Anal. Chem. 1991, 63, 2397-2400
for the characterization of chemisorbed species on silver under different environmental conditions. Registry No. Ag, 7440-22-4; HN03, 7697-37-2.
LITERATURE CITED Flelschmann, M.; Hendra. P. J.; McWUen, A. J. J . Chem. Phys. Len. 1974, 26, 163-166.
2397
(7) Goudenned. J. P.; Begun, 0.: Arakawa. E. Chem. Phys. Len. 1982, 92, 197. (8) Msler, M.; Wokaun, A.; VeDlnh, T. J . Chem. Phys. 1985, 89, 1843. (9) Boa, D. W.; Oh, W. S.; Klm, M. S.; Kim, K.: Lee, H. Chem. pIzvs. Len. 1985. ., 720 -.131. 301. -(10) Miller. S. K.; Balker, A.; Meier, M.; Wokaun, A. J . Chem. Soc.,Faraday Trans. 11984, 80, 1305. (11) Garoff. S.: Stephens, R. E.; Haanson. C. D.; Sorenson, 0. K. O D ~ . Commun. 1082, 41, 257. (12) W e b , D. A.; Oaroff, S.; Gersten, J. L.; Nitran, A. J . Chem. Phys.
.-,.
'
Jeanmake, D. L.; van Duyne, R. P. J . Ektroanal. Chem. Interfacial Ekcirochem. #rr. 84. I. Alkecht, M. 0.;Crelghton, J. A. J . Am. Chem. Soc. 1977, 99, 5215. van Duyne, R. P. In Chemkal and B b d w n b l Appmcetkns of Lasers; Moore, C. E., Ed.; Academic Press: New York, 1979 Vol. 4, 101-185.
cheng, R. K.. Futtek, T. E., E&. Suface Enhencsd Ramn Scattehg;
Plenum: New York. 1982.
V N n h , T.; Hlromoto, M.; Begun, G.; Moody, R. Anal. Chem. 1984, 56, 1667.
inaa. ----. -78.- . ~ 3 2 4 .
(13) Sandroff,C. J.; Herschbach, D. R. J . Phys. Chem. 1982, 86, 3277. (14) Mo, Y.; Morke. L.; Wachter, P. Surf. Sci. 1983, 733, L452.
RECEIVED for review March 26,1991. Accepted July 3,1991. The project is financially supported by the National Science Foundation of China.
Preparation of Phosphate Samples for Oxygen Isotope Analysis Ronald A. Crowson*J and William J. Showers Department of Marine Earth and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina 27695-8208 Ellen K. Wright and Thomas C. Hoering Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015 The potential of oxygen isotopic analysis on natural phosphates has long been known but has not been fully realized for want of a simple analytical technique. For example, paleotemperature measurements based on lsO/lsO ratios of fossil carbonates are well established (I). In principle, the corresponding phosphate paleothermometer should be more stable and resistant to alteration in the sedimentary environment because a phosphate ion in a crystalline lattice exchanges oxygen isotopes with water more slowly than carbonate ion. This phosphate paleothermometer, however, is not nearly as well developed and exploited as the one based on carbonate primarily because of the relative difficulty of the phosphate preparation technique (2). A method for the 6lSO isotopic analysis of phosphate was presented by Tudge (2). Subsequent modifications were made by Longinelli and co-workers (3-7) and by Kolodny and coworkers (8-10). In this procedure, phosphate ions are isolated as BiP04.H20 after a three-stage, wet chemical separation. The product is dehydrated to a-BiP04, which is hygroscopic. Karhu and Epstein (11) converted the anhydrous a phase to the leas hygroscopic 0 phase. The resulting bismuth phosphate is reacted quantitatively with bromine pentailuoride to yield 02,that is converted to C02for isotopic analysis in a ratio mass spectrometer. The bismuth phosphate method is not optimal because (1) the preparation method is tedious multistep and time consuming, (2) a relatively large sample is required, and (3) bismuth phosphate is hygroscopic. We have simplified this procedure by using anion-exchange chromatography for isolation and purification of phosphate ions for geological matrices. Phosphate in slightly alkaline solution exists as a trivalent anion that is retained strongly on an anion-exchange resin. Mono- and divalent ions can be washed out completely without loss of phosphate. Using an eluant solution of ammonium nitrate removes the dihydrogen phosphate ion sharply in a minimum volume. Silver phosphate is then precipitated by the method of Firsching (12). Silver phosphate was chosen because it is one of the few phosphates that precipitates from Present address: Geophex, Ltd., 605 Mercury St., Raleigh, NC
27603-2343.
0003-2700/9 1/0363-2397$02.50/0
aqueous solution in a simple stoichiometry without a water of crystallization and is not hygroscopic. Baxter and Jones (131,in a classic study, determined the properties of Ag3P04 and found it suitable (pure, stable, nonhygroscopic) for determining the atomic weight of phosphorus. A preliminary report on the feasibility of the silver phosphate method for isotopic analysis was published by Wright and Hoering (14) in which several problems were identified. These problems have been addressed, and the refined methodology for isotopic analysis is presented here.
EXPERIMENTAL SECTION Materials. Chemicals used in the present work were reagent grade. The NBS 12012reference material (Florida Phosphate Rock Standard) was obtained from the National Institute of Science and Technology, Gaithersburg, MD. The AgBP04internal laboratory reference material is Aldrich No. 33.738-2. The ion-exchange resin is Amberlite IRA-400(OH),a strongly basic gel-type resin (Aldrich Chemical Co.). High-purity bromine pentafluoride (Ozark-MahoningChemical Co., Tulsa, OK), containing less than 1%contaminants, was used to react the silver phosphate. Instrumentation. All samples were digested and prepared in a dedicated room and fume hood system to avoid airborne contamination. Glassware and plastic centrifuge tubes used in this procedure were rinsed repeatedly in deionized redistilled water. All glassware was precombusted at 500 "C for 4 h in an annealing oven prior to use. Silver phosphate samples were reacted in a fluorination reaction line (Figure 1)constructed of all-nickeltubing (No. 201) silver-solderedto monel bellows valves (Nupro No. BF-4BK). Each reaction vessel was constructed of solid nickel stock and connected to a monel bellow valve by a welded solid nickel VCR fitting. The entire reaction line had a total volume, includingthe reaction vessel, of less than 0.2 L. The fluorination reaction l i e was totally dedicated to silver phosphate and non-ferrous silicate minerals (reaction of ultramafic minerals in fluorination lines has been related to slight positive isotopic deviations). Vacuum on the fluorination side of the line was provided by an oil-free,molecular sieve, cryogenic pump (lo-' Torr; Vacsorb by Varion No. 941-6501). Released oxygen gas was purified through two nickel U-traps immersed in liquid nitrogen and converted to C 0 2 in a 600 "C platinum-catalyzed graphit.e 02/C02conversion furnace. The COzwas passed through a silver wool furnace at 650 OC to remove any halogen gas. Vacuum on the borosilicate/quartz glass side of the line used for 02/C02 Q 199 1 Amerlcan Cbmlcal Sockty
23@8
ANALYTICAL CHEMISTRY, VOL. 63,NO. 20, OCTOBER 15, 1991
NI~KER L E A C ~ I O NVESSELS
Fburr 1. Diagram of nickel fluorination reaction line and glass O2 to COP conversion line constructed at NCSU.
conversion was provided by a Hg diffusion pump (lo4 Torr) isolated from the line by a large reentrant liquid nitrogen trap and isolated from the mechanical forevac pump (Sargent Welch 8811) by a similar reentrant liquid nitrogen trap preceded by a 5-A molecular sieve forevac trap (MDC KMST-1002). These two vacuum pumping systems provide an oil-free vacuum for the fluorine reaction and O z / C 0 2conversion lines. Line blanks in this system range from 0.25 to 0.5 pmol of COPand have an average blQ value of +10.5 per mil SMOW. Size of the gas samples were measured by using an Omega pressure transducer (0-5 psi; No. PX-81-005GV) with a resolution of 0.05 pmol over a range of 0.1-100 pmol of gas. C02 gas samples were cryogenically transferred and sealed in borosilicate breakseals (6-mm borosilicate tubing (15)) and transferred to the ratio mass spectrometer (RMS). Gas sampleswere isotopicallyanalyzed by using a Finnigan MAT 251 ratio mass spectrometerwith a modified inlet system and small volume cold fingers (16). With these modifications, gas counting statistics are below 0.02 per mil (al- P O )for samples from 100 to 0.1 pmol of COP The RMS machine standard was calibrated against the NBS-28 stable isotope reference material (assuming a NBS-28 calibration value of 9.64 per mil SMOW) and results are reported as per mil SMOW. Thermal gravimetric analysis (TGA) was carried out by using a Du Pont Series 99 thermal analyzer, equipped with a thermal gravimetric analyzer. Procedure. The following procedural description for precipitation of Ag3P04from phosphate material contains slight modifications from the technique described by Wright and Hoering (14). Approximately 30 mg of phosphate material was dissolved in 2 M HF at room temperature. Digestion was generally completed over a 24-h period. The phosphate solution and residue composed of calcium fluoride was separated by centrifugation and decanted into a clean 15-mL polypropylene centrifugetube. The remaining calcium fluoride and phosphate solution was rinsed once with 2 mL of deionized redistilled water centrifuged and decanted into the first phosphate solution. The decantant was then neutralized with 2.2 mL of 2 M potassium hydroxide. Amberlite IRA-400(0H) (2 mL in water) was then added to the neutralized solution after the ion-exchange resin had been washed free of chloride ions with deionized redistilled water. Polypropylene centrifuge tubes containing the ion-exchange resin with the neutralized solution were placed on an orbital shaker table and gently shaken for 24 h. The excess liquid was discarded and the Amerlite washed three times with deionized redistilled water. To elute the phosphate, 13 mL of 0.5 M ammonium nitrate was added and gently shaken for 5 h. The Amberlite and the solution were then separated by slowly washing the Amberlite on a 63 pm stainless steel sieve using 17 mL of 0.5 M ammonium nitrate solution. Silver phosphate was precipitated from the wash solution by adding 15 mL of silver nitrate solution and slowly warming to 50 O C while a constant liquid level was maintained by periodically adding distilled water. Silver phosphate precipitates from
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400
600
800
1000
1200
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Flgurr 2. Thermal gravimetric analysis of NBS 120c standard reference material (Florida Phosphate Standard) under nltrogen atmospbe, warmed at 10 "Clmin. Lack of weight loss below 400 "C indicates that silver phosphate does not absorb atmospheric moisture.
the eluate by the method of Firsching (12). Because the silver phosphate has a high gravimetricfactor, the precise determination of phosphate is possible. The silver phosphate crystals were concentrated by centrifugation, washed three times in deionized redistilled water, and air-dried at 60 O C . At this stage, the crystala contain some organic contamination derived from an organic solution derived from the Amberlite ion-exchange resin, and is a greenish brown color.
RESULTS AND DISCUSSION Atmospheric Water Absorption on Ag304. Absorption of atmospheric water vapor on silver phosphate was investigated by allowing several grams of the Aldrich Ag3P04 standard to be stored in a room with >70% humidity for more than 2 months. The standard was not placed in a drybox or desiccator as is normal for storage of most isotope standards and bismuth phosphate. Thermal gravimetric analysis (TGA) of the exposed silver phosphate indicated no detectable weight loss between 20 and 500 "C (Figure 2). This indicates insignificant atmospheric water absorption by Ag3P04 and suggests that dryboxes and desiccators normally used for storage and processing of bismuth phosphate are not required for silver phosphate handling. Reaction Temperature of Ag3P04 with BrFs. Optimum temperatures for the Ag3P04reaction with BrFs were determined by reacting 10-15 mg of the Aldrich silver phosphate with a 6:l to 1 0 1 mole excess of BrF, for a 22-h period (Figure 3). Because bismuth phosphate is reacted a t 150 "C and quartz is reacted at 600 O C (In,the reaction temperature was varied from 250 to 700 "C. Consistent b1*0 values for the
ANALYTICAL CHEMISTRY, VOL. 63, NO. 20, OCTOBER 15, 1991 2389 =115.12 I I
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NBS lzOe
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200
400 500 600 700 REACTION TEMPERATURE (C) 300
800
Flgw 3. Comperlson of reaction temperatwe and Isotopic value (per mil SMOW) of the Aldrlch silver phosphate and NBS 12Oc standard reference materlal (Florida Phosphate Rock). Consistent analytical results are observed for reaction temperatures above 425 "C. The mean of the >425 "C analysis Is 19.64 f 0.08 per mil SMOW for A#lch silver phosphate and 21.33 f 0.05 per mll SMOW for NBS
12oc.
Ag3P04/BrF5reaction are obtained for temperatures greater than 425 "C. Eleven samples reacted at or above 425 "C had mean isotopic values for the Aldrich Ag3P04reagent of 19.64 per mil SMOW with a u1 of 0.08 per mil (n = 11). Samples reacted at or below 400 "C show an isotopic depletion that is temperature dependent. These results suggest that Ag3P04 should be reacted with BrF5 at or above 425 "C,but this temperature threshold must be verified with Ag3P04crystals precipitated from phosphate material to ensure that other interferences are not present. Organic Contamination Removal. Organic contaminant found in the precipitated silver phosphate crystals most likely originated from the organic ion-exchangeresin used to extract phosphate from the HF solution (14). Contaminated silver phosphate crystals were generally dark brown to greenish brown in color and cohesive. Organic contaminants are effectively removed from carbonate samples prior to isotopic analysis by vacuum roasting; treatment with chlorox, hydrogen peroxide, and plasma ashing have also been employed with varying degrees of success. Heating under vacuum was selected as the best method to remove organics from silver phosphate because it did not employ the use of an oxidizing agent, thus reducing the potential for isotopic fractionation. To investigate the efficiency of vacuum heating for removal of organic contaminants from Ag3P04,crystals produced from NBS 120c were heated a t 106 Torr for 1h. The temperature was varied from 200 to 500 OC and the product reacted with BrF6at 425 "C for 22 h (Figure 4). Consistent isotopic values were obtained when the samples were heated under vacuum above 400 "C. Below 400 "C negative deviations from the average NBS-12Oc value were observed, most likely due to the incomplete removal of organic contaminants. Differences in isotopic values of samples heated at temperatures below 400 "C in different precipitation batches were most likely due to varying amounts of organic material in the Ag3P04crystals resulting from slightly different phosphate/Amberlite concentrations during the ion-exchange process. The isotopic resulta of varying reaction temperatures for NBS 12012(Florida Phosphate Rock Standard) (Figure 3) agree well with the Aldrich AgaO, reagent reaction temperature data. Consistent 6% values were obtained for crystala precipitated from NBS 120c phosphate material at reaction temperatures above 400 "C.
Variation of Isotopic Values as Related to Duration of Reaction. The effect of reaction time on isotopic value and yield was determined by reacting heated silver phosphate extracted from NBS 120c with bromine pentafluoride at 450 "C. Reaction time was stepped a t 2-h intervals from 8 to 22 h. Consistent gas yields of 100% were observed for reactions that were 12 h or longer (Figure 5). However, consistent isotopic results were not obtained unless the reaction went 16 h or longer (Figure 5). NBS 120c samples that were reacted
20.7 20.6 4
100
200 300 400 500 HEATING TEMPERATURE
Figure 4. Comparison of heating temperature at lo-' Torr of silver
phosphate produced from NBS 12Oc standard reference materiel
(Fkrida phosphate Rock) and isotopic value of oxygen (per mil SMOW). Standards were heated for 1 h. Different symbols represent two separate runs. Consistent values were obtalned above 400 "C.
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PERCENT RECOVERY
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25
Figure 5. Comparison of reaction time vs percent recovery vs bl8O of sifver phosphate produced from NBS 12Oc (Florida phosphate Rock). Percent recovery Is expressed as 1OO(pM CO2(yielded)lpMAg,PO,(reacted)). Error bars are 0.4% recovery, which is u1 of the values of the analyses >12 h. 6"O of NBS 120c is expressed in per mil SMOW, error bars are 0.049 per mil which is u, of the values of the analyses >16 h. A line is drawn across the 100% recovery level and the NBS 12Oc value of 21.33. Consistent percent recovery Is observed for reaction times greater than 12 h, while consistent isotopic results are observed for reaction times greater than 16 h. All samples were reacted at 450 "C.
less than 16 h had negative isotope deviations, indicating incomplete reaction. Differences between the results indicated by yield and isotopic data suggest that the SleO measurements were more sensitive in recording complete reactions than percent yield calculated from sample weights and the size of C02 gas samples.
Effects of Sample Size and Extraction Efficiency of Ion-ExchangeResin. To determine optimum relationships between sample size and quantity of ion-exchange resin, varying amounts of NBS-120c ranging from 1to 101 mg were digested and placed in exactly 2 mL of resin. Phosphate was then extracted and precipitated as silver phosphate and anal+ for percent recovery and PO. Samples containing more than 43 mg of NBS-120c had yields significantly lower than 100% (Figure 6). The 6 l 8 0 value of low yield samples was also more positive, indicating a loss of lighter isotopic anions in the r i n s i i procedure, which most likely resulted from anion overloading of ion-exchange resins. NBS 12012contained approximately 33.34% P205by weight, as well as several other potentially interfering anions that could have been adsorbed onto the ion-exchangeresin. These other ions could have contributed to exchange resin overloading but did not interfere with precipitation of Ag3P04 after elution from the ion-exchange resin (14). Because different phosphate material can contain different proportions of potentially interfering anions and the proportion of Amberlite used in relation to sample weight may vary, the overloading threshold
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Flgurr 6. 6'6 values plotted against the percent recovery of silver phosphate and sample welght produced from various amounts of NBS 120c loaded onto 2 mL of btwxchange resin. The posithre deviation
in isotopic values above 40 mg and reduced percent recovery are due
to overloading the resin.
should be determined for each type of phosphate sample material analyzed. For NBS 12012,approximately 2-30 mg of sample material loaded onto 2 mL of ion-exchange resin (suspended in water) gives consistent results. Precision of the Ion-Exchange Technique. The mean for all NBS 120c analyses that were completed for a >16-h reaction time and a >42.5 OC reaction temperature is +21.33 per mil SMOW ( n = 15) with an analytical precision (al)of 0.05 per mil. Analytical precision of the a-bismuth phosphate technique is *0.3 per mil (9, 10). The a-bismuth phosphate method yielded P O values for NBS 120b of +20.1 per mil (n = 13, u1 = 0.3 per mil (10)). The @-bismuthphosphate yielded 6% values for NBS 120b of +20.5 per mil (n = 5, a1 = 0.1 (10)). Karhu and Epstein (11)stated that the difference between the a-bismuth phosphate technique and the 0-bismuth phosphate technique was +1.1to +1.9 per mil SMOW. However, standard deviation between the two bismuth phosphate techniques varied from 0.45 per mil to 1.9 per mil (11). Our average of +21.33 f 0.05 per mil for NBS 120c was outside the range of values given by Shemesh et al. (9, 10)for NBS 120b using the a-bismuth phosphate technique. However, given the differences between the two bismuth phosphate techniques, values for NBS 120c obtained by the Ag3P04 technique were not unreasonable. These discrepancies could be related to analytical procedure differences or inhomogeneities related to different aliquots of the NBS standard reference material (Florida Phosphate Rock, NBS 120b vs NBS 120~1,but not to interlaboratory calibration problems. The three labs that have presented data for NBS 120 Florida Phosphate Reference Material (Hebrew University, Cal Tech, NCSU) have also run the NBS 28 Quartz standard, the Cal Tech Rose Quartz standard, and the NCSU Quartz standard. The analytical results suggest that all three labs agree within the stated precision of replicate analyses (al= 0.07 to 0.4 per mil). Differences between the NBS 12Oc value presented here and the NBS 120b value of Shemesh et al. (9,10)are also in the right direction, if Karhu and Epstein's (11)suggestion is correct that the a-bismuth phosphate technique is susceptible to atmospheric water contamination. Our results prove that the Ag3P04technique is not susceptible to atmospheric water problems. Karhu and Epstein (11) stated that analytical precision of the anhydrous bismuth phosphate technique is 0.12 per mil (al)for phosphates from chert samples, while repeated fluorinations of bismuth phosphate powder have a precision of 0.09 per mil. Repeated fluorinations of the Aldrich Ag3P04yielded an analytical precision of 0.08 per mil (al,n = 111, which was similar to the analytical precision of the total Ag3P04 procedure using NBS 120c.
CONCLUSIONS The Ag3P04technique developed by Wright and Hoering (14) and presented in refined form here has been demonstrated to be a viable alternative to the bismuth phosphate
technique. Problems resulting from organic contamination, time and temperatures of the Ag$04 reaction with BrF5, ratio of sample weight to amount of ion-exchange resin, and analytical precision of the Ag3P04technique have been resolved. Utilizing the Ag3P04technique, we have been able to analyze the NBS 120c standard reference material (Florida Phosphate Rock with sample size ranging in size from 2 mg to 30 mg) with a standard error of *0.05 per mil (al). Major advantages of the Ag3P04technique are that the method is simple (one digestions and precipitation) and that the final product is not hygroscopic. Application of this new method to small phosphate samples is especially attractive, because the sample size can be reduced without increased analytical error resulting from contamination from atmospheric water. The Ag3P04 separation and purification technique is simple and labs can prepare samples without elaborate handling procedures or concern for detrimental effects of contamination by atmospheric water prior to fluorination. Reduction in sample size will enable investigation of the P O content of individual grains of sedimentary phosphate systems. This is important in order to assess the susceptibility of various grain types of diagenesis and checking the validity of phosphate paleotemperature records (18).
ACKNOWLEDGMENT We are indebted to B. Genna for technical assistance at North Carolina State University, Dr. Stanley R. Riggs at East Carolina University, and P. Hare a t the Geophysical Laboratory of the Carnegie Institution of Washington. We would also like to express thanks to the late I. Lynus Barnes and the Inorganic Analytical Research Division of the National Institute of Standards and Technology (NIST) for providing the NBS 120c Florida Phosphate Rock Standard. We acknowledge Samuel Epstein and Elinor Dent of the California Institute of Technology for providing us the Cal Tech Rose Quartz standard and interlaboratory calibrations of NBS 28 Quartz, NCSU Quartz, and the NBS 120b Phosphate Reference Material. We also acknowledge Yehoshua Kolodny of Hebrew University for providing interlaboratory calibrations of NBS 28 Quartz, NCSU Quartz, and the NBS 120b Phosphate Reference Material.
LITERATURE CITED (1) Hoefs, J. Stable Isotope Geochemistry;Springer-Verlag: New York, 1980; 208 pp. (2) Tudge, A. P. Geochim. Cosmhim. Acta 1960, 18, 81-93. (3) Longinelli, A.; Nuti, S. Earth Planet. Sci. Lett. 1966, 5 , 13-16. (4) Longinelli, A. Nature 1965, 207, 716. (5) Longinelli, A.; Nuti, S. Earth Planet. Sci. Lett. 1973, 19, 373. (8) Longinelli, A.; Nuti, S. Earth Planet. Sci. Lett. 1973, 20, 373. (7) Lonsinelli, A.; Barteiloni, M.; Cortecci. G. Earth Planet. Sci. Lett. 1976, 32, 389. (8) Kolodny, Y.; Luz, E.; Navon, 0. Earth &net. Sci. Lett. 1963, 64, 389-404. (9) Shemesh, A.; Kolodny, Y.; Luz, B. Earth Planet. Sci. Lett. 1863, 64, 405-416. (10) Shemesh, A.; Kolodny, Y.; Luz, E. Geochim. Cosmochim.Acta 1968, 52, 2565-2572. (11) Karhu, J.; Epstein, S. Geochim. Cosmochim. Acta 1866, 50, 1745-56. (12) Firsching, F. H. Anal. Chem. 1961, 33, 873-87. (13) Baxter, G. P.; Jones, G. J . Am. Chem. SOC. 1910. 32, 298-318. (14) Wright. E. K.; Hoerlng, T. C. Annu. Rep. Dk. Geophys. Lab., Camgie Inst. Washington 1969, 2150, 137-41. (15) DesMarais, D. J.; Hayes, J. M. Anal. Chem. 1976. 48, 1651-1652. (16) Showers, W. J.; Genna, B.; Palczuk. N. Unpublished work. (17) Clayton, R. N.; Mayeda. T. K. Gmchim. Cosmhim. Acta 1963, 27, 43-52. (18) Crowson, R. A.; Showers, W. J.; Rlggs, S. R. Geol. Soc.Am. Abstr. progs. 1990, 22.
RECEIVED for review January 17,1991. Accepted July 10,1991. Support for this research was provided by the National Science Foundation Grant No. OCE87-10311. Portions of this work were presented at the Annual Geological Society of America meeting in Dallas, TX,Nov 1,1990 (Abstract No. 11179). This work will be included in the dissertation of R.A.C. to be submitted in partial fulfillment of the requirements for the Ph.D. degree from North Carolina University.
