities

^are also about an order of

magnitude

smaller than what one would expect ^{if the}

binding

between the chains were

predominantly

Van der Waals type

(e.g., for solid neon, k = 29.6

^x

10 -12 cm2/dyne [7]).

It

might

be instructive to compute values for the elastic moduli

Cll, C22

^and

C33

^{from eq.}

⁽¹⁾ by using

the linear

compressibilities given by (2)

^and

neglecting,

as a first

approximation,

^the

off-diagonal

^constants.

As we shall see

later,

^{this is not a bad}

approximation.

This

procedure gives

A value of

C22

^{can also be}

directly computed

^from

the initial

slope

^{of the}

dispersion

^{curve for}

longi-

tudinal acoustic

phonons propagating along

^{the chain}

axis

[010].

^An

analysis

of this acoustic mode

dispersion

curve

[8] gives C22

^{= 1.9 ± 0.3 x}

¹⁰¹¹ dyne/cm2

ⁱⁿ

excellent agreement with the value obtained above.

This

justifies

^our

neglecting

^the

off-diagonal

^constants.

It should be noted that values for

C22

^{have also}

been

reported by

Barmatz et al.

[9]

^and

by Ishiguro [10]

from a measurement of the

longitudinal

^sound

velocity along

the b-axis. The former used the

vibrating-reed technique [ 11 ]

^and

gives C2 2

^{= 0.27 x}

^{1 O 11} dyne/CM 2,

while the latter

employed

^the conventional. ultrasonic

pulse

method and reports

C22

^{= 0.96 x}

1011’dyne/cm2.

We would like to mention that it would be unwise to

rely

^on these values since the

experimental

^uncer-

tainties involved in both cases are

large, particularly

so in the

vibrating

reed method where the

validity

^of

its use is

questionable.

We now consider the

significance

^{of our} results and

,

present

^a

qualitative

discussion intended to serve as a

guide

^for future work on

TTF-TCNQ.

The intrachain bond

(along b-axis)

is of the metallic type. ^The

equilibrium

intermolecular distance

along

the chain direction results from the

interplay

^{of the}

electron contribution

(overlap

of molecular orbitals

and resultant band

width)

^to the cohesive _energy and the

repulsive

forces due

(at

^least

partially)

^{to the}

Coulomb

repulsion

^between

similarly charged

^mole-

cules in the chain. The

equilibrium

^{band width is}

quite

small

(~0.5

^eV

[12]).

^The

compression along

^the

b-axis increases this band width

[13]

and results in ^a

negative

electron contribution to the deformation energy

proportional

^{to the}

equilibrium

band width

[ 14].

However,

since this width is small and since the

equili-

brium distance is

comparatively large (stacking

^dis-

tance 3.475 and 3.166

A, respectively,

^{for TTF and}

TCNQ

^chains

[15]),

the variation of cohesive _energy with intermolecular distance

along

the chain is small.

This should result in a

relatively high compressibility

and low elastic modulus as we have observed.

The values of the

compressibility along

^{the a-}

and c-axis directions indicate a

predominantly

^ionic

or Coulombic type interchain interaction. The observed low values for the transverse

conductivity

(~tt/~-L ~ ¹⁰² [16])

and the interchain

hopping

^or

tunnelling amplitude [17]

^{lead to small interchain}

overlap integrals.

Their contribution to cohesion is thus

negligible

ⁱⁿ

keeping

^{with our} observation.

The

binding along

^the a-axis direction is due ^to the Coulomb attraction between the

oppositely charged

TTF and

TCNQ

molecules. An

appreciable proportion

of the

charge

^transfer

presumably

^{occurs between}

the S atoms of TTF and N atoms of

TCNQ [18].

^These

atoms are

quite

^close

(3.20 ^A [15])

^which

^gives

^some

additional

stability

^{to the} structure. The sum of the Van der waals radii of the N and

S atom ( = 3.35 A [ 19])

is of the order of the short N-S

distance,

^which

indicates that the

repulsive

^{forces are} of the usual

origin.

The

packing

^of

similarly charged

molecules in the b-c

(011) planes

^{can not be}

explained

^{within the}

point-charge

model for Coulomb forces. This model

obviously prefers charge

alternation

along

^{the c-axis}

direction,

^{as is found to occur in}

HMTTF-TCNQ

and

HMTSF-TCNQ

structures

[20]. Indeed,

^cal- culations of the

Madelung

energy made

by

^various

authors

[21, 22]

^{show that this} energy is insufficient

by

^{itself to} stabilize the

TTF-TCNQ

^structure.

Consequently,

other contributions to the

binding

energy,

viz.,

the Van der Waals

interaction,

^the

exchange

energy, and the

polarization

energy have to be taken into account. We do not see any ^reason

why

the usual Van der Waals and

exchange energies

^should

be much different in

TTF-TCNQ

and HMTTF-

TCNQ

^or

HMTSF-TCNQ

structures. One is thus forced to invoke the contribution of the

polarization

energy in order to

explain

^the

stability

^{of the different}

structure

types.

^The

polarization

energy is the _energy

gained through

the interactions of

fluctuating dipoles

induced on

neighbouring

molecules due to their

high polarizability.

^The

resulting dynamically

^induced

dipolar

attraction can be

quite

strong in certain cases,

especially

when the distance of

separation

^of

adjacent

molecules is

small,

^and may overwhelm the

monopole

L-230 JOURNAL DE PHYSIQUE - ^LETTRES

repulsive

effect when

similarly charged

^{molecules are}

stacked

together

^{as in}

TTF-TCNQ. If MA

^and

MD

^are

the

dynamically

^induced

dipole

^{moments associated}

with the acceptor ^{and donor}

molecules,

^{R the distance} of

~eparation

^of

adjacent

^molecules

along

^{the c}

^axis,

and

EM the gain in Madelung

^{energy in}

going

^{from the}

TTF-TCNQ

^{to the}

HMTTF-TCNQ

^{or HMTSF-}

TCNQ

^structure type

(note

^that

EM

^is

necessarily positive) stacking,

^then

simple reasoning

^{shows that}

the former

type

^of

stacking

^is

energetically

^more

favourable when the condition

(MD - MA)2/R6

>

EM,

is satisfied. We

suggest

that this condition is satisfied in

TTF-TCNQ,

^which

explains

^the

stacking

^of

similarly charged

^molecules

along

the c-axis direction.

Note that the TTF molecule is

significantly

^shorter

[15]

than either the HMTTF or HMTSF molecule

[20]

resulting

^{in a}

larger

^c

parameter

^{and hence R value in} the latter two

compounds.

^{Since we do not}

^expect (MD - MA)2

^{to vary}

^much,

^{if at}

^all,

ⁱⁿ

going

^from

TTF-TCNQ

^{to the other two}

compounds,

^{it is}

quite possible

that the condition cited above is no

longer

satisfied in

HMTTF-TCNQ

^and

HMTSF-TCNQ

because of the increased value of R. This will then result in

charge

alternation

along

^{the c axis as observed.}

The main idea is the

following.

^When the molecules are

highly polarizable,

^{a small}

separation

^between

adjacent

molecules causes a

dynamical charge

redistribution in the molecular

planes converting

^{each into a}

fluctuating

molecular

dipole.

^The

bonding

then results from the dominant attractive interaction between

adja-

cent

dipoles.

^In

^fact,

^such

polarization

^{or enhanced}

Van der Waals

bonding

^is

perhaps responsible [23]

^for

the cohesion in

organic

^aromatic solids with less than Van der Waals

interplanar spacing

^{as in}

naphthalene

or anthracene. It is

interesting

^{to note} that the linear

compressibilities

^{of these two}

organic

^solids

[6]

^{fall in}

the _range of those we have observed for

TTF-TCNQ.

In such a case, ^one also expects ^a strong ^anharmonic effect. This is

quite

apparent ⁱⁿ

figure

^2.

It also seems reasonable to think that the

charge

transfer from TTF to

TCNQ

goes ^to the same

wing

^of

the molecule for all the molecules

along

^{the same}

c-axis direction in order to minimize the coulomb energy. This

requirement

^limits

presumably

^the

charge

transfer itself

[24].

It is also

likely

^{that the}

wing

^{of the}

molecule which receives the

largest part

^{of the}

charge

transfer alternates

along

the b axis. In

fact,

^{such an} alternation will add to the

binding

energy

along

^the

b-axis direction.

In

conclusion,

^we venture to say that our results

conclusively

establish that the interchain

bonding

ⁱⁿ

TTF-TCNQ

^is

quite strong

and is the result of an

interplay

between Coulombic and

polarization

^ener-

gies.

Both contributions overwhelm _any cohesion

resulting

from electron

hopping

^or

tunnelling

^between

chains.

Thus, although quasi-one

dimensional in its

electronic _transport properties, TTF-TCNQ

^{is a}

fully

three-dimensional material as far as

crystal binding

^is

concerned.

Acknowledgments.

^- The authors wish to thank Dr. P. Mériel for his interest and encouragement ^for this work.

They

^{feel indebted to} Pr. J. Friedel and Pr. L. P. Gorkov for several

illuminating

^discus-

sions and clarifications. The authors are also

grateful

to Dr. M.

Weger

^{for a critical}

reading

^{of the manus-}

cript

^and

appreciate highly

the interest shown

by

Drs D.

Cribier,

^A. Landesman and M. Lambert in this work.

They

^{are thankful to Dr. M. Perrin for his}

help

in some of the measurements.

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therein.

[2] COMÈS, R., in Proceedings of the NATO Summer School ^on

Chemistry ^and Physics of One-Dimensional Metals, August 1976, Bolzano, H. G. Keller Editor (Plenum Press) ^1977.

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HOROVITZ,

B., GUTFREUND, H., WEGER, M., Phys. ^{Rev. B 12} (1975) ^3174.

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[17] SODA, G., JÉROME, D., WEGER, M., FABRE, ^{J. M.} and GIRAL, L., Solid State Commun. 18 (1976) ^1417.

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and Semiconductors, Siofok, Hungary, 1976, ^{to be} publish-

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WEGER, ^{M. and} FRIEDEL, J., ^J. Physique ³⁸ (1977) ^241.

[19] PAULING, L., The Nature of ^the Chemical Bond (Cornell University Press) 1960, p. 260.

[20] PHILIPS, ^T. E., KISTENMACHER, ^T. J., BLOCH, ^{A. N. and} COWAN, D. O., ^{JCS Chem. Commun.} (1976) ^334.

GREENE, ^R. L., MAYERLE, J. J., SCHUMAKER, R., CASTRO, G., CHAIKIN, ^P. M., ETEMAD, ^{S. and} LAPLACA, ^S. J., ^Solid State Commun. 20 (1976) ^943.

[21] EPSTEIN, ^{A. J., LIPARI, N.} O., SANDMAN, ^{D. J. and} NIELSON, P., Phys. ^{Rev. B 13} (1976) ^1569.

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5098.

[23] WALLWORK, ^C. S., J. Chem. Soc. (London) 1961, 494.

[24] ^The charge ^transfer p has been determined accurately by

diffuse X-ray scattering experiments. ^For TTF-TCNQ,

p ⁼ 0.59 electron/molecule according ^to

DENOYER, ^{F. et} al., Phys. Rev. Lett. 35 (1975) ^{445. The corres-} ponding value for HMTSeF-TCNQ ^{is 0.74} electron/

molecule according ^to WEYL, C. et al., Solid State Commun.

19 (1976) ^925.