2516
J. Pbys. Chem. 1991, 95,2516-2519
electrolyte solutions at concentrations 1 1 0 mM is attributable to a lack of structure in the ion atmosphere around the reference ion and its failure above 10 mM to the onset of structural features in the ion atmosphere. The GCMC simulations carried out here appear to indicate that a dielectric continuum representation of solvent provides with a viable alternative to fully discrete simulations including explicit waters for the purposes of calculating thermodynamic properties of polyelectrolyte solutions. The calculated excess chemical potentials suggest that in the case of simple electrolytes ([NaCI],,) the interionic interactions become stronger with increasing salt concentrations, resulting in more negative excess chemical potentials and activity coefficients much less than unity. In the case of a mixture of simple and polyelectrolyte solution ([NaCl NaDNA],,), at low salt, the stronger attractive interactions between the counterions (Na+) and the polyanion (DNA) and the repulsive interactions between co-ions with themselves and with the polyanion lead to positive co-ion (Cl-) excess chemical potentials. The co-ion excess chemical
+
potentials become more negative with added salt, since more counterions become available for favorable interionic interactions. The opposite trends hold true for counterion excess chemical potentials, with the latter dominating the total excess chemical potential. Thus, nonideality in a polyelectrolyte and simple electrolyte mixture increases with dilution contrary to the behavior in simple electrolyte solutions.
Acknowledgment. This research is supported by grants from the NIH (GM-37909), from the Office of Naval Research (N-0014-87-K-0312), and via the Bristol Myers Corp. and State of Connecticut High Technology Research and Development Award. Supercomputer time was provided on the Cray Y-MP by the Pittsburgh Supercomputing Center. The authors are thankful to Dr. S.Swaminathan, Dr. K. Sharp, and Prof. B. Honig for useful discussions on this project. The authors also express their gratitude to Prof. H. L. Friedman and Prof. M. T. Record, Jr., for their extremely valuable comments on the manuscript. Registry No. NaCI, 7647-14-5.
New Phase of Oxygen at High Pressure and Low Temperature W. B. Carter,* D. Schiferl,* M. L. Lowe, and D. Gonzales Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received: April 10, 1990; In Final Form: July 16, 1990)
We have extended the phase diagram of oxygen to 34 GPa at 20 K with Raman spectroscopy on samples in diamond anvil cells. At 25.0 GPa and 20 K,a new phase, which we term {-02, appears. In going from c-O2to {-02, the two low-frequency intermolecular vibrational modes split abruptly by about 10 cm-l, while the vibron remains a single peak. The transition appears to be first order.
Introduction The properties of solid oxygen have been of considerable interest for many years. At low temperatures and pressures, the two ?r* electrons on each O2 give rise to crystal structures in which magnetic ordering plays an important At pressures on the order of 10 GPa, oxygen begins to show dramatic color changes as the nature of the bonding in the solid changes?-' The effect of these changes on the magnetic properties of oxygen is currently unknown. After an uncertain start, the phase diagram of oxygen at high pressures now seems reasonably understood. Early work included reports of new phases which could not be subsequently confirmed, and many phase lines were incorrectly determined primarily due to poor temperature calibration in the high-pressure cells. The situation was further complicated by the discovery of two metastable phases! The confusing history of the oxygen phase diagram up to 1984 was carefully reviewed by Olinger, Mills, and Roofs8 They introduced a consistent notation for naming the established phases. Hochheimer and co-workers9 and Jodl, Bolduan, and Hochheimer'O extended the phase diagram to low temperatures to include pressures up to approximately 10 GPa at 10 K. Yen and Nicol" added the high-temperature region up to 17 GPa and 650 K. These authors provided a critical review of the experimental situation up to 1987 and presented their conclusions as their Figure 8. Recently, preliminary X-ray diffraction results indicate that t - 0 2 is the stable form at room temperature up to at least 65 GPa.l* The results of these groups of workers8-12seem to be in very close agreement, although there are still some minor problems at low temperatures and pressures. In this paper we follow the phase notation of Yen and Nicolll and Olinger et a!.* Authors to whom correspondence should be addressed.
0022-3654/91/2095-2516$02.50/0
The purpose of this work was to extend the phase diagram of oxygen to much higher pressures at cryogenic temperatures. A new phase, which we term C-O2,appears above 25.0 GPa at 20 K, as described below. Experimental Section We used four different Merrill-Ba~sett'~diamond anvil cells to study samples of 1602 between 10 and 34.2 GPa over the temperature range 10-327 K. Because such high pressures are not routinely reached with Merrill-Bassett cells, we provide the main details of their construction here. Cell 1 was constructed to Inconel 718 and had 0.25-carat diamonds with 600-pm culet diameters. Cell 2 was constructed of beryllium copper and fitted ( I ) Donohue, J. The Sfructure of the Elements; Wiley: New York, 1974. (2) Etters, R. D.; Kobashi, K.; Belak, J. Phys. Rev. B Condens. Matter 1985, 32, 409. (3) LeSar, R.; Etters, R. D. Phys. Rev. B: Condens. Matter 1988, 37, 5364. (4) Nicol, M.; Hirsch, K. R.; Holzapfel, W. B. Chem. Phys. Lett. 1979, 68, 49. (5) #Amour, H.; Holzapfel, W. B.; Nicol, M. J . Phys. Chem. 198L8.5,
131. (6) Schiferl, D.; Cromer, D. T.; Schwalbe, L. A.; Mills, R. L. Acra Crystallogr., Sect. B.: Struct. Crystallogr. Crysr. Chem. 1981, 89, 153. (7) Nicol, M.; Syassen, K. Phys. Rev. B Condens. Matter 1983.28, 1201. (8) Olinger, 9.; Mills, R. L.; Roof, R. B. J . Chem. Phys. 1984,81,5068. (9) Hcchheimer, H. D.; Jodl, H. J.; Henkel, W.; Bolduan, F.Chem. Phys. Lett. 1984, 106, 79. (10) Jodl, H. J.; Bolduan, F.; Hochheimer, H. D. Phys. Rev. B Condens. Matter 1985, 31, 7316. (11) Yen, J.; Nicol, M. J . Phys. Chem. 1987, 91, 3336. (12) Desgreniers, S.; Vohra, Y. K.; Ruoff, A. L. Bull. Am. Phys. Soc. 1988, 33, 521 [Paper 512-81. (13) Merrill, L.; Bassett, W. A. Rev. Sci. Instrum. 1974, 4.5, 290. (14) Schiferl, D. High Temp.-High Pressures 1977, 9, 71.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2517
New Phase of Oxygen with 750-pm culet diamonds. Cell 3, which was originally intended for very high pressure single-crystal X-ray diffraction studies on eoz,was constructed of Inconel 718, with specially prepared Kawecki-Berylco HIP50 beryllium (now discontinued) backing plates, and 300-rm culet diameter 0.25-carat diamonds. Cell 4 was constructed of Inconel 718, with 400-pm culet diameter diamonds. The highest pressures, 34.2 and 32.1 GPa, were achieved with cell 3. The bulk of the data in the pressure range from 10 to 30 GPa was taken with cells 1 and 4. Initially only cell 1 was used, but since it was limited in pressure to 26.6 GPa, cell 4 was loaded to check continuity with points taken with cell 3. Cell 2 was used to check some of the low-pressure data taken with cells 1 and 4. Temperature control and measurement were identical for each cell. The cell was mounted on the cold finger of a Model DE-202 Displex refrigerator. Thermocouples were attached to the front, back, and gasket of the cell, as well as to the cold finger of the refrigerator. A Scientific Instruments Series-5500 temperature controller was used to monitor these thermocouples and to control a heating element attached to the cold finger of the Displex. Temperatures within the range 10-350 K could be held within f 2 K for several hours with this arrangement. Temperature gradients across the cell (face to face) were measured to be no more than A 2 K. For pressure measurements, we used the ruby l~minescence'~~' method with temperature corrections. The pressure P in GPa was calculated from the equation P = 380.3{[vo(T)/vp(T)]~- 1) where vp( 7) is the measured frequency of the R1 ruby peak at pressure P and temperature T and vo(T) is the corresponding frequency of the R1 peak at zero pressure and the same temperature T. The zero-pressure R 1 ruby peak frequency vo( T ) is obtained from the empirical expressionts 169.77(T/300)' VO(T) 14422.0 - 36.612(T/300)'/2 264.54(T/300)s/2 + 1 12.14(T/300)3
s8
0
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(15) Forman, R. A.; Piermarini, G. J.; Barnett. J. D.; Block, S.Science 1972, 176, 284. (16) Barnett, J. D.;Block, S.;Piermarini. G. J. Reo. Sci. Imrrum. 1973. 44, 1. (17) Mao, H. K.; Bell, P. M.;Shaner, J. W.; Steinbcrg, D. J. J. Appl. Phys. 1978, 49, 3276. (18) Buchsbaum, S.; Mills, R. L.; Schiferl, D. J . Phys. Chrm. 1984.88, *e**
LJLL.
(19) Lowe. M.;Kutt, P.; Blumenroeder, S.Compur. Phys. Commun. 19%8,
50, 367.
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Both the ruby luminescence pressure measurements and the Raman spectra were taken with a Spex Model 1403 0.85-m doublegrating spectrometer. A backscattering geometry was used. For the pressure measurements, the 647.1 - and 476.2-nm laser lines from a Spectra Physics 164 krypton ion laser were used. Only the 647.1-nm line was effective in obtaining Raman spectra. Light was detected by an RCA C3 1034 low dark count photomultiplier tube, which was refrigerated by means of a Products for Research thermoelectric cooler. The laser power incident on the sample was 50-100 mW. At low temperatures, this heated the sample only 1 or 2 K. An IBM-PC-based data collection and analysis system was used in acquiring the Raman data.lg The Displex refrigerator was equipped with feedthroughs to allow pressure to be changed at low temperature. Although this was done nominally at 20 K, the heat conducted to the cell when the drivers engaged the pressurizing bolts increased the sample temperature to between 30 and 50 K. In order to check the possibility of hysteresis or metastable phases, the pressure was increased sometimes at low temperature, and at other times at room temperature, followed by cooling. The new t phase was discovered after cell 3 was cooled from 295 to 20 K. The pressure rose during cooling due to differing thermal contraction of the various elements of the cell, from 29.0 to 34.2 GPa. We decided not to change the pressure of this cell because the sample is also ideally suited for future X-ray diffraction experiments. A second run was made about a year later,
160.0
39
: m.0
m.0
m.0
206.0
RamanShlft (an") Figure 1. Appearance of the vL1 peak in eo2at 20 GPa and 2'.02 at 26 and 32 GPa. The solid lines are calculated by using results obtained from the Lorentzian fitting program. For each spectrum, the fitted Lorentzian functions and linear background are given by solid lines, along with their sum, which is the solid line going through the data points. (a) illustrates a typical r - 0 2 peak at 19.8 GPa and 20 K, with rLI = 11.0 f 0.3 cm-I, vLI = 167.6 f 0.1 cm-I, and ILl= 670 f 17, m = 0.11 f 0.16,b = 175 f 31, and fit x i = 1.92. (b) shows the unresolved doublet found at 29.6 = 7.3 f 0.5 cm-I, vLla = 192.9 f 0.2 cm-l, ILI, GPa and 20 K, with rLla = 472 f 39, r L l b 10.9 h 0.3 "I, YLlb = 201.8 f 0.1 Cm-', ILlb 1410 f 40, m = -1.4 f 0.2 cm, b = 494 f 36, and x i = 1.29. (c) contains a characteristic high-pressure {-oxygen peak at 32.3 GPa and 20 K, with rLI.= 4.0 0.2 cm-I, vLla = 201.2 h 0.1 cm-I, ILI. = 706 h 27, r L l b = 6 . 3 f 0 . 2 c m - ' , v L l b = 2 1 1 . 8 f 0 . 1 cm-l,ILlb=1 0 6 0 + 3 0 , m = - 9 . 1 f 0.3 cm, b = 2596 i 58, and x i = 0.95.
after the pressure in cell 3 relaxed to 28.8 GPa at rmm temperature. When the cell had oooled to 20 K, the pressure increased to 32.1 GPa. No other diamond anvil cells suitable for reaching pressures in excess of 30 GPa were available.
2518 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
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of the goodness of fit was provided by the reduced chi-square xfn given by
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xi, = x 2 / m where m = N - n is the number of degrees of freedom when fitting N data points to n parameters, and x2 has the standard definition2'
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18 24 90 sa R e a w e (wa) Figure 2. Pressure dependence of uLI, vL2, and v,ibmn at 20 K. Solid squares indicate the presence of the {phase, and the solid circles indicate the presence of the z phase. (a) uLI vs P (b) vLz vs P and (c) vVibronvs P. 12
A Lorentzian fittingaJ1 program was used to determine whether the observed Raman peaks were singlets or unresolved doublets. Each spectrum was deconvoluted by using one or two Lorentzian curves and a linear background. The Lorentzians had to form r2
I ( v ) = Io r2
+ 4(v - uo)2
where Io is the maximum height of the peak, r is the full width at half-maximum, and uo is the frequency at maximum. The linear background used in the fit had slope m and intercept b. Figure la-c illustrates the results obtained from this program. A measure (20) Brister, K. Private communication. (21) Bevington, P.R.Dota Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969. ( 2 2 ) Johnson, S . W. Private communication. (23) Schiferl, D.; Johnson, S. W.; Zinn, A. S . High-pressure Res. 1990, 4, 293.
Results The principal result of this work is the discovery of a new phase of solid oxygen, which we designate as {-0,. The {and t phases are distinguished from each other by differences in their lowfrequency Raman modes. There are two such modes, uLI and uL2, in eo2.On transforming to {-02, each of these modes splits into a pair of modes, uLlaplus VLlb and uLza plus YL2br respectively. The splitting of the uL1 peak is better resolved than that of the uL2 and was therefore used as the primary indicator for the transition. Figure la-c shows the appearance of the uLI peak as it splits with increasing pressure at 20 K. The vLI peak is single up to 25.0 GPa and is an unresolved doublet up to about 30 GPa. By 32.1 GPa, the vL1 peak is a resolved doublet. This result was confirmed by noting that we could clearly best fit uLI up to 25.0 GPa with single-Lorentzian peaks, while double Lorentzians separated by about 9 cm-' were required at pressures above 25.0 GPa. At these pressures the Raman line widths I' of the lattice modes do not exhibit any significant trends. Furthermore, the intensity ratio of the doublet lines does not seem to change with pressure. The uL2 peak was scanned initially but, because of limited time, was not followed on later runs. Consequently, the behavior of the vL2 peak has not been so well characterized as that for vLI. At 32.1 and 34.2 GPa, and 20 K, the vL2 peak exhibits a striking asymmetry. However, at lower pressures where vLI was shown to be asymmetric, no splitting in the vL2 peak could be resolved with the fitting techniques available. In contrast to the low-frequency modes, the vibron frequency vvibron does not exhibit any splitting. No new modes with frequencies markedly different from the values of vL1, uL2, and uVih in t were found. Figure 2 depicts the pressure dependence of vL1, vL2, and v,ib,on at 20 K. There appears to be no radical shift in frequency at the transition for uLlrand the separation of the doublet which makes up the uL1 peak above the transition apparently does not change greatly between 25.0 and 34.1 GPa. The uU and uVih branches of the spectrum do not appear to shift abruptly in frequency at the transition, but have not been studied as carefully as uLI. A run was made using cell 3 where the temperature of the sample was increased from 20 to 300 K in increments of 50 K and was held a t each temperature long enough to determine the pressure and to measure uLl, uLZ,and vvibron. Figure 3 shows the variation of vL1 during this run. In {-02, the separation of the doublets making up the vLI branch remains essentially constant until it collapses into the single peak characterizing e - 0 2 . The
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2519
New Phase of Oxygen
A0
4!0
SA0
6LO
700
T(KI
F i 4. Phase diagram of oxygen: (-O,, eo2 Filled squares represent existence of the {phase, and filled circles denote the t phase. Note that the error bars for each point are smaller than the symbols used. Also, near the transition some points are omitted to preserve clarity. The structure of the low-pressure, low-temperature region of the diagram is somewhat uncertain in the literature and is left blank. The remaining phase lines are drawn from refs 8-1 I .
pressure in the cell changed with increasing temperature due to unequal thermal expansion between parts of the cell but changed reproducibly during each run. With cell 3, the transition was observed to take place between 29.7 f 0.2 GPa at 200 f 2 K and 28.7 f 0.9 GPa a t 200 f 2 K. However, results from another run, using cell 4, indicate the transition occurring between 29.1 GPa a t 160 K and 29.4 GPa and 180 K. The transition with temperature is, therefore, ill-defined at present.
Discussion The structure of the orthorhombic 6 phase of oxygen has been shown to be similar to that of the monoclinic a phase. Preliminary X-ray diffraction data show that the e and Q phases have monoclinic structures that are also related to the a-O2structure.22
The splitting in 5-0,of the vLI and vL2 branches of e - 0 2 suggests that the 5 phase is a further perturbation of the monoclinic structure. The vibrons Seem unaffected, although we do not have enough pressure points to determine whether there is a jump in any of the frequencies at the e5 transition. This transition appears to be first order because the splittings appear abruptly and remain essentially constant in {-02.That the low-frequency modes both split strongly suggests that the e-5 transition involves a doubling of the unit cell. It is possible that the splitting is the result of a mixture of two phases. However, this seems unlikely due to the fact that the L l a and L l b lines split symmetrically from the L1 line as shown in Figure 2a. Furthermore, neither the line widths nor the relative intensities of the L l a and L l b change with increasing pressure above 25 GPa. The phase diagram of oxygen is presented in Figure 4. The solid symbols represent the P,T points where e and 5-0, have been observed in this work. AT 20 K, 5-O2appears at pressures above 25.0 GPa. On heating at around 29 GPa, 5-O2transforms back into e-O2between 160 and 250 K. This observation is consistent with that of Desgreniers, Vohra, and Ruoff,I2 who found the e phase to be stable up to at least 65 GPa a t room temperature. Based on their finding and data presented in this paper, approximate limits on the phase boundary between 5-O2and e-O2 can be seen. Because the transition currently is ill-defined, the phase boundary is not indicated. The boundaries of the stable phases described by Yen and Nicol," however, are included in Figure 4. Our discovery of the 5 phase suggests the possibility that more phases may be found in oxygen at low temperatures and even higher pressures.
Acknowledgment. We are grateful to Dr. K. Brister (Cornell) for providing a copy of his excellent Lorentzian peak fitting program. We also appreciate the help of C. A. Vanderborgh in transferring the program to our computer and in using it. Dr. S.K. Schiferl offered invaluable advice on the subtle properties of Lorentzian functions. We also thank Dr.P. Kutt for the data acquisition software. Finally, it is a pleasure to thank Dr.R. L. Mills, Dr. R. LeSar, and Professor M. F. Nicol for stimulating discussions as this work was being done. This work was supported by the U.S.Department of Energy. Registry No. 02, 7782-44-7.
