Use of a Modified Coulter Counter for Determining Size Distribution of Macroinclusions Extracted from Plain Carbon Steels D. A. Flinchbaugh Homer Research Laboratories, Bethlehem Steel Corporation, Bethlehem, Pa. 180 16 This paper describes the use of a modified Coulter Counter to extend upward the diameter range over which the size distribution of oxide inclusions in plain carbon steels can be determined by chemical extraction and Coulter Counter measurement techniques. When used with a standard Coulter Counter electronic module, an aperture apparatus of new design makes it possible to accurately and precisely size and count macroinclusions u p to at least 130 microns in diameter. Evaluation tests were performed by taking silicon carbide particles through the residue purification and counting procedures. Results showed an average particle recovery of 99% with an average standard deviation of 11%. The precision of the method depends on the homogeneity of the inclusion phases in the steels tested. Also included a r e examples of size distribution data of the type used in studies on the effect of macroinclusions on the mechanical properties of steel. THEDELETERIOUS effect of large oxide inchsions on the mechanical properties of steel has been recognized for some time ( I ) . It is generally accepted that only those inclusions above a critical size may cause failures ( 2 , 3), the critical size being dependent in each case o n the configuration of the part to be made and o n the strength and thickness of the steel. In general, lower-strength steels can tolerate larger inclusions than can higher-strength steels. In the case of the lower strength plain carbon steels, the maximum allowable inclusion size can be quite large. Therefore, the inclusions of greatest interest in investigations of low-strength steels are those a t the very large diameter end of the frequency distribution curve. Size distribution measurements o n these large inclusions are helpful in studies aimed a t defining the maximum allowable inclusion size-and-frequency parameters for each application and also in studies to alter processing practices to prevent such macroinclusions from nucleating and growing. As can be seen in Table I, the inherent analytical problems associated with measuring the size distribution of macroinclusions become obvious when one considers the relationship between macroinclusions and the total inclusion population of a given grade of steel. The table shows results from a 70-ppm-oxygen ingot-cast AI-killed sheet steel. Given the very small fractions of the total inclusion population that are represented by these macroinclusions, it becomes virtually impossible to find them, let alone measure such size distributions by even the most sophisticated metallographic techniqbes. The primary advantage of inclusion extraction and residue analysis methods for making this type of determination is that these methods are capable of dealing with large volumes of steel and can therefore provide reasonable numbers of macroinclusions for counting and size-distribution measurement. A review of the work done in our own and other laboratories to apply extraction techniques to inclusion size-distribution
(1) B. P. Barnsley. J . Ausr. Z m f . Metals, 14, 65 (1969). (2) R. Kiessling, “Non-metallic Inclusions in Steel, Part 111,” The Iron and Steel Institute Publication 115, London, England, 1968. (3) R. Kiessling, Jernkontorers Ann., 153, 295 (1969). 178
determinations was described in a recent paper ( 4 ) . Our approach is to use halogen-in-organic-solvent extraction, oxygen-plasma residue purification, and Coulter Counter size-distribution measurements. Our results showed that: the extraction techniques are suitable for quantitative analysis; the residue purification procedures destroy the filter and the elemental carbon and sulfur in the residue without altering the size distribution or losing any of the inclusions; and the Coulter Counter is capable of providing reliable size distribution measurements on the extracted and purified inclusions. The method just described provides reliable results on about 3- to 40-micron inclusions extracted from AI-killed and rimmed sheet steels. However, at diameters greater than about 40 microns, the reliability of the data diminishes as the population density of the large particles in the electrolyte decreases, because with a standard Coulter Counter that portion of the sample drawn through the aperture is lost and cannot be recovered. Therefore, only a small fraction of the total sample suspension can be sacrificed for each data point on the distribution curve. One possible solution to the problem is to provide a n aperture apparatus capable of recycling large fractions of the sample suspension through the aperture as often as is needed to provide optimum counting reliability. The development and evaluation of such a device was described in a recent paper (5). The present paper describes how the new aperture apparatus can be used with the inclusion extraction and analysis techniques to provide accurate information o n the size distribution of macroinclusions in steel. A description of the apparatus and procedures used to make the determinations is followed by data demonstrating the precision and accuracy obtainable with the method. EXPERIMENTAL
The procedures for extracting and analyzing inclusions that were outlined in previous papers ( 4 , 6) have since been optimized and adapted for macroinclusion size-distribution work as follows. Apparatus. EXTRACTION.Our extraction apparatus is essentially that of Bohnstedt (7)-with a few minor changes. The volume of the sample flask is increased from 250 to 500 ml. Also, glass hooks have been added to both the flasks and the reflux condensers to accommodate the use of wire springs. The stopcock regulating the solvent drop rate has been replaced with a Manostat Needle Valve (Catalog No. 78-425-01). Pressure between the extraction flask and the atmosphere is equalized by means of a Tygon tube by-pass around the needle valve. When extractions are to be carried out with ultrasonic agitation, the extraction apparatus is placed in a stainless steel water tank containing an immersible ultrasonic transducer. (4) D. A. Flinchbaugh, ANAL.CHEM., 41, 2017 (1969). (5) D. A . Flinchbaugh, ANAL.CHEM., 43, 172 (1971). (6) R. G. Smerko and D. A . Flinchbaugh, J . Metals, 20 (71, 43 (1968). (7) U. Bohnstedt, 2. And. Chem., 199 (lo), 114 (1964).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971
Before use, the bromine is prefiltered with a FILTRATION. standard glass filter funnel equipped with Whatman No. 41 filter paper. Electrolyte and the sodium hydroxide wash solution are filtered through a Gelman Alpha-6-Metricel filter (0.45 p pore size) o n a Millipore membrane filter holder equipped with a stainless steel support screen. The halogen extraction solution containing the inclusion residue is filtered through a Whatman 41H paper mounted on a Millipore membrane filter holder having a sintered glass filter support. We use a Tracerlab Model 600L. RESIDUE PURIFICATION. Dry Asher operated at full power, about 350 W , with a n oxygen flow rate of about 70 cc/min. The dry-ashing boats are made of 1/16-in,plate glass and measure ll/z in. wide by in. high. 31/? in. long by 1 SIZE-DISTRIBUTION MEASUREMENT.The size-distribution measurements are made with a Model B-M Coulter Counter equipped with the new aperture apparatus described in detail in a recent article (5). Reagents. All reagents are ACS grade o r better. The bromine, the sodium hydroxide wash solution, and the electrolyte are prefiltered before use. The electrolyte is prepared by mixing 125 ml of a 4.8% sodium chloride solution with 125 ml of glycerine and adding 10 drops of a 4.0% aqueous solution of Triton X-100 (Rohm and Haas, Philadelphia). Sampling. Samples can be taken at any stage of steel processing, from ingot through finished rolled product, and can be cut in almost any configuration. Millings and drillings are not satisfactory because of surface oxidation and because inclusions are frequently lost during the milling and drilling operation. About 250 grams of steel are taken for macroinclusion size-distribution analysis. Procedure. EXTRACTINGOXIDES FROM FULLYKILLED WITH BROMINE-IN-METHANOL. Add 25 grams of steel STEELS and a Teflon-coated magnetic stirring bar to each of 10 extraction flasks. Add 50 ml of bromine. Mount the extraction flask o n the stir-plate and attach the condenser. Put 125 ml of methanol in the addition funnel and adjust the drop rate at 1 drop every 5 to 6 sec. Adjust the hot plate at about 50 "C. Be sure that the stirrer remains off. The dissolution reaction begins several seconds after the first of the methanol is added and should continue at a mild rate until the steel is completely dissolved. The reflux line of the reaction mixture should not be allowed to rise into the condenser. If this occurs, cool the reaction flask and temporarily slow down o r stop the methanol addition. After about 1 'Iz hours, most of the steel is dissolved. Turn on the stirrer and increase the methanol drop rate a t 1 drop every 1 to 2 sec such that all of the remaining methanol is added to the reaction mixture within a total reaction time of about 2 hr. The samples are now ready to be filtered. EXTRACTINGOXIDESFROM SEMIKILLEDAND RIMMING ACETATE. Place a stainless STEELWITH BROMINE-IN-METHYL steel tank on the stir-plates used for the bromine-in-methanol extractions. Put an immersible transducer in the bottom of the tank and then fill the tank about 3/4 full with water. Mount a water-cooled "cold finger" in the water bath to keep the water temperature from exceeding about 40 "C during the extraction operation. Add 20 grams of steel to each extraction flask. Add 40 ml of bromine. Using springs, attach the flask to a condenser-dropping funnel combination of the type used for the bromine-in-methanol extractions. Position the apparatus in the water bath so that the flask is submerged in about 11/2 in. of water. Put 100 ml of methyl acetate into the addition funnel and set the drop rate at about 1 drop every 4 sec. Turn on the ultrasonic generator. (The reaction is gentler than in the bromine-in-methanol case and therefore does not present a control problem.) After about 2 hr, the dissolution is complete and the solution is ready to be filtered. FILTERING AND WASHING. Vacuum-filter the extraction solution through Whatman 41H paper. (It is frequently
Table I.
Characterization of Macroinclusions in a Commercial AI-Killed Sheet Steel Fraction of inclusion population Parameter Total > 4 3 p a >76pa > 9 6 p a No. of oxides per gram of steel -lo6 19 1 0.4 ppm O2in steel 70 2.8 0.6 0.2 of total O2 content 100 4.0 0.8 0.3 a Equivalent spherical diameter.
necessary t o add some methanol to methyl acetate extraction solutions to make them sufficiently fluid to filter.) Wash the residue with methanol until the wash solution remains clear. I n the case of residues from Al-killed steels which contain aluminum nitride, cut the vacuum and add 20 ml of a warm (60 "C) 1 % N a O H solution. Wait 2 min. Restore vacuum and repeat the N a O H treatment. Finally, wash the residue with warm water and then with methanol. Place the filter into a dry-ashing boat, residue down. Each boat holds two filters. DRYASHING. Place the sample boats into the dry-asher chambers, attach the chamber lids, and slowly evacuate the system to about 0.1 mm Hg. Strike the plasma, adjust the forward power to 350 W, and set the oxygen flow rate a t 70 cc/min. Final-tune the plasma for minimum reflected power. After about 1 hr, the blue color from the filter oxidation process disappears, indicating the end of the first dry-ashing cycle. Shut off the plasma and oxygen flow and then slowly bleed the sample chamber until atmospheric pressure is reached. Remove the same boat from the dry asher, add about 10 ml of acetone, and disperse the samples for about 15 sec in a low-power ultrasonic bath. Evaporate the acetone o n a low-temperature hot plate and then return the sample boats to the dry asher for another cycle. At the completion of the second cycle, examine the residue under about SOX to determine the effectiveness of the purification procedure. At this point, any large unashed fibers can be hand-picked from the residue. A third dry-ashing cycle is usually required t o complete the residue purification. It is essential that the inclusions be free of foreign material prior to Coulter Counter measurement. SIZE-DISTRIBUTION MEASUREMENT. Disperse the sample in electrolyte and wash the inclusions into the sample beaker of the new aperture apparatus. Dilute to 250 ml. Take the size-distribution measurements as given in the Procedure section of the recent paper (5). Record the data as number of particles equal to o r greater than each instrumental diameter. Calculate the results as number of particles per gram of steel. EVALUATION OF THE METHOD The validity and practicality of the extraction-analysis approach to determining the overall size distribution of oxide inclusions was demonstrated in a previous paper ( 4 ) . The main points demonstrated in this connection were: extraction techniques are capable of quantitatively extracting oxide inclusions from most plain carbon grades; dry ashing removes all but a n insignificantly small trace of the non-inclusion material from a n as-filtered residue without losing, sintering, or agglomerating the inclusions; and the Coulter Counter can be used to provide reliable overall size-distribution measurements o n the purified inclusions. All of these conclusions were based o n tests with bulk quantities of material. The objective of the present study was to adapt the generalpurpose extraction-analysis method-specifically through the incorporation of the new aperture apparatus into the Coulter
ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971
179
Table 111. Precision Tests on a 70-ppm Oxygen Ingot-Cast AI-Killed Sheet Steel (Sample 17) Diameter, p
212 167 133 106 96 84 76 66 60 53 48 42 38 a nd
i
13
rn 3
*
3
$i m
m
3
4 m
v1
Y
vi
0
I
0
3
d I-
Icl
,E
.-
e
b
m
U e
180
o
Number of particles per Test 1 Test 2 Test 3 0.00 0.00 nda 0.04 0.02 0.04 0.08 0.06 0.06 0.20 0.15 0.26 0.25 0.41 0.42 0.63 0.54 0.90 1.05 0.66 1.31 1.90 1.44 2.09 2.80 2.60 3.63 4.87 3.93 8.02 7.25 6.67 10.6 11.4 11.2 17.3 17.0 16.2 25.8 = not determined
gram Test 4 nd 0.01 0.06 0.27 0.41 0.78 1.10 1.74 2.97 4.98 6.88 11.3 16.9
> stated size 2
U
0.00
0.00
0.03 0.06 0.22 0.37 0.71 1.03 1.79 3.00 5.45 7.85 12.8 19.0
0.02 0.01 0.04 0.07 0.10 0.24 0.26 0.43 1.77 4.34 3.00 4.56
Counter-so that the method would be capable of accurately sizing and counting very small numbers of large inclusions in the total inclusion population extracted from a steel sample. Therefore, it was necessary to show that specific numbers of large particles could be put through the analytical procedure and then be quantitatively recovered by the modified Coulter Counter. It was also necessary to determine the precision obtainable on actual steel samples. Results of these two types of experiments are given below. Recovery Tests on Simulated Inclusion Residues. We have already determined that known numbers of particles of the type found in steel as inclusions can be counted with the modified Coulter Counter with an estimated accuracy of 100% and a precision of f10% at the one standard deviation level (5). This experiment was designed to verify the ability to carry a few large simulated inclusion particles (silicon carbide) through the filtering and dry-ashing procedures and to count them with the modified Coulter Counter. Three samples were prepared by microscopically counting about 2000 particles of silicon carbide that had been presieved at 105 and 150 microns. These particles were washed onto a filter through which a large quantity of prefiltered bromine-inmethanol waste solution had been passed. The synthetic residue was then washed with NaOH solution (since this would be done to destroy AlN if the procedure were being conducted on actual steel specimens) and dry-ashed. The size distribution was then determined with the modified Coulter Counter. For each sample, one measurement was made at each diameter setting; this sequence of measurements was repeated two more times, giving a total of three runs (Table 11). Since the original silicon carbide was greater than 105 microns in diameter, it is possible to estimate the precision and accuracy of the determinations from these data. As is also shown in Table 11, the overall recovery was 99 i 11 %. These values compare favorably with the 101 + 11 recovery previously reported ( 5 ) on presieved alumina powder that had been similarly microscopically counted and put directly through the Coulter Counter. These extremely close recovery values prove that very large particles can be carried through the procedure-filtration, dry-ashing, and measurement with the modified Coulter Counter-without being lost or broken. Precision Tests on Steel Samples. To determine the precision obtainable on actual steel samples, we performed preci-
ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971
Test 1 2 3 4
a
Slope (a) -4.500 -4.331 -4.519 -4.023
Table IV. Precision Data on Steel 17 (70-ppm oxygen) Number of particles per gram of steel 2 stated size ( N ) Intercept (b) 40 p 50 1.1 60 p 70 y 8 0 ~ 90 I* 100 15.4 5.6 2.5 1.2 0.68 0.40 0.25 8.396 2.4 1.2 0.69 0.42 0.26 8.083 13.9 5.3 1.00 3.7 1.8 0.59 0.36 22.9 8.3 8.600 0.88 2.8 1.5 0.55 0.36 7.600 14.3 5.8
Average -4.343 =t1 u 0.239 5.53 RSDa % Av RSD RSD = Relative standard deviation
Test 1 2 3 4
Slope (a) -4.399 -4.564 -4.765 -4.835 -4.580
5
8.169 0.435 5.34 =
1 g/Average
i lu
RSD % Av RSD
=
6.3 1.4 22.2
2.8 0.56 20.2
1.4 0.28 19.2 20.6
8.676 0.372 4.29
18.8 5.6 29.8
sion tests on five different Al-killed sheet steels. Each sample contained material from the entire width of the sheet. Three to five 250-gram samples of each steel were taken through the extraction, purification, and analysis procedures. For each residue, one particle count was recorded at each diameter setting. The modified Coulter Counter results from one of the steels are shown in Table 111. Visual inspection of the data shows that the agreement among 250-gram samples of the same steel is quite good, considering that the data were taken at the extremely large particle end of a 1 to 3-micron-median-diameter population numbering about lo6 particles per gram of steel. A statistical estimate of the run-to-run precision of each steel was made as follows. The data from each run were fitted to the straight line equation: =
a (log d)
+6
(1)
where
N a
= =
d =
b
=
0.49 0.09 19.0
0.31 0.06 19.6
100.
6.6 1.7 26.1
1.4 0.29 20.8 21.7
2.8 0.66 23.2 ~~
log N
0.81 0.15 18.8
Table V. Precision Data on Steel 21 (50 ppm oxygen) Number of particles per gram of steel 2 stated size ( N ) Intercept ( b ) 40p 50y 60p 70 p 80 p 90 p 100 p 1.2 8.200 0.67 0.40 0.25 14.2 5.3 2.4 1.2 8.494 0.64 0.38 0.23 15.2 5.5 2.4 8.912 1.3 0.70 0.40 0.24 19.0 6.6 2.8 1.9 9.197 1 .o 0.34 0.56 28.3 9.6 4.0 0.73 0.42 1.3 8.578 17.4 6.2 2.7 0.26
-4.629 0.173 3.74
Av
16.6 4.2 25.4
number of particles per gram of steel 3 the stated diameter, d slope of the straight line equivalent spherical diameter of the particles as measured by the Coulter Counter intercept
Run-to-run comparisons were made by calculating the relative standard deviations of the calculated slopes and intercepts for each steel. The slope and intercept values were then used to calculate particle-count data for each run at 10-p diameter intervals from 40 through 100 1.1. The run-to-run precision at each 10-1.1interval was then determined for each steel. The results of these calculations are shown in Tables IV through VIII. Run-to-run repeatability varied among the steels tested. Steels 17, 21, and 27 showed the best precision of those tested. For these materials, the relative standard deviations of the slopes and intercepts calculated from Equa-
0.75 0.14 18.8
0.43 0.26 0.07 0.04 17.2 15.8 ~-
~
~
tion l averaged 4.4 % and 5.4 %, respectively, while the average relative standard deviations of the particle count values were in the +20% range. On the other hand, as shown in Table VI1 and VIII, the analytical precision of steels 12 and 14 was generally three to five times worse than that of steels 17, 21, and 27. Closer inspection of the data from steels 12 and 14 shows that the particle-count precision is better for steel 14 than for steel 12 in spite of the less precise slope and intercept values for steel 14. Because of wide differences in precision obtained o n the test steel, when the method is used in metallurgical studies, it is advisable to make replicate determinations, particularly when small differences exist in the population density of macroinclusions. DISCUSSION
Precision Differences between Results on Simulated and Actual Residues. In view of the greater number of variables in the steel residue experiment, it is natural for the method to lose some of its precision when an actual rather than a simulated residue is used. First, consider the sampling variable. When measuring extreme ends of a size distribution, such as is the case with macroinclusions, one would expect to find some variation in both the number of large inclusions and in their diameter distribution-even among 250-gram samples taken from the same steel. These variations in both total number of macroinclusions and in the slope of their distribution curve contribute significantly to the variation in the average coefficients of variation shown in Tables IV-VIII. (Recall that the simulated inclusion tests were designed to eliminate this variable by counting only the total number of particles in a sample.) The second consideration is the effect of the day to day variation in the particle-size calibration of the Coulter Counter. Normally, the maximum variation is on the order of i 5 % of the supposed true volume of the particle. This means that at an instrument setting of 42 1.1 in diameter, the actual instrument response could vary from 41.3 to 42.7 p .
ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971
181
Table VI. Precision Data on Steel 27 (50 ppm oxygen) Number of particles per gram of steel 3 stated size ( N) Slope (a) Intercept (b) 40p 50p 60 p 70 p 80p 9Op 1OOp -4.908 9.040 15.0 5.0 2.1 0.96 0.50 0.28 0.17 -4.530 8.239 9.6 3.5 1.5 0.76 0.41 0.24 0.15 -4.750 8.817 16.1 2.4 5.6 1.1 0.60 0.34 0.21 -5.317 9.845 21.2 6.5 2.5 1.1 0.53 0.28 0.16 -4.718 8,787 16.9 5.9 2.5 1.2 0.64 0.37 0.22
Test 1 2 3 4 5 Av i lu
z
RSD, Av RSD
Test 1 2 3 Av i l u
z
RSD Av RSD
Test 1 2 3 4
Av i l u RSD Av RSD
z
-4.845 0.197 4.07
Slope ( a ) -4.891 -4.889 -3.958 -4.580 0.482 10.5
8.945 0.582 6.51
15.8 4.2 26.6
2.2 0.41 18.6
1 .o 0.18 17.0 19.2
0.54 0.09 16.5
0.30 0.05
16.7
0.18 0.03 17.4
Table VII. Precision Data on Steel 12 (50 ppm oxygen) Number of particles per gram of steel 3 stated size ( N ) Intercept (b) 40 p 50p 60 p 70 p 80 1 90 p 100 p 9.329 31.1 10.5 4.3 2.0 1. o 0.59 0.35 9.188 22.7 7.6 3.1 1.5 0.76 0.43 0.26 7.860 33.0 13.6 6.6 3.6 2.1 1.3 0.88 8.792 0,808
9.21
28.9 5.5 19.0
10.6 3.0 28.5
4.7 1.8 38.2
2.4 1.1 46.9 45.1
1.3 0.72 54.6
0.78 0.48 61.4
0.50 0.33 67.4
Table VIII. Precision Data on Steel 14 (50 ppm oxygen) Number of particles per gram of Slope (a) Intercept (b) 40p 50 p 60p 70p -5.978 9.501 23.2 7.5 2.9 1.4 -4.721 8.876 20.5 3.0 1.5 7.2 -4.081 7.751 16.3 6.6 3.1 1.7 -2.778 5.428 9.5 5.1 3.1 2.0
steel 3 stated size ( N ) 80 p 90 1.1 100 p 0.69 0.38 0 22 0.78 0.45 0.27 0.96 0.60 0.39 1.38 1.0 0.74
-4.164 1.02 24.4
0.95 0.31 32.4
7.889 1.81 22.9
17.4 6.0 34.4
With a plot of the average particle count data in Table V, as a n example, the 18.8 particle count a t 40 p could have varied from 17 to 20 particles. This is equivalent to a range of approximately i1.5 particles per gram or about is% of the particle count at 40 p . Recall that this type of error could not have affected the results of the simulated inclusion residue test, because in that test all counts were taken o n the portion of the size distribution curve that did not change with diameter setting. Versatility of the Method. The method described is useful for studying deoxidation products and other types of phases that are relatively homogeneously distributed throughout the matrix. At present the method is generally not intended for application in studies on heterogeneously distributed exogenous phases such as refractory erosion products and entrapped slag. Many operations of the procedure can be readily modified to meet analytical requirements different from those associated with analyzing sheet steels. First, the amount of steel taken for analysis can be varied over wide ranges to provide the number of particles required to achieve reliable analyses. Second, the extraction and residue purification procedures can be modified where needed to provide suitable residues for the analysis of other grades of steel. Finally, the size of the orifice in the aperture apparatus can be changed to facilitate the analysis of particles of other size ranges. However, changes in orifice diameter must be made judiciously. Decreasing the orifice diameter 182
5.3 1.1 21.4
6.6 1.0 16.0
3.0 0.069 2.2
1.6 0.29 17.7 29.5
0.60 0.28 45.9
0.41 0.24 58.1
makes it possible to count smaller particles at lower electronic background noise rates but also reduces the flow rate of the sample suspension through the particle-sensing zone. Increasing the orifice diameter makes it possible to count larger particles, with the added advantage of achieving faster flow rates. However, when working with particles larger than those studied in the present work, one must make certain that the large particles are adequately suspended in the electrolyte prior to their being drawn through the orifice. T o sum up, the method consisting of inclusion extraction, residue purification, and size-distribution determination with the modified Coulter Counter provides the most practical of the methods available for characterizing macroinclusions in steel. The method can be modified to size and count macroinclusions in different steels. ACKNOWLEDGMENTS
The author thanks a number of colleagues at the Homer Research Laboratories, in particular D. L. Harper for helpful discussions, B. S. Mikofsky for assistance in the preparation of the manuscript, and R. J. Noll, B. M. Thomas, and R. F. Wetzel, and S. Knochs, Jr. for technical assistance. RECEIVED for review July 13, 1970. Accepted November 2, 1970. An abbreviated form of this paper was presented at the Pittsburgh Conference o n Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 4,1970.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971
