1 REVISED RUBY PRESSURE SCALE Peter I. Dorogokupets, Artem R. Oganov* Institute of the Earth’s Crust, Irkutsk, Russia dor@crust.irk.ru *Laboratory of Crystallography, Dept. of Materials, ETH Zurich, CH-8092, Switzerland a.oganov@mat.ethz.ch The ruby pressure scale where pressure is measured using the ruby R 1 luminescence line shift, is one of the most commonly used standards in diamond anvil cell experimental studies of PV relations of minerals on the room-temperature isotherm. Up to now the ruby pressure scale of Mao et al. [1], who have measured the ruby R 1 luminescence line shift in argon medium up to pressure 80 GPa, was the most widely used calibration. The pressure was determined from Cu and Ag room isotherms calculated by Carter et al. [2] from shockwave data. As a result, the pressure scale in the following form gained acceptance in the literature P = A [(1 + λ ) B − 1] , (1) λ0 B where A=1904 GPa, B=7.665 (Fig. 1). Almost at the same time Alexandrov et al. [3] have published a significantly different high pressure scale based on an a priori diamond equation of state. Alexandrov et al. [3] have performed simultaneous measurements of the ruby R 1 luminescence line shift in diamond anvil cell in helium pressure medium and a first-order Raman light scattering spectra in diamond up to compression x=V/V 0 =0.93 . The scale with parameters A=1918 GPa, B=11.7 begins to differ from the scale of Mao et al. [1] at pressures above 20 GPa and results in significant differences in the pressure range above 50 GPa (Fig. 1). Although Zha et al. [4] confirmed the scale of Mao et al. [1], recently on the basis of detailed analysis of the present X-ray, ultrasonic, theoretical and shock-wave data for diamond Holzapfel [5] has proposed a new ruby scale in the form: P = A [exp(( B + 1)(1 − λ ) −C ) − 1] , B +C C λ0 (2) where A=1820 GPa, B=14, C=7.3 (Fig. 1). In order to find the reasons for such discrepancy between scales Mao et al. [1986], Zha et al. [2000] [1], [3] and [5], it is necessary to Aleksandrov et al. [1987] check the Cu and Ag room Holzapfel [2003] BM3 A=1896, B=9.63 isotherms from Carter et al. [2], 0.04 which have been calculated only from shock-wave data. By now the range of shock-wave data on Cu and Ag has expanded, which 0.03 together with ultrasonic, X-ray and thermochemical data allows one to obtain reliable equation of state for these metals. Therefore 0.02 the purpose of our study is to 40 50 60 70 80 90 100 Pressure, GPa develop an equation of state for Cu and Ag on the basis of Fig. 1. Ruby pressure scales contemporary data and comparison of calculated room isotherms with Carter et al. [2] isotherms. Then from Mao et al. [1] data we calculate the Cu and Ag volume that permits us to revise the pressure of the ruby pressure scale. Thermal equations of state for Cu and Ag have been developed on the basis of recent thermochemical, X-ray, ultrasonic, theoretical and shock-wave data using formalism from [6]. Parameters of equation of state for Cu and Ag with cold isotherm according to a third∆λ/λ0 0.05 2 order Birch-Murnaghan equation are given in Tab. 1. Deviations of calculated functions from experimental measurements are 0.5-1.5% over the whole PVT range. Therefore hereinafter we will compare the calculated room isotherm of Cu and Ag with Carter et al. [2] data. Fig. 2 shows the difference between newly calculated pressures on room isotherm and the pressures recommended by Carter et al. [2]. This figure suggests that equations of state for Ag from our data and [2] are close but at the same time differences between equations of state for Cu are significant and reach 2 GPa at pressure equal to 70 kbar. Thus, data from Fig. 2 suggest that the ruby pressure scale of Mao et al. [1] underestimates the pressure at each given ruby R 1 line shift by up to 2 GPa. Pressures obtained at given ruby R 1 line shift may be approximated by a third-order Birch-Murnaghan equation with A=1896 and B=9.63 parameters. Here A-parameter was fixed according to initial slope of quasihydrostatic conditions [7]. Dependence obtained for the ruby R 1 line shift with Table 1. Parameters of the equation of state of Cu and Ag. Parameters Cu Ag V0 , cm3 7.113 10.272 K0 , GPa 133.9 100.0 5.24 5.99 K’ 47.24 120.72 ΘB1o , K d1 1.990 39.325 mB1 0.001 1.121 146.57 112.63 ΘB2o , K d2 6.450 4.266 mB2 0.471 0.436 286.65 191.86 ΘE1o , K mE1 1.549 1.443 181.32 – ΘE2o , K mE2 0.980 – 1.975 2.439 γ0 1.100 1.655 γ∞ 2.722 5.089 β a 0 , K–1 -15.95E-6 6.495 g –1 e0, K 10.66E-6 23.27E-6 Pcal-Pexp, GPa pressure gives pressures intermediate 2.5 between the Mao et al. [1] scale and Cu BM3 the Holzapfel [5] independent scale. 2 Ag BM3 Thus, equations of state for Cu and Ag have been developed, which in the 1.5 range of experimental error are consistent with shock-wave, 1 ultrasonic, X-ray and thermochemical 0.5 data in the temperature range from 1020 K to melting temperature and 0 compression x=0.6. From comparison of calculated room isotherms with -0.5 those recommended by Carter et al. 0 20 40 60 80 [2], it follows that the latter deviates Pressure, GPa from our isotherm by up to 2 GPa at Fig. 2. Deviations of pressure on room70 Gpa-pressure, which implies a temperature isotherms of Cu and Ag from data systematic error in the ruby pressure Carter et al. [2]. scale of Mao et al. [1]. We recommend a new ruby pressure scale, which is intermediate between the Mao et al. [1] scale and the Holzapfel [5] scale. Financial support by RFBR, grants N 02.05-64062 and 02-07-90324. References: 1. Mao H.K., Xu J., Bell P.M. // J. Geophys. Res. 1986. V. 91B, P.4673–4676. 2. Carter W.J., Marsh S.P., Fritz J.N. McQueen, R.G. // NBS Spec. Publ. 1971. V 326, P.147–158. 3. Aleksandrov I.V., Goncharov I.V., Zisman A.N., Stishov S.M. // JETP. 1987. V. 93, P.680-691. 4. Zha C.-S., Mao H.-K., Hemley R.J. // Proc. Nat. Acad. Sci. 2000. V. 97, 13494–13499. 5. Holzapfel W.B. // J. Appl. Phys. 2003. V. 93, P. 1813-1818. 6. Dorogokupets P.I. // Geochemistry International. 2002. V. 40, P.132–144. 7. Piermarini G.J., Block S., Barnett J.D., Forman R.A. // J. Appl. Phys. 1975. V. 46, P.2774–2780. 3 Electronic Scientific Information Journal “Herald of the Department of Earth Sciences RAS” № 1(21)′2003 Informational Bulletin of the Annual Seminar of Experimental Mineralogy, Petrology and Geochemistry – 2003 URL: http://www.scgis.ru/russian/cp1251/h_dgggms/1-2003/informbul-1_2003/mineral-3e.pdf Published on July 15, 2003 © Department of the Earth Sciences RAS, 1997-2003 All rights reserved