Energetics and structural stability of Cs3C60

Energetics and structural stability of Cs3C60

Solid State Communications 130 (2004) 335–339 www.elsevier.com/locate/ssc Energetics and structural stability of Cs3C60 Susumu Saitoa,b,c,*, Koichiro...

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Solid State Communications 130 (2004) 335–339 www.elsevier.com/locate/ssc

Energetics and structural stability of Cs3C60 Susumu Saitoa,b,c,*, Koichiro Umemotoc,d, Steven G. Louiea,b, Marvin L. Cohena,b a

Department of Physics, University of California, 366 Le Conte Hall 7300, Berkeley, CA 94720-7300, USA b Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA c Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan d Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Received 23 December 2003; accepted 6 February 2004 by P. Sheng

Abstract Using the ab initio pseudopotential total-energy method and the density– functional theory, we study the energetics of facecentered-cubic Cs3C60 which is a material of great interest as a possible high transition-temperature superconductor. At the optimized lattice constant the volume per C60 is found to be smaller than the the most-stable hexagon-coordination A15 phase, while the total energy of the fcc phase is about 0.9 eV higher than the A15 phase. These results indicate that a low-temperature and high-pressure synthesis method might be a possible way to produce the fcc Cs3C60 phase. In addition, it is also found that the A15 Cs3C60 should show a phase transformation from a hexagon-coordination phase to a pentagon-coordination phase under hydrostatic pressure. q 2004 Elsevier Ltd. All rights reserved. PACS: 61.48. þ c; 74.70.Wz; 64.60. 2 i Keywords: A. Fullerenes; A. High-Tc superconductors; A. Nanostructures; C. Crystal structure and symmetry

The macroscopic production of spherical C60 fullerenes and the simultaneous discovery of crystalline solid C60 [1] helped to bring reality to the dream of theorists to use clusters as atom-like building blocks of materials [2 –4]. Since then, C60 fullerenes have been studied in many fields of materials science and engineering, and various kinds of C60 compounds have been produced. The alkali and alkaline-earth doped C60 fullerides have been studied most intensively because of their wide variety of crystalline lattice geometries and their rich transport properties including superconductivity [5]. In the case of K and Rb fullerides (denoting the alkali by ‘A’), A3C60, A4C60, and A6C60 have the face-centered cubic (fcc), body-centered tetragonal (bct), and body-centered cubic (bcc) structure, respectively (Fig. 1(a) – (c)) [6 –8]. In contrast, for the case of Ba fullerides, Ba3C60 and Ba4C60 possess the A15 and body-centered orthorhombic (bco) structure, respectively * Corresponding author. Tel.: þ 1-5106433374; fax: þ 15106439473. E-mail address: [email protected] (S. Saito). 0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2004.02.011

(Fig. 1(b) and (d)) [9,10], while Ba6C60 takes the bcc structure as in the case of A6C60 [11]. In Sr fullerides, the same lattice geometries as those of Ba fullerides are observed: A15 Sr3C60, bco Sr4C60, and bcc Sr6C60 [10]. Among a variety of these alkali and alkaline-earth fullerides, fcc A3C60 fullerides have received most attention because they are superconductors with high transition temperatures ðTc Þ; e.g. 29 K in Rb3C60 [12]. For A3C60 in the fcc structure, the electronic-structure studies reveal that the conduction band composed of the lowest-unoccupied t1u states of the C60 molecule is half filled by three electrons per unit cell which are transferred from alkali valence states [13]. The Tc values of a series of the fcc A3C60 fullerides with A ¼ K, Rb, or the mixture of Na, K, Rb, and Cs, are known to be a monotonic function of the fcc lattice constant [14,15], which is longer for heavier alkali elements since Kþ, Rbþ, and Csþ ions are larger than the tetrahedral interstitial site of the pristine fcc C60 lattice. Hence, heavier Aþ ions give rise to an expansion of the lattice when they are accommodated in the tetrahedral interstitial sites. Because the C60 radius should remain the

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Fig. 1. Schematic pictures of alkali and alkaline-earth doped C60 fullerides, (a) face-centered cubic phase observed in alkali fullerides A3C60 (A ¼ K, Rb, or mixture of Na, K, Rb, and Cs), (b) body-centered orthorhombic phase observed in Cs4C60, Sr4C60, and Ba4C60, (c) bodycentered cubic phase observed in alkali fullerides A6C60 (A ¼ K, Rb, or Cs) and alkaline-earth fullerides Sr6C60 and Ba6C60, and (d) A15 phase observed in Cs3C60 and Ba3C60. In the case of K4C60 and Rb4C60, they possess not the bco lattice but the body-centered tetragonal lattice due to the merohedral disorder of C60 reported to be present in these A4C60 fullerides. In the case of the A15 phase, the metal-ion positions fit not with the body-centered cubic lattice but with the simple-cubic lattice. Therefore, the orientation of the center C60 can rotate by 908 to give rise to the pentagon-only coordination or the hexagon-only coordination for the three metal ions. In the Ba3C60 fulleride, it has been reported that the Ba ions occupy the pentagon sites, and other three interstitial sites surrounded by four hexagons remain empty as is shown in the figure. As for the A15 Cs3C60, we consider not only this pentagon-coordination phase but also the other hexagon-coordination phase. The fcc A3C60 fullerides show superconductivity with high transition temperatures. Among these superconducting A3C60 fullerides, Na2RbC60 and Na2CsC60 fullerides possess simple-cubic (A3C60)4 unit cell with orientationally inequivalent four C60 molecules. The bco Sr4C60 and Ba4C60 fullerides also show superconductivity.

same in these A3C60 fullerides, this lattice expansion in turn gives smaller spatial overlap of the adjacent C60 p states and, therefore, a narrower t1u conduction band. Consequently, the density of states at the Fermi level ðNðEF ÞÞ becomes larger. This is consistent with the observed higher Tc for larger lattice-constant A3C60 because the larger NðEF Þ should give higher Tc not merely in the BCS model but also in the McMillan and even more sophisticated theories of superconductivity. The highest Tc (33 K) observed so far in the fcc A3C60 fullerides is, on the other hand, not in Cs3C60 but in Cs2RbC60 [16]. Although the fcc Cs3C60 has been the material of the highest interest in the above context, its production has not been reported so far. While cesium is an alkali element, Cs fullerides are known to possess mostly the same lattice geometries as Ba fullerides: A15 Cs3C60 [17], bco Cs4C60 [18], and bcc Cs6C60 [8]. In addition, in the case of Cs3C60, not only the A15 phase but also the bco phase with the fractional occupation, (Cs0.75)4C60, has been found to be another stable phase [19]. Although the fractional occupation is rather unusual in C60 fullerides, it has been revealed in our previous work that the total energy of the bco phase is only slightly higher than that of the A15 phase [20]. Interestingly, the relative production ratio of A15 and bco Cs3C60 phases is known to depend on the samplepreparation procedure using liquid ammonia [19,21]. Therefore, one may be able to produce the third phase, i.e. the fcc Cs3C60 by using another experimental procedure if the phase is not so energetically different from the other two phases. In this respect, the relative stabilities of these three Cs3C60 phases are of high interest. In this communication, we report the energetics of the fcc Cs3C60 phase obtained by

using the ab initio pseudopotential density – functional theory (DFT) [22 – 24], and discuss the relative stabilities of three phases. In addition, we also discuss the structural stability of the A15 phase under hydrostatic pressure, because superconductivity at as high as 40 K under pressure has been reported in the Cs3C60 sample which contains the A15 phase [17]. In this study we use pseudopotential density– functional calculation, and the local-density approximation with the Ceperley – Alder exchange-correlation functional in the DFT [25,26]. For the pseudopotentials, we adopt the Troullier– Martins soft pseudopotentials [27] with d and s references for C and Cs, respectively. In the case of Cs, in order to obtain the best energetics for Cs3C60, we treat the 5p state not as a core state but as a valence state and include it into the self-consistent electronic-structure calculation [28]. In addition, the Kleinman– Bylander separable approximation is used [29]. The plane-wave basis set is used with a cut-off energy of 50 Ry. At each given lattice constant, the internal geometry is relaxed by using the conjugate-gradient procedure [30]. In Fig. 2, the total energy of fcc Cs3C60 obtained is shown as a function of the lattice constant. The lattice constant which gives the total-energy minimum ðafcc Þ is ˚ , which is about 1.6% longer than that found to be 14.685 A of the fcc Cs2RbC60. As discussed above, the superconducting transition temperature Tc in the fcc A3C60 is a monotonic increasing function of the lattice constant. Considering the observed Tc values of 18 K in K3C60, 29 K in Rb3C60, and 33 K in Cs2RbC60 with the lattice ˚ , respectively, constants of 14.240, 14.384, and 14.455 A [31], fcc Cs3C60 with this afcc might possess a Tc of around

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Fig. 2. Total energy of the fcc Cs3C60 obtained as a function of the lattice constant. Energy is measured from its minimum value observed at the ˚. lattice constant of 14.685 A

45 K. This optimization result gives, therefore, more evidence for the importance of this possible fcc Cs3C60 phase. In our previous work [20], we also studied the energetics of the experimentally observed Cs3C60 phases, i.e. bco and A15 phases, using the same computational procedure as used here for the fcc phase. To study the bco (Cs0.75)4C60 phase, we removed one of four Cs ions of the bco Cs4C60 lattice. Since there are two kinds of metal sites in the bco fullerides, the removal of one of Cs ions can give rise to two kinds of bco Cs3C60 lattices. In each case, we optimized three lattice constants (a, b, and c) as well as the internal geometry. The optimized lattice constants for the two cases  b ¼ 12:180 A;  and c ¼ 11:364 A  (‘type are, a ¼ 12:037 A;  b ¼ 12:552 A;  and c ¼ 11:685 A  1’), and a ¼ 12:275 A; (‘type 2’), respectively. The average values of these two  b ¼ 11:866 A;  and c ¼ 11:525 A;  cases are, a ¼ 12:156 A; which are found to be close to the experimental values of  b ¼ 11:8437 A;  and c ¼ 11:4646 A  [19]. a ¼ 12:2207 A; The total energies for the type 1 and 2 bco phases obtained are found to be close to each other. They differ by about 4 meV with a slight preference for the type 2 case. In the case of the A15 Cs3C60, on the other hand, there are two possible distinct phases, one with Cs ions surrounded only by pentagons (Fig. 1(d)) and the other with Cs ions surrounded only by hexagons. We studied the total energies of both pentagon-coordination and hexagon-coordination phases as a function of the A15 simple-cubic lattice constant, and interestingly, the hexagon-coordination Cs3C60 phase with the optimized lattice constant of ˚ has been found to be energetically lower than the 11.67 A pentagon-coordination phase. Although this is opposite to

the preference of the pentagon-coordination phase observed in the Ba3C60, Rietveld analysis of the A15 Cs3C60 reported actually gives a slightly better fitting result for the hexagoncoordination phase than for the pentagon-coordination phase [19]. In Fig. 3, we plot the total energies of the two A15 phases as a function of the volume per C60 together with that of the fcc Cs3C60 obtained in the present study, and with those of the two bco cases at the optimized lattice constants. As one can see from the figure, the most stable phase is the hexagon-coordination A15 phase, and the bco phase is energetically slightly higher than the A15 phase. The difference between the total energy of the fcc Cs3C60 phase and the hexagon-coordination A15 phase is found to be about 0.9 eV. These results are consistent with the experimental observation of bco and A15 phases but not the fcc phase in the Cs3C60 fulleride. The geometry of the fcc lattice is, on the other hand, considerably different from the observed body-centered lattices. In addition, as is evident from the figure, the energy-minimum volume of the fcc phase is found to be considerably smaller than that of the A15 and bco phases. Therefore, the production of the fcc Cs3C60 phase by using low-temperature and high-pressure synthesis method might be an interesting challenge experimentally. Finally, we discuss the relative stability of the two A15 phases under external hydrostatic pressure. As is discussed above, the hexagon-coordination phase is energetically more stable than the pentagon-coordination phase. On the other hand, it is also evident from Fig. 3 that the pentagoncoordination phase is softer than the hexagon-coordination phase, and it should possess a lower free energy when above

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Fig. 3. Total energies of the fcc phase (solid line), two bco phases (þ and £ for type 1 and 2, respectively) and two A15 phases (dashed lines) obtained as a function of the volume per C60. In the case of A15 phases, the hexagon-coordination phase is found to have a lower total-energy  3 ) than the pentagon-coordination phase. minimum (at V ¼ 855 A

the critical pressure ðPc Þ which can be obtained from the common tangent of the two curves. Using this approach, the estimated value of the critical pressure for the transformation from the hexagon-coordination to the pentagoncoordination phase is found to be Pc ¼ 2:0 GPa: It has been shown that the pentagon and hexagon faces of C60 possess different spatial distributions of the t1u conductionband states, with much larger amplitude on pentagons than on hexagons [32]. Therefore, a transformation from the hexagon-coordination to the pentagon-coordination phase in the A15 Cs3C60 fulleride should give rise to an stronger interaction between the C60 t1u state and the Cs states, which might give stronger metallic behavior in the high-pressure pentagon-coordination phase. In this context, it is interesting to note that the value of the critical external pressure obtained here for the A15 phase transformation is just around the hydrostatic pressure applied experimentally when superconductivity at up to 40 K was observed (from 1.21 to 1.43 GPa) [17]. In summary, by using the ab initio pseudopotential density – functional method, we have studied the energetics of the fcc Cs3C60 which has been a material of highest interest as a possible new high-transition temperature superconductor. While the total energy at the optimized lattice constant is found to be higher than that of the moststable hexagon-coordination A15 phase by about 0.9 eV, the optimized volume per C60 is found to be considerably smaller than that of the A15 phase. This indicates that a

low-temperature high-pressure experimental approach might be a possible way to synthesize fcc Cs3C60. In addition, we have also found from studying the energetics of the two A15 phases that there should be a phase transformation from the hexagon-coordination phase to the pentagon-coordination phase under hydrostatic pressure of about 2.0 GPa. This should give rise to a change of the electronic transport properties of the material.

Acknowledgements We would like to thank for Prof Y. Iwasa and Prof Y. Kubozono for useful discussions. We also would like to thank Prof A. Oshiyama, Prof T. Nakayama, Dr M. Saito, and Prof O. Sugino for the LDA program used in the present study. This work was supported by the 21st Century Centerof-Excellence Program at Tokyo Institute of Technology ‘Nanometer-Scale Quantum Physics’ from the Ministry of Education, Culture, Sports, Science, and Technology of Japan, by US National Science Foundation Grant No. DMR00-87088, and by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, US Department of Energy under Contract No. DE-AC03-76SF00098. Some of numerical calculations were performed at the Research Center for Computational Science, Okazaki National Institute.

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References [1] W. Kra¨tschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huffman, Nature 347 (1990) 354. [2] S. Saito, S. Ohnishi, Phys. Rev. Lett. 59 (1987) 190. [3] A. Rose´n, B. Wa¨stberg, Z. Phys. D 12 (1989) 387. [4] S. Saito, Mater. Res. Soc. Symp. Proc. 206 (1991) 115. [5] A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez, A.R. Kortan, Nature 350 (1991) 600. [6] P.W. Stephens, L. Mlhaly, P.L. Lee, R.L. Whetten, S.-M. Huang, R. Kaner, F. Diederich, K. Holczer, Nature 351 (1991) 632. [7] P.W. Stephens, L. Mlhaly, J.B. Wiley, S.-M. Huang, R. Kaner, F. Diederich, R.L. Whetten, K. Holczer, Phys. Rev. B 45 (1992) 543. [8] O. Zhou, J.E. Fischer, N. Coustel, S. Kycia, Q. Zhu, A.R. McGhie, W.J. Romanow, J.P. McCauley Jr., A.B. Smith III, D.E. Cox, Nature 351 (1991) 462. [9] A.R. Kortan, N. Kopylov, R.M. Fleming, O. Zhou, F.A. Thiel, R.C. Haddon, Phys. Rev. B 47 (1993) 13070. [10] C.M. Brown, S. Taga, B. Gorgia, K. Kordatos, S. Margadonna, K. Prassides, Y. Iwasa, K. Tanigaki, A.N. Fitch, P. Pattison, Phys. Rev. Lett. 83 (1999) 2258. [11] A.R. Kortan, N. Kopylov, S. Glarum, E.M. Gyorgy, A.P. Ramirez, R.M. Fleming, F.A. Thiel, R.C. Haddon, Nature 355 (1992) 529. [12] M.J. Rosseinsky, A.P. Ramirez, S.H. Glarum, D.W. Murphy, R.C. Haddon, A.F. Hebard, T.T.M. Palstra, A.R. Kortan, S.M. Zahurak, A.V. Makhija, Phys. Rev. Lett. 66 (1991) 2830. [13] S. Saito, A. Oshiyama, Phys. Rev. B 44 (1991) 11536. [14] K. Tanigaki, I. Hirosawa, T.W. Ebbesen, J. Mizuki, Y.

[15]

[16]

[17] [18] [19]

[20] [21]

[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

339

Shimakawa, Y. Kubo, J.S. Tsai, S. Kuroshima, Nature 356 (1992) 419. M.J. Rosseinsky, D.W. Murphy, R.M. Fleming, R. Tycko, A.P. Ramirez, T. Siegrist, G. Dabbagh, S.E. Barrett, Nature 356 (1992) 416. K. Tanigaki, T.W. Ebbesen, S. Saito, J. Mizuki, J.S. Tsai, Y. Shimakawa, Y. Kubo, S. Kuroshima, Nature 352 (1991) 222. T.T.M. Palstra, O. Zhou, Y. Iwasa, P.E. Sulewski, R.M. Fleming, B.R. Zegarski, Solid State Commun. 93 (1995) 327. P. Dahlke, P.F. Henry, M.J. Rosseinsky, J. Mater. Chem. 8 (1998) 1571. S. Fujiki, Y. Kubozono, M. Kobayashi, T. Kambe, Y. Rikiishi, S. Kashino, K. Ishii, H. Suematsu, A. Fujiwara, Phys. Rev. B 65 (2002) 235425. K. Umemoto, S. Saito, to be published. Y. Kubozono, S. Fujiki, K. Hiraoka, T. Urakawa, Y. Takabayashi, S. Kashino, Y. Iwasa, H. Kitagawa, Y. Mitani, Chem. Phys. Lett. 298 (1998) 335. M.T. Yin, M.L. Cohen, Phys. Rev. B 26 (1982) 5668. P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. K. Umemoto, PhD Thesis, Department of Physics, Tokyo Institute of Technology, 2000. L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. O. Sugino, A. Oshiyama, Phys. Rev. Lett. 68 (1992) 1858. I. Hirosawa, PhD Thesis, Department of Physics, Tohoku University, 1995. T. Miyake, S. Saito, Chem. Phys. Lett. 380 (2003) 589.