mL of seawater was reduced to 10 mL of CHC& solution of Pb(DDC)2. The extraction yield of the three metals with the volume ratio of 50:l was tested with radioactive traces and was beyond 99% at pH 2-3. No activity of the three metals was found in the ampoule from the second extraction. Figure 2 shows the y spectrum after 6-h irradiation at a neutron flux of 2 X 10” n cm-’s-l and 10-h cooling time. It is clear that a large amount of Na and Br in seawater was removed by the preconcentration procedure (only a trace of bromine remained and was found in the y spectrum), The y energy for the determination of each metal is as follows: 77.6 keV for Hg, 411.8 keV for Au, 511.0 keV for Cu. Covell’s method was used for the calculation of the peak areas (23,24). The possible interference of the 70.8 keV Hg x-ray from ”‘Au to the 77.6 keV lg7Hgy ray was found negligible in the case of our seawater sample. This was confirmed by the following experiment. The y peaks of both known amounts of lg8Au and lg7Hgwere measured independently. They were then mixed together and the y peaks were re-measured. The contribution from the 70.8 keV Hg x-ray of ”‘Au to 77.6 keV lg7Hgwas examined for various combinations. It was found that the contribution was less than 0.5% when the ratio of mercury content to gold content is larger than 1.5 as is the case in our seawater sample. Copper can be determined with the 511.0 keV annihilation peak without subtracting the similar annihilation peak from Na or other metals because of their absence in the y spectrum as can be seen in Figure 2. Copper-64 was also confirmed by half-life measurement. The content of the three metals in the coastal surface seawater from the Taiwan Strait located at 24’ 51’ N and 120’ 54’ E was determined as Hg 0.102 f 0.012 ppb, Au 0.072 f 0.010 ppb, and Cu 2.34 f 0.09 ppb, respectively, with the error indicated by standard deviation. The gold content compares well with the result for the surface seawater of San Francisco (12). The copper content is in good agreement wth several reported results (25-27). The mercury content was found to be somewhat higher than the average of the surface sea water reported in literature (28-30). This may be due to the fact that the location of sampling is near the mouth of a river into which industrial wastes and/or fungicides containing mercury might have been discharged.
ACKNOWLEDGMENT The authors thank the National Science Council for financial support. They are also indebted to S. Tanaka of the Institute for Nuclear Study of the University of Tokyo for reading the manuscript and suggestions.
LITERATURE CITED
(16) (17) (18) (19) (20)
(21) (22) (23) (24) (25) (26) (27) (28) (29) (30)
F. W. Wilshire, J. P. Lambert, and F. E. Butler, Anal. Chem., 47, 2399 (1975). S. Meloni, V. Caramella-Crespi, M. T. Ganzerli-Valentini, and P. Borroni, Radiochem. Radioanal. Lett., 25, 117 (1976). J. A. Buono, R. W. Karln, and J. L. Fasching, Anal. Chlm. Acta, 80, 327 (1975). H. J. Kramer and B. Nedhart, Radbchem. Radioanal. Lett., 22,209 (1975). H. A. Van Der Sloot and H. A. Das, Anal. Chim. Acta, 73, 235 (1974). M. H. Yang, P. Y. Chen, C. L. Tseng, S. J. Yeh, and P. S. Weng, “Determination of Trace Elements by Neutron Activation Analysis Using DinonylnaphthaleneSulfonic Acid as a Preconcentration Agent”, 1976 InternationalConference on Modern Trends in Activation Analysis, Munich, September 13-17, 1976. A. Wyttenbach and S. Bajo, Anal. Chem., 47, 1813 (1975). E. C. Kuehner, R. Ahrarez, P. J. Paulsen, and T. J. Murphy, Anal. Chem., 44, 2050 (1972). C. Feldman, Anal. Chem., 46, 99 (1974). J. M. Lo and C. M. Wai, Anal. Chem., 47, 1869 (1975). D. R. Christrnann and J. D. Ingle, Jr., Anal. Chim. Acta., 86, 53 (1976). H. V. Weiss and M. G. Lai, Anal. Chim. Acta, 28, 242 (1963). R. Thiers, “Trace Analysis”, J. Wiiey and Sons, New York, N.Y., 1957. B. Sjostrand, Anal. Chem., 36, 815 (1964). Mercury Analysis Working Party of BITC, Anal. Chim. Acta, 84, 231 (1976). H. Cherrnette, J. F. Colonat, and J. Tousset, Anal. Chim. Acta, 80, 335 (1975). A. Wyttenbach and S. Bajo, Anal. Chem., 47, 2 (1975). H. Bode and K. J. Tusche, Fresenius’ 2.Anal. Chem., 157, 414 (1957). R. Wickboid, Fresenius’ 2.Anal. Chem., 152, 259 (1956). G. Eckert, Fresenius’ 2. Anal. Chem., 155, 23 (1957). J. Stary and K. Kratzer, Anal. Chim. Acta, 40, 93 (1968). J. Ruzicka and J. Stary, “Substoichiometry in Radiochemical Analysis”, Pergamon Press, Elmsford, N.Y., 1968. D. F. Covell, Anal. Chem., 31, 1785 (1959). K. Heydorn and W. Lada, Anal. Chem., 44, 2313 (1972). Y. P. Virmani and E. J. Zeller, Anal. Chem., 46, 324 (1974). E. D. Goklberg, “Chemical Oceanography”, Academic Press, New York, N.Y., 1965, p 163. K. Kremling and H. Petersen, Anal. Chim. Acta, 70, 35 (1974). H. V. Welss and T. E. Crozier, Anal. Chim. Acta, 58, 231 (1972). H. V. Weiss, S. Yamamoto, T. E. Crozier, and J. H. Mathewson, Environ. Sci. Technol., 6, 645 (1972). T. M. Leatherland, J. D. Burton, M. J. McCartney, and F. Culkin, Nature (London), 232, 112 (1971).
RECEIVED for review December 8, 1976. Accepted March 23, 1977.
Radiometric Determination of Alkyl Aromatic Sulfonates in Crude Oils David M. Clement2 Chevron Oil Field Research Company, P.O. Box 446,
La
Habra, California 90631
A method for determining sulfonate concentration in crude 011s has been developed. I t is based on the method of Taylor and Waters [Analyst (London), 97, 533 (1972)l in which a stable, chloroformgoluble complex is formed between sulfonates and ”Fe labeled ferroin [Fel‘( l,lQ-phen),12+. Appllcatlon of thls technlque to crude 011s has revealed that each oll has the ablllty to deactivate a specific amount of sulfonate.
Detection of alkyl aromatic sulfonates in crude oils and brines is essential to proper evaluation of modern tertiary oil recovery schemes such as micellar and surfactant flooding. Laboratory and field estimates of surfactant loss and measurements of surfactant slug breakthrough at producing wells depend on the ability to accurately measure sulfonate con1148 * ANALYTICAL CHEMISTRY, VOL. 49, NO. 8 , JULY 1977
centration in the produced fluids. Until now, however, the available methods of sulfonate detection have been either ineffective in dark-colored crude oils and brines [the colorimetric Hyamine ( 1 ) and methylene blue (2) techniques] or very time consuming [liquid chromatography ( 3 ) ] . This report describes the application of a new analytical method, the Radiometric Sulfonate Determination (RSD), to this problem. Rapid and accurate, the method is not limited by the color of the parent phase. In addition, it has provided hard evidence that sulfonates can become deactivated in crude oils, probably through complexing with heavy end components. Detection of sulfonates in ground water and potable water using this new method has already been clearly demonstrated ( 4 ) . Preliminary experiments showed that the method was effective for oil-field brines and for crude oils. The objective
of this study was to modify the procedure for the determination of sulfonates in crude oils.
EXPERIMENTAL The basis for this analysis is the reaction between sulfonates and a stable chloroform-insoluble complex cation, ferroin [Fe"(l,10-phen)3]2+,(phen = phenanthroline) which is radioactively labeled with iron-59. A chloroform-soluble product is formed via the following equation:
The amount of radioactively labeled ferroin extracted into the chloroform is therefore directly proportional to the amount of sulfonate present. A small sample of sulfonate-containing liquid (either oil or water) is introduced into an aqueous ferroin/CHC13 mixture and extracted, the CHC13 layer is counted, and the concentration is determined from a standard curve. Modification of Procedure. Since the procedure as described by Taylor and Waters (4) was developed for aqueous surfactant solutions, modifications were required to adapt the procedure to oils. Petroleum sulfonate (pas.)425, an oil-soluble, mixed molecular weight surfactant containing approximately 65% active sulfonate by weight, was chosen for the procedure. This material is a sulfonated distillate fraction of a California crude oil prepared by Chevron Chemical Company, Los Angeles, Calif. Standard solutions were prepared by dissolving weighed amounts of p.s. 425 in toluene, chloroform, chloroform + 0.1% toluene, a heavy gasoline from the Chevron Bakersfield refinery-Bakersfield Heavy Gasoline (BHG), and Chevron Base Oil C (BOC-a colorless kerosene). Crude oil samples containing active sulfonate in concentrations greater than several hundred ppm must be diluted. Solvent type was found to have a pronounced effect on the activity extracted in blanks. Activity extracted by 1 mL of blank solvent decreases in the order: chloroform + 0.1% toluene > toluene > chloroform > BHG > BOC. Apparently, aromatics or small amounts of pure aromatics in CHC&adversely affect partitioning of the ferroin between the two phases. Base Oil C, having demonstrated the lowest blanks, was chosen as the standard diluent for crude oil samples. A change in the volume ratio of aqueous phase to solvent phase in the extraction also changed the extraction efficiency. For convenience, the volume of the CHC13 layer was kept at 6 mL, which included 1 mL of the sulfonate solution of interest, while the aqueous phase was kept at 20 mL. The modified procedure as used in the remainder of this study follows. Radiometric Determination of Sulfonate in Oil Samples. The general experimental approach to determining sulfonate in crude oils is to: (1) prepare a standard curve, (2) dilute the oil sample, (3) run the extraction, and (4) measure the radioactivity and plot the data. Normal procedures for safe handling of the radionuclide are followed. Reagents required for the analysis are as follows. Actiue Ferroin Reagent. To a 100-mL volumetric flask, add 5 mL stock solution: mix the following aqueous solutions; ferrous M, 5 mL); hydroxyl ammonium ammonium sulfate (17.9 X chloride (O.l%, 5 mL); iron-59 as soluble salt (100 pCi); 1,lOphenanthroline (0.4%, 25 mL). Dilute the mixture to 100 mL with water. Dilute reagent: dilute the stock solution (10 mL) to 100 mL with water. Buffer Solution, p H 4. Adjust 2 M sodium acetate solution to pH 4 with 2 M acetic acid. Chloroform. Analytical reagent grade. Equilibrate daily by shaking with an equal volume of distilled water. Standard Surfactant Solution. Use petroleum sulfonate 425 (or any other of interest) in Base Oil C to give a stock solution of 1 pequiv active sulfonate/mL. Check this exactly via the Hyamine titration. Standard Curue. A standard curve must be prepared with the surfactant of interest dissolved in the solvent used to dilute the ail. This standard curve should have enough points to determine the linear response range in concentration for that particular sulfonate. This should generally be 0.005-0.10 pequiv/mL of
surfactant solution. Beyond the upper limit, the activity vs. concentration plot becomes nonlinear as the ferroin becomes limited. Once the overall limits have been established, a three-point standard curve, taking points just within the limits and a center point, should be run with each daily set of samples. Extraction. To an approximately 30-mL disposable vial with polyethylene cap add 5 mL CHC13,1mL dilute surfactant solution, 19 mL distilled HzO,0.5 mL of ferroin reagent, and 0.5 mL N d c buffer. Cap tightly and shake vial vigorously for 1 min on a ehaker table with spill tray. Separate layers by centrifugation or Whatman 1P/S phase separating paper, transfer 4 mL of CHC13 layer to counting vial, and determine count rate of sample relative to standards. With each batch, measure total daily activity by including separate counting vial Containing 0.5 mL ferroin reagent and 3.5 mL H20. Modified Methylene Blue Method of Sulfonate Analysis. An independent check of the radiometric method was made using a modification of the methylene blue method (2). An acidic methylene blue solution is prepared (0.120 g Eastman Kodak methylene blue chloride + 200 g Na2S04anhydrous, + 26 mL concd H2S04,all in a total of 4 L of deionized water). One mL of this solution is added t o 9 mL of H20 in a 25-mL vial. Then 5 mL of CHC13and 1 mL of surfactant solution (diluted with solvent if necessary) are added. The vial is shaken vigorously for 1 min and the amount of methylene blue in the CHC13layer is measured colorimetrically using a standard curve. Although the error (&10-20% depending on the concentration) in the results from this technique is much larger than the radiometric, this method did provide a check on the results which follow. Sulfonate Titration of Crude Oils. Prepare a stock solution of 1000 pequiv/mL sulfonate in Base Oil C . Two 25-mL burettes are required, one containing BOC and the other containing the stock solution. At least 150 g of crude oil should be available for the titration as outlined below. However, the end-point in pequiv/g is independent of the amount of crude used and the BOC/crude ratio, so any convenient quantity will work. Disposable 30-mL vials are used for mixing the crude and the surfactant. Prepare two sets of vials numbered 1-11. To the fist pair, add 5.0 mL BOC; to the second, add 4.5 mL BOC and 0.5 mL stock; to the third, add 4.0 mL BOC and 1.0 mL stock; and so on in 0.5-mL increments until vials No. 11are 0 mL BOC and 5.0 mL stock. Add 5 g of crude oil to each vial and mix well. Dilute all samples 1/100 with BOC and analyze 1mL via RSD. Determine the crude oil density to allow conversion to volume for concentration terms. Data may be plotted as shown in Figure 4. The value at the end point is then divided by 5 g to get the STN (pequiv deactivated/g crude).
RESULTS AND DISCUSSION Figure 1 shows a standard curve of the activity of various p.s. 425 solutions. On the same graph is plotted the activity ratio (A.R.) of these solutions. This quantity, defined as the activity of the solution divided by the total activity originally added to the aqueous layer, is a measure (*5% depending on concentration) of the amount of iron-59 extracted in relation to the total amount available for extraction. Since the radionuclide has a half-life of 45 days, the activity ratio is useful for comparing data in which there is a long elapsed time between batch measurements. The plot is linear only out to approximately 0.1 pequiv of p.s. 425/mL. Beyond that it bends toward the abscissa as the amount of ferroin in the aqueous layer becomes limited. The data are found to conform to the chemical equation:
F
t 2s
FS,
(2)
where F and S represent the ferroin and sulfonate, respectively, and FSz represents the ferroin-sulfonate complex. The equilibrium constant can be shown to be represented by:
.J-
Keq
=
( f - x ) ( s - 2x)2
where n = [FS,], f = [F] initial, s = [SI initial. ANALYTICAL CHEMISTRY, VOL. 49, NO.
8, JULY 1977
1149
Table I. Measurement of Ferroin-Extractable p.s. 425, in Counts per Minute Extracted, in Two Crude Oils at Two Different Concentrations Compared to the Extractable Amount in Base Oil C 1%wt pes.425 in:
Sulfonate activity, countslmin
Base Oil C Crude Oil A Crude Oil B
930 146 76
1 0 % wt
BOC
Sulfonate activity, counts/min
Blank, counts/min
BOC
16 7
1156 861 966
21 21 11
74 84
%
Blank, counts/min
of
29
2 9
%
of
0.14 /
-
/
/
0.12
-
0.10
I-I
/ /
/
/
/
0
, ,
t
o,o//’
0O o02 4[
t’
” 09 0
0.04
0.02
0.06
0.08
0.10
0 12
0.14
HYAMINE l p q l m l )
Flgure 2.
Ip.5, 4251 & eq&Jl
Standard curve for radiometric sulfonate determination of p.s. 425 in Base Oil C Figure 1.
Comparison of Hyamine titration and RSD for pes. 425 anaiysls
in Base Oil C 1500
The experimental data can be fit to the following equation:
+
l o g ( k ) = 1.39 log (S - 2 ~ )2.24
(lo6)
(4)
with a correlation coefficient of r = 0.995. The last term in the equation is an estimate of Kes,since the coefficient of log (s - 2x) is 1.39 rather than 2. Thus, the ferroin/p.s. 425 complex is highly favored. The theoretical detection limit in crude oils is approximately 0.5 ppm p.s. 425 using 1 mL of undiluted oil. Solutions of varying amounts of p.s. 425 in Base Oil C were analyzed via both the Hyamine and radiometric methods. Comparison is made in Figure 2. Within the radiometric optimum range, excellent agreement between the two methods is reached. Outside that region, radiometric yields lower values than Hyamine because of the nonlinearity of the standard curve. Introduction of sulfonate into crude oils, however, yields an unexpected result. Two California crude oil samples and one Base Oil C sample containing approximately 1%wt of p.s. 425 were prepared in an identical manner. AU were diluted with Base Oil C to give approximately 0.022 pequiv p.s. 425/mL, then analyzed via the radiometric method. The results are presented in Table I. The blanks observed in all three systems are extremely low, implying that there are no compounds in the raw crude which react with the ferroin reagent. There is, however, a striking difference in measured sulfonate activity. A t the 1 % level, measured activity in the crude oil is only approximately 10-15% of that observed in the base oil. If this observation is due to extraction efficiency in the crude oil systems, then longer shaking times should increase the amount extracted. 1150
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1000 I
3e c
->8 k
500
0
Figure 3.
1
2 3 SHAKING TIME [mini
Effect of shaking time on extraction of
4
5
425 (0.0155 pequlv)
As Figure 3 demonstrates, shaking time has no effect on extraction efficiency in the crude oils. If solutions containing approximately 10% p.s. 425 in these same oils are prepared and diluted to give approximately 0.022 pequiv/mL, the percent extracted is significantly higher than from the approximately 1% solutions. Evidently, there is a fixed amount of material in the crude that reacts with the sulfonate in an essentially irreversible manner causing deactivation.
P.S. 425 CONCENTRATION ADDED ( p e d 5 9 CRUDE)
Flgure 4. Sulfonate titration of Crude Oil A. The sulfonate titration number (STN) is defined as the end point in p s . 425 added divided by the amount of crude titrated (yequivlg crude) to obtain loss per gram of oil
This concept is verified by what is essentially a titration curve on the crude oil A. Figure 4 shows the measured p.s. 425 concentration of solutions containing 5 g of crude oil and 5 g of Base Oil C solutions containing various amounts of p.s. 425. A distinct break in the plot of actual vs. measured p.s. 425 occurs at approximately 220 wequiv added. Beyond that point (verified experimentally out to 2000 pequiv/5 g added) the line parallels the ideal curve. There is a fixed, titratable amount of material in the crude oil that can deactivate the sulfonate. Once this amount has been satisfied, the detection of sulfonate in crude oil is linear but displaced from the ideal by this finite amount. This observation was corroborated by an independent method of sulfonate analysis on these identical solutions. Extraction of the methylene blue cation from aqueous solutions by these solutions dissolved in CHC13was measured. The results are shown in Figure 5 superimposed on the titration data from the radiometric results. The end point for this “methylene blue titration” is approximately the same as with the radiometric titration. The large error and narrow detection ranges associated with the methylene blue method preclude its use for routine analysis but it does give credence to the radiometric observations. Apparently, a reaction has occurred in the crude oil of the form: Crude
+ Sulfonate e Crude/Sulfonate C o m p l e x (5)
In order to test the reversibility of this reaction, the titration was repeated using a 10-times more concentrated solution of ferroin. The end point observed was essentially the same, indicating that the crude/sulfonate complex does not readily dissociate with added ferroin. Another test of the crude oil/sulfonate complex stability can be performed by calculating the equilibrium constant of formation. The value of the ferroin-sulfonate equilibrium constant (I&) was calculated above as ~ 2 ( 1 0 )implying ~, a very favorable reaction. Using data obtained from the titration of crude oil A as an example, one can calculate a theoretical equilibrium constant for the reaction:
where C* represents the species in the crude oil which complexes sulfonate and n represents the moles of sulfonate complexed. The calculated equilibrium constant, Keq,is 1.4 (lo7)and n is approximately 2. Thus, formation of the crude
RSD - SOLID LINE MME-
80 /
/
1
0
20 0
40 0 60 0 ACTUAL 425 CONCENTRATION ( P E q ’ g l
I
80 0
100 0
Figure 5. Comparison of RSD with modified methylene blue method for measuring concentration of p.s. 425 in various solutions of Crude Oil A
oil/sulfonate complex is theoretically favored over the ferroinlsulfonate complex by a power of ten. Experiments were performed to verify the relative magnitude of the interaction strengths suggested by the equilibrium constants. Solutions of p . ~ 425 . in Base Oil C at a concentration of 0.05 yequiv/mL were analyzed via the radiometric method. In one case the test was done in the usual manner with no crude oil present. An additional 0.5 mL of Base Oil C was injected into the CHC13 layer to maintain a constant volume throughout the experimental series. The activity (directly proportional to concentration) observed was 5461 counts per minute (counts/min). The analysis was repeated but a 0.5-mL aliquot of crude oil A was introduced into the CHC13layer prior to shaking with the ferroin. The activity observed was 17 counts/min. This meant that very little ferroin was transferred to the CHCIBlayer and demonstrated the ability of tne crude oil complexing agent to prevent the sulfonate from complexing with ferroin. In a third analysis, the ferroin-sulfonate complex was formed first and then a 0.5-mL aliquot of crude oil was added to the CHC13 layer and the sample shaken again. The measured activity of the chloroform layer was 539 counts/min. This showed that the crude oil/sulfonate complex was more favored and was ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1151
able to dissociate the ferroin/sulfonate complex. The exact cause of sulfonate deactivation by crude oil is not known at this time. There does appear to be some correlation between the amount lost and the nature of the crude oil heavy ends. Positive nitrogens in the asphaltene and resin fraction and heavy metal centers are a likely source of complexing (5). The amount of sulfonate lost to various crude oils varies, undoubtedly because of structural differences in the heavy ends. It will likely also vary from one sulfonate to another because of differences in equivalent weight and molecular structure. For purposes of comparing one crude to another, the “sulfonate titration number” (STN) is defined as the amount of a given surfactant (in pequiv) that can be complexed by 1g of crude oil as obtained from a titration of the crude with the sulfonate. The range of STN values for different crudes observed to date is 1 to 44 wequiv/g
(f5-10%). The titration procedure as described above should be used before each series of analyses of sulfonate in a particular crude to obtain the STN of that crude. RSD’s on samples before
and after sulfonate addition will allow one to estimate: (1) the capacity of a particular crude oil to deactivate sulfonate, (2) the amount of free sulfonate in a sample, (3) the amount of complexed sulfonate in the sample. These quantities can be valuable in planning surfactant floods for tertiary oil recovery (5).
ACKNOWLEDGMENT Appreciation is expressed to B. A. Fries of Chevron Research Company, Richmond, Calif., for his assistance in the radioactive method development and to W. E. Gerbacia, Chevron Oil Field Research Company, La Habra, Calif., for many helpful discussions.
LITERATURE CITED (1) (2) (3) (4) (5)
P. I. Brewer, J . Inst. Pet., 58, 41 (1972). C. H. Wayman, USGS Prof. Pap., 450-6, 8117 (1962). W. R. Ali and P. T. Laurence, Anal. Chem., 45, 2426 (1973). C. G. Taylor and J. Waters, Analyst (London), 97, 533 (1972). D. M. Clementz, J. Pet. Techno/., in press.
RECEIVED for review January 10,1977. Accepted April 4,1977.
Simultaneous Determination of Composition and Mass Thickness of Thin Films by Quantitative X-ray Fluorescence Analysis Daniel Lagultton and Willlam Parrish” IBM San Jose Research Laboratoty, San Jose, California 95193
A new method of simultaneous determination of composition and mass thickness of alloy films has been developed. It uses the matrix effect correction by the fundamental parameters method and is performed automatically on a computer by the LAMA program. Only pure element bulk standards are required and no prior knowledge of the thickness of the specimen Is necessary. The iteration method is described, and the results are compared with those of electron microprobe, interferometry, and atomic absorption spectroscopy. The method is rapid, nondestructive, and has an accuracy slmilar to the above methods.
Since its discovery, x-ray fluorescence has been a very fascinating analytical tool, because it is nondestructive, rapid, precise, and potentially very accurate. This latter point, however, has been the limiting factor in the practical development of the method because the concept of the matrix effect correction used to transform experimental fluorescence intensities into weight fractions, involves a large number of fundamental parameters which in many instances are only approximately known. Other methods have been more or less successively developed to overcome the inherent difficulties of the fundamental parameters method (1,2). These include the dilution technique (3),the multiple regression method (4), the alpha or beta coefficient methods (5, 6), and the equivalent wavelength methods (7). Although all these methods could in principle be handled by use of calibration standards to reduce calculations to a minimum, a significant improvement 1152
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
has been made in their application by the introduction of modern computers. For instance, regression or alpha coefficients can now be generated more easily by a computer (8-1 0). Besides the various simplifications that were necessary, these matrix effect correction schemes were applied only to thick specimens because the preparation of thin f i i standards required special procedures and were difficult to characterize by chemical methods. However, in recent years, the situation has significantly changed and the preparation of thin film specimens has undergone a considerable development as well as the resulting attempts to characterize thin film materials. The determination of fundamental parameters such as the mass absorption coefficients has also made important progress, and the greater availability of computers in research laboratories has made it easier to handle the somewhat complex equations describing the matrix effect correction by the fundamental parameters method (1,2). This paper presents the results of the application of computers to the determination of the composition and the mass thickness of thin f i i s by the fundamental parameters method.
THEORY The equation relating the measured fluorescence intensity of a line to the composition of a thin matrix is given in Equation 1, and the meanings of all symbols used are given in Table I (11-14). In order to cancel the effect of the efficiency of the spectrometer, one usually measures the ratio of the intensity of a characteristic line of the specimen to the intensity of the same line of a standard of known composition. As shown in Equation 1, besides the fundamental parameters which characterize each element, the matrix as a whole is
