Solid State Communications, Vol.5|,No.5, pp.275-279, 1984. Printed in Great Britain.

0038-I098/84 $3.00 + .00 Pergamon Press Ltd.

ANION SIZE AND THE STRUCTURAL PROPERTIES OF (TMTSF)2X SALTS: INTRACOLUMNAR EFFECTS

Thomas J. Kiateomacher

Milton S. Eisenhower Research Center, Applied Physics Laboratory, The Johns Hopkins University, Laurel, Maryland 20707, USA

(Received 2 February 1984 by J. M. Rowell)

It is analytically demonstrated that dimerization of the donor colunm in (TMTSF)2X salts, as Judged by the difference in the separation of molec- ular centers of mass, increases as the size of the counter ion X in- creases. Interestingly, one of the two independent center-of-mass separations appears to be constant across the series of salts, while the second is variable. This differing behavior is traceable to the differ- ent manner in which alternate donor pairs interact with the anion sub- structure. The general increase in the dimerization of the donor column parallels the increasing critical pressure necessary to achieve the superconducting ground state.

Several recent studies I-6 have investigated

the crystal structures of and crystal structure-

physical property relationships for the novel

family of organic superconductors, (TMTSF)2X ,

based on the electron donor tetramethyltetra-

selenafulvalene, TMTSF, and a host of complex

inorganic anions, X. A particular emphasis of

these studies has been the effect of complex

anion sIze and symmetry on both macroscopic

(e.g., cell-axis length) 2-5 and microscopic

(e.g., Interdonor Se...Se interaction dis-

tances 1,2'5 and particular donor-anlon inter-

actlons 2) structural parameters.

Some of these studles 2'5 have considered

the effect of the anion on the structural para-

meters for the zig-zag column of partially

Ionized donor molecules indigenous to all known

salts (see Figure I). In the crystalline motif

(space group symmetry P~) universally adopted by

these materials, all donor molecules have iden-

tical environments, lie in parallel planes by

inversion symmetry, but only alternate spacings

between parallel planes are required to be

equivalent by translational symmetry (a direct

consequence of the presence of the anions).

Previous empirical efforts 2 have focused on the

mean separations between molecular planes (de-

noted herein as DN) , with the most reliable

derivation of these interplanar distances based

solely on the well-determlned Be atom coordi-

nates. As can be seen in Table 1 (and else- where), 2 the difference in mean separation

between alternating sets of donors (denoted

~(D@) in Table I) is small (ca___. 0.01 - O.03A)

and correlation with anion slze 2 is hampered by

the fact that 6(D@) is of the same order of

magnitude as the deviation of individual Se

atoms from the mean plane. Part of the reason

for considering the variation of 8(D@) with

anion size stems from the theoretical work of

Emery, Bruinsma and Barlslc, 6 who noted that the

degree of dimerlzation of the donor column can

be taken as a measure of the coupling constant

g3 for electron-electron umklapp scattering and

should be correlatable with the critical pres-

sure necessary for the achievement of the super-

conducting ground state. 7 In this report, empirical relationships are

investigated for two fundamental structural

parameters for the donor column in these salts:

the angle between the normal to the mean plane

of Be atoms and the stacking axis (designated

INn) and the distance between molecular centers

of~mass along the stacking axis (designated

AMa). It will be shown that ~N a is a slgnifi-

ca~t variable of anion size - i~creasing as the

anion size increases, and that one of the two

independent values of AM a is effectively con-

stant, while the second ~f these values is

variable - also significantly increasing as the

aulon size increases.

For various reasons, computations were

carried out within an orthogonal coordinate

system defined by the a%es ~, b" and c* (this is

the same axis system commonly employed in opti-

cal studles 8 on these salts). Furthermore, all

derived quantities were based solely on Se atom

coordinates. Since all donor planes are paral-

lel, only a single mean plane calculation per

salt needed to be done to give ~N a. However,

the calculation of the two independent values

for AM a required center-of-mass coordinates for

three ~onors (with original coordinates (x,y,z)

- molecule A of Figure I; (-x,l-y,l-z) - mole-

cule B of Figure I; and (l-x,l-y,l-z) - molecule

C of Figure I). It is also to be noted that the

center-of-mass coordinates for these donor

molecules are probably as well determined as any

275

276 THE STRUCTURAL PROPERTIES OF (TMTSF)2X SALTS

D

Figure 1. (Top) An isolated columnar array of interacting donors in the structure of (TMTSF)2CI04. Thin lines denote Intracolumnar Se...Se interactions; thicker lines (interrupted by open circles) trace the zig-zag pattern of the molecular centers of mass (and the inversion symmetry elements). The labeled molecules are of the following coordinate types: A(x,y,z); B(-x,]-y,l-z); C(l-x,l-y,l-z); D(-l+x,y,z); E(l+x,y,z). (Middle) Molecular overlap pattern for donors of the types A and C. (Bottom) Molecular overlap pattern for donors of the types A and B.

derived structural parameter, in that various

random (and possibly systematic) errors in the individual Se atom coordinates may well be averaged out. 9 Finally, all the computations reported here are based on room-temperature structural data. I0

Results of these computations for the

(TMTSF)2X salts for which coordinates are avail- able in the literature I0 are presented in Table I. It has been established previously 5 that empirical correlations of physical and structur- al parameters with anion size for the (TlqrSF)2X series are most instructive when salts with centrosymmetrlc and non-centrosymmetrlc anions are treated as members of independent statisti- cal sets, and it is within this guideline that the data of Table ] will be interpreted here.

Vol. 5l, No. 5

It is immediately noticeable that ~N a increases smoothly as the ion diameter [DI vdW ~(a van der Waals-like estimate of anion size)] 5 increases

for the four salts with non-centrosymmetric anions, while LN a is essentially identical for the two salts with centrosymmetric anions. In fact, it is this variation in ~N a that is large-

ly responsible for the absence o7 a significant

variation in D N or 6(DN) with anion size (al- though it is seen from~Table I that Z(DN) and I~I do increase smoothly with increastn~ DI vdW for salts with non-centrosymmetrlc an-

ions). ~re dramatic is the varlatlon of AM a

across the series of salts presented in Tabl~ I. It is readily seen that AM a for the set of donors A(x,y,z) and B(-x,l-y,12z) is virtually independent of anion, with a range (over all six

salts) of only 0.006A [the mean value for AMa(A,B) is 3.583A, with an estimated standard

deviation of the mean o~ ~ 0.003A]. Thus, AMa(A,B) is either only very weakly dependent on or~independent of anion. In contrast, ~M a for

the set of donors A(x,y,z) and C(l-x,l-y,~-z) is dependent on anion, showing a range of 0.067A

across the series of four salts with non-centro- symmetric anions (Table I). Plots of AMa(A,B) and AMa(A,C) versus DlVdW are presented ~n

Flgure~2, where the invarlance of AMa(A,B )

and the variability (possibly nonlinear) of AMa(A,C) are particularly clear. II

~ The antecedents of the differing behaviors of AMa(A,B) and AMa(A,C) seem to be directly related to the different manner in which these alternate pairs of donors interact with the

anion substructure. As depicted in the (001) projection of the crystal structure of

3.8

3.7

~s

3.6

3.5 5.2

Figure 2.

I I I

- ~ ( A , C)

- - = • (A , B} NO~ BF~ CiO~ ReO~

I I I 5 .6 6 . 0 6 .4

Ion diameter (vdW) (A)

AM a versus ion d i a m e t e r (295K).

Plots of AM a (T = 295K) versus ion dlamete~ (DlVdW): • between molecules of the types A and C; • between molecules of the types A and B.

68

Vol. 51, No. 5 277 THE STRUCTURAL PROPERTIES OF (TMTSF)2X SALTS

Table I. Intracolumnar parameters for several (TMTSF)2X salts

(~) (deg.) (A) (A) (~) (A) (A) (A) d4(A) d5(A)

a) c e n t r o s y m m e t r i c a n i o n s

PF 6- 5.90 1.661 3.630 b 7.294 0.034 3.587 b 7.297 0.123 4.067

3.664 c 3.710 c 3.927

AsF 6- 6.10 1.641 3.625 b 7.274 0.024 3.583 b 7.277 0.III 4.053

3.649 c 3.694 c 3.918

b) non-centrosymmetrlc anions

NO 3- 5 .28 1.255 3 .612 b 7 .215 - 0 . 0 0 9 3.581 b 7 .217 0 .055 4.041

3.603 c 3.636 c 3 .913

BF 4- 5.44 1.559 3.620 b 7.252 0.012 3.583 b 7.255 0.089 4.054

3.632 c 3.672 c 3.952

CIO 4- 5.68 1.865 3.626 b 7.263 0.011 3.581 b 7.267 0.105 4.031

3.637 c 3.686 c 3.934

ReO 4- 6.24 2.018 3.632 b 7.279 0.015 3.581 b 7.284 0.122 4.037

3.647 c 3.703 c 3.924

aEqual to the magnitude of the a-axis for each salt.

bBetween molecules of the coordinate types (x,y,z) and (-x,l-y,l-z).

CBetween molecules of the coordinate types (x,y,z) and (l-x,l-y,l-z).

4.044 3 .983

3 .874

4 .026 3 .970

3 .874

3 .965 3 .899

3.850

4.031 3.958

3.873

4.033 3.964

3.871

4.043 3.979

3.873

(TMTSF)2CI04 of Figure 3, columns of donors are immersed in both the interaction potential of contiguous donor columns (notably through speci- fic intercolumnar Se...Se Interactions) 1,2 and that of the anions (principally through interac- tions involving the methyl groups of the donors and the Coulomb field of the complex anions). In this rendition of the crystal structure of the perchlorate salt~ the anions have been depicted as spheres of diameter equal to DI vdN - which in the present context will be considered to represent the maxlmal "sphere of influence" of the anion. It is readily evident from Figure 3 that donor pairs of the type A,B lle within the same set of anion spheres in the bc" plane, while donor pairs of the type A~C lle between alternate planes of anions along a. It is almost surely t h i s difference in donor-pair/ anion interaction that accounts for the differ- ing trends in AM a dlsplayed in Figure 2.

Finally~ it~is interesting to briefly consider the variations in intracolumnar Se... Se 12 distances as a function of anion size. It is expected that the variation of these dis- tances within the donor pair ADB (d 4 and d 5 of Figure 1) ought to be reasonably constant across the serles~ and this seems to be well borne out in the numerical data of Table 1. A somewhat larger variation is expected for the Se...Se distances internal to the AsC donor pair

0 8

Figure 3. The (001) projection of the crystal structure of (THTSF)2CIO 4. The perchlorate anions are represented by spheres of diameter equal to DIvdW.

( d l , d 2 and d 3 of F i g u r e I ) . In F i g u r e 4, p l o t s of d l , d 2 and d 3 v e r s u s DI vdW a r e p r e s e n t e d . 13 The c o n t a c t d i s t a n c e d 3 shows t h e l a r g e s t v a r i a - t i o n , w i t h a s h a r p downturn i n i t s v a l u e f o r t h e nitrate salt. In this contextt the center of mass d i s t a n c e s a l o n g t he b ' and c* a x e s (Ta b l e 2) a r e r e l e v a n t . I t i s Imme d la t e ly r e c o g n i z e d t h a t AMc, i s ve ry weakly de pe nde n t on a n i o n s i z e ( t h e r e ~s no r u f f l i n g of t he donor p l a n e s ) . Th i s i s a l s o t r u e f o r AMb, , w i t h t h e e x c e p t i o n o f t he n i t r a t e s a l t f o r which an a n o m a l o u s l y low v a l u e f o r ~M b, i s o b s e r v e d . I t i s p r o b a b l e t h a t t he

278

4.1

4.0

qD

3. 5.2

® 3.9 o~

ThE STRUCTURAL PROPERTIES OF (TMTSF)2X SALTS Vol. 51, No. 5

Table 2. Center of mass distances

F i g u r e 4.

I I I

_ • ~ d 2 -dl

_ ~ ~ m d3 • ,,,,,,,'lr BrO~ ReOj

c,oi FSO~

--B

I I I 5.6 6.0 6.4 6.8

Ion diameter (vdW) (A)

dl, d 2 or d 3 versus ion dismemr (295K).

Plots of dl, d 2 and d 3 (T = 295K) ver- sus DI vdW (see Figure I for defini- tions of dl, d 2 and d3).

sharp downturn in d 3 (and also d 2) at the ni- trate salt Is directly related to Its anomalous

v a l u e f o r AMb,, and t h i s e f f e c t may w e l l be d l r e c t l y t r a ~ e a b l e to t he p l a n a r symmetry of t he nitrate anion.

In summary, i t has been demonstrated that the fundamental donor-column parameters IN a and

AM a for the family of (TMTSF)2X salts are Flg- n l ~ I c a n t variables of anion size. In addition,

one of the two independent center-of-mass dls- tances between donors appears to be constant

across the series of salts, while the other is

along b" and c*

vdW X D I A~, AMc,

(A) (A) (A)

a) c e n t r o s y m m e t r t c a n i o n s

PF 6- 5.90 0.714 1.355

AsF 6- 6.10 0.722 1.349

b) non-centrosymmetrlc anions

NO 3- 5.28 0.612 1.366

BF 4- 5 .44 0 .739 1.387

CIO 4- 5 .68 0.686 1.392

ReO 4- 6 .24 0 .701 1.372

variable. Importantly, t h e difference [~(AMa) ] between center-of-mass-separatlons

Increases with increasing anion size. This increasing dlmerlzation of the donor column is expected to lead to an enlargement of the elec- tron-electron umklapp coupling constant g3 ,6 a

shift of the g-ology phase diagram (notably the

phase separation boundary between SS and BDW or CDW ground states), 7 and to parallel the in-

creased critical pressure necessary ~-7 for the achievement of a superconducting ground state wlth increasing anion size. 14

Support of this research by the National

Science Foundation (under Grant No. DMR-8307693) and the U.S. Naval Sea Systems Command (under

contract No. N00024-83-C-5301) is gratefully

acknowledged.

REFERENCES

I. F. Wudl, J. Am. Chem. Soc. 103, 7065 6. (1981).

2. J.M. Williams, M. A. Beno, J. C. Sullivan, 7. L. M. Banovetz, J. M. Braam, G. S. Black- man, C. D. Carlson, D. L. Greet and D. M. L o e s t n g , J . Am. Chem. Soc. 105, 643 (1983) ; J. M. Williams, M. A. Beno, E. H. Appleman, 8. F. Wudl, E. Aharon-Shalom and D. NalewaJek, blol. Cryst. Liq. Cryst. 79, 319 (1982); J. M. Williams, M. A. Beno, J. C. Sullivan, L. M. Banovetz, J. Braam, G. S. Blackman, C. 9. D. Carlson, D. L. Greet, D. M. Loeslng and K. Carnelro, Ph___ys. Rev. B28, 2873 (1983).

3. S. Flandrols, C. Coulon, P. Delhaes, D. Chasseau, C. Hanw, J. Gaultler, J. M. Fabre and L. Giral, Mol. Cryst. Llq. Cryst. 79j 307 (1982).

4. S.S. Parkln, F. Cruezet, M. Pdbault, D. I0. Jerome, K. Bechgaard and M. Fabre, Mol. Cryst. Liq. Cryst. 79, 249 (1982).

5. T.J. Klstenmacher, Phys. Rev. B, in press.

V. J. Emery, R. Bruinsma and S. Barlsic, Phys. Rev. Lett. 46, 1039 (1982).

See also, B. Horovitz, 9. Gutfreund and M. Weger, Mol. Cryst. Liq. Cryst. 7q, 235 (1982).

C. S. Jacobsen, D. B. Tanner and K. Bech- gaard, Mol. Cryst. L~q" Cryst. 79, 25 (1982).

It appears that the structural study on (TMTSF)2BF 4 is somewhat less accurate (unusual Se-Se intramolecular distances, etc.) than those of the other salts consid- ered here. It Is expected, however, that thls lack of accuracy does not seriously affect the center-of-mass coordinates for this salt.

Coordinates for the salts considered here were taken from the following sources: a) hexafluorophosphate salt - N. Tnorup, G. Rindorf, H. Soling and K. Bechgaard, Acts Crystallogr. B37, 1236 (1982); b) hexafluoroarsenate salt - from ref. I;

Vol. 51, No. 5

c) nitrate salt - H. Soling, G. Rindor~ and N. Thorup, Cr~st. Struct. Commnn. 11, 1975 (1982); d) tetrafluoroborate salt - H. Kobayashi, A. g~bayashl, G. Salto and ~. Inokuchl, Chem. Lett., 245 (1982); e) per- chlorate and perrhennate salts - G. Rin- doff, H. Soling and N. ~'norup, Act 9 Cr~s- ~ B38, 2805 (1982).

II. If the nitrate salt is excluded, AMa(A,C) for the three tetrahedral salts has~a good linear correlation with ion size [AMa(A,C) = 0.04DivdW + 3.47 (r 2 = 0.971)]. ~

12. The definitions of the intramolecular Se...So distances given in Figure 1 are slightly different from those commonly

THE STRUCTURAL PROPERTIES OF

13.

14.

(TMTSF)2X SALTS 279

employed (ref. 2) in that d 3 and d 5 have been interchanged so that dl, d 2 and d 3 are associated with the donor pair A,C and d 4 and d 5 are associated with the donor pair A,B.

Published values for dl, d 2 and d 3 for (TMTSF)2BrO 4 and (TMTSF)2FSO 3 (both taken from ref. 2) are also included in Figure 4.

Incorporation of structural and critical pressure data for other salts in the (TMTSF)2X series into the empirical framework developed here awaits further experimentation or the availability of primary crystallographic data.