Inorganic Materials, Vol. 37, No. 7, 2001, pp. 669–672. Translated from Neorganicheskie Materialy, Vol. 37, No. 7, 2001, pp. 796–799. Original Russian Text Copyright © 2001 by Gunicheva, Babushkin, Shkerin.
Electrical Properties of Sulfur at Very High Pressures: An Impedance Spectroscopy Study Yu. A. Gunicheva*, A. N. Babushkin**, and S. N. Shkerin*** * Institute of Metal Physics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 18, Yekaterinburg, 620219 Russia ** Ural State University, pr. Lenina 51, Yekaterinburg, 620083 Russia *** Institute of High-Temperature Electrochemistry, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 20, Yekaterinburg, 620219 Russia e-mail:
[email protected] Received July 25, 2000
Abstract—The electrical properties of sulfur at very high pressures (20–50 GPa) were studied by impedance spectroscopy. Measurements were carried out in diamond anvil cells at room temperature and frequencies in the range 1 Hz to 100 kHz. The anomaly in impedance observed around 37 GPa was attributed to structural disordering.
INTRODUCTION High-pressure effects on the properties of sulfur have been a field of extensive investigation [1–13] because sulfur has a complicated phase diagram and can form polymeric structures [1]. At high pressure, sulfur passes into a metallic state and shows a superconducting transition [2–6]. Optical studies of sulfur at pressures in the range 20–50 GPa revealed a few phase transitions [7–10]. Experimental evidence for a metallic state of sulfur at pressures above ⯝23 GPa was first reported by David and Hamann [3]. According to Dunn and Bundy [4, 5], the transition to a metallic form occurs between 40 and 50 GPa. Luo et al. [7] observed a phase transformation between 23 and 30 GPa. The structural changes observed around 25 GPa [10] are likely to result from reversible amorphization. According to Akahama et al. [9], crystallization of the amorphous phase begins at 37 GPa. Superconductivity in sulfur at very high pressures was also observed in the dc electrical measurements reported in [12, 13]; in addition, the polymerization temperature was shown to depend on pressure and thermal history. In our previous study [14], ac electrical measurements also revealed dielectric anomalies at pressures from 30 to 40 GPa. As is well known, the results of electrical measurements can be distorted by interfacial effects, carrier locking in electrodes, space charge formation and relaxation, intercrystalline barriers, etc. The contributions of these effects to the total conductivity of the system can be assessed by measuring its complex impedance over a wide range of frequencies (impedance spectroscopy) [15, 16]. At very high pressures, materials undergo complex structural and electronic transformations with large
thermal and baric hystereses, resulting in nanocrystalline structures. Impedance spectroscopy is a valuable tool for probing the dynamics of high-pressure transformations, nucleation of new phases, their stability, etc. The purpose of this work was to investigate the electrical properties of sulfur by impedance spectroscopy at pressures from 20 to 50 GPa. EXPERIMENTAL Measurements were carried out in taper–plane anvil cells made of polycrystalline synthetic diamond (carbonado) [17]. An important feature of such cells is good conductivity, due to the presence of conducting intergranular inclusions in carbonado, which eliminates the need for wire leads in electrical measurements. The pressure was determined by the technique described elsewhere [18], which was checked on a large number of materials over wide ranges of temperatures and pressures. Complex conductivity was measured at frequencies from 1 Hz to 100 kHz using a four-probe geometry with two electrodes [19] and an FRA-1174 impedance analyzer (Solartron Electronic) with an ECI-1186 interface. In interpreting experimental data, allowance must be made for the frequency-dependent impedance of the high-pressure cell. To this end, we carried out preliminary measurements on model systems—an “ideal” conductor and “ideal” dielectric. In the former case, the anvils were short-circuited by Al foil; in the latter, the anvils were insulated with paper. The foil and paper
0020-1685/01/3707-0669$25.00 © 2001 MAIK “Nauka /Interperiodica”
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thicknesses (15–20 µm) were the same as the sample thickness. When the anvils were short-circuited, the cell resistance was 15 Ω, independent of frequency and pressure. From the complex impedance plot for the insulated-anvil cell (Fig. 1), it follows that the cell can be represented by the equivalent circuit displayed in Fig. 2. The parameters of the equivalent circuit were found to depend little on pressure and insulating material. The sulfur samples studied (99.99% purity) had an orthorhombic structure. RESULTS AND DISCUSSION The impedance of the sample can be represented by resistance R and constant-phase element CPE2 connected in parallel (Fig. 2b). The conductance of CPE2 is Y = B(i2πf )α, where i = – 1 , f is the measuring frequency, and B and α are constants. The concept of constant-phase element (CPE) is widely used in modeling complex electrochemical systems—exponential distributions of the parameters of
Fig. 2. (a) Equivalent circuit of the anvil cell with a sample: R1 ⯝ 20 MΩ is the input resistance of the measuring system and cell, R2 and CPE1 are the parameters of the anvils, R3 ⯝ 15 Ω is the real resistance of the anvils, and Ims is the sample impedance. (b) Equivalent circuit of the sample.
electrochemical reactions involving charge and mass transfer through energy barriers, the fractal structure of electrodes, etc. [20]. At the same time, CPEs can be used to formally describe the impedance of objects of complex physical nature. In the widest sense, CPEs can be regarded as a manifestation of fractal properties in the frequency space. In studies of some real objects, CPEs are included in more complex impedance structures reflecting the diversity of the processes involved. Figure 3 shows the complex impedance plots for the measuring cell with a sulfur sample. In the pressure range 23–35 GPa, the plot contains an arc which intercepts a resistance at high frequencies (the plot is shifted to the right from the origin along the real axis). The center of the arc is shifted downward, indicating that the equivalent circuit includes a CPE [16]. At pressures above 37 GPa, the CPE vanishes (Fig. 4). Below a critical frequency fc , the impedance scatters widely. The critical frequency depends on pressure (Fig. 5). With increasing pressure, the arc becomes shorter and disappears at 37 GPa. The spectrum reduces to a single, frequency-independent resistance. Above 37 GPa, the phase shift between the current and voltage changes sign (Fig. 3). The sample generates a charge, which flows to the electrodes. This provides indirect evidence that, at pressures above 37 GPa, spontaneous INORGANIC MATERIALS
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The sample resistance R decreases steadily with increasing pressure (Fig. 6), as observed in earlier studies. The slope of the curve changes around 37 GPa.
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We think that these features are due to the phase transition of sulfur. The break at 37 GPa results from structural disordering accompanied by the formation of electrically active complexes, responsible for the resonant absorption of electromagnetic energy. It seems likely that, under the effect of the ac electric field or as a result of structural changes, an excess space charge appears, or polarization of molecular dipoles occurs. Vol. 37
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Fig. 5. Pressure dependence of the critical frequency.
polarization sets in. As the pressure is reduced, the arc appears again at about 33 GPa.
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Fig. 6. Variation of the sulfur resistance (with no contribution of the cell) with (1) increasing and (2) decreasing pressure.
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ACKNOWLEDGMENTS This work was supported in part by the US Civilian Research and Development Foundation (grant no. REC-005) and the Russian Foundation for Basic Research (grant no. 01-03-96494). REFERENCES 1. Meyer, B., Elemental Sulfur, Chem. Rev. (Washington, D. C.), 1976, vol. 76, no. 3, pp. 367–388. 2. Yakovlev, E.N., Stepanov, G.N., Timofeev, Yu.A., and Vinogradov, B.V., Superconductivity in Sulfur at High Pressure, Pis’ma Zh. Eksp. Teor. Fiz., 1978, vol. 28, no. 6, pp. 369–371. 3. David, H.G. and Hamann, S.D., Sulfur: A Possible Metallic Form, J. Chem. Phys., 1958, vol. 28, no. 5, p. 1006. 4. Dunn, K.J. and Bundy, F.P., Electrical Behavior of Sulfur up to 600 kbar—Metallic State, J. Chem. Phys., 1977, vol. 67, no. 11, pp. 5048–5053. 5. Bundy, F.P. and Dunn, K.J., Electrical Behavior of Te, Se, and S at Very High Pressures and Low Temperatures: Superconduction Transition, Phys. Rev. B: Condens. Matter, 1980, vol. 22, no. 7, pp. 3157–3164. 6. Stuzhkin, V.V., Hemley, R.J., Mao Ho-Kwang, and Timofeev, Yu.A., Superconductivity at 10–17 K in Compressed Sulphur, Nature (London), 1997, vol. 390, no. 27, pp. 382–384. 7. Luo, H., Desgrenier, S., Vohra, Y.K., and Ruoff, A.L., High-Pressure Optical Studies on Sulfur to 121 GPa: Optical Evidence for Metallization, Phys. Rev. Lett., 1991, vol. 67, no. 21, pp. 2998–3001. 8. Peansky, M.J., Jurgensen, C.W., and Drickamer, H.G., The Effect of Pressure on the Optical Absorption Edge of Sulfur to 300 kbar, J. Chem. Phys., 1984, vol. 81, no. 12, pp. 6407–6408. 9. Akahama, Y., Kobayashi, M., and Kawamura, H., Pressure-Induced Structural Phase Transition in Sulfur at 83 GPa, Phys. Rev. B: Condens. Matter, 1993, vol. 48, no. 10, pp. 6862–6864. 10. Luo, H. and Ruoff, A.L., X-ray-Diffraction Study of Sulfur to 32 GPa: Amorphization at 25 GPa, Phys. Rev. B: Condens. Matter, 1993, vol. 48, no. 1, pp. 569–572.
11. Luo, H., Greene, R.G., and Ruoff, A.L., β-Po Phase of Sulfur at 162 GPa: X-ray Diffraction Study to 212 GPa, Phys. Rev. Lett., 1993, vol. 71, no. 18, pp. 2943–2946. 12. Babushkina, G.V., Kobelev, L.Ya., and Babushkin, A.N., Electrical Properties of Sulfur near the Polymerization Temperature at Very High Pressures, Vysokomol. Soedin., Ser. B, 1988, vol. 30, no. 9, pp. 643–644. 13. Babushkin, A.N., Kobelev, L.Ya., and Babushkina, G.V., Sulphur Electric Properties at Superhigh Pressure around the Polymerization Temperatures, High Pressure Res., 1990, vol. 3, pp. 177–179. 14. Gunicheva, Yu.A., Babushkin, A.N., Volkova, Ya.Yu., and Ignatchenko, O.A., Dielectric Relaxation in Sulfur at Very High Pressures, Neorg. Mater., 2000, vol. 36, no. 2, pp. 191–193 [Inorg. Mater. (Engl. Transl.), vol. 36, no. 2, pp. 140–142]. 15. Grafov, B.M. and Ukshe, E.A., Elektrochimicheskie tsepi peremennogo toka (AC Electrochemical Circuits), Moscow: Nauka, 1973, p. 128. 16. Solov’eva, L.M., Analytical Approach to Constructing Complex Resistance and Conductance Plots of Electrochemical Equivalent Circuits, in Elektrodnye protsessy v galogenidnykh i oksidnykh elektrolitakh (Electrode Processes in Halide and Oxide Electrolytes), Sverdlovsk Ural Otd. Akad. Nauk SSSR, 1981, pp. 68–82. 17. Vereshchagin, A.F., Yakovlev, E.N., Stepanov, G.N., et al., 2.5-Mbar Pressure in Carbonado Anvil Cells, Pis’ma Zh. Eksp. Teor. Fiz., 1972, vol. 16, no. 4, pp. 240–242. 18. Babushkin, A.N., Pilipenko, G.I., and Gavrilov, F.F., The Electrical Conductivity and Thermal Electromotive Force of Lithium Hydride and Lithium Deuteride at 20−50 GPa, J. Phys.: Condens. Matter, 1993, vol. 5, pp. 8659–8664. 19. Physics of Electrolytes: II. Thermodynamics and Electrode Processes in Solid State Electrolytes, Hladic, J., Ed., London: Pergamon, 1972. Translated under the title Fizika elektrolitov: Protsessy perenosa v tverdykh elektrolitakh i rastvorakh, Moscow: Vysshaya Shkola, 1977, p. 400. 20. Stoynov, Z.B., Grafov, B.M., Savova-Stoynova, B., and Elkin, V.V., Elektrokhimicheskii impedans (Electrochemical Impedance), Moscow: Nauka, 1991, pp. 30–36.
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