Pressure dependence of the thermoelectric power of TTF-TCNQ

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Pressure dependence of the thermoelectric power of TTF-TCNQ

C. Weyl, D. Jérome, P.M. Chaikin, K. Bechgaard

To cite this version:

C. Weyl, D. Jérome, P.M. Chaikin, K. Bechgaard. Pressure dependence of the thermoelectric power of TTF-TCNQ. Journal de Physique, 1982, 43 (7), pp.1167-1172. �10.1051/jphys:019820043070116700�.

�jpa-00209491�

Pressure dependence ^{of the} thermoelectric _power of TTF-TCNQ

C. Weyl, ^D. Jérome, ^{P. M. Chaikin} (*)

Laboratoire de Physique ^des Solides, Université de Paris-Sud, ⁹¹⁴⁰⁵ Orsay, ^France

and K. Bechgaard

H. C. Oersted Institute, Universitetsparken 5, ^{DK 2100} Copenhagen, ^Denmark (Reçu le 2 avril 1981, révisé le 2

1982, accepté ^{le 22}

1982)

Résumé.

Nous

mesuré le pouvoir thermoélectrique ^de TTF-TCNQ ^dans

intervalle de température

allant de 300 à 4 K pour des pressions comprises ^entre

atmosphère ^et 15 kbar. Le pouvoir thermoélectrique,

à la température ambiante, décroît de ~ - 30 03BCV/K ^{à ~ - 10} 03BCV/K ^dans

^{domaine de} pression indiquant que la conductivité relative de la chaîne de TTF par rapport ^à celle de la chaîne de TCNQ ^croît

^même temps que la

pression. ^{Dans le domaine où la} transition métal-isolant

lieu, ^le pouvoir thermoélectrique change ^de signe; ^la plus ^haute température de transition correspond ^{donc à la} disparition ^des porteurs ^de charges

les deux chaînes.

Lorsque ^la pression augmente ^cette transition affecte de plus

plus ^{la chaîne} de TTF par rapport ^à la chaîne de

TCNQ.

Abstract.

We have measured the thermoelectric power of TTF-TCNQ ^{in the} temperature region from 300 K- 4 K for pressures from atmospheric ^{to 15 kbar. The}

temperature thermopower decreases from ~ - 30 03BCV/K

to ~ - 10 03BCV/K in this pressure range indicating that the relative conductivity of the TTF chain to the TCNQ

chain increases with pressure. In the temperature regime of the metal-insulator phase transition

find that the

sign ^of thermopower changes. ^The highest temperature transition therefore corresponds ^{to the}

freezing-out

of carriers

both chains. As pressure increases this transition increasingly effects the TTF chain relative to the

TCNQ ^chain.

Classification

Physics ^Abstracts

72.15J

72.20P

Measurements of the properties ^of highly ^conduct- ing quasi-one-dimensional organic crystals

^{a func-}

tion of hydrostatic pressure have proven particularly

useful [1-3]. This results from the high compressibility

of the crystals and the fact that _pressure is the only

method for continuously varying ^{the most funda-}

mental quantities ^of physical interest in these narrow-

band systems namely : ^the longitudinal ^{and transverse}

bandwidths and the cation-anion charge ^transfer.

Most of these compounds undergo metal-insulator transitions due to the instability ^of one-dimensional electronic systems against Peierls’ distortions [4].

Application of pressure strongly effects this phase

transition. In the

of TTF-TCNQ pressure studies have indicated

complicated ^{set of} phase transitions

(*) ^{Permanent address :} Department ^of Physics, ^Univer- sity ^of California, ^Los Angeles, California 90024, A. P. Sloan Foundation Fellow, ^work partially supported by ^NSF

DMR-79-08560.

which at high pressure (19 kbar) ^{evolve to a} single

first order commensurate transition [5]. ^More recently

studies

(TMTSF)2-PF6 have shown that the Peierls transition can be suppressed completely by ^the application ^{of 10} kbar and that the material then becomes superconducting [6].

The organic charge ^transfer compound ^{which has}

been most widely studied is TTF-TCNQ. ^{At atmo-} spheric pressure TTF-TCNQ remains metallic from above 300 K to 53 K at which temperature ^{it under-}

goes the first of at least three transitions which even-

tually ^{leave it} insulating ^{in its low} temperature ground

state [7]. ^The phase diagram ^as

function of pressure has been obtained from conductivity measurements and more recently ^{from neutron} scattering ^studies [ 8].

In order to further explore ^{the metallic state as}

well as the phase diagram ^of TTF-TCNQ ^under

pressure, ^we have measured the thermoelectric _power.

Along with the Hall effect [9] ^the thermopower ^is capable ^of distinguishing ^the sign ^{of the} charge

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019820043070116700

1168

carriers. This is particularly important ^{in linear} charge transfer materials where both chains are

conducting ^with carriers of opposite sign [10]. ^It

allows the investigation of the relative conductivity

contributions of the two chains and in the ^case of metal-insulator transitions provide information about which chain is predominantly ^involved.

The thermopower ^{was measured in an} apparatus which allows simultaneous measurement of four

probe conductivity. ^The apparatus is described in detail elsewhere [11]. ^The temperature gradient ^is

established through the pressure medium, ^{in this}

case isopentane. The pressure ^was measured with a

manganin ^strain gauge, but often the pressure depen-

dence of the conductivity ^of TTF-TCNQ ^{served as a}

very good pressure gauge.

In figure ^{1 we show the} conductivity and thermo- power for TTF-TCNQ ^{measured at room} tempera-

ture 291 K as a function of _pressure. The conducti-

vity ^{is in} very good agreement ^with previous ^measu-

rements.

The absolute thermopower ^{was measured on four}

different samples ^at separate ^{times to} study ^different

pressure regimes ^as

function of temperature. ^In

Fig. ^1.

a) Normalized conductivity ^and b) absolute ther- mopower

function of _pressure at

temperature;

solid line is guide ^to the eye only.

figure ^{one, two} samples ^are plotted up ^to 20 kbar, however, ^all samples measured fell within the limits of those shown.

The room temperature thermopower ^falls quite rapidly with pressure attaining one-third of its ambient pressure value by ^{20 kbar. If} TTF-TCNQ ^{were a} simple ^carrier system ^or if the relative conductivities of the two carriers remained the same this would

imply ^a change ^{in bandwidth of a factor of 3. The} thermopower ^{of a} one-dimensional material with ^a

tight binding ^{band is} given by

where _p is the number of conduction electrons per

molecule, ^{W is the bandwidth and}

^{is the} scattering

time. The first term clearly ^{varies as the} reciprocal

bandwidth as long ^{as there is no} strong ^variation of _p. The second term involves an energy derivative of the scattering time and has been estimated to be

as significant ^{as the first term} [10]. ^{However, as far}

as the metallic behaviour is concerned at room tempe-

rature for the elastic scattering T ^{can be assumed as} having only

moderate variation with

(kB T/EF 1).

Its energy dependence ^makes

similar contribution to S as the band term : S oc (4 t) - ’, where t is the longi-

tudinal transfer integral. ^{Thus S}

^{W - 1.}

For two conducting chains the thermopower ^is

the conductivity weighted average ^or

We would

like to explore how much of the observed change ⁱⁿ thermopower ^can be accounted for by ^{the known} changes ⁱⁿ charge transfer between chains and the bandwidth change ^{as a} function of pressure. Within tight binding theory ^{we can estimate}

the _pressure dependence ^{of the} thermopower ^{of each}

chain by using equation (1). Although ^the particular

form of the energy dependence ^{of the} scattering ^rate

is important for this calculation it should typically

vary ^as the characteristic energy for the system (sF)

and hence as the « band term » or first term in _equa- tion (1). ^Conwell [12] ^has argued ^{that for one} phonon

processes the scattering ^term is in fact identical to the band term. For two phonon (or ^libron processes)

it has the same dependence ^on bandwidth and slower

dependence ^on charge ^transfer [13, 12].

The neutron scattering ^data [14] ^shows

charge transfer of 0.59 electron/molecule ^{at one bar and}

0.616 electron/molecule ^{at 5 kbar or}

and confirms [15] ^an average value of 0.90 %/kbar up

to 14.5 kbar. The change ⁱⁿ the bandwidth can be

calculated from the compressibility ^and theoretical

values for the transfer integral ^{as a function of lattice}

constant [16,

171.

^This yields variations for a ln W

of 2-3 %/kbar ^{for the} TCNQ chain. A less reliable method is fitting the pressure dependence ^{of the}

Drude edge ^which gives OP

¹ %/kbar [ 18].

The initial dependence ^of thermo power ^on pres-

sure can be obtained for each chain by taking ^the logarithmic derivative of equation (1), ^with respect

to pressure. ^We take the band term as representing

the functional dependence of the total thermopower

on p and W. This will produce ^{the most} rapid ^varia-

tion for each chain. Using ^{an initial} charge density

of _p

0.59 electron/molecule ^{we have :}

The charge ^{transfer term then} reliably gives ^a

decrease of 2.3 %/kbar. ^The bandwidth contribution is from - 1 to - 3 % kbar and the total reduction from these effects is

(3-5) %/kbar. ^{From the} experimental ^{data of} figure ¹ the initial pressure

dependence ^is

10 %/kbar. The conclusion is that a uniform change ^{of the} properties ^{of the two}

chains is not sufficiently rapid ^to explain ^{the obser-}

vations in the low pressure domain.

The conductivity of the TTF chain must be increas-

ing ^{relative to that on the} TCNQ chain. Since

the signs ^{of the} thermopowers ^{of the two chains are} opposite ^from equation (1). ^The TCNQ chain domi- nates the conductivity ^{at room} temperature ^and atmospheric pressure. As pressure increases the con-

ductivity of the TTF chain becomes relatively ^more important. ^{This same} conclusion was reached from

previous ^studies of the Hall effect in TTF-TCNQ [9].

One theory postulated before these experiments

were done attempted ^to predict ^the thermopower

a

function of pressure in ^terms of

electron-electron

scattering ^model. However, ^the model could not forsee the large ^relative conductivity change ^between

the two chains which dominate the _pressure depen-

dence [J9].

If we look at the change ⁱⁿ thermopower up ^to 8 kbar

that it has been reduced by ⁵⁰ %.

About 30 % ^{of this} change ^{is due to} the bandwidth and charge ^{transfer term} already discussed. Previous estimates of the relative conductivity ^at atmospheric

pressure show O’Q 1’-1 ^{5 Op.} Assuming that the thermo- powers of SQ ^and SF ^are comparable the ratio of the conductivities at 8 kbar is UQ/ CF - ^{2.5. If the change}

were entirely associated with the more rapid ^increase

in bandwidth of TTF compared ^with TCNQ ^the

ratio would be

smaller due to the smaller TTF

thermopower. ^{A similar} analysis of the Hall effect data also gives - ^{2 at 8 kbar} [9].

Fig. ^2.

^Absolute thermopower

^{function of} tempera-

ture for several values of pressure. (A - 12.5 kbar, e - ⁸ kbar,

x -

4.6 kbar, D - ^2.5 kbar, 0 -1 kbar).

The temperature dependence ^{of the} thermopower

at various _pressures is shown in figure ^{2. In the} temperature region ^{above 60 K} the behaviour is

quite ^{similar at all} pressures shown. At high tempe-

rature (from ^{100 K-300} K) ^the thermopower ^{is small}

and approximately linear in temperature indicating

the metallic state. Between 100 K-60 K there are

deviations from this simple behaviour which _pro-

bably arise from the competition between the sign

of the thermopower ^{of the two} chains. The relative conductivities are changing ^with temperature ^with the TTF chain becoming ^more important. ^This change in relative conductivity may arise simply ^from

different temperature dependent mobilities or from fluctuation effects preceding the metal-insulator transition [20]. Either the thermopower ^or the conduc-

tivity ^{on the} TCNQ ^{chain is} decreasing ^with respect

to the TTF chain.

At low temperatures (below ²⁰ K) ^the rapid ^increase

in the thermopower ^to large values indicates the low temperature insulating ^{state. Note} that the low tem-

perature sign ^is negative for all these pressures. Both

signs ^{have been} previously ^{found in} samples ^from

different sources [21].

The most interesting temperature region is that of the cascade of phase transitions from - 60 K to

-

20 K [7]. Figure ^{3 shows}

results in this transi-

tion region ^{in more} detail. At 1 kbar the thermo-

power is similar to what has been observed at 1 atm.

1170

Fig. ^3.

^Absolute thermopower

^{function of} tempera-

ture in the region ^{of the} metal-insulator transition for several pressures.

[21 ]. ^{At 1 atm. the} thermopower is flat with

value

-

+ 30 pV/K ^{between 50 K and 40 K and then} monotonically ^{rises to} high values in either positive

or negative

depending ^on sample origin. ^In

the present ^case the o flat » region ^{is from 43 K to}

33 K and is followed by

positive dip before it becomes

strongly negative ^and semiconducting ^{at - 20 K.}

The usual interpretation of the ambient _pressure

thermopower ^{is that there is an} upper transition

(TH - ^{53 K) which} predominantly effects the TCNQ

chain [10]. ^{As we have seen the} TCNQ ^{chain has a} negative thermopower and when these carriers are

frozen out by ^the opening ^{of a} gap the thermopower quickly ^becomes

positive. Between 50 K and 40 K the conductivity ^{is dominated} by ^carriers

the TTF chain which has positive thermopower.

Finally ^{at - 40 K}

^{well defined gap} develops ^on

the TTF chain and the material is a traditional semi- conductor. The thermopower then becomes large

and its sign ^is determined by ^what impurities ^are present ^to slightly shift the Fermi _energy closer to the valence or conduction band. ESR susceptibility

measurements have led to similar conclusions con-

cerning the claims involved in the transitions [22].

This picture ^{is not what one} finds in the inter-

pretation ^{of the} X-ray ^{and neutron} scatterings ^stu-

dies. The model of Bak and Emery suggests ^{that the} 53 K transition involves a distortion associated with

one order parameter (usually ^and probably ^mista- kenly associated with one chain-TCNQ) ^{with trans-}

verse order period ²

^A second transition at 49 K associated ^{with a} second order parameter ^{on the}

TTF chain with incommensurate transverse perio- dicity ^{and a} third transition at 38 K in which both order parameters ^{lock at a} commensurate value of wavevector transverse to the conducting ^axis namely

4 a [23]. Transport ^and susceptibility studies tend to show electronic _gaps forming ^at only the first and

last transitions although ^{there is}

^small anomaly

at 49 K in the resistivity [24].

For the present

^will stay with the conventional

interpretation ^{of the} thermopower. ^As pressure is increased the temperature ^{of the} upper transition remains practically ^constant. Below this transition however, ^the thermopower ^becomes increasingly ^more negative ^as pressure is increased, crossing ^{zero at}

-

7 kbar. This implies that the carriers are changing

from predominantly ^{TTF at low} pressure ^to predo- minantly TCNQ ^{at 12.5} kbar. If the _upper transition

were

previously associated with TCNQ ^{at 1} atm., ^at 12.5 kbar it must be associated with TTF.

A consequence of this model is that it would be necessary for the lower transition of the TTF chains to « pass through » ^the TCNQ chain transition. The

problem is that such

picture would involve the

crossing ^{of two} phase transition lines with four

phases meeting ^at

point ⁱⁿ P-T space. This is forbidden for a one component system by ^{the Gibbs} phase ^rule [25]. ^The only tenable solution is that the

simple decomposition of the transitions as being

associate with each chain is incorrect. The order parameter ^{for the} upper transition must involve distortions and _gaps

both conducting ^{chains but}

not equally. ^{At low} pressure the TCNQ ^is mainly

effected and at high pressure the TTF is mainly

effected.

Again ^{there is}

evidence of an intermediate transition from the thermoelectric _power at different pressures. The lower transition is apparent ^{in the} data shown at 1 kbar and at 12.5 kbar. For _many of the other pressures it is clear that immediately ^below

the _upper transition the compound ^{is not} insulating

but becomes insulating (from ^the thermopower) ^over

a

temperature region which extends over 20 K without _any obvious transitions. The thermopower

in the semiconducting ^{state is} given approximately by

where we merely ^{wish to} point ^{out the} simplest

variation with gap ^A and temperature. By analogy

with the resistivity, ^{if we wish to} look for the _pre-

sence of a phase transition, ^{we must look for} rapid changes ^{of A with} temperature. ^For resistivity ^{this is}

done by Y looking g ^at O(IIT) ðlnR ^{For the} thermo power ^the

a(1/T) ^p

analogous g derivative is as

O(IIT)

Since we have taken both resistivity and thermo- power measurement

each sample ^{at each} pressure

we can plot ^the phase diagram ^{as obtained} by ^the approximate derivative of the two measured quanti-

ties. The phase diagram which results is shown in

figure ^{4. The} resistively ^{defined curve is in} good

agreement ^with previous measurements. The thermo-

power defined curve is similar except ^{for the} region

between 2.5 kbar and 8 kbar where no lower transi-

Fig. ^4.

^Phase diagram of TTF-TCNQ ^{obtained from the} thermopower ^and resistivity anomalies. Circles

from

analysis ^of resistivity ^data. Squares

^from thermopower

data.

tion has been observed as a peak ⁱⁿ .O(IIT) . ^This

is the _pressure region in which the _upper transition is crossing ^{over from} predominantly TCNQ ^to pre-

dominantly ^{TTF and hence at these} pressures the transition affects both chains comparably. ^{The non-}

observation of the lower transition _may simply ^be

an experimental artifact due to the fact that neither chain dominates the transport. ^On the other hand the fact that the _upper transition is comparable

both chains _may change ^{the nature} of the lower transition which is still observed in resistivity.

Recent neutron scattering studies have revealed a

quite complicated phase diagram ^for pressures up ^to 5 kbar [26]. These studies indicate that the transition

temperature associated with the TTF chains and

longitudinally polarized CDW increases with pres-

sure. This is not in disagreement ^with thermopower

measurements presented here. Below 54 K the beha- viour of the absolute thermopower in the range 3.5-8 kbar does not allow

accurate determination of the lower transition as already mentioned. Addi-

tionally they ^{find that at 5} kbar there is a single phase

transition in possible agreement with the thermo- power measurements. The resistively determined lower

phase transition is not seen.

The suggestion ^was made that at 5 kbar TTF-

TCNQ ^is very similar to TSeF-TCNQ ^both having

the same value of 2 k and

single ^{neutron deter-}

mined phase transition. While our data suggests that the conductivities of both chains are comparable

at the transition temperature ^{for the two} compounds,

the thermopowers ^measured through ^this region ^are quite different. TSeF-TCNQ ^{shows a} large gap and hence large thermopower forming directly ^{below the}

transition. TTF-TCNQ ^{retains a small} thermopower

for - 20 K below the transition.

In conclusion the thermopower measurements in the metallic state show that the conductivity ^{of the}

TTF chain increases faster with _pressure than that of the TCNQ. At ambient conditions the ratios are

aQl aF - ^{5 while at 8} kbar the ratio is O’Q/O’F -...; ^2.5.

In the region of the metal-insulator transitions the effect of _pressure is to change ^the upper transition from predominantly ^{on the} TCNQ ^{chain at 1 atmo-} sphere ^to predominantly

^{the TTF chain at 10 kbar.}

This implies ^{a more} complicated phase diagram ^and requires ^{the order} parameters ^to involve distortions

on both chains. The usual simplified picture ^of

Peierls distortions

each chain associated with different transition temperatures ^{is no} longer appro-

priate.

We would like to acknowledge useful discussions with S. Barigid, ^M. Weger, ^R. Comes, ^S. Megtert,

J. P. Pouget, ^E. Conwell and P. Seiden.

References

[1] JÉROME, ^{D. and} WEGER, M., Chemistry ^and Physics of One-Dimensional Metals, ^{H. J.} Keller editor

(Plenum ^{Press, N.} Y.) ^1977.

[2] JÉROME, D., Proceedings NATO Advanced Study ^Insti-

tute

Low Dimensional Solids, Portugal, 1979,

edited by L. Alcacer (D. Reidel, ^N. Y.) ^1980.

[3] COOPER, ^J. R., WEGER, M., JÉROME, D., ^LE FUR, D., BECHGAARD, K., BLOCH, A. N. and COWAN, D. O., Solid State Commun. 19 (1976) ^749.

[4] DENOYER, F., COMÈS, R., GARITO, ^{A. F. and} HEEGER,

A. J., Phys. Rev. Lett. 35 (1975) 445 ;

COMÈS, R., SHAPIRO, ^S. M., SHIRANE, G., GARITO,

A. F. and HEEGER, ^A. J., Phys. ^{Rev. Lett. 35} (1975) 1518 ;

WEYL, C., ENGLER, ^E. M., BECHGAARD, K., JEHANNO,

G. and ETEMAD, S., Solid State Commun. 19

(1976) ^925.

[5] FRIEND, ^R. H., MILJAK, ^{M. and} JÉROME, D., Phys.

Rev. Lett. 40 (1978) ^1048.

[6] JÉROME, D., MAZAUD, A., RIBAULT, M. and BECH- GAARD, K., ^J. Physique-Lett. ⁴¹ (1980) ^L-95.

[7] FERRARIS, ^J. P., COWAN, D. O., WALATKA, V. V. and

PERLSTEIN, ^J. H., J. Am. Chem. Soc. 95 (1973) 948;

COLEMAN, ^L. B., COHEN, ^M. J., SANDMAN, ^D. J., YAMAGISHI, ^F. G., GARITO, A. F. and HEEGER,

A. J., Solid State Commun. 12 (1973) 1125 ; Highly Conducting One-dimensional Solids, ^edited by

J. T. Devreese, R. P. Evrard and V. E. Van Doren

(Plenum Press, ^N. Y.) ^1979.

[8] ^FINCHER Jr., C. R. and SHIRANE, G., COMÈS, ^{R. and} GARITO, ^A. F., Phys. ^{Rev. B 21} (1980) ^5424.

[9] COOPER, ^J. R., MILJAK, M., DELPLANQUE, G., JÉROME, D., WEGER, M., FABRE, J. M. and GIRAL, L.,

J. Physique ³⁸ (1977) ^1097.

1172

[10] CHAIKIN, ^P. M., KWAK, ^J. F., GREENE, ^R. L., ETEMAD, S. and ENGLER, E., ^{Solid State} Commun. 19

(1976) 1201 ;

CHAIKIN, P. M., GREENE, ^R. L., ETEMAD, ^{S. and} ENGLER, E., Phys. ^{Rev. B 13} (1976) ^1627.

[11] CHAIKIN, ^P. M., WEYL, ^{C. and} JÉROME, D., ^{Rev. Sci.}

Instrum. 52 (1981) ^1397.

[12] CONWELL, ^E. M., Phys. ^{Rev. B 19} (1979) 2409, ^also CONWELL, ^E. M., ^{Proc. NATO Advanced} Study Institute

on

Low Dimensional Solids, Portugal 1979, ^edited by L. Alcacer (D. Reidel, ^N. Y.) ^{1980 and CONWELL}

E. M., Phys. ^{Rev. B 22} (1980) ^1761.

[13] GUTFREUND, ^{H. and} WEGER, M., Phys. ^{Rev. B 16} (1977) 1753 ;

GUTFREUND, H., WEGER, ^{M. and} KAVCH, N., ^Solid State Commun. 27 (1978) 53 ;

WEGER, M., Proc. NATO Advanced Summer Institute

of Low Dimensional Solids, Portugal, 1979, ^edited by ^{L. Alcacer} (D. Reidel, ^N. Y.) ^1980.

[14] MEGTERT, S., COMES, R., VETTIER, C., PYNN, ^{R. and} GARITO, ^A. F., ^Solid State Commun. 31 (1979)

977.

[15] MEGTERT, S., COMÈS, R., VETTIER, C., PYNN, ^{R. and} GARITO, ^A. F., ^Solid State Commun. 37 (1981)

875.

[16] DEBRAY, D., MILLET, R., JÉROME, D., BARI0160I0106, S., FABRE, ^{J. M. and} GIRAL, L., ^J. Physique ^{Lett. 38} (1977) ^L-227-231.

[17] ^{COOPER, J. R.,} Phys. ^{Rev. B 19} (1979) ^2404.

[18] ^WELBER, B., SEIDEN, ^P. E., GRANT, P. M., Phys. ^Rev.

B 18 (1978) ^2692.

[19] ^SEIDEN, P. E. and GRANT, ^P. M., ^Proc. of the ^Inter-

national Conference

Quasi One-Dimensional Con- ductors I » (Dubrovnik), ^edited by ^S. Bari0161i0106,

A. Bjeli0161, ^{J. R.} Cooper and B. Leonti0107 (Springer- Verlag, Berlin, Heidelberg, ^N. Y.) ^1979.

[20] HORN, ^{P. M. and} RIMAI, D., Phys. ^{Rev. Lett. 36} (1976)

809.

[21] ^{CHAIKIN, P.} M., KWAK, ^J. F., JONES, ^T. E., GARITO,

A. F. and HEEGER, ^A. J., Phys. Rev. Lett. 31

(1973) 601.

[22] TOMKIEWICZ, Y., ^Proc. of ^NATO Advanced Summer Institute of Low Dimensional Solids, Portugal, 1979, ^edited by L. Alcacer (D. Reidel, ^N. Y.)

1980.

[23] ^{PER BAK and} EMERY, ^V. J., Phys. Rev. Lett. 36 (1976)

978.

[24] CHU, ^C. W., HARPER, ^{J. M.} E., GEBALLE, ^{T. H. and} GREENE, ^R. L., Phys. Rev. Lett. 31 (1973) ^1491.

[25] ^{LANDAU and} LIFSHITZ, Statistical Physics (Pergamon Press, ^N. Y.) 1969, p. 275.

[26] MEGTERT, S., COMÈS, R., PYNN, R., VETTIER, ^{C. and} GARITO, ^A. F., Summer Institute of ^{Low Dimen-}

sional Solids, Portugal, 1979, ^edited by ^{L. Alcacer}

(D. Reidel, ^N. Y.) ^1980.