Descriptive analysis of the crystal structure of the 1-D semiconducting TCNQ salt : TEA(TCNQ)2, as a function of temperature. - I. Intermolecular distortions of the conducting TCNQ columns

HAL Id: jpa-00209986

https://hal.archives-ouvertes.fr/jpa-00209986

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Descriptive analysis of the crystal structure of the 1-D semiconducting TCNQ salt : TEA(TCNQ)2, as a function of temperature. - I. Intermolecular distortions

of the conducting TCNQ columns

J.P. Farges

To cite this version:

J.P. Farges. Descriptive analysis of the crystal structure of the 1-D semiconducting TCNQ salt :

TEA(TCNQ)2, as a function of temperature. - I. Intermolecular distortions of the conducting TCNQ

columns. Journal de Physique, 1985, 46 (3), pp.465-472. �10.1051/jphys:01985004603046500�. �jpa-

00209986�

Descriptive analysis ^{of the} crystal ^{structure of the 1-D} semiconducting ^TCNQ

salt : TEA(TCNQ)2, ^{as a function of} temperature.

I. Intermolecular distortions of the conducting ^{TCNQ columns}

J. P. Farges

Laboratoire de Biophysique, Université de Nice-Valrose, 06034 Nice Cedex, ^France (Reçu ^{le 28 mai} 1984, révisé le 16 octobre, accepté ^{le 6 novembre} 1984 )

Résumé.

On montre qu’avec ^des approximations raisonnables, ^{la structure} d’une colonne conductrice de TCNQ peut être caractérisée au moyen de six paramètres. ^{Deux de ces} paramètres définissent la colonne régulière équi- valente, ^{et les} quatre ^{suivants se} rapportent ^aux distorsions intermoléculaires. Deux des paramètres de distorsion sont associés à une dimérisation de la colonne, ^{et les deux autres à une} tétramérisation.

On fait ensuite apparaître ^{comme un fait} expérimental que seulement deux de ^ces six paramètres varient d’une

façon significative ^{avec la} température. ^Le premier ^décrit simplement ^la dilatation thermique normale de la colonne.

Le second est associé à une composante de la tétramérisation perpendiculaire à l’axe de la colonne.

Les implications possibles ^{de ces résultats sur les} propriétés semiconductrices du matériau sont également

discutées.

Une analyse complémentaire de la distribution des charges ^sur les molécules d’une colonne conductrice de

TCNQ ^sera développée ^{dans un} prochain ^article.

Abstract

Within reasonable approximations, ^{the structure of a} conducting TCNQ column is characterized

by ^six parameters. ^Two parameters define the equivalent regular column, ^{and four} parameters ^{refer to the inter-} molecular distortions. Two of the distortional parameters ^are associated with a dimerization in the column, ^while

the other two parameters ^are associated with a tetramerization.

It is then shown, ^{as an} experimental fact, ^that only ^two of these six parameters ^are significantly temperature

dependent. ^{The first one} simply ^accounts for the usual thermal expansion of the column. The second one is asso-

ciated with a component of the tetramerization perpendicular ^to the column axis.

The possible implications ^{of these} findings ^with respect ^{to the} semiconducting properties ^{of the material are also}

discussed.

In complement ^{to the} present article, ^{a second one will concern an} analysis ^{of the} charge distribution on the

TCNQ molecules of a conducting ^column.

Classification

Physics ^Abstracts

61.50L - 72.80L

Introduction.

This study ^is concerned with the material triethyl-

ammonium (tetracyano-7,7,8,8,p-quinodimethane)2,

or TEA(TCNQ)2, ^a material for which the solid state properties, ^and particularly the electrical _pro-

perties, ^{have been} quite extensively investigated ⁱⁿ

the past [1]. However, ⁱⁿ spite ^{of the} progressive

accumulation of various and detailed experimental data, the basic problem ^{of how} charge transport proceeds ^{in this} semiconducting material is still _open.

This situation is similar for many other TCNQ ^salts

of crucial interest. The difficulty ^resides primarily ⁱⁿ

the lack of information about the crystal ^structures

which are usually ^known only ^{at room} temperature.

As these structures are highly deformable and even

unstable, they should be a priori expected ^to undergo complex modifications when the temperature ^is varied,

which in turn may significantly affect the physical properties of the material.

An invaluable contribution to this problem ^has

been provided recently by ^{Filhol and Thomas} [2].

These authors have reported, mainly ^{ffom their own} experimental work, ^{a detailed} compilation ^{of accurate} crystal ^{data for} TEA(TCNQ)2 ^{at six} temperatures from 40 K to 345 K [3]. ^Their work, currently unique

in this field, greatly reinforces the interest in this

particular ^material. Benefiting from these data, ^the present paper develops ^a descriptive analysis ^{of the}

intermolecular distortions of the TCNQ ^{columns in} TEA(TCNQ)2.

TEA(TCNQ)2 ^{is a} member of the extended class

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004603046500

466

of the TCNQ ^{salts, a class of} crystalline organic

materials with potentially high electrical conducti-

vities [4].

Basically, ^the crystal ^{structure of} these salts consists of a highly ^selective aggregation ^{of the} planar TCNQ

molecules into parallel ^{and well} separated ^molecular

columns. In the _process of salt formation, ^the TCNQ

molecules are partially negatively charged, ^{the mean} charge per molecule being ^a function of the stoichio-

metry of the material. The counter-ions, for instance TEA+ in TEA(TCNQ)2, occupy regular positions

between the TCNQ columns in the lattice.

Within each column, ^a strong ^n-orbital overlap

results from the ability ^{of the} TCNQ ^{molecules to}

stack closely plane ^to plane. The columnar axis defines in the crystal ^a special direction in which

charge transport, and hence electrical conduction,

are greatly facilitated. As a consequence, the TCNQ

salts also exhibit a considerable anisotropy ^{in their}

electrical properties, ^{to such an extent that} they ^can

be regarded ^as nearly one-dimensional (1-D) systems.

The best, metal-like conductors of the class are

materials in which the conducting columns have a

regular structure, ^{at least at room} temperature (the overlap ^{between one} TCNQ molecule and the next in the column being large ^and unchanged by ^trans- lation).

For most of the TCNQ salts, however, ^columnar distortions are present ^{at room} temperature, ^cor-

responding ^{to a} periodical modulation of the mole- cular overlap. ^{In this case} the electrical conductivity

is lower and it exhibits the activated character of a

semiconductor.

TEA(TCNQ)2 ^{has a} tetramerized columnar struc- ture and is an example of the second category ^{of salts.}

However, the deviations in the actual columns from

a regular ^{structure are} small in this salt. The electrical

conductivity ^{is still} appreciable in the direction of the TCNQ columns, ^{with a room} temperature ^value

approaching 10 K2 - I cm - ’. In addition, the activa- tion _energy is low, of the order of 0.1 eV, ^{but there} is a significant variation between 60 K and 400 K [5].

It is conceivable that the variation of the activation energy is due, ^{at least in} part, ^to structural changes

in the conducting ^{columns; this} hypothesis ^{will be}

examined in the last part ^{of this} paper.

1. General column considerations, ^and approximations.

From the crystal ^{data of Filhol and Thomas}

on TEA(TCNQ)2 [2], ^the following salient features of a TCNQ column will be outlined :

1) ^{We first assume that the} TCNQ ^monomers constituting the column are all planar (with ^a D2h symmetry), ^{all identical} (whatever their electronic

charge), ^{and all} parallel. ^{The out of} plane ^deviations

of the atoms are ignored ^{and we} simply identify ^the

mean plane ^{of the} quinonoid ring [2] with the mole- cular plane ^{of the monomer.}

2) ^The TCNQ ^{monomers first interact} strongly ⁱⁿ pairs ^to form identical dimers, basic molecular units of the column.

3) ^{The dimers then interact more} loosely ^{to form} irregular ^{tetramers which are} characteristic of the distortion of the TCNQ columns in the material.

The molecular overlap ^between any TCNQ ^mono-

mer and the next one in the column will generally

involve three parameters. One is the interplanar

distance D (> 0) ^measured along the normal N to the molecular plane. ^{The other two are the} longitu-

dinal and transverse molecular shifts d and t (> ⁰

or 0) ^defined respectively along ^{the two} orthogonal

axes L and T of the molecular plane, ^L being ^the elongation axis of the molecule and T its transverse axis (Fig. 1).

Fig. ^1.

^A schematic view of the TCNQ monomer, with the molecular plane and the three molecular axes.

In the first stage ^{of the} present analysis, it has been established from the experimental ^{data that the axis}

of the column, ^{the axis of the dimer} (joining ^the symmetry ^{centres of the two} monomers), ^{as well as}

the axis of the tetramer (joining ^the symmetry ^centres of the two dimers), ^{were all out} of the normal-molecular

plane (N, L) by ^{less than} 40, ^{at all} temperatures.

Hence, ^a good approximation ^{is to} identify ^these

three axes with their projections ^on the normal- molecular plane, thereby gaining ^a considerable

simplification ^{of the} analysis. ^The latter, thus reduced to a two-dimensional _one, ignores ⁱⁿ consequence the

transverse shifts ^t (by assuming ^that they ^{have a zero} value) ^and only considers the two last parameters ^D and d.

2. Definition of the structural parameters ^{of a column.}

Starting with the dimer as the basic unit (also ^the strongest ^molecular association) ^{in the} column, ^we

first define the two intradimer parameters D 1 (// N)

and d1 (#’L), ^{as in this} picture t 1

0(//T) (Fig. 2).

A dimerized column, ^{viewed as a} regular ^succession

of identical dimers, requires ^two additional interdimer

parameters D1 ^{+ L1} (with ^d > 0) and d1 ^{+ 6} (Fig. 2).

Fig. ^2.

Formation of a dimerized column. Definition of the intradimer and interdimer parameters, and of the tilt

angle ^0.

The mean parameters ^{of the column are then}

In figure 2, ^z is the axis of the column and y ^{is an} orthogonal ^axis. They ^are both in the plane (N, L)

and defined by :

For a regular column, ^{A = 6}

^0.

A tetramerized column _may be viewed as a dimerized

one in which one dimer in two is shifted by ^{A’ /,z}

and by 6’/y (Fig. 3a).

The column is then a regular alternation of unshifted

dimers, ^{or dimers} I, and of shifted dimers, ^{or dimers} II,

the centres of which are related by (considering only

the adjacent neighbours) :

(Fig. 3a).

The resulting periodicity in the column is _c, defined

by ^{c cos 0=4} Do, ^{and the} repeat ^{unit now consists} of a tetramer formed by ^{one dimer I and one dimer} II, taken in this order in the z direction. The axis of the tetramer is z’, ^{with tan} (z’, z)

Y(I-li)/Z(I-ii).

The mean parameters Do ^and do ^{of the column} (as

well as the intradimer parameters D1 ^and d1) ^{are left} unchanged. The interdimer parameters ^{are now} D2 and d2 ^{within a tetramer and} D3 ^and d3 ^between adjacent ^tetramers (Fig. 3b), ^with D2, D3 > D1, ^but

the mean interdimer parameters ^are unchanged :

It should be already ^{noted as an} experimental ^fact

that both d1 and d2 ^are positive whereas d3 ^is negative

in TEA(TCNQ)2, ^{as shown in} figure ^{3b. It is} clear, then, ^{from this} figure, ^that if 6’ decreases (d’ being

Fig. ^3.

Formation of a tetramerized column. a) ^Defini-

tion of the distortion parameters ^{d’ and 6’.} b) ^Definition

of the intermolecular distances and shifts. ^{The four mono-}

mers in a tetramer are denoted A, B ^{in dimer I, and A, B}

in dimer II, ^as in reference [2]. ^{S and S’ are two inversion}

centres in the column.

unchanged), D3, d2 and I d3 I also decrease whereas

D2 increases. More specifically, considering figures ^3a

and 3b, ^we get ^the following geometrical ^relation- ships :

The Z-axis of the tetramerized column (which ^is

also one of the crystallographic ^{axes of the} material)

is simply ^{the z-axis of the} dimerized column shifted

by 6’/2 ⁱⁿ the y direction. Thus, (Z, N) = (z, N)

^0.

On the Z-axis, ^{the centres} S and S’ of the two respec- tive segments ^{I-II and 11-1 are the} two centres of symmetry of the column (Fig. 3b).

For a dimerized column, ^d’

^{6’ = 0.}

Instead of the two parameters ^{A and d defined} above, ^{it is} preferable ^{to introduce two} dimensionless parameters ^{K and K’} free from ^thermal expansion effects. They ^are respectively ^and equivalently ^defined by :

with

In summary, ^a quantitative description ^{of the}

temperature dependence ^{of the columnar structure}

may ^now be developed (as ^a two-dimensional analysis) by considering ^six parameters :

-

the mean parameters Do ^and do ^{of the actual}

column, ^i.e. the parameters defining ^the equivalent

regular column,

468

-

the two dimerization parameters ^{K and} 6,

-

the two tetramerization parameters ^{K’ and 6’.}

The two dimerization parameters ^are defined with respect ^to the molecular axes L and N, ^{and the two} tetramerization parameters ^are defined with respect

to the columnar axes y and ^z.

These six parameters entirely ^{determine the struc-}

ral properties ^{of a} TCNQ column, ^at any temperature, by ^{means of the} following ^{set of} equations :

3. Numerical analysis ^of the structural parameters.

The values of the above six parameters may be obtained at each temperature ^{from the} data of Filhol and Thomas, by ^{means of the} following equivalent

definitions :

All the distances and angles occurring ^{in these} expres- sions are tabulated in the work of Filhol and Thomas,

for six temperatures :

The numerical results ,are reported ⁱⁿ figure ^4. The,

two parameters ^{K and K’ are} both found to be

remarkably ^{constant from 40 to 345 K.} Additionally,

the two parameters do ^{and 6,} which show only ^a

weak variation with temperature, may also be consi- dered as constants, ^{in view} of their relative _accuracy evaluated to - 1 % (from the estimated standard deviations reported ^{in reference} [3]). These four parameters ^{are shown in} figure 4, normalized to their

mean values, ^{which are :}

A quite distinct behaviour is however observed for the last two parameters Do ^{and 6’, which are found}

to vary significantly ^and regularly ^{with T. In} figure 4, they ^are both shown normalized to their values at 40 K, ^{which are :}

Fig. ^4.

Temperature dependence of the six parameters ^of

a column, defined in the text (the ^{values at two successive} temperatures ^are joined by ^a straight line). Do ^{and 6’ are}

normalized to their values at 40 K (their relative accuracy is + 0.2 %). The four other parameters ^are normalized to their mean values (the relative accuracy for do and 6 is ± ¹ %).

Here, ^a relative accuracy of - 0.2 % is evaluated for both of them.

By allowing only ^{the two} parameters Do ^{and 6’ to}

vary with T, ^and by considering ^{the last four} para- meters as constants, ^we shall be able to reproduce

the details of the columnar structure during its thermal evolution. In the following study (Sect. 4), ^{the mean}

values will be substituted for K, K’, do ^{and 6, whereas} Do and 6’ will be allowed to vary according ^{to the} T-dependence ^{shown in} figure ^4.

Some variation must be allowed to the tilt angle ⁰

which the TCNQ ^monomers make with the columnar axis Z. In the present description, ^{it is} entirely ^attri-

buted to the. T-dependence ^of Do through ^{the equa-}

tion :

Numerically, ^from this relation 0 is found to decrease

slightly from 17.30 at 40 K to 16.50 at 345 K (repro- ducing ^the experimental ^{values of 0 to} better than half ^a degree).

The corresponding change ^{of cos 0} is, however, practically negligible, being much smaller than the

change ^{on 0} (or ^sin 0). ^{From the two} relations :

D1 = 2(1 - K) Do ^and ccosO=4DO, ^it may be

predicted ^that Do, D 1 ^{and c} should have the same

temperature dependence. ^It will be shown in the next

section that this prediction ^is correct, confirming ^the

specific ^role of the basic dimer to impose ^{its own} thermal evolution on the whole column. Do ^{is the} pertinent parameter to account for the thermal

expansion ^{of the column.}

The last T-dependent parameter, 6’, ^{is associated} with a transversal tetramerization of the column.

Thus, it is the only ^relevant parameter involved in the thermal evolution of the distortion of the column, and it decreases smoothly ^{as T increases.}

More specifically, ^{dimers I on one} hand, ^and

dimers II on the other, ^form two identical and parallel

sub-columns. Between the two sub-columns, ^there

exists a constant longitudinal ^shift (K’

const.) ^and

a decreasing transversal shift (6’), ^{as T} increases, such that they progressively penetrate ^into each other.

4. Detailed quantitative description ^{of a} TCNQ

column.

We consider here numerically ^{the set of} equations

obtained at the end of section 2, ^{which in this} approach entirely determines the columnar structure at any temperature.

We introduce in these equations ^{the mean values}

of the parameters K, K’, do ^{and 6,} already reported

in section 3.

We also neglect ^the slight variation of the tilt

angle 0, ^and simply identify ^{it to its mean} value which is : 0

16.9° (sin ⁰

0.291, ^{cos 0}

0.957).

The equations thus become (all ^distances being expressed ⁱⁿ angstrom units, 1 A

10 -10 m) :

Finally, by allowing ^{the last two} parameters Do ^and

6’ to vary according ^{to the} T-dependence ^{shown in} figure ⁴ (it is recalled that Do increases and 6’ decreases with increasing T), the numerical results summarized in figures 5, ^{6 and 7 are obtained.}

Figures ^{5 and 6 refer to the} three intermolecular distances and to the columnar periodicity; figure ⁷

refers to the three intermolecular shifts (the ^numerical

values at two successive temperatures ^are joined by

a straight ^{line on these} figures).

For comparison, figures 5, ^{6 and 7 show the cor-} responding experimental ^{results obtained} by ^Filhol

and Thomas [2], ^{as well as} the actual variations of the two parameters Do ^{and 6’.}

It is clear from these figures that, ⁱⁿ spite ^{of its}

Fig. ^5.

Temperature dependence of the intermolecular distances and of the columnar periodicity c, shown norma-

lized to the mean intermolecular distance Do (experimental

values are joined by straight ^dotted lines, ^{and calculated}

values by straight ^full lines). a) Interdimer distances ^with

6

constant. b) Interdimer distances with 0 allowed to vary.

Fig. ^6.

Temperature dependence of the intermolecular distances and of the columnar periodicity (experimental

values are joined by straight ^dotted lines, and calculated values by straight ^full lines). a) 0

constant, b) 0 ^allowed

to vary. The T-dependence ^{of the} parameter Do ^{is also}

indicated.

470

Fig. ^7.

Temperature dependence of the intermolecular shifts (experimental ^{values are} joined by straight ^dotted lines, ^and calculated values by straight ^full lines). ^The T-dependence ^{of the} parameter 6’ is also indicated.

remarkable simplicity, ^the underlying ^{set of} equa- tions is able to reproduce accurately, ⁱⁿ nearly ^all

aspects, ^the experimental behaviour of the columnar structure in TEA(TCNQ)2 (only ^the transverse mole- cular shifts t being ignored).

This thereby indicates the soundness of the present

analysis.

It may be observed that as T increases, D2 ^increases

more and D3 ^{less than} D1, ^{and that} both d2 and I d3 I

decrease with their difference conserving ^a nearly

constant value. On the basis of the present analyse,

these distortional effects can be conclusively regarded

as the consequence of the decrease in the parameter 6’ as T increases.

Additionally, ^the prediction made in section 3 that Do, D1 ^{and c have the same} T-dependence ^is clearly demonstrated in figures ^{5 and 6} [6].

A slight refinement of the above description may be subsequently ^achieved by considering ^the (small)

variation of the tilt angle 8, which results from the relation : tan 0

0.978 (A)/Do. ^As discussed in section 3, this variation of 0 leaves cos 0 practically unchanged, ^{so that} only ^the intermolecular distances

are modified. The values for D2 ^and D3 ^corrected

for 0 are also shown in figures ^{5 and 6.}

It may be observed that this small correction allows the model to account now for the cross-over of the interdimer distances D2 ^and D3, ^at nearly ^{the same} temperature ^{as in the} experimental results. The

experimental temperature ^{is close to 340} K, just

below the _upper limit (345 K) ^{of the} investigated T-range.

Extrapolation of these results to higher tempera-

tures would imply ^{that the two} interdimer distances

diverge again, rather than stabilize at their identical values at 340 K. For T greater ^{than 340} K, ^we expect D2 ^{to become} greater ^than D3 and their difference to increase with increasing ^T.

A very rough evaluation in the limit T

oo gives 6’IDO ^{0.5 and} D3/D2 ^{0.98, whereas at 40} K, D3/D2

^1.04.

Thus, considering only ^the interdimer distances, ^we

would obtain the following ^scheme (already suggested

in reference [2]) :

Such a scheme is, however, greatly ^obscured by ^the

additional variations of the interdimer longitudinal

shifts d2 ^and d3, ^and transverse shifts t2 ^and t3. ^In fact, ^{it is} firmly established that ^K’

constant :f. 0.5 and 6’ 0 0, ^at any T, hence, ^the ideally ^dimerized

column is never achieved, ^{even at 340 K.}

5. Discussion

1) ^{In the} past, Peierls-like distortional effects, ^intra-

molecular as well as intermolecular effects, ^have

been suggested by various authors in order to explain

several aspects ^{of the} physical properties ^of TEA(TCNQ)2 [7-9, 2].

It is found, here, ^{that the two} parameters ^{K and} 6, associated with the dimerization of the column, ^do

not exhibit _any significant modification between 40 and 345 K. The dimer formation which basically

occurs in this material thus appears ^{as an} intrinsic property, probably attributable to both the parti-

cular 1 : 2 stoichiometry, ^{i.e. one} donor molecule for two acceptor molecules, ^{and to the} complete ^ioniza-

tion of the donor molecules. In this respect, ^the dimerization of the conducting TCNQ ^columns may be regarded ^{as a} permanent ^and highly commensurate intermolecular (4 KF) Peierls-like distortion. It is also questionable whether the subsequent ^tetra-

merization of the column is driven by ^electronic properties ^and may be considered as a (2 KF) ^Peierls-

like distortion. It is shown here that, whatever its

origin is, the tetramerization of the column undergoes only a transversal modification (according ^{to the}

variation of 6’), ^{and not a} longitudinal ^one (K’ = const.).

In this process, the resulting modification of the interdimer distances is a consequence of the non-

vanishing value of the tilt angle ⁰ (Fig. 3).

2) ^{It is now well} established, mainly from the work of Filhol and Thomas [3], ^{that a} structural transition

occurs at 210 K in TEA(TCNQ)2.

From the results summarized in figures 5, ^{6 and} 7,

there is no evidence for an abrupt modification of

the columnar structure, attributable ^to the transition

at 210 K. On the whole, ^{the structure} appears ^to evolve regularly ^{from 40 to 345 K.} However, ^the

variation of the parameter 6’ is found to be signifi- cantly ^{modified at the} transition temperature, ^indi- cating ^{that the} tetramerization of the column evolves

differently below than above 210 K. Both 6’ and its

derivative db’/dT I ^{are shown as} functions of T in

figure ^{8. There is an inherent} uncertainty ⁱⁿ joining

the discrete values of 6’ by ^{a smooth curve.} However,

the fact that I db’/dT is ^{found to reach a well defined}

maximum in the vicinity ^{of the} transition tempera-

ture (and ^most probably ^{in the} T-range : ^{205 ± 15} K)

is quite remarkable and should be noted.

Fig. ^8.

^The interpolated behaviour of 6’, ^{as a function}

of T, ^obtained tentatively ^{from the} calculated discrete values

(dark circles), ^{and the} corresponding derivative db’/dT 1.

3) The electrical as well as the optical properties

of the material [1] unambiguously establish its semi-

conducting ^character.

Referring ^{to the} electrical conductivity u 1 measured in the direction of the columnar axis, ^{the function} (J 1 (1) ^can always be considered to have the general

form :

in which all the thermal evolution of _al is included in the function E1(T), ^{defined as the activation}

energy for conduction (k being ^{the Boltzmann} constant).

In the most general ^{case, the} physical significance

of E1(T) ^is quite complex (involving mobility ^{as well}

as production ^{rates of} carriers). ^{In the} simplest case, it reduces to a constant whose magnitude represents half the semiconducting gap of the material.

Conversely, the function E1(T) ^is obtainable from the function (J1 (T), by :

S,(T) being ^an intermediate function, already ^deter-

mined in the past [5]. S1( T) ^{is found to increase} smoothly from 0.13 eV at 60 K ^to a maximum of 0.22 eV near 220 K, ^{then to} decrease back to 0.1 eV at 400 K. The temperature dependence of 81 ^bears

a close resemblance to the temperature dependence

of the derivative I db’/dT I ⁱⁿ figure ^{8. The function} E1 (T), which results from an integration of the above differential equation (under ^the hypothesis ^that E1

is constant at 0.13 eV below 60 K), is shown in

figure ^9. E1 (T) is found to decrease considerably ^from

a value of 0.13 eV below 80 K to less than 0.025 eV above 350 K: As a consequence, the conductivity ^at

300 K is about 70 times higher ^{than the} conductivity extrapolated from the low-T results, using ^{a constant}

activation _energy of 0.13 eV. There is, ⁱⁿ fact, ^a quasilinear dependence ^of El ^{on 6’,} also shown in

figure ^9.

Fig. ^9.

^The integrated activation energy E1, ^{as a function}

of T (lower scale), ^{and as a} function of 6’ (upper ^scale).

In summary, the present discussion suggests ^{that :} a) ^{there is a} significant correlation between the decrease in the activation _energy El of the electrical

conductivity measured in the column direction, ^and

the decrease in the parameter 6’ associated with the transverse component of the tetramerization of the

columns;

b) both the variations of El ^{and 6’ are} influenced,

at least in part, by the structural transition occurring

in the material at 210 K.

6. Conclusion.

In the present paper, ^a quantitative analysis ^{of the}

temperature dependence ^{of the columnar structure}

in TEA(TCNQ)2 ^was developed ^{on the basis of} recently published experimental ^data.

The aim of this analysis ^{was to} determine the main

structural invariants, ^{the most critical} variables, ^and

472

to achieve a reasonable parametrization ^{of the}

intermolecular distortions of the conducting TCNQ

columns. This is an essential step ^{towards a better}

understanding ^{of the} electrical properties ^{of this} specific ^material.

In spite ^{of the} apparent complexity ^{of the thermal}

evolution of the columnar structure, ^{it was} possible

to reproduce nearly all the details of this evolution

accurately, by ^{means of} extremely simple ^linear expressions, involving only ^{two variable} parameters

(any experimental distance, _except ^{the transverse} shifts t, being reproduced ^to better than 0.02 A at any T).

It is hoped that such an analysis ^will encourage further experimental ^{work on the} crystal structures,

allowing for its extension to other TCNQ ^{salts of}

still greater interest in the future.

The columnar distortion in TEA(TCNQ)2 ^results

from the combination of a strong T-independent

dimerization and a weak T-dependent tetrameriza- tion. The latter, ^which probably governs the T-

dependence ^{of the} activation energy for conduction,

also reflects an influence of the structural transition which occurs at 210 K.

No effort was made here to clarify ^the origin ^{of the}

columnar distortion. An answer to that important question undoubtedly requires consideration of all the structural components ^{of the 3-D material. In} fact, it should explicitly ^{take into account the cations}

TEA +. As discussed in section 5, the cations certainly

have a key ^{role in} the existence of the distortion, ^at least in the dimer formation.

The structural data also indicate that the cations

are strongly disordered in the lattice, ^{and that} they undergo considerable thermal motions as the tempe-

rature is increased [2, 3]. ^In addition, ^{recent NMR} data indicate that the disorder of the cations turns from a static regime ^{to a} dynamic ^{one above the}

structural transition temperature ^{of 210 K} [10].

It would thus be appropriate ^{to look for a correla-}

tion between the motional change ^{of the} cations and the variation of the relevant distortional parameter 6’ which was reported ^{in this} paper.

An analysis of the distribution of negative charges

transferred from the cations onto the conducting TCNQ columns, ^{as a} function of temperature, ^will be presented ^{in a next} paper.

Acknowledgments.

The author wishes to thank A. Filhol and M. Thomas from the Laue-Langevin ^{Institute in} Grenoble, France, for the kind communication of their work, prior ^to publication, and for useful additional comments on

the structural data of TEA(TCNQ)2. ^{B. Pater} (I.L.L.

Grenoble) ^{is also} acknowledged ^{for his} help ^{in the} English translation.

References

[1] ^{For a recent review on} TEA(TCNQ)2, ^see the article

by ^{FARGES, J.} P., ⁱⁿ Physics ^and Chemistry of Low-

Dimensional Solids, Proceedings of ^{the NATO ASI}

in Tomar, Portugal, ²⁶ August-7 September 1979, L. Alcacer Ed. (Dordrecht : Reidel) 1980, p. 223- 232.

[2] FILHOL, ^{A. and} THOMAS, M., ^Acta Cryst. ^{B. 40} (1984)

44.

[3] ^The crystal ^{structure of} TEA(TCNQ)2 ^{at 40 K is a}

neutron structure which was the subject ^{of a} separate publication : FILHOL, A., ZEYEN, ^{C. M.} E., CHENAVAS, P., GAULTIER, ^{J. and} DELHAES, P., Acta Cryst. ^{B 36} (1980) ^2719-2726.

[4] ^{For a recent review on the 1-D} conducting systems ^and the TCNQ salts, ^{see : La} Physique ^{et la Chimie}

des Métaux Synthétiques ^et Organiques, ^Proceed- ings ^{of the} Colloque International du CNRS in Les Arcs, France, 14-18 December 1982, ^J. Phy- sique Colloq. ⁴⁴ (1983) ^C3.

[5] BRAU, ^{A. and} FARGES, ^J. P., Phys. ^Status Solidi (b)

61 (1974) ^257.

[6] ^An inspection ^of figures ^{5 and 6 also} suggests ^an intringuing ^{result :} c/4

D2 ⁺ D3 - D1, ^or 1/cos ^03B8

2(3 K - 1) (giving 03B8

^{0 when K}

0.5).

[7] RICE, ^M. J., Solid State Commun. 25 (1978) ^1083.

[8] CARNEIRO, K., ALMEIDA, ^{M. and} ALCACER, L., ^Solid State Commun. 44 (1982) ^959.

[9] STEIGMEIER, ^E. F., AUDERSET, H., BAERISYL, D., ALMEIDA, ^{M. and} CARNEIRO, K., ^J. Physique Colloq. ⁴⁴ (1983) ^C3-1445.

[10] TRAVERS, ^J. P., DEVREUX, ^{F. and} NECHTSCHEIN, M.,

J. Physique Colloq. ⁴⁴ (1983) ^C3-1295.