cavity size versus anion size in (tmtsf)2x salts: possible implications for the uniqueness of...

Solid State Communications, Vol.50,No.8, pp.729-733, 1984. Printed in Great Britain.

0038-1098/84 $3.00 + .00 Pergamon Press Ltd.

CAVITY SIZE VERSUS ANION SIZE IN (TMTSF)2X SALTS:

POSSIBLE IMPLICATIONS FOR THE UNIQUENESS OF (TMTSF)2CI04

Thomas J. Kistenmacher

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

(Received 19 December 1983 by A. G. Chynoweth)

A simple, effective method for deducing the fit of the complex anion, X, within its structural cavity for (TMTSF)2X salts with tetrahedral anions is presented. Subsequent analysis suggests that an electronic instability is operative over the full range of salts, becoming coincident with or leading to anion ordering and an insulating ground state above some critical fit of the anion within its structural cavity. Moreover, (TMTSF)2CI04 can be considered unique in that the perchlorate anion is too small for anion ordering to be the critical instability, yet large enough for anion ordering to occur at a finite temperature.

It has recently become clear that several structural I-~ (e.g., unit-cell axis lengths, unit-cell volume, interchain Se...Se contact distances) and physicalS-7(e.g., critical pressure, spin-flop magnetic field, spin-resonance linewldth, metal-insulator transition temperature) properties of the family of organic super- conductors, (TMTSF)2X, based on the electron donor tetramethyltetraselenafulvalene, TMTSF, and a host of complex inorganic anions, X, are functions of the symmetry and size of the complex anion. It has also become evident 8 that anion ordering is a prerequisite for the achievement of a superconducting ground state. Thus, a means for the comparison of anion size with cavity size in this series of salts would seem to be of considerable interest.

To this end, a very simple, but apparently effective, empirical scheme is outlined here. The structural base for the proposed method is largely derived from the work of Williams and co-workers, 9 who noted that the cavity in which the complex anion resides is principally deter- mined by the terminal methyl groups of the TMTSF donor (see Figure I). The quantitative aspects of the immediate environment about the complex anion for several salts are documented in Table I, where the quoted distances are those between the carbon of the interacting methyl group and the origin of the unit cell (the center of mass of the disordered anion in the hlgh-temperature phase). Implementation of the proposed method requires a knowledge of three quantities: RI vdW - a van der Waals-like estimate of the radius of the complex anion, X; RMe vdW - the van der Waals radius of a methyl group; and, R(C) - the "radius" of the cavity surrounding the complex anion. Values for RI vdW for several anions have been previously calculated and tabulated 3 (see also Table i), and RMe vdW is taken as 2.0A - the value given by Pauling. I0 It remains then to give some estimate of the radius of the cavity. Table I lists the various methyl groups closest to, and their distance from, the center of mass of the disordered anion for those salts

X

Fig. I. The (100) projection of the crystal structure of (TMTSF)2CI04. The perchlorate anions are represented by spheres of radius equal to RI vdW. The labeled donors have the following coordinate transformations: A(x,y,z); B(x,-l+y,z); C(x,-l+y,-l+z).

729

730 CAVITY SIZE VERSUS ANION SIZE IN (TMTSF)2X SALTS

Table I. Anion environment for several (TMTSF)2X salts

Vol. 50, No

vdW Atom (symmetry transforms) Distance (A) R I

(1) salts with centrosymmetric anions

(I) (TMTSF)2PF6 a

C(4:x,-l+y,-l+z;-x,l-y,l-z) 4.177(RsPF6 ) 2.95 C(14:x,-l+y,z;-x,l-y,-z) 4.278 C(15:x,y,z;-x,-y,-z) 4.376

(2) (TMTSF)2AsF6b

C(4:x,-l+y,-l+z;-x,l-y,l-z) 4.246(RsASF6 ) 3.05 C(14:x,-l+y,z;-x,l-y,-z) 4.290 C(15:x,y,z;-x,-y,-z) 4.412

(ii) salts with non-centros~mmetric anions

(3) (TMTSF)2N03 c

C(4:x,-l+y,-l+z;-x,l-y,l-z) C(15:x,y,z;-x,-y,-z) C(5:x,-l+y,-l+z;-x,l-y,l-z)

(A) ARs(O (A)

(4) (TMTSF)2BF4 d

C(4:x,-l+y,-l+z;-x,l-y,l-z) C(15:x,y,z;-x,-y,-z) C(14:x,-l+y,z;-x,l-y,-z)

- 0 . 7 7 3

-0.804

(5) (TMTSF)2CI04 e

C(4:x,-l+y,-l+z;-x,l-y,l-z) C(15:x,y,z;-x,-y,-z) C(14:x~-l+y,z;-x,l-y,-z)

3.630(RsNO3 ) 2.64(ip) -1.010 4.024 2.13(op) -0.500 4.111 2.81(sp) -I.180

(6) (TMTSF)2Re04 f

C(4:x,-l+y,-l+z;-x,l-y,l-z) C(14:x,-l+y,z;-x,l-y,-z) C(15:x,y,z;-x,-y,-z)

4.041 (RsBF4) 4.167 4.230

2.72 - 0 . 6 7 9

2 .84 - 0 . 7 6 5

3.12 -0.941

4.075(RSCI04 ) 4.265 4.273

4.179(RsRe04 ) 4.210 4.379

a(TMTSF)2PF6: coordinates taken from ref. II;

b(TMTSF)2AsF6: coordinates taken from ref. I;

C(TMTSF)2NO3: coordinates taken from ref. 12; the various van der Waals radii for the nitrate

anion are its in-plane radius [RlVdW(ip)], its out-of-plane height [2RlVdW(op)], and that for a

sphere [RlVdW(sp)] whose volume is the same as the van der Waals cylinder [~(RlVdW(ip)) 2

(2RlVdW(op))];

d(TMTSF)2BF4:

e(TMTSF)2CI04:

f(TMTSF)2ReO4:

coordinates taken from ref. 13;

coordinates taken from ref. 14;

coordinates taken from ref. 14.

Vol. 50, No. 8

for which coordinates are available in the literature.l,ll-l~ The distribution of these methyl groups about the anion is required only to be centrosymmetric, and the actual distribution (for the six closest interacting groups of Table I) Is that of a skewed, trigonal anti- prism. For simplicity, the cavity radius is taken here to be coincident with the shortest distance (denoted RsX in Table I) of a methyl group from the center of mass of the anion. It should be noted that this definition of R(C) is at least consistent across the series of salts, as the same methyl group [C(4:x,-l+y,-l+z) and its symmetry mate C(4:-x,l-y,l-z)] provides the estimate for R(C) in each case.

The proposed scheme can be quantified by providing a measure of the "fit" of the anion to the observed cavity:

ARs(C) = Rs(C) - [Zl vdW + RMeVdW], (I)

with increasingly more negative values for ARs(C ) signifying a tighter fit. Based on eqn. (I), values for ARs(C ) are easily computed (Table I), and a plot (excluding the nitrate salt) of ARs(C ) versus RlVdW is presented in Figure 2. Guided by previous indications, 3-q it is likely that salts with anions of tetrahedral symmetry ITd) will follow a different empirical correlation than salts with anions of octahedral symmetry I Oh). Following this guideline, it appears from Figure 2 that for the three salts with T d anions (tetrafluoroborate, perchlorate and perrhennate) there is a linear correlation of ARs(C ) with anion size:

ARs(C) = -0.65RIVdW + 1.09 (r 2 = 0.9990), (2)

with the perrhennate anion most tightly bound in its crystalline cavity and the tetrafluoroborate anion the most loosely fit. Too little data is available on salts with O h anions to be confi- dent of a correlation for ARs(C ) with RlVdW. It is interesting, however, that ARs(C ) for these salts lles well off the linear correlation for the salts with T d anions. Equation (2) can be employed to give ARs(C) for hypothetical T d anions with the same RlVdW as for the PF 6- and AsF 6- anions. The resulting ARs(C ) for these hypothetical T d anions are, respectively, 0.06A and O.09A more negative than those for their O h congeners - giving a seml-quantltive measure of the apparent tendency of T d anions to more strongly interact with their crystalline environment than O h anions. 2,9

Continuing in a more speculative vein, it would seem that ARs(C ) ought to provide some measure of the structural driving force for anion ordering. Direct scattering evidence for anion ordering is available for three pertinent (TMTSF)2X salts: (TMTSF)2CI0415 [TA_ 0 = 24K; ~ =

(0,I12,0)]; (TMTSF)2Re0416 [TA_ 0 = 180K; ~ =

(I/2,1/2,1/2)]; and (TMTSF)2FS0317 [TA_ 0 = 87K;

q = (1/2,1/2,1/2)]. To proceed further, three ~ssumptlons will be made: [I] TA_ 0 for the perchlorate salt is anomalous - consistent with its unusual distortion wavevector; 15 [2] ARs(C) for (TMTSF)2FSO 3 is identical with that e~Icu- lated [Table I] from the available structural data for (TMTSF)2CI0414 - consistent with the

CAVITY SIZE VERSUS ANION SIZE IN (TMTSF)2X SALTS

-06 l

73]

-08 -

-1.0 2.6

Fig. 2.

Re02~

I I 2.8 3.0 3.2 Ion radius (vdW) {A)

ARs(C) versus ion radius (295K).

Plot of ARs(C) versus RI vdW. The solid line represents the least- squares fit to the data for the tetrafluoroborate, perchlorate and perrhennate salts.

equivalence of RI vdW for the two anions 3 and the nearly identical structural parameters for the two salts; 14'18 and, [3] that TA_ 0 is linearly correlated with ARs(C ) . Following assumptions [2] and [3], the data for the fluorosulfate and perrhennate salts yield eqn. (3):

TA_ 0 = -528.41ARs(C) - 317.23. (3)

This result can then be combined with eqn. (2) to obtain TA_ 0 expressed as a linear function of RlVdW ~ eqn. (4):

TA_ 0 = 343.62RlVdW - 891.40. (4)

Equation (4) immediately recalls a previously deduced 3 empirical relationship between the metal-insulator transition temperature (TM_I) and RI vdW for salts with non-centrosymmetric anions, eqn. (5):

TM_ I = 351.13RI vdW - 914.46. (51

The equivalence (within statistical error) of TM_ I and TA_ 0 as expressed by eqns. (4) and (5) could have been anticipated by noting that TM_ I and TA_ O are identical for (TMTSF)2Re0416 and (TMTSF)2FSO3.17,18 The notion of a general equivalence of anion ordering and the transition to an insulating ground state at ambient pressure for salts with T d anions would seem to be buttressed by data for the isostructural salt (TMTTF)2CI04 (where TMTTF is the S analogue of TMTSF), which exhibits resistive, magnetic and specific heat anomalies at 75K, 6'19 concurrent with anion ordering at a normal distortion wavevector [S = (I/2,1/2,1/2)] "20

732

It is, of course, the exceptions to this general equivalence of TM_ I and TA_ 0 that are potentially the most interesting. The collation of TM_ I and TA_ O data for (TMTTF)2CI04 within the framework of the (TMTSF)2X salts suggests a minimal dependence on the nature of the hetero- fulvalene donor (TMTSF vs. TMTTF), requiring only isostructural crystalline motifs and anions of similar symmetry. Following in this vein, it is noted that both (TMTSF)2BF421 and (TMTTF)2BF419 have TM_ I = 40K, as expected from eqn. (5). Furthermore, utilizing the published coordinates for (TMTTF)2BF4 ,22 it is found that the methyl group environment about the BF 4- anion in this salt is very similar to that in (TMTSF)2BF4.13 In particular, Rs(C) is calculated (based again on the shortest methyl group contact) to be 4.018A[Rs(C ) = 4.041A for the TMTSF salt, Table i], yielding a ARs(C ) value [from eqn. (I)] of -0.702A, which is very close to the value, -0.679A, calculated for (TMTSF)2BF 4 and suggestive of similar anion- ordering temperatures (40-50K) according to eqn. (3) for both salts. Taking this argument one step further, the equivalence of TA_ 0 for these two salts is also expected from eqn. (4), which is solely a function of RivdW. However, there are no published data supporting anion ordering at finite temperature (or concomitantly super- conductivity at any applied pressure) 18 for (TMTSF)2BF4, and the specific heat anomaly near 41K in (TMTTF)2BF 4 is very weak and suggestive of minimal anion ordering at best. 19

One rational means for rectifying this failure is to assume that eqns. (3) and (4), which were derived under assumptions [2] and [3] and based on data for the fluorosulfate

[RIVdWIFsO3- ) = 2.84~] and the perrhennate

[RIVdWIReO4-- ) = 3.12A] salts, are limiting laws,

holding only for large values of RivdW. The universal validity of eqn. (5) for TM_ I over the full range of RI vdW and the complete temperature scale suggests, however, a pervasive driving force that either induces anion ordering or becomes coincident with the structural driving force for salts with large anions. Primary candidates for this prevalent driving force would seem to be charge- or spln-denslty wave correlations associated with electronic instabi- lities congenital to the donor column. 24-25 In addition, this driving force is contingent on the donor in the sense that the critical value for RivdW [or interchangeably the critical value for ARs(C)] above which anion ordering is concomitant with a strong metal-lnsulator transition is apparently donor dependent. An in- triguing speculation as to where this crossover occurs for different donor salts as RI vdW de- creases can be inferred from the divergent properties of the perchlorate salts of TMTSF and TMTTF. As noted above, (TMTTF)2CIO 4 exhibits simultaneous metal-lnsulator and anlon-orderlng transitions near 75K, 6'19 with a normal distortion wavevector. 20 In contrast, (TMTSF)2CIO 4 exhibits anion ordering at 24K, 15 an anomalous distortion wavevector, and only a weak anomaly at this temperature in hlgh-resolutlon resist- ance data. 26 These two results suggest that the critical value of RivdW for the (TMTTF)2X salts lies below RI vdW for the perchlorate anion,

CAVITY SIZE VERSUS ANION SIZE IN (TMTSF)2X SALTS Vol. 50, No. 8

while the critical value of RI vdW for the (TMTSF)2X series lles above that for the perchlorate anion. It is apparent then that these different critical values for RI vdW [ARs(C) ] provide a major source of differentiation between the (TMTTF)2X and (TMTSF)2X salts. In this context, (TMTSF)2FSO 3 would need to be considered anomalous in that its metal-lnsulator and anion-ordering temperatures are coincident - a result that may be credited to its dipolar character, which presumably enhances anion ordering so that this salt appears "normal" according to eqns. (4) and (5). The culmination of this train of thought is that (TMTSF)2BF 4 and (TMTSF)2CIO 4 ought to display common crystal physics. The uniqueness of the perchlorate salt is directly attributable to the size of the perchlorate anion, which is too small for the structural driving force to be the critical instability leading to an insulating ground state, yet large enough for anion ordering to occur at a finite temperature. 27

Finally, there are synthetic overtones associated with the notion of a donor--dependent critical anion size. For the (TMTTF)2X series of salts, the low projected critical value for R vdW I poses serious problems in that anions with RI vdW below this limit may not achieve anion ordering at finite temperature. For the (TMTSF)2X series, the perchlorate salt will remain unique, unless another (non-polar) anion of similar size and symmetry is available for which anion ordering is achievable at a finite temperature. Most interestingly, if the apparent increase in critical anion radius on pro- ceeding from TMTTF to TMTSF were to continue for the tellurium analogue TMTTeF (as yet unreport- ed), and an isostructural series of (TMTTeF)2X salts can be obtained, then it is possible that salts with T d anions larger than (and possibly including) perchlorate may achieve superconduc- tivity at ambient pressure and with possibly higher critical temperatures.

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 (1981). 2. J. M. Williams, M. A. Beno, J. C. Sullivan,

L. M. Banovetz, J. M. Braam, G. S. Blackman, C. D. Carlson, D. L. Greer, and D. M. Loes- ing, J. Am. Chem. Soc. 105, 643 (1983); J. M. Williams, M. A. Beno, E. H. Appleman, F. Wudl, E. Aharon-Shalom, and D. NalewaJek, Mol. Cryst. Liq. Cryst. 79, 319 (1982); J. M. Williams, M. A. Beno, J. C. Sullivan, L. M. Banovetz, J. Braam, G. S. Blackman, C. D. Carlson, D. L. Greer, D. M. Loesing, and K. Carneiro, Phys. Rev. B28, 2873 (1983).

3. T. J. Kistenmacher, Phys. Rev. B, submitted. 4. T. J. Kistenmacher, to be submitted. 5. S. S. Parkln, F. Cruezet, M. Ribault, D.

Jerome, K. Bechgaard, and M. Fabre, Mol. Cryst. Liq. Cryst. 79, 249 (1982).

6. S. Flandrols. C. Coulon, P. Delhaes, D. Chasseau, C. Hauw, J. Gaultler, J. M. Fabre,

Vol. 50, No. 8 CAVITY SIZE VERSUS ANION SIZE

and L. Giral, Mol. Cryst. Liq. Cryst. 79, 307 ( 1 9 8 2 ) .

7. A. Maaroufi, C. Coulon, S. Flandrols, P. Delhaes, K. Mortensen, and K. Bechgaard, Solid State Commun. 48, 555 (1983).

8. P. Garoche, R. Brusetti, and K. Bechgaard, Phys. Rev. Lett. 49, 1346 (1982); S. Kago- shima, T. Yasunaga, T. Ishiguro, H. Anzai, and G. Saito, Solid State Commun. 46, 867 ( 1 9 8 3 ) .

9. M. A. Beno, G. S. Blackman, P. C. W. Leung, and J. M. Williams, Solid State Commun. 48, 99 ( 1 9 8 3 ) .

I0. L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca (1960).

II. N. Thorup, G. Rindorf, H. Soling, and K. Bechgaard, Acts Crystallogr. B37, 1236 ( 1 9 8 2 ) .

12. H. Soling, G. Rindorf, and N. Thorup, Cryst. Struct. Commun. 11, 1975 (1982).

13. H. Kobayashi, A. Kobayashi, G. Saito, and H. Inokuchi, Chem. Lett. 245 (1982).

14. G. Pdndorf, H. Soling, and N. Thorup, Acta Crystallogr. B38, 2805 (1982).

15. J. P. Pouget, G. Shirane, K. Bechgaard, and J. M. Fabre, Phys. Rev. B27, 5203 (1983).

16. R. Moret, J. p. Pouget, R. Comes and K. Bechgaard, Phys. Rev. Lett. 49, 1008 (1982).

17. R. Moret, J. P. Pouget, R. Comes and K. Bechgaard, Proceedings of the International Conference on Physics and Chemistry of Synthetic and Organic Metals, Les Arcs, 1982 ( J . Phys . ( P a r i s ) , i n p r e s s ) .

18. F. Wudl, E. Aharon-Shalom, D. NalewaJek, J . V. Waszczak, W. M. Walsh, L. W. Rupp, P. Chaikin, R. Lacoe, M. Burns, T. O. Poehler, M. A. Beno and J. M. Williams, J. Chem. Phys. 76, 5497 (1982).

19. C. Coulon, P. Delhaes, S. Flandrois, R. Lagnier, E. BonJour and J. M. Fabre, J. Phys. (Paris) 4__33, 1059 (1982).

IN (TMTSF)2X SALTS 733

20. J. P. Pouget, R. Motet, R. Comes, K. Bech- gaard, J. M. Fabre and L. Giral, Mol. Cryst. Liq. Cryst. 79, 129 (1982).

21. K. Bechgaard, C. S. Jacobsen, K. Mortensen, J. H. Pedersen and N. Thorup, Solid State Commun. 33, 1119 (1980).

22. J. L. Galinge, B. Liautard, S. Peytavin, G. Brun, M. Maurin, J. M. Fabre, E. Torreilles and L. Giral, Acta Crystallogr. B35, 1129 (1979).

23. For recent reviews, see: K. Bechgaard, Mol. Cryst. Llq. Cryst. 79, I (1982); J. Frledel and D. Jerome, Contemp. Phys. 23, 583 (1982); D. Jerome and H. J. Schultz, Adv. Phys. 31, 299 (1982).

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

25. In this context, it is noted that diffuse scattering at the wavevectors 2k F and 4k F is often observed (see refs. 15-17 and 20) in addition to superlattlce reflections associated with anion ordering.

26. See, for example, D. U. Gubser, W. W. Fuller, T. O. Poehler, J. Stokes, D. O. Cowan, M. Lee and A. N. Bloch, Mol. Cryst. Liq. Cryst. 79, 225 (1982).

27. Numerous previous suggestions of an instability or dimensionality crossover (see ref. 23 and references therein) or a unique fit of the perchlorate anion to its cavity (ref. 9) have appeared in the literature. The realization of a universal dependence of metal-insulator transition temperature on anion size for the (TMTSF)2X and (TMTTF)2X salts, the seml-quantitatlve analysis of the fit of the anion to its structural cavity, and the concept of a "critical" fit of the anion to its cavity as a measure of the uniqueness of (TMTSF)2CI04 appear, however, to be espoused for the first time in this report.

cavity size versus anion size in (tmtsf)2x salts: possible implications for the uniqueness of...

Documents