1711
Anal. Chem. 1984, 56, 1711-1715
Retention volume increased with increasing sample concentration, which was similar to that reported previously using conventional SEC columns (7, 10, 11).
ACKNOWLEDGMENT The authors wish to express their appreciation to Yasuhiko Nishimura for technical assistance. Registry No. Polystyrene (homopolymer), 9003-53-6.
l5I-
LITERATURE CITED 1
- 41
01
02 0.3 04 Concentration (%)
Figure 7. Effect of concentration on retention volume. Conditions are the same as those in Figure 5.
injection volume and the amount of variation is significant below 10 pL. This observation is similar to the result on the conventional SEC columns, where the amount of increase in retention volume when the injection volume increased from 0.1 to 0.25 mL was 15-20 times larger than that from 0.25 to 0.5 mL (7).
(1) Siemion, C. C. J. Liq. Chromafogr;,1983, 6 , 765-775. (2) Snyder, L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography”, 2nd ed.; Wlley: New York, 1979;pp 217-219. (3) Takeuchi, T.; Ishii, D.; Morl, S. J. Chromafogr. 1983, 257, 327-335. (4) Mori, S. J. Cbromafogr. 1979, 174, 23-33. (5) Kirkland, J. J. J. Chromafogr. 1976, 125, 231-250. (6) Limpert, R. J.; Cotter, R. L.; Dark, W. A. Am. Lab. (Fairfield, Conn.) 1974, May. 63-69. (7) Mori, S.J. Appl. Polym. Sci. 1977, 2 1 , 1921-1932. (8) Little, J. N.; Waters, J. L.; Bombaugh, K. J.; Paupils, W. J. J. folym. Sci., Pari A-2 1969, 7 , 1775-1783. (9) Chuang, J.-Y.; Johnson, J. F. Sep. Sci. 1975, 10, 161-165. (IO) Boni, K. A.; Siiemers, F. A.; Stickney, P. B. J. Polym. Sci., fart A-2 1968, 6,1567-1578. (11) Spatorico, A. L. J. Appl. Polym. Sci. 1975, 1 9 , 1601-1610. ’
RECEIVED for review March 6, 1984. Accepted April 18, 1984.
Some Fundamental Aspects of Surface-Film Analysis with Variable Angle Ultrasoft X-ray Fluorescence Spectrometry George Andermann* and Francis Fujiwara
Department of Chemistry, University of Hawaii at M a m a , Honolulu, Hawaii 96822
The use of varlabie angle ultrasoft X-ray fluorescence spectrometry Is suggested as a nondestructive method for “real world” surface-flim analysis. The fundamental aspects of the film emlssion, substrate line attenuatlon, and ultrasoft scattered X-rays are evaluated. I t Is shown that In the ultrasoft X-ray region the fluorescent radiation escape depth reaches values around lo2 A at low exlt angles and lo3 A at conventional exit angles, thus providing the possibility of sample depth proflling wlth the film emission method. The substrate line attenuatlon technique is proposed for thln film structural and thickness studies. The use of ultrasofl scattered X-rays Is suggested as an internal standard In surface-film analysis as well as for correcting for surface lrreguiaritles at grazing angles.
In discussing surface analysis Hercules (1) has recently pointed out a number of pertinent features. Most importantly he cited that “true” surface analysis involves the outermost 1-5 atomic layers of a solid. According to Hercules, of the large number of spectroscopic techniques XPS (X-ray photoelectron spectrometry),AES (Auger electron spectrometery), SIMS (secondary-ion mass spectrometry), and ISS (ionscattering spectrometry) appear to be most useful for such analysis. All of these methods (and UPS (ultraviolet photoelectron spectrometry) also) are based on the quantitative manipulation of ejected particles (electrons or ions). All of 0003-2700/84/0356-1711$01.50/0
the above are associated with escape, Le., critical depths, d,, which are in the range of about 5-25 A, thus fulfilling the requirement of a “true” surface analytical tool, and, therefore, automatically requiring the use of UHV (ultrahigh vacuum) conditions at least in the sample chamber. Photon methods were indicated by Hercules to involve d, values of lo3 8, in the IR region and lo4 8, using 103-eV X-rays. Clearly, therefore, according to the viewpoint suggested by Hercules none of the photon methods could be considered to be “true” surface-thin film analytical tools. Aside from the importance of clearly delineating which spectroscopic techniques fulfill the role of “true” surface characterization, Hercules’ review is useful also because it shows that none of the techniques reviewed by him have d, values in the range of 50 8, to lo3 A, indicating a serious gap in analytical capability. As indicated by Hercules there are at least two other fundamental capabilities that need to be looked at in comparing the various techniques, and these are spatial resolution and chemical speciation capabilities. Only AES has microprobe capabilities and only XPS, UPS, and AES provide chemical speciation capabilities. Not reviewed by Hercules specifically is the Rutherford backscattering (RBS) method which has d, values in the range of 50 to lo3 8, but which provides only atomic information and cannot be used as a microprobe. Hercules’ comments on “true”surface analysis are especially noteworthy for solid samples for which there is a reasonably sharp distinction between bulk and surface properties and where surface properties are present for layers which are 25 0 1984 American Chemical Society
1712
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
A or less. On the other hand, there exists a host of materials encountered in corrosion, embrittlement, weathering, ion implantation, thin film coatings, epitaxial growth, lubricants, adhesives, etc., where the thickness of the layers involved is usually in the range of several hundred to a few thousand angstroms. These thicker layers do not correspond to “true” surfaces as defined by Hercules, yet they constitute a separate phase or phases distinct from the bulk phase. For the sake of convenience we shall designate these layers as surface films. Currently sample depth profiling for these surface films must proceed with XPS, UPS, AES, SIMS, and ISS via a number of destructive methods such as particle bombardment, ion etching, etc., Le., in controlled discrete steps where very thin layers are removed energetically under UHV conditions. Aside from the fact that in some instances it might be preferred not to destroy a sample, it is also important to note that especially with respect to chemical speciation studies, perhaps better designated as molecular or band electoronic structural characterization, the energetic stripping of surface layers may significantly alter the surface which is to be evaluated after the stripping. Moreover, it is becoming more and more apparent (2)that any method which has to employ HV or UHV sample chamber conditions may involve experiments which are significantly removed from real world problems. Consequently, an important fundamental analytical problem of depth profiling capability for surface films may be formulated as follows: “Is it possible to obtain information in a non-destructive manner concerning (a) surface-film physical uniformity, (b) elemental composition, (c) chemical speciation as a function of depth, (d) either with or without spatial resolution?” Clearly, RBS does provide a useful capability for category (b). Before presenting the arguments on how, in principle, (US) ultrasoft (A > 10 A) X-ray fluorescence spectrometry (XFS) can provide all four capabilities nondestructively, we provide a brief review on previous efforts on studying films and coatings via XFS. The use of XFS using (H) hard (X < 2 A) or soft (S) X-rays ( 2 A < X < 10 A) for elemental analysis of films, and coatings, where the film or coating thickness (t)is about 103A or greater, is textbook information (3, 4 ) . In fact, Ebel (5) has even reported on varying the exit angle as an aid in obtaining chemical analysis. To date, however no one has suggested the use of variable angle XFS to provide sample depth profiling of films or coatings. Moreover, a cursory examination of the literature reveals no information on chemical speciation studies of films in any wavelength region or any sort of surface-film characterization (elemental or molecular) with USXFS (ultrasoft X-ray fluorescence spectrometry). This finding is particularly surprising since one would expect USXFS techniques to be able to characterize films with t values much lower than lo3 A simply by using grazing incidence and/or exit angles with respect to the sample. Our group has already carried out some preliminary experiments and we have reported on one rather interesting application of USXFS, namely, the characterization of naturally occurring nickel oxide on the surface of high purity Ni (6). THEORY We discuss variable angle XFS in terms of three possible techniques, namely, (1)film emission (FE) method, ( 2 ) substrate line attenuation (SLA) techniques, and (3) the scattered X-ray internal standard (SXIS) method. While acknowledging the possible importance of optical properties, for example, refractive index effects, at low angles of incidence and/or exit, these will be ignored in this treatment for the sake of simplicity. By considering only polycrystalline specimens, we shall also ignore possible anisotropic emission complications from single crystals of low symmetry. While in principle much of what we discuss below would be applicable to molecular
Flgure 1. Experimental arrangements for surface-film FE method:
=
e, + e,
= 900.
C#J
surface films, we shall emphasize elemental analysis. (1) The Film Emission (FE) Method. The use of the FE method a t fixed oblique angles with HXFS (hard X-ray fluorescence spectrometry) and SXFS (soft X-ray fluorescence spectrometry) for elemental analysis is covered thoroughly in Bertin’s text ( 3 ) . The simplification underlying this approach is that optical constant (refractive index, reflection) effects may be ignored completely. With conventional sample geometry, low optical resolution, and for core electron transitions, such a model is rigorously accurate. In the treatment offered below for unconventional, i.e., grazing angle geometries, even at high optical resolution, and even for valence electron transitions, we adopt the above simple model, since, as it turns out, it provides a number of useful guidelines for surface-film characterization. A highly simplified version of the geometry of sample irradiation and fluorescence production with the FE method is shown in Figure 1. In this illustration the angle 4, which represents the sum of the angle of incidence 8, and the angle of exit Be, corresponds to 90°, as in our present experimental arrangement. Characterization of surface films proceeds according to the formulation well known in the hard X-ray region (7) namely where
+
+ pUecosec e,)
= p(A B) (2) with p and p representing the appropriate mass absorption coefficients and density values, respectively, and where Id represents the fluorescence intensity at any given surface-film thickness, d, and I , stands for the intensity corresponding to an infinitely thick film. In order to calculate the value of critical depth d,, it is necessary to assign an arbitrary value to r a n d this may be anywhere from 0.95 to 0.99. Clearly, in order to obtain a minimum value of d, at any given value of r, it is necessary to increase the value of q. An increase in the value of q is obtained as Bi and Be are decreased and as pe and p, are increased. While optimizing q in terms of p, and ps depends on the specific sample itself, nevertheless, it is possible to gain some qualitative insight by noting a few well-known facts or practices. Since the objective is to obtain high values of pe and pi, clearly increasing A and increasing Z favor such requirements. In general, for effective monochromatic excitation pi > pe, and, in fact, it is possible to have pi reach values of rip, to 9pe, or approximately p1 lope both for K a and La excitation with appropriate monochromatic excitation. In view of the above considerations on B1,Be, pi, and pe, it is informative to examine some limiting cases with p, lope. If 0, 90°, but Be lo, A < B and q pB. On the other q = p(pi cosec Bi
-
-
-
-
-
ANALYTICAL CHEMISTRY, VOL. 58, NO. 9, AUGUST 1984
1713
Table I. Some d , Values at Different Conditions d, values (lo3A)d
Cu Ka Be
Bi
1" 1" 4O
1" :30°
4" 7" 7" 30" 30"
80"
1" 1"
30" 1" 30"
a Incident radiation. angle considerations.
0.9gc
@
0.95' 5.60 12.0
8.70 19.0
2" 31" 5" 34" 8" 37" 31" 60"
9.90 160
15.0 250
Emitted radiation.
Cr K Si K
cu L Ni L
Ni K b
'I d l d -.
0.99
0.95
0.190 0.300
0.120 0.200
0.410 1.90
0.270 1.30
0.99 3.70 22.7
4.24 106
CK Si L
0.95 2.40 14.8
2.74 68.9
0.99
0.95
0.060 0.700 0.070 1.30
0.041 0.440 0.043 0.860
Some entries were left blank for clarity or because of critical
-
-
hand, if Oi lo and if 6, >> lo,then q pA. Thus, the maximum improvement in going from Bi = 90' to 6i = 1' is a factor of about 10. It should be noted that this improvement can be realized only in the hard (H) X-ray region (but only with long focal length grating optics), since, as X increases higher values of Oi need to be used to avoid specular reflection effects. For Ni K a 6i,H > 0.25O, but, in fact, for practical reasons 6i,Hprobably has to be -lo. For Ni La 6i,us > 2' and, therefore, a gain of about 2 is realizable in going from 6i 90° to Oi 2 O with USXFS. On the other hand, for Si 6i,s loand Oi,"S To, and therefore, using low angle incidence for very high X gains only a factor of about 1.1. Consequently, in general, low (or grazing) angle incidence yields only a factor of 1.1to 2 with USXFS. It is also instructive to examine briefly why the ultrasoft x-ray region is far more favorable for surface-film studies with the FE method than the hard X-ray region. If we let G stand for the gain in going from K a studies to La studies, then, under the stipulation that pi lop,, we have the following formulation: 10 cosec Oi.L+ cosec lo G N -= PL-KYL-K (3) pe,K 10 cosec ei,K cosec lo
-
- - -
-
-
+
For Ni, pLK 30 and Y L K 0.6,yielding a G value of about 20. For Si, on the other hand, G has a value of 77. Next it is pertinent to ascertain what sort of d, values one can expect for various substanceswith USXFS using eq 1. For these calculations at r = 0.99 we picked NiO, FeOC1, and SOz. Ni was chosen because it represents a problem of current experimental interest to us. FeOCl was chosen because it represents an interesting corrosion problem and SOz,because it represents a limiting high X situation. For Ni K excitation we used W La (1.47 A) and for Si K we used Cr K (2.28 A) excitation. For Ni and Fe L and 0 K excitation in our calculations we used Cu L (Xi = 12.2 A), whereas for C1 and Si L radiation we utilized C K excitation (A = 44.6 A). In Figure 2 we illustrate the calculated dependence of d, on 6, for the various elements with 4 = 90' and assuming that for p we can use well-known bulk values. As this figure shows in every case as 6, is changed from 45O to lo, d, value lowerings are in the range of 15 to 30. For 6, = lo,in going from Ni L to Si L, d, values decrease from about 450 A to about 65 A. With minimum permissible values for 6i, d, values of 180 A and 50 A are calculated to be achievable for Ni L and Si L determinations at r = 0.99. If the requirement on r is relaxed to 0.95, d, values of 110 to 35 A me calculated to be achievable with USXFS. It should also be noted that by going to Oi and Be values of 0.5O, another factor of 2 to 3 is achievable, and, therefore, only surface irregularities and angle definition would appear to offer the lowest limit to d, values by USXFS. In Table I we summarize the above findings for Ni and Si at -2
I
0
IO
20
30
40
50
9 ;
Figwe 2. Calculated dependence of d , on 6, for various eiements with c$ = goo.
various combinations of r, Oi, and 6,. The US region P values utilized for calculating the entries for Table I and for Figure 1were taken from Henke's studies (8,9). From the point of view of sample depth profiling the significance of Figure 2 is self evident. For any given value of 4, 6, can be readily changed from some lower limit, BeC, to some higher limit, e,, yielding dc,Land d , U values. The analytical capabilities to probe a surface film can, therefore, with FE studies be divided into three different kinds of cases depending upon the relationship of sample thickness layer t to d,. Case I dc,L< t < d,," Case I1 t < dc,L Case I11 t > d,," Case I. By changing 6, from 6, to Be,, in small increments, we should be able to monitor changes in an "incremental fashion" in intensity at a given analyte line peak or changes in spectral contour (or even new peaks possibly). Intensity changes may reflect changes in density and/or in composition. Changes in spectra may reflect changes in chemical speciation as a function of depth. It is for this case for which XFS provides the most unique analytical capability over all of the other spectroscopic techniques precisely because of the in-
1714
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
t
Figure 3. Attenuation of substrate element line by film. 1.0-
‘d -
h O C l CI-L
.5-
‘In
d(%) Fkgure 4. Calculated dependence of I,lI on film thickness, d , for 0 L in FeOCl and 0 K In Fe20,.
herent potential to extract valuable information as a function of depth. Case 11. Since t < dc,L, our method merely provides an “averaged” response exactly in the same manner as all other techniques with exponential dependence except for somewhat higher values of t . Case 111. With t > d , U our method provides a nondestructive probe down to d , U in the same way as in case I, and then, in order to get beyond dc,U, it would be necessary to remove a desired portion of t with some destructive method but perhaps with greater practical ease. Finally, it is interesting to ascertain whether or not USXFS might be used with the FE method to determine the thickness of thin films on a surface. We have examined this problem theoretically for the use of Ni, FeOC1, and Fe203with q5 = 90’ and 0, = lo. In Figure 3 we have plotted for the C1 L in FeOCl and the 0 K in Fe203,Id/I.. ( = r ) values vs. film thickness. Since r values of, say 0.1, are achievable at t = 10 A, it would appear that the present limitations of this XFS method are due to uniform film density, surface regularity, and surface contamination for very low values of t. (2) The Substrate Line Attenuation (SLA) Method. For some problems the so-called substrate line attenuation (SLA) method (10) may be preferable. As shown schematically in Figure 4, the reference sample corresponds to the substrate and provides an unattenuated intensity I,. The intensity of both the incoming and outgoing beam is attenuated by the film and may be designated as I80 As a crude approximation the absorption of the incoming beam may be ignored (for 4 = goo), and then also ignoring refractive index effects for a constant p (4). In WI,d = l ~ p t (4)
As shown with the f i i emission technique, so with the SLA method for 4 = 90°, the outgoing beam angle Be has a great bearing on sensitivity. In fact, this method may have a good potential for uniformity and chemical analysis purposes for the following reasons. (a) It may be possible to choose substrates such that the absorption by the film matrix is greater for the substrate
element line than for the film analytic line. This capability could make the SLA method more sensitive for small values of film thickness t. (PI Whereas the FE method provides a good signal to noise ratio for large t values, the SLA method should have good signal to noise ratio values for cases where t is very low. In this sense the two methods would be complementary. (7)In case we are interested in evaluating the variation of structure” for a single element density due to nonuniform “fib surface film, then in principle a single substrate analytical line may be sufficient, recalling that the FE method provides the other set of measurements. On the other hand, if the film has n elements, then it appears that at least n substrate elements not present in the film would be necessary. It may be highly informative to indicate the tremendous sensitivity of the SLA method in the SXFS and USXFS region for studying Ni thin film on a glass substrate. For example, for 0, = lo,and assuming that experimentally we can see 5% difference between I, and IBf, then if the substrate line is Si Ka, the thickness of a Ni film is only about 3 A. Moreover, if we were to use Si L the value of it would be 0.1 A. Clearly, this puts the SLA method at very low values of ee into the “true surface” category. If fact, it appears that this capability with SLA might be universally true in the ultrasoft (US) X-ray region since if (pp) > 5 X lo3, then t I20 8, a t Be = lo. Consequently, in order to study “real-world”, i.e., dirty Samples, high 0, values are necessary. But, also note that in this sense the SLA method provides the only method with continuity between “true surface” thin film and surface-film studies, at least for elemental and uniformity studies. Unfortunately, the SLA method provides no information about the chemical speciation of film constituents but it does about the substrate constituents, or perhaps about interfacial layers as well. (3) The Method of Scattered X-rays as an Internal Standard (SXIS). So far, we have considered soft and ultrasoft X-ray fluorescence from the film and the substrate. Unavoidably, however, the incoming Bremsstrahlung is scattered both by the film and possibly by the substrate, and shows up as the background radiation. Andermann in 1954 discovered that scattered X-rays in the hard X-ray region could be used as a powerful analytical tool for correcting for variable sample packing, density, shape of sample surface, and the so-called interelement effects in multicomponent analysis (11). Additional studies confirmed the early observations of the SXIS method and a limited rationalization was offered by Andermann and Kemp subsequently (12). A more rigorous theoretical rationalization and an extension to the soft X-ray region were accomplished subsequently by Taylor and Andermann (13, 14). In principle there does not appear to be any reason that the SXIS method could not be extended for sample depth profiling studies with SXFS and USXFS techniques. However, a flag of caution needs to be raised because, at a given Be, d , values for the scattered X would be lower than for the outgoing fluorescence line. Presumably this could be Calibrated for, or the anode in the X-ray tube would incorporate an element which would behave more like the analyte line in the film. Another possibility for the use of SXIS, as we have already observed (15) is to correct at least partially for variable surface roughness at low values of Be (and/or 0,) in the same manner as in the hard X-ray region for visually obvious surface irregularities.
DISCUSSION In the previous section we have considered the fundamental aspects on nondestructive surface-film elemental analysis with emphasis on sample depth profiling. However, we merely
ANALYTICAL CHEMISTRY, VOL. 56, NO. 9, AUGUST 1984
indicated the qualitative suitability of the technique. The quantitative aspects of sample depth profiig present the next set of challenges. These include the extraction of “incremental”information as 8, is varied and the manipulation of the fluorescence production equations for multicomponent surface films. In addition to elemental analysis there are other analytical capabilities inherent in the USXFS technique, namely, chemical speciation and sample spatial resolution. As it turns out XFS in general and USXFS in particular are eminently capable of solving chemical speciation (valence electron structural) problems. In fact, there are a dozen groups in the world, including ours, which have been active in the past 15 years in this frontier area, but, of course, in terms of bulk properties only. While a relatively useful review of XFS capability for such studies is offered by Urch (IO), it may be appropriate to list the two most important and unique capabilities with X-ray emission. (i) The number of opportunities to sample the filled valence electron structure of a compound increases with increasing heteronuclearity. For each heteroatom we can have at least K and possibly L (or even M) initial states and, therefore, K a and L2,3types of emission which involve the filled valence levels. Thus, for a substance with three different kinds of atoms of sufficiently high 2 we would have at least six valence spectra. Note that for all of the other techniques discussed previously, except for Auger, only a single valence spectrum is obtained. To date the complexity of the Auger phenomena, however, has prevented its general utilization for valence electron strucutral studies. (ii) Only with the X-ray emission technique is it possible to utilize the experimentally observed intensity to obtain quantitiative information about the makeup of the individual valence electron orbitals (molecular orbitals). XFS spatial resolution capability development was announced recently (7).With a synchrotron as a source, brute force technique appears to offer microprobe capability with a spatial resolution of about 1pm. Use of grazing exit angles would deteriorate this resolution to about 10-20 pm, but this is still well within the desired resolution capabilities of many possible applications. Finally, it is appropriate to comment on two important instrumentation requirements, namely, the achieving of well-defined low values of 8, in order to carry out meaningful
1715
sample depth profiling and the availability of instrumental resolution of at least 0.5 eV and preferably as low as 0.1 eV in order to perform valence electron structural studies. It turns out that high focal length grating optics provide both capabilities. Flat crystal optics do not lend themselves to reaching low values of 8, at all, and with curved crystal optics well defied, low values of 8, are difficult to achieve. Moreover, for X > 20 8, only soap crystals are available and neither flat nor Johann soap crystals provide high optical resolution. On the other hand with grazing incidence grating optics of large focal length such as in our 5-m focal length grating instrumentation, the optical resolution is about 0.1 eV a t 10 8, and 0.005 eV at 100 8, (16). Moreover, for an incidence angle of 1.5O for 8, = lothe definition is +0.3’ and - 0 . 2 O when we illuminate the entire 4-cm width of our gratings.
ACKNOWLEDGMENT We thank I. Enoki for some of the calculations and C. S. Fadley for his useful comments. LITERATURE CITED (1) Hercules, D. M. Anal. Chem. 1978, 50, 734A-744A. (2) “Science Update-Anal. Chem.” Chem. Eng. News 1982, 22. (3) Berth, E. P. “Princlples and Practice of X-Ray Spectrometric Analysis”, 2nd ed.; Plenum Press: New York, 1975; pp 621-627, 811-828. (4) Llebhafsky, H. A,; et al. “X-Rays, Electrons and Analytical Chemistry”; Wlley-Interscience: New York, 1972; pp 290-293. (5) Ebel, H. A&. X-R8yA/78l. 1970, 13, 68-79. (6) Andermann, G.; Lawson, M.; Fujiwara, F. Spectrosc. Lett., in press. (7) Gordon, B. M. ”Book of Abstracts”, 82nd National meeting of the A m erlcan Chemlcal Society, New York, Aug 1981; American Chemical Society: Washington, DC, 1981; PHYS 123. (8) Henke, B. L.; Tester, M. A. ”Advances in X-Ray Analysis”; Plenum Press: New York 1975; Vol. 18, pp 76-104. (9) Henke, E. L.; et ai. “Atomic Data and Nuclear Data Tables, Low Energy X-Ray Interaction Coefficients”; Academic Press: New York, 1982; VOI. 27, NO. 1, pp 1-144. (10) Urch, D. S. In “Electron Spectroscopy, Theory, Techniques and Appllcatlons”; Academic Press: New York, 1979; Voi. 3, pp 1-39. (11) Hasler, M. F.; Kemp, J.; Andermann, 0. Proceedings of the Conference on Industrlal Applications of X-Ray Analysis, 4th 1954. (12) Andermann, G.; Kemp, J. W. Anal. Chem. 1958, 30, 1306-1309. (13) Taylor, D. L.; Andermann, G. “Advances in X-Ray Analysis“; Plenum Press: New York, 1970; Vol. 13, pp 80-93. (14) Taylor, D. L.; Andermann, G. Anal. Chem. 1071, 4 3 , 712-716. (15) Andermann, G.; Lawson, M., unpublished results. (16) Andermann, G.; et ai. Rev. Scl. Instrum. 1980, 5f (6).814-820.
RECEIVED for review December 23,1983. Accepted March 27, 1984.
