Sensitivity Calibration in Spark Source Mass Spectrometry John F. Jaworski and George H. Morrison' Department of Chemistry, Cornell University, lthaca, N. Y. 14850
Relative sensitivity coefficients have been determined for over 23 elements in geological, metallurgical, and biological matrices. Special attention was given to elimination of errors due to interferences, inhomogeneity, variation of instrumental parameters, and inconsistent photographic measurement. Results Indicate that RSC's varied from matrix to matrix by only 10-30% on the average. RSC's were readily calculable using an existing theory based on thermodynamic considerations.
Quantitative analysis by spark-source mass spectrometry (SSMS) requires that relative sensitivity coefficients (RSC's) be determined by analysis of calibration standards. The RSC is defined as the ratio of the measured relative concentration of an element to its certified relative concentration in a calibration standard. In theory, the RSC is used to correct for the different ionization efficiencies, instrumental ion transmission factors, and photoplate sensitivities of the various elements to be determined. In practice, the RSC may contain other factors such as that representing a line-width correction. Numerous investigators (1-17) have reported RSC determinations in a number of materials and matrices. Most (2, 4-6, 13, 16) have indicated that there are significant differences in RSC values for various elements in the same matrix and, as well, for the same element in different matrices. A number of workers (7, 8, 10) have observed that, for certain groups of elements, the RSC's corresponding to one element in different matrices changed by only 25% or less. A thorough study of RSC's and matrix effects is described here using groups of standards representing three principal and widely differing types of samples normally analyzed by SSMS: geological, metallurgical, and ashed biological material. Photoplate evaluation was performed through the use of peak areas to eliminate any effects due Author to whom reprint requests should be addressed (1) J. G. Gorman, E. J. Jones and J. A. Hipple, Anal. Chem., 23, 438 (1951). (2) E. I. Hamilton and M. J. Mlnski, hf. J. Mass Specfrom. /on Physics, 10, 77 (1972). (3) B. Chakravarty, V. S. Venkatasubramian, and H. E. Duckworth in "Advances in Mass Spectrometry," Vol. 2, R . M. Elliott. Ed., Pergamon. Oxford, 1963, pp 128-134. (4) G. D. Nichols et ab, Anal. Chem., 39, 585 (1967). (5) W. D. Bratton and C. H. Wood, Appl. Specfrosc., 24, 409 (1970). (6) C. M. Judson and C. W. Hull, ASTM-E14 Conf. on Mass Spectrometry, 1963, p 470. (7) H. Kawano, Nippon KagakukaiBull., 37, 697 (1964). (8) F. Konishi, N. Nakamura and K. Kusao in "Recent Developments in Mass Spectrometry," K. Ogata and T. Hayakawa, Ed., Univ. of Tokyo Press, 1970, p 323. (9) J. M. McCrea, lnt. J. Mass Specfrorn. /on Physics, 5, 83 (1970). (10) M. Desjardins, NBS Symposium on Trace Characterization, paper 66, Gaithersburg, Md.. 1966. ( 1 1) D. W. Oblas, Appl. Specfrosc., 25, 325 (1971). (12) P. F. S.Jackson and J. Whitehead, Analyst (London). 91, 418 (1966). (13) A. J. Ahearn in "Trace Characterization-Chemical and Physical." NBS Monograph 100, National Bureau of Standards, Washington, D.C., 1967, pp 347-376. (14) H. G. Short and B. J. Keene, Talanta, 13, 297 (1966). (15) R . J. Conzemius and H. J. Svec. Talanta, 20, 575 (1973). (16) R. E. Honig in "Advances in Mass Spectrometry," Vol. 3, W. L. Mead, Ed., Elsevier, Amsterdam, 1966, pp 101-129. (17) A. J. Socha and E. M. Matsumoto. AS-E-14 Conference on Mass Spectrometry, 1967, p 179.
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to change of relative line-widths with matrix. Internal standards were incorporated into the SSMS electrodes by a precise solution doping technique (18) allowing more reliable comparisons to be made among the RSC's. Unresolvable interferences, inhomogeneity errors, and measurement errors were reduced by analyzing a number of standards representing the same matrix but having large differences in composition. The final results, representing information gathered from measurement of over 60,000 mass spectral lines, indicate that, for the matrices examined, significant differences exist among RSC's for different elements in the same matrix, while the RSC of an individual element did not change significantly from matrix to matrix.
EXPERIMENTAL Instrumental Parameters. All standards were run under the identical operating conditions detailed in Table I. Geological Standards. Six rock standards G-2, AGV-1, BCR-1, W-1, PCC-1, and DTS were obtained in powder form from the U S . Geological Survey (USGS). All standards were treated identically: one gram of powdered rock was weighed into a polystyrene vial. One gram of solution-doped graphite (146 ppm In, 5.9 pprn Re) was then added along with several polystyrene mixing beads. T h e six resulting mixtures were each shaken for one hour in a Spex mixer mill, ground for one hour in an agate ball and mortar (Geoscience Instr. Inc., Mount Vernon, N.Y.) and then pressed into electrodes according to a previously published method (19). Four photoplates were run on a t least two pairs of electrodes a t each of two magnet settings: high dispersion such that masses 6 to 140 were displayed on the 16-in. photoplate, and normal dispersion such that masses 10 to 238 were displayed on the photoplate. The high dispersion setting was used in order to optimize the analysis of low mass elements. Biological Standards. Two biological standard materials, SRM 1571 Orchard Leaves and SRM 1577 Bovine Liver were obtained from the National Bureau of Standards. Each standard was dried, weighed, and then ashed in a low temperature ashing unit (Tracerlab, Inc.) until constant weight was reached. Ashing was performed to reduce mass spectral interferences due to organic molecular ions. A number of elements, e g . , As, Sb, Hg, halogens, etc., may be partially lost by volatilization under certain operating conditions. Cooling the sample holder externally by use of liquid nitrogen can help to minimize this effect. Equal weights of ash and doped graphite (100 ppm Y) were then mixed together, made into electrodes, and run as above. Metal Standards. Three NBS steel standards, numbers 661, 663 and 665 were chosen to provide widely differing concentration levels for as many elements as possible. As the standards were in rod form, they were cut to the proper length, etched in dilute nitric acid, washed in reagent grade methanol, and then run as above. Internal Standards. Internal standards were chosen on the basis of freedom from interferences and absence of that element from the sample. Geological standards were analyzed using In as internal standard for elements of atomic number 3 to 49 while Re was used for elements of atomic number 50 or greater. Biological standards were analyzed using Y as sole internal standard. The steel standards were analyzed using Cu as internal standard for elements with atomic number below 50 and using Sb for elements of atomic number 50 or greater. The solution doping method used has recently been described (18). In brief, a solution of the internal standard is added to high purity graphite. A slurry is formed, homogenized and then freezedried t o yield the doped conducting medium. (18) J. F. Jaworski, R. A. Burdo, and G. H. Morrison, Anal. Chem., 46, 805 (1974). (19) G. H. Morrison and A. T. Kashuba, Anal. Chern.. 41, 1842 (1969).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 14, DECEMBER 1974
Table I. Instrumental Parameters Instrument Nuclide Graf-2 Source vacuum Torr Analyzer vacuum -IO-* Torr S p a r k pulse duration 100 p s e c S p a r k repetition rate 100 Hz (high dispersion) 320 Hz (normal D i s p e r s i o n ) S p a r k voltage 60 kV Accelerating voltage 1 6 kV Detector Ilford Q2 photoplates Resolution -2900 at m a s s 121
Photoplate Evaluation. Photoplates were read with a JarrellAsh Model 23-100 scanning microdensitometer interfaced with a PDP 11/20 minicomputer. Peak areas were used to calculate apparent elemental concentrations free from variability due to changes in line-width and line shape (20). To compensate for the mass dependence of the photographic emulsion, each result was corrected by a factor equal to the square root of the respective isotopic mass. Apparent concentrations for each standard were averaged and then ratioed with the certified values to yield individual sets of RSC'sgrouped according to matrix. The RSC's for each element in a matrix were then compared and, when possible, were averaged. I n s t r u m e n t a l I o n Transmission. Identical series of exposures were made on four photoplates at varying magnetic field strengths using NBS 665 steel for electrodes as that standard exhibited superior homogeneity characteristics. Ion intensities were measured and relative percent ion transmission was calculated with 100% taken as the ion transmission measured a t the low mass end of the photoplate (see Figure 1). These transmission factors were used to correct the RSC's to values more representative of the relative ion intensities present in the source.
RESULTS AND DISCUSSION The observed relative sensitivity of an element may be considered to be the relative sensitivity at the source (ie., the relative populations of plus one ions in the source) modified by ion extraction, energy discrimination, ion transmission, and photoplate sensitivity factors. The RSC's presented here are not equal to those representative of the conditions in the source as they still contain ion extraction and energy discrimination factors. Nevertheless, as will be shown later, these effects do not appear to be pronounced even among widely differing matrices. Different Elements, Same Matrix. Figure 2 shows a plot for the geological standard W-1 of the RSC's experimentally and theoretically obtained us. the atomic numbers of the respective elements. Calculated RSC's will be discussed later. Similar results were obtained for the other matrices examined. It is evident that the RSC's vary greatly with the changing chemical properties of the elements. This variation along with several theoretical approaches to its calculation will be considered later in this paper. RSC Invariance within One Matrix. Table I1 gives the ranges of major and minor element composition found in the chosen geological, metallurgical, and biological standards. In most cases, the elemental concentrations span one or more orders of magnitude in a given matrix. Hence, i t was possible that some matrix effects could be observed. To determine what was a significant difference in RSC's, the precision of our results were examined. Table I11 lists typical results of three different RSC determinations for the USGS standard W-1. These determinations were performed over the space of two years. Each time, different batches of photoplates and doped graphite were used. The average % RSD for all the RSC's determined was 12% al(20) R. A. Burdo, J. (1974).
R. Roth, and G. H. Morrison, Anal. Chem., 46, 701
3
4
B
12
16
20
24
28
32
36
45
Distance From Low Mass End (cm)
Figure 1. Relative ion transmission of
magnetic analyzer
_ _ _ Colculaled - Experimental
f
Iv
011
c'
A t o m i c Number
Figure 2.
Experimental and calculated RSC's of elements in
W-1
though some elements had much higher % RSD's due, probably, to inhomogeneities in the standard. Thus, differences in RSC on the order of 15% for real samples may be explained simply in terms of SSMS imprecision without invoking any matrix effects. Overall average % RSD's calculated for the RSC's of each matrix were 21% for the geological standards, 15% for the metallurgical standards, and 14% for the biological standards. Table IV lists, for comparison, precisions obtained by several authors for RSC's in various matrices. Allowing that many of the USGS standard values were not stated to the same confidence level as were those of the NBS certified standards, it may be concluded that at the level of precision allowed by SSMS, the RSC for a given element in a particular matrix should be invariant. Simultaneous analysis of a graded series of rock samples by SSMS and neutron activation (NAA) using W-1 as reference standard for both techniques has shown this to be true for many elements. Since NAA is free of matrix effects, agreement between SSMS and NAA for widely differing levels of a series of elements is good indication that matrix effects are not noticeable even amongst widely differing representatives of the same matrix. Results indicative of the agreement obtained are listed in Table V for several lunar rock and soil samples of widely differing compositions. Errors in RSC Determination. Although in principle the RSC of an element in a given matrix is invariant, in practice RSC values obtained often contain large systematic errors due to inhomogeneity, incorrect certification of standards, spectral interferences, and measurement errors. Most standards contain at least some microinhomogeneities. Ingamells and Switzer (21) have shown that for many existing rock standards, the sampling weight necessary to ensure a relative subsampling error of 1% for a given element may be more than 0.3 gram. Hence the neglect of singularly high values obtained on one photoplate for an element may yield erroneously low values for the bulk analysis even though the resultant precision may be high. Micrograins containing large amounts of one or more elements (21)
c 0.lngamells and P. Switzer,
Talanta. 20, 547 (1973)
ANALYTICAL CHEMISTRY, VOL. 46, NO. 1 4 , DECEMBER 1974
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Table 11. Ranges of Compositions of Standards (wt %) Rock
Steel
C Mn P Si
Si 18.9-32.3 AI 0.13-9.15
Fe Mg Ca Na
1.86-9.40 0.40-30.0 0.11-7.79 0.01-3.16 K 0.001-3.75 Ti 0.008-1.32 Mn 0.026-0.14 P 0.001-0.25
0
S
Ni
Cr V MO AI
Biological
N K Na Fe CU Zn Mg
0.008-0.57 0.0057-1.50 0.0025-0.029 0.008-0.74 0.0059-0.017 0.041-1.99 0.0072-1.31 0.0006-0.31 0.005-0.19 (0.0007)‘-0.24
2.76-10.6 0.97-1.47 0.008-0.24 0.027-0.030 0.0012-0.019 0.0025-0.013 (0.061)0-0.62
Recommended but not certified. ~
Table 111. Triplicate Determination of RSC’s for W-1
Table V. Agreement of NAA a n d SS,MS L u n a r Analysesa
Typical RSC Values Element
B P Mn
Rb Y Sn Ce
Ho Pb Th O v e r a l l average
Range
0.42 0.40 1.0 1.7 0.27 1.8 1.0
0.84 1.0 0.53
RSD
0.59 0.48 1.2 2.0 0.43 1.9 1.3 0.91 1.4 0.63 = 12%
Composition (ppm) Sample 60315
M RSD
19 9.2 8.3 7.1 24
Element
Cr Co Ni
cu
5.1
Zr
12 5.1 19 10
Yb Lu
Iron alloys Bowen’s Kale NBS steels Rare earth oxides TiOz
In\ estigator(s)
Short and Keene ( 1 4 ) Hamilton and Minski (2) McCrea (9) Conzemius and Svec (15) Jackson and Whitehead (12)
a
Overall RSD il
37 25 18 16 8
occur in many types of samples but most frequently in rocks. Analysis of W-1 for Zr has consistently yielded apparent results that range from 20 to 110 ppm. However, when large numbers of plates are run (10 or more) in groups, average RSC results from the various groups exhibit an RSD of 20% or less if no values are ignored. Standards often have widely differing estimated relative errors in their certified values. For example, the NBS steel standard number 663 has at most a 0.6% relative uncertainty in its Mn value while the relative uncertainty in its Au value is 20%. Hence, the precisions of the standard values must be taken into account when comparing RSC’s obtained from different standards; otherwise it will be impossible to ascertain when a significant change in RSC has taken place. Estimated ranges for possible relative error in certified values are listed in Table VI for some of the standards used. The presence of unresolvable interferences due to molecular lines and multiply-charged species has always been a major problem in SSMS. NAA has been used repeatedly in this laboratory t o verify the accuracy of SSMS in a n unfamiliar matrix. Agreement between the two methods when using the same comparative standard t o analyze widely dif2082
*
1600
&,\A
1400 83 95 1600 1400 9.5 10.8 800 1000 10.0 1 3 . 0 1.8 2.0
Sample 62255 SSMS
36 1.4 ND 0.82 1.0 0.080 0.08
NAA
24 1.3
ND 1.09 0.82
0.071 0.07
Sample 74220
SA4
SSMS
4900
4400 65 90 70 30 34 150 180 4.5 4.3
75
0.7
Av 5 dev
Table IV. Precision of Experimentally Derived RSC’s \htnX
SS.MS
15.2 21.9 Both using W-1 as comparative standard.
0.5 18.4
Table VI. Range of Estimated E r r o r s i n Certified Values of Selected Standards Standard
O r c h a r d Leaves Bovine L i v e r NBS 661 NBS 663 NBS 665
Number of elements certified
19 12 29 22 17
Range of uncertainty, 96
1.4-18.1 5.2-23.5 0.5-45.5 0.7-31.3 1.7-33.3
Average il uncertainty
8.5 9.4 14.2 7.3 10.1
~
fering samples has been the basis for concluding that RSC’s remain constant in the same matrix. Disagreement between the two methods can be a n indication of inhomogeneities, measurement error, interferences, as well as a matrix effect. Interferences are generally indicated when larger and larger RSC values are encountered as the absolute concentration of the element decreases t o the detection limit. Elements which did not exhibit RSC values invariant over several orders of magnitude change in absolute concentration were generally excluded from the final results. In cases where the effects of interferences became clearly discernible only a t relatively low absolute concentrations, RSC values from standards having much higher levels of that element were used. Even here, caution was exercised as drastic changes in interference patterns may cause apparent changes in RSC even at relatively high levels of the element being considered. The use of isotope ratios to recognize the presence of interferences is helpful but limited in complex matrices by the fact that often all the isotopes of an element with the possible exception of one are interfered with. Furthermore, in some complex matrices, interference pat-
ANALYTICAL CHEMISTRY, VOL. 46, NO. 14, DECEMBER 1974
~
~~~
Table VII. Comparison of Artifact and Accepted Isotopic Abundance Values for Selected Elements in Josephinite Isotope
lolRUh ‘”Ru 157Gd i 5 8 ~ d b
4rti fact a abundance
17.07 30.30 18.20 5.72 22.70
Literature abundance
Table VIII. RSC’s for Three Matrices Element
Li B
17.07 31.61 15.68 5.72 21.90
‘“Gd Abundances in 1 e , Ru and Gd were absent from the sample both columns set equal to prmit comparison of other abundances.
terns may reproduce very closely the isotopic patterns of certain elements even though subsequent NAA showed that the elements in question were below the detection limit. This is clearly shown in Table VI1 where, for the rock Josephinite, molecular line patterns closely resemble the isotopic patterns of Ru and Gd; NAA had conclusively proved that both elements were absent from the sample despite the fact that SSMS signals indicated levels for both elements well above the NAA detection limits. The lines observed in the mass spectrum are therefore attributable to molecular interferences and not to Ru and Gd. The analyses of elements whose concentrations are very high or are near the detection limit result in highly variable RSC values because of the basic inability to measure very strong or very weak lines photographically. The same type of measurement error occurs when matrix lines are used as internal standards, i.e., measurement of very low exposures as well as photographic lines of widely differing intensity and position on the photoplate doubtless introduces errors which can swamp out any gains achieved from reduction of internal standard homogeneity problems. Impurity lines falling near matrix lines have always vielded widely varying RSC results. Space charge (15) and Gariable background effects (22) have been invoked to explain this observation. Examples of such cases are IIB when carbon is used as the conducting medium and S5Mn in an iron matrix. In general, keeping instrumental parameters constant is straightforward; however, maximizing the charge collection by applying an offset to the accelerating potential changes the position of the energy-selecting window and, hence, changes the sample of the ions being viewed a t the photoplate. Woolston and Honig (23) have indicated that, for a given element, very similar energy distributions are observed whether the element is the matrix or a minor constituent. Therefore, keeping the accelerating potential constant for samples of widely differing matrices (as was done in this work) will keep discrimination a t the energy selecting slit constant to a t least a first-order approximation. Variation in plate sensitivity along the mass focusing plane periodically introduces mass dependent differences in RSC’s obtained from a set of supposedly identical plates. However, when plates are run in groups of four or more, the effects of such sensitivity variability tend to cancel out or a t least tend to be minimized when results from individual plates are averaged. Scope of RSC Invariance. Erroneous RSC values attributable to the above mentioned factors were deleted from the data sets for all matrices. Average RSC’s were then calculated for each element in each matrix. Each re(22) K. D. Schuy and J. Franzen, Fresenius, Z. Anal. Chem., 225, 260 (1967). (23) J. R . Woolston and R. E. Honig, AS-E-14 Conference on Mass Spectrometry, 1964. p 377.
P Ti V Cr Mn
Fe
co Ni CU
Zn
As Rb Sr Zr
Nb Sn sb
La Ce Pr
Pb a
Geological average
Biological average
0.83 0.42 0.53 0.56 0.83 1.00 0.91
0.77 0.33
0.77
0.83 0.91 1.0 0.59 1.9 1.5 0.50 0.42 0.33 1.2 1.00 0.63 0.77 0.77 0.77
... 0.24 0.56
... ...
0.71 1.00 0.77
0.63 0.83
Metallurgical averaqe
0.77 0.67
1.00 2.0= 0.77
0.67
...
0.72
0.72 0.48 1.0“ 1.9 0.31
1.4
... ... ... 1.00 ... ... ...
0.59
2.0
...
...
0.50 0.40 0.91 1.00 0.83 0.91 1.0 1.3
Averagc all matncer
0.80 0.33 0.55 0.67 0.74 1.00 1.2 0.72 0.78 0.82 1.0 0.54 1.6 1.7 0.41 0.46 0.37 1.1
A RSD all maeices
5.3 27.2 3.9 22.3 11.3
...
54.9 11.2 11.9 16.5 32.9 14.5 33.7 16.6 33.2 12.3 13.6 19.4
1.00
...
0.73 0.84 0.89 0.89
19.4 11.8 18.4 41.6
Possible error, see text
sult was corrected for the differential ion transmission of the magnetic analyzer by application of the appropriate correction factor obtained from Figure 1. To compare results for different matrices, RSC’s for all elements with atomic number 49 or less were normalized to an RSC value of unity for Cr, while all elements with atomic numbers greater than 49 were normalized to an RSC value of unity for Sb. Cr and S b were chosen to be reference elements as each had two interference-free mass spectral lines and both elements were present a t measurable levels in most of the standards. These final results are listed in Table VIII. Only those elements where RSC’s were determined in two or more matrices are listed. Certain elements could not be included in the comparisons for the following reasons: a) the signals for those elements were not measurable in the given matrix, e.g., heavy rare earth elements in biological ash; b) the elements were not certified in the particular standards, e.g., Mo in the biological standards; c) the mass spectral lines of the elements suffered significant interference, e . g . , Sc in the geological matrix, and d ) elements such as the alkali metals exhibited significant thermal ionization contribution to the spark excitation necessitating their exclusion. The average RSD determined from Table VI11 by averaging the listed RSD’s is 20.6%. When two RSC’s were rejected, that for Mn in steel (possibly affected by the strong matrix lines on either side) and that for As in biological ash (possibly lost during low temperature ashing), the value of the average RSD dropped to 17.8%.This is close to the 15% originally stated to be the level of imprecision of SSMS analysis by this particular method. Therefore the results in Table VI11 indicate that the RSC of an element is independent of the matrix in which the element is contained. Hence, provided the previously mentioned sources of error are excluded, RSC’s derived for analysis within one matrix may be used quantitatively in the analysis of other matrices. A further test was performed to evaluate the influence of the chemical form of the element upon its SSMS sensitivity. High purity graphite was doped with a solution contain-
ANALYTICAL CHEMISTRY, VOL. 46,
NO. 14,
DECEMBER 1974
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I o n Energy Distributions of Selected Elements
Table IX. Standard Addition to W-1
Li
Element
Li
Cr
15 5
160
16 5
170
175
Ni cu Sr Y Ba La
Expected signal, ppm
22. 241.
Experimental signal, ppm
198.
24. 242. 203.
248.
271.
300.
290. 33.6 200.
32.7 200. 8.8
7.8
Deviation, ?4
9.1 0.41 2.5 9.3 3.0 2.8
0 11.
Overall RSD = 4.8%
Energy ( L V I
Figure 3. Ion energy distributions of selected elements
ing precise amounts of the nitrates of Li, Cr, Ni, Cu, Sr, Y, Ba, and La. One gram of this graphite was then mixed with one gram of W-1 and run as before. Table IX lists the signal in ppm (by weight) expected if the sensitivities of the elements are identical in both the rock and the nitrate salts doped onto the graphite. Immediately beside the expected values are the experimentally determined results and the percent deviation from the expected values. Barring selective volatilization and thermal ionization problems, it appears that the chemical form of the element is not an important factor in determining its SSMS sensitivity. Guidoboni and Evans (23) have shown that by doping both samples and standards onto high purity silver powder, matrix-free synthetic standards could be used for the analysis of steel and aluminum samples, i.e., elemental sensitivities remained constant when the chemical forms of the elements were similar, if not identical, in both sample and standard in spite of the presence or absence of a matrix component in the electrodes. In the light of the results presented in Tables VI11 and IX, it appears that this observed reduction of the so-called matrix effect is due to the greater precision with which operating conditions can be maintained constant when the major component of the electrodes remains the same, e.g., in the selection of the correct accelerating potential offset to assure consistent positioning of the energy-selecting window a t the electrostatic analyzer. Desjardins (10)has analyzed steel and aluminum matrices directly and reported that RSC values were essentially independent of the matrix. Hence, it seems that it is the difficulty in exactly reproducing certain critical operating conditions and not the sample chemistry which is primarily responsible for the observation of matrix effects. Therefore, the solution doping method may be used not only to overcome gross sample inhomogeneity but also be used to rapidly prepare made-to-order standards for the analysis of unfamiliar samples. Furthermore, the method may be used to check for the presence of interferences in unfamiliar matrices by adding known amounts of elements to standards representing those matrices, determining the signal change corresponding to the addition and, hence, by comparison, the purity of the original line measured in the standard. Theoretical Interpretation of RSC Results. Theoretically derived RSC’s do not contain correction factors representing ion extraction, transmission, or discrimination a t the energy selecting slit. Hence, comparisons of theory and experiment should be made where experimental values are all likely to have been affected to the same extent by these factors, i.e.,observed differences in ion intensities for these elements will be due primarily to the different physical properties of the elements and will reflect the relative ion (24) R. J. Guidoboni and C. A. Evans, Anal. Chern.,44, 2027 (1972).
2084
populations in the source. Figure 3 contains three characteristic types of ion energy distribution curves and indicates which elements exhibit these distributions. The curves in Figure 3 were obtained by sparking electrodes composed of a complex material and observing the variation of spectral line intensities as an offset was applied to the accelerating potential. In the case of Bi, the curve was obtained by observing the relative rates of beam monitor charge collection as a function of offset to the accelerating potential while sparking pure Bi electrodes. These curves are remarkably similar to those obtained by Woolston and Honig (23) indicating that these distributions probably do not change drastically from instrument to instrument. Hence, experimental and calculated RSC’s should be comparable for the following elemental groupings provided results are properly normalized within each group: 1) P, S, As; 2) Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb; 3) rare earth elements, Y. One of the earliest proposals for the theoretical calculation of RSC’s was that of Goshgarian and Jensen (25). Their general equation for the RSC of a given element is shown below.
CR is the covalent radius of the element in question, here squared to approximate the ionization cross section, .VI, is the heat of sublimation of the element, I , is the first ionization potential of the element (as the relative sensitivities of the singly charged positive ions are being considered), and M is the mass of the isotope in question, its square root being a correction factor for the mass dependence of the photoplate response. Figure 2 shows that the agreement of theoretical and experimental results is quite good for those groups of elements having the same ion energy distribution curves. On the average, the overall relative deviation of calculated and experimentally determined RSC’s was 20.1%. If results for Ti and Yb were not included, the average relative deviation dropped to 16.7% for 22 elements. This value approaches the precision of analysis of “real” samples by SSMS using photoplate detection. ACKNOWLEDGMENT The authors thank R. I. Botto for assistance in analyzing the steel standards as well as for the data used in Table VIII. RECEIVEDfor review May 17, 1974. Accepted August 2, 1974. Financial support was provided by the National Science Foundation under Grant No. GP-30940X and through the Cornell Material Sciences Center. (25) B B Goshgarian and A V Jensen, AS-E-14 Conference on Mass Spectrometry, 1964, p 350
ANALYTICAL CHEMISTRY, VOL. 46, NO. 14, DECEMBER 1974
