LETTERS Novel chain structures in group VI elements OLGA DEGTYAREVA1*, EUGENE GREGORYANZ1, MADDURY SOMAYAZULU2, PRZEMYSLAW DERA1, HO-KWANG MAO1 AND RUSSELL J. HEMLEY1 1 Geophysical Laboratory, Carnegie Institution of Washington,5251 Broad Branch Road NW, Washington, District of Columbia 20015, USA HPCAT, Carnegie Institution of Washington, APS, 9700 South Cass Avenue, Argonne, Illinois 60439, USA *e-mail: o.degtyareva@gl.ciw.edu 2 Published online: 23 January 2005; doi:10.1038/nmat1294 R Present study: -ll Meltin S-ll, trigonal S-l to S g curv e S-l, orthorhombic S-lll, tetragonal 800 600 S-lll to metallic -lll Temperature (K) 1,000 to S 152 1,200 S-ll ecent developments in high-pressure methods and advances in X-ray crystallography have led to a new level of understanding of phase diagrams and structures of materials under pressure. Recently discovered phenomena such as complex phases of alkali metals1,2, incommensurate host–guest structures3,4, and incommensurately modulated structures5,6 have rendered obsolete our conventional wisdom about the range of structures possible in the elements7. Using new in situ difraction techniques, we have resolved the long-standing problem of the phase-transition sequence of sulphur in its non-metallic state. We demonstrate that it is very diferent from that previously proposed7,8, with only two phases stable between 1.5 GPa and 83 GPa (the pressure of metallization), and temperatures from 300 K to 1,100 K. he phases have a triangular chain and a squared chain structure. he same squared chain structure is found in the heavier group VI element selenium. Polymorphism of sulphur has been studied over the years by a wide range of techniques. Different experiments have produced conflicting results, mostly because all structural studies on lowerpressure phases have been performed only on quenched samples9. In fact, some 12 solid and 5 liquid phases have been reported, making the phase diagram of sulphur one of the most complicated among the elements7. Recent efforts with greatly improved experimental in situ high-pressure techniques, such as optical, spectroscopic or resistivity measurements, have revealed a wealth of interesting physical phenomena in sulphur, such as metallization at about 95 GPa (ref. 10), onset of superconductivity at 93 GPa with critical temperature Tc = 10 K (refs 11,12), increase of the superconducting transition temperature up to 17 K at around 160–200 GPa (refs 11,13), and existence of non-metallic and metallic liquids14. In situ high-pressure diffraction studies on the metallic phase of sulphur report a base-centred orthorhombic (b.c.o.) structure above 83 GPa (refs 15,16), which transforms at 162 GPa to a β-Po structure16. These metallic phases of sulphur are isostructural with the high-pressure metallic phases of the heavier group-VI elements selenium and tellurium17–19. The crystal structure of sulphur in the intermediate pressure range below metallization is unclear. Some in situ diffraction experiments8 indicated a pressureinduced amorphization at 25 GPa, but the energy-dispersive X-ray diffraction technique used in that study can be misleading if large crystallites with preferred orientation form. Indeed, a 400 Metallic 200 0 20 40 60 80 100 Pressure (GPa) Figure 1 Reaction and transformation diagram of sulphur. Selected P–T paths of this study are shown with arrows, where the direction of the arrows indicate the increase/decrease of pressure/temperature. Blue arrows indicate the S-I phase, green arrows the S-II and red arrows the S-III phase. Melting curve up to 3 GPa, shown by the black solid line, is taken from ref. 9, melting curve up to 5 GPa, shown by grey solid line, is taken from ref. 21 and melting curve from 5 GPa to higher pressures, shown by dashed area, is taken from ref. 14. The boundaries for the transitions S-I to S-II and S-II to S-III observed in the present study are shown by dashed lines. phase with large crystallites has been reported above 25 GPa in an angle-dispersive X-ray diffraction study on sulphur but without structural determination15. The most recent in situ study on the low-pressure phase diagram of sulphur20,21 provided the first high-quality diffraction data on high-pressure sulphur. This study showed a transformation of the ambient-pressure S8 ring molecule of the orthorhombic Fddd phase nature materials | VOL 4 | FEBRUARY 2005 | www.nature.com/naturematerials ©2005 Nature Publishing Group LETTERS b a 60 100 Counts Counts 150 80 S-l at 5.8 GPa and 300 K on pressure increase λ = 0.4028 Å S-ll at 5.8 GPa and 800 K on pressure increase λ = 0.4028 Å 40 20 50 0 0 –20 2.0 4.0 6.0 8.0 10.0 12.0 14.0 2.0 16.0 4.0 6.0 2θ (deg) 8.0 10.0 12.0 14.0 16.0 2θ (deg) c d S-lll at 12 GPa on pressure decrease λ = 0.3683 Å 1.0 0.5 * * 0.0 2.0 4.0 6.0 Se-Vll at 16.2 GPa on pressure decrease λ = 0.4028 Å 1.5 Counts (×104 ) Counts (×103 ) 1.5 8.0 10.0 2θ (deg) 1.0 0.5 0.0 12.0 14.0 16.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 2θ (deg) 20.0 Figure 2 In situ X-ray diffraction data. X-ray spectra of a, S-I at 5.8 GPa and 300 K collected on pressure increase; b, S-II at 5.8 GPa and 800 K collected on pressure increase; c, S-III taken on pressure decrease at 12 GPa and 300 K; and d, Se-VII, taken on pressure decrease at 16 GPa and 300 K after heating to 450 K at 20 GPa. The spectra of S-I, S-II and Se-VII are taken with λ = 0.4028 Å; the spectrum of S-III is taken with λ = 0.3683 Å. Full structure Rietveld refinement is shown for the S-II, S-III and Se-VII phases. Red crosses, green solid lines and purple lines represent experimental, modelled and difference spectra. The ticks below profiles indicate the predicted peak positions. Asterisks in the S-III profile indicate the reflections from the pressure-transmitting medium N2. S-I to a new phase S-II, consisting of chains with trigonal geometry. Phase S-II is reported to form only on heating of S-I (because of a kinetic barrier) at pressures above 1.5 GPa. This study20,21, however, was restricted to pressures of 5 GPa, leaving the behaviour of S-II in the pressure range between 5 and 83 GPa unknown. To understand the high-pressure behaviour of sulphur, we have conducted several angle-dispersive X-ray diffraction experiments using diamond anvil cells and monochromatic high-energy high-brilliance synchrotron radiation over a broad pressure–temperature (P–T) range. Samples of S (99.999% purity, Puratronic) were loaded in hightemperature Mao-Bell cells with different openings allowing probing up to 22 degrees of 2θ. Different pressure-transmitting media (that is, He, Ne, N2 and no medium) were used for different loadings. To determine the pressure, we used in situ fluorescence measurements of ruby chips loaded in the sample chamber. In the case of heating experiments, pressure was measured before and after heating and did not change appreciably. The temperatures were measured to within ±5 K by thermocouple. The high-temperature technique is described in greater detail in ref. 22 and references therein. Powder diffraction data were collected at beamline 16-ID-B (HPCAT) at the Advanced Photon Source. Focused, monochromatic beams of different wavelengths (λ = 0.36 – 0.42 Å) were used and the data were recorded on a MAR CCD (charge-coupled device) or image plate calibrated with a CeO2 or silicon standard. Diffraction data were integrated azimuthally using FIT2D23, and structural information was obtained by Rietveld refinement of the integrated profiles using GSAS24. Figure 1 shows the thermodynamic paths followed during this study. In all the runs, our diffraction data show that the starting material was always the known ambient S-I phase. On heating at pressures above 3 GPa, S-I transforms to S-II at temperatures very close to the melting line of sulphur (Fig. 1). The phase transition from S-I to S-II is of first order, and is associated with marked changes in the diffraction pattern (Fig. 2). The diffraction patterns of phase S-II were indexed with trigonal unit cell (a = 6.9082(3) Å, c = 4.2593(6) Å, atomic volume V = 19.54 Å3 at 5.8 GPa and 800 K). Rietveld refinement confirmed that the S-II phase forms the trigonal structure with space group P3221, reported in ref. 20, that consists of triangular chains, running parallel to the trigonal c-axis, with three atoms per turn (Fig. 3). Our Rietveld refinement (Fig. 2) showed that the atoms occupy the following positions: 3(b) (0.876(4) 0 1/6) and 6(c) (0.230(3) 0.534(2) 0.051(3)), close to those reported previously20, and yielded R-factors Rwp =7.6%, Rp = 5.4%. The S-II phase closely resembles ambient polymorphs of the heavier group VI elements selenium and tellurium7, consisting of atomic chains with similar geometry (Fig. 3). The bond angle and the torsion angle in S-II are very similar to those in Se-I and Te-I. But the structure of S-II with two symmetry-independent spirals per nature materials | VOL 4 | FEBRUARY 2005 | www.nature.com/naturematerials ©2005 Nature Publishing Group 153 LETTERS 4.5 a Se-l S-l S-ll (trigonal) S-l S-lll (tetragonal) S-ll S-lll Interatomic distances (Å) 4.0 3.5 3.0 2.5 2.0 0 10 20 30 40 50 60 70 80 90 Pressure (GPa) 4.5 b Se-l (trigonal) Se-Vll (tetragonal) Interatomic distances (Å) 4.0 3.5 3.0 2.5 Figure 3 Crystal structures of Se and S. Structure of Se-I with black line indicating Se-I cell and green line indicating S-II cell; S8 ring molecule of S-I; trigonal chain structure of S-II and tetragonal chain structure of S-III. The bonds up to 2.10 Å for S and 2.32 Å for Se are shown. The structures drawn for Se-I and S-I are based on the data from ref. 31. unit cell is more complex than the structure of Se-I and Te-I with one spiral per unit cell. In S-II, the spirals are rotated around the c-axis, if compared with those in Se-I (Fig. 3). The peculiar behaviour of the spiral chains in Se-I and Te-I in stretching under pressure, associated with an increasing c lattice parameter19,25, is not observed in sulphur, where the c lattice parameter decreases slightly with pressure. If sulphur is pressurized above 36 GPa at 300 K or heated at pressures between 22 and 35 GPa to temperatures shown in Fig. 1, it transforms into a body-centred-tetragonal phase S-III, quenchable in temperature down to 300 K (Fig. 2). The transformation also appears to be of first order. The S-III phase is stable up to 83 GPa at 300 K, where it transforms to the known metallic S-IV phase15,16. On pressure decrease at 300 K, S-III can be retained in a metastable form down to 3 GPa, where it transforms to another (metastable) phase with very broad diffraction peaks, the structure of which could not be determined. This phase transforms to S-I on decompression. Other (metastable) phases were observed on pressure decrease if sulphur was heated up to 850 K in the pressure range of 5–15 GPa (these phases are not discussed here). The patterns of S-III were indexed with the cell parameters a = 8.5939(9) Å, c = 3.6179(5) Å 154 0 5 10 15 20 25 Pressure (GPa) Figure 4 Pressure dependence of interatomic distances for S and Se. Data on S-II at 5.8 GPa, S-III and Se-VII are from present work. The interatomic bonds for S-I at atmospheric pressure and for S-II at 3.0 GPa are calculated using the data from refs 31 and 20, respectively. Data for Se-I are taken from ref. 25. Intrachain (intramolecular) interatomic distances are shown by solid symbols, whereas interchain (intermolecular) interatomic distances are shown by open symbols. The arrow shows the discontinuous change in c-lattice parameter (chain step) at the transition from S-II to S-III. and V = 16.70 Å3 at 12 GPa and 300 K on pressure decrease. The diffraction pattern of sulphur at 76.3 GPa reported previously15 is likely to correspond to the S-III phase. The Rietveld refinement for S-III (Fig. 2) shows that the S atoms occupy 16(f) position (x x+1/4 1/8) of the space group I41/acd (origin choice 2), with x = 0.1405(3) at 12 GPa and 300 K (R-factors Rwp = 5.1%, Rp = 3.4%). The S-III structure consists of squared chains, running parallel to the tetragonal c-axis, with four atoms per turn (Fig. 3). This is a novel structure type. Similar chains of S atoms have been reported26 for a high-pressure phase of H2S, but the closest S–S distance in this structure (3.05 Å at 14 GPa) is much larger than 2.10 Å in S-III. nature materials | VOL 4 | FEBRUARY 2005 | www.nature.com/naturematerials ©2005 Nature Publishing Group LETTERS We have reproduced the S-I to S-II transition several times at different pressures and temperatures (Fig. 1). The S-II phase always forms just below the melting line and after re-crystallization from the liquid state, and is quenchable in temperature down to 300 K. This phase is stable at 300 K up to 36 GPa, and has a negative slope of transformation to S-III, similar to that observed27 in molecular phases of N2. The experiments carried out at high pressures, loading sulphur in different pressure-transmitting media and following different P–T paths by heating S-I or S-II at different pressures, all resulted in the formation of S-III above 36 GPa at room temperature. We carried out diffraction experiments on the next member of the chalcogen family, Se, taking its trigonal polymorph as a starting material. It is found to transform at elevated pressures and temperatures to a tetragonal phase of squared chains, identical to S-III, called here Se-VII. At 16.2 GPa, Se-VII has unit cell parameters of a = 9.0753(1) Å, c = 3.6206(1) Å and V = 18.63 Å3 (Fig. 2). Rietveld refinement gives the atomic position parameter x = 0.1293(2) (R-factors Rwp = 2.4% and Rp = 1.3%). Unlike S, Se-VII can be reached only by heating (for example, 450 K at 20 GPa), and can be quenched to ambient temperature and pressure. If further pressurized at room temperature, Se-VII transforms at 29 GPa to the known metallic Se-IV phase5,18. Diffraction patterns similar to Se-VII have been observed in recent high-pressure studies28 of orthorhombic Se in the pressure range 12–23 GPa. The diffraction data for S-II, S-III and Se-VII measured as a function of pressure provide a direct determination of the equation of state (see Supplementary information Fig. S1). Our results demonstrate that the S8 molecular rings of S-I break under pressure and form triangular chains of S-II, which at higher pressure rearrange into squared chains of S-III with a tighter spiral pitch and denser structure. Through the pressure-induced conformational transformation of atomic chains from trigonal to tetragonal geometry, the shortest covalent S–S (Se–Se) interatomic distance of ~2.10 Å (~2.32 Å) and the next-nearest intrachain distance remain essentially invariant (Fig. 4). The change in bond angle through the phase transitions is not large (100–108°). However, the torsion angle is much smaller in S-III (46.7° at 12 GPa) than the 98.7° in S-I at ambient pressure and 97.5° in S-II at 5.8 GPa. Our findings show parallels with the ground-state structures and energy landscapes predicted in density functional calculations for isolated molecules and clusters (ref. 29 and references therein; ref. 30). Specifically, the calculations predict the stability of both rings and chains with nearly constant S–S bond lengths together with comparable bond angles and conformational freedom about torsion angles. Comparison between theory and experiment indicates that the structures in S and Se are controlled to first order by localized bonding properties over a broad range of compression (that is, up to metallization). Received 4 March 2004; accepted 5 November 2004; published 23 January 2005. References 1. Hanfland M., Syassen, K. Christensen, N. E. & Novikov D. L. New high-pressure phases of lithium, Nature 408, 174–178 (2000). 2. Nelmes, R. J., McMahon, M. I., Loveday, J. S. & Rekhi, S. Structure of Rb-III: novel modulated stacking structures in alkali metals. Phys. Rev. Lett. 88, 155503 (2002). 3. Nelmes, R. J., Allan, D. R., McMahon, M. I. & Belmonte, S. A. Self-hosting incommensurate structure of barium IV. Phys. Rev. Lett. 83, 4081–4084 (1999). 4. McMahon, M. I., Degtyareva, O. & Nelmes, R. J. Ba-IV-type incommensurate crystal structure in group-V metals. Phys. Rev. Lett. 85, 4896–4899 (2000). 5. Hejny, C. & McMahon, M. I. 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The Structures of the Elements (Krieger, Florida, 1982). Acknowledgements We thank V. F. Degtyareva for helpful discussions. This work and HPCAT is supported by DOE-BES, DOE-NNSA, DOD-TACOM, NSF, NASA and the W.M. Keck Foundation. The authors acknowledge financial support from NSF, through grant EAR-0217389. The Advanced Photon Source is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-Eng-38. Correspondence and requests for materials should be addressed to O.D. Supplementary Information accompanies the paper on www.nature.com/naturematerials. Competing financial interests The authors declare that they have no competing financial interests. nature materials | VOL 4 | FEBRUARY 2005 | www.nature.com/naturematerials ©2005 Nature Publishing Group 155 28 25 26 3 Atomic volume ( Å ) 3 Atomic volume (Å ) S-I (orthorhombic) 20 S-II (trigonal) 15 S-III (tetragonal) 10 S-IV 0 10 20 30 40 50 60 70 80 90 24 Se-I (trigonal) 22 Se-VII (tetragonal) 20 18 Se-III 16 0 5 10 15 20 25 Pressure (GPa) Pressure (GPa) Supplementary Figure 1. Equations of state for S and Se. Data on S-I (blue circles), S-II (green triangles), S-III and Se-VII (red squares) are from present work. Data for Se-I (green triangles) are taken from Ref. [1]; data for S-IV and Se-III are taken from Ref [2] and [3], respectively. The data collected on pressure increase are shown with open symbols, data collected on pressure decrease are shown with solid symbols. The fitting of the pressure-volume data with the second-order BirchMurnaghan equation of state (shown by solid lines) gives for S-II Ko= 34(2)GPa, V/Vo=0.867(1), and for S-III Ko=37(1)GPa, V/Vo=0.804(1), with Vo=25.56Å and Ko’ = 4 for both phases. The volume difference between the S-II and S-III phases is 6.5% at 6.2 GPa, and between the Se-I and Se-VII phases, it is 5.6% at ambient pressure. [1] R. Keller, W.B. Holzapfel, and H. Schulz, Effect of pressure on the atom positions in Se and Te, Phys. Rev. B 16, 4404 (1977). [2] Y. Akahama, M. Kobayashi, H. Kawamura, Pressure-induced structural phase transition in sulfur at 83 GPa, Phys. Rev. B 48, 6862 (1993). [3] C. Hejny and M.I. McMahon, Complex crystal structures of Te-II and Se-III at high pressure, Phys. Rev. B 70, 184109 (2004). © 2005 Nature Publishing Group