Quantitative Analysis of Aluminosilicates and Other Solids by X-ray Photoelectron Spectroscopy John M. Adams, Stephen Evans,* Paul I. Reid, John M. Thomas, and Michael J. Walters Edward Da vies Chemical Laboratories, University College of Wales, Aberystwh, SY23
Relative photoionlratlon cross sectlons for the 1s (Li-F), 2s (Na-K), and 2p (Na-K) subshells (for an angle of 90’ between the incident Mg K a photon and the ejected electron) are deduced from XPS peak intensity measurements on compounds. The conslstency of the data with the interpretatlve model employed demonstrates that XPS can be USBd as a bulk quantitative analytical technlque to determine atom ratios for the principal constltuents of homogeneous sollds with an accuracy, on average, of 5 % This conciuslon is confirmed by comparisons with established methods d analysts In studles of APYNBS standard (and other) aiuninoslllcate mkrerals. The unique potential of XPS, as a proven quantltative analytical technique, for sutface analysis is demonstrated In a preliminary study of freshly-exposed cleavages in lepidolite, muscovlte, and phlogopite.
.
The analytical potentialities of x-ray photoelectron spectroscopy (XPS) were recognized even a t the inception of the technique as we know it today in the coining of the acronym “ESCA” (Electron Spectroscopy for Chemical Analysis) by Siegbahn and coworkers in 1967 (1);but its subsequent evolution into a truly quantitative tool has been slow. Two main categories of analytical study have emerged: attempts to determine “relative elemental sensitivities” (or, more precisely, partial relative photoionization cross sections) from measurements on compounds (2-7) or elements (7,8); and the development of experimental techniques to enable specified elements to be determined in inhomogeneous samples (Le., mixtures) where cross-section data alone are insufficient to permit a reliable analysis (9, 10). The present study falls largely in the first category. The earliest comprehensive study of relative peak intensities in compounds, by Wagner (2), suffered certain drawbacks as a source of quantitatively useful analytical information. First, the number of determinations of each interelement intensity ratio was, in general, not sufficient to reduce the inevitable errors to a level low enough for reliable quantitative analysis; nor was this, indeed, the principal aim of the work. Second, no specific allowance was made for the substantial surface contamination of specimens in the relatively poor vacuum (IO4 Torr) of the IEE-15 instrument, and, finally, no explicit correction was applied for the decrease in escape depth with decreasing photoelectron kinetic energy (KE). [This last omission should not be significant when using X P S in a purely analytical role (provided the escape depth has the same functional variation in all materials) but it should be taken into account in comparisons with calculated photoionization cross sections.] The progressive reductions in peak intensity for the slower photoelectrons caused by these last. two factors were, however, offset to an indeterminate extent by the approximately linear decrease in analyzer transmission with increasing photoelectron KE (2, 11). The experimental work of Nefedov et al. (3,4) suffered similar deficiencies (although the problems were again recognized), while J4rgensen and Berthou, in their compilations (5, 6), in addition took no account of the variability of peak widths from material to material [widths are not constant even for the same element
IN€, U.K.
and core level (12)], and tabulated only peak heights. The cross-section table recently derived from their data (11) consequently cannot be relied on for quantitative purposes. Janghorbani e t al. (7), compared peak intensities from clean elemental surfaces; but they neglected the variation of electron inelastic mean free path between different elemental solids, an omission which could lead to errors of several hundred percent in extreme cases (13, 14). Attempts have also been made to calculate the relevant photoionization cross-section ratios (3, 4, 15, 16), but the accuracy of these calculations remains largely untested. The few experiments so far reported (3, 4, 14, 17) are not conclusive, but suggest that the calculated values may not infrequently be as much as 30% in error. However, one must also bear in mind that intrinsic (18)two-electron processes (shakeup and shakeoff) can seriously reduce the intensity of the experimental primary photoelectron peak (19): the significance of such effects is well-established for the first-row transition elements (14,20), but the extent to which, if any, they constitute a detectable factor in the quantitative determination of other elements by XPS has not been adequately investigated. Although shakeup and shakeoff losses usually amount to 10-20% of the total intensity, the fraction lost has been calculated not t o vary much from atoms of one pure element t o those of another (21); were a similar result to hold for solid compounds this source of error could be neglected. Ambiguity can also arise in distinguishing structure arising from inelastic losses occurring subsequent to photoionization from such intrinsic features: this difficulty is acute in studies of metallic transition-element systems (14) but is unlikely t o cause major errors in work on main-group elements. Nevertheless, it must be admitted that the exact form of the inevitable correction for the background of inelastically scattered photoelectrons is not readily predictable, and that some small uncertainty must in consequence always remain (22). A need however clearly exists for the more careful determination of experimental relative cross sections (11). In the present work we extend our previous studies (14,23) on a more limited range of elements, and report experimental relative cross sections for the photoionization by Mg K a x-radiation of the 1s (Li-F) and 2s and 2p (Na-K) shells. Results for the 3p (K-Zn) and suitable shells of heavier elements are detailed elsewhere (14, 23, 24); the results reported here provide a sufficient data base for our present objective, the evaluation of XPS as a quantitative technique. The difficulties of obtaining relative interelemental sensitivity data should not, however, be allowed to obscure the more subtle problems associated with the XPS analysis of mixtures. Wyatt, Carver, and Hercules (10) have shown convincingly how the variation in electron escape depth between particles of different constitution will invalidate analyses made simply from peak intensity ratios between different components in a mixture: but the remedy advocated-fusion of the element(s) to be analyzed into a uniform matrix-is by no means universally applicable. The selection of specimens suitable for the evaluation of XPS as a quantitative technique is not therefore as simple as it might appear a t first sight.
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ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
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“132
,..-idu
,“*e
31
-3
, tcrec < E _ /ev _
Figure 2. Detail XPS scan (Mg Ka) for lepidolite. The vertical llnes Figure 1. Wide scan (Mg K a ) of a freshly cleaved flake of lepidollte:
recording tlme 850 s
It will be obvious from the foregoing, and especially considering the expense and expertise required, that X P S is hardly likely to displace established techniques for general-purpose bulk chemical analysis. Nevertheless, once the practicability of performing bulk analyses by X P S has been established, the special attributes of solid-state photoelectron spectroscopy may be utilized with advantage in analytical contexts where few, if any, other techniques could be used. X P S possesses a surface sensitivity almost unique among analytical techniques, since the total sampling depth is rarely and is often as little as 20 A (25). Auger greater than 100 i% electron spectroscopy shares this surface sensitivity, but is intrinsically much more difficult to quantify (26,27),and in addition the intense incident electron beam essential to this technique often causes serious surface damage ( 2 8 ) . While such a small probing depth may occasionally confer unacceptable surface bias in the analysis of bulk materials, it should prove invaluable in, for example, studies of the surface composition of mineral specimens, the analysis of catalyst surfaces and, indeed, of thin coatings in general. This feature of X P S has in fact already been used to great advantage in stud.ies of chemisorption (29, 30),although, once again, adequate cross-section data have not always been to hand. An important incidental consequence of this extreme surface sensitivity in the application of X P S in bulk analysis is that careful attention to sample preparation is necessary to ensure that the surface is, in fact, representative of the bulk material. X P S is unique among analytical methods in detecting all elements (except H, He) with a sensitivity which varies only relatively little from element to element: a routine “wide scan” (cf., Figure 1) usually reveals all elements present in 15% concentration. The intensity of the most prominent X P S signal increases fairly steadily with atomic number, the overall variation being about 100-fold from Li to U (2). This universal sensitivity is especially valuable in mineralogical analysis, where unexpected elements may occur quite frequently; even a semi-quantitative analysis in addition to the qualitative result would be valuable in numerous geochemical contexts. T h e sheet aluminosilicates in particular provide a very convenient subject for the evaluation of XPS as a quantitative analytical tool; these solids, of variable composition, often possess structures interfused a t the unit cell level (or subtle patterns of solid solution) and are not, in general, physical (macroscopic) mixtures. They consist essentially of A1 (or Mg)Oe octahedra and S i 0 4tetrahedra combined in a layered framework within which substitution may take place (e.g., Al for Si, Mg or Fe for Al), the charge imbalance thereby introduced into the structure being relieved by cations interspersed between the aluminosilicate layers (31). The major problems associated with the analysis of physical mixtures should not therefore arise, as the solid through which the photoelectrons escape is essentially uniform despite the wide variations possible in chemical constitution. The occurrence of relatively small percentages of free silica or alumina in these minerals is not uncommon, but since the electron escape depths in silica, alumina, and aluminosilicates are likely to 2002
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
show the position of core level peaks for other elements commonly found In layered alumlnoslllcates, and are Included to ald rapld asslgnment. The SI and AI peaks show negligible shlfts between dlfferent alumlnoslllcate minerals (42) and may consequently be used In allgnlng the spectra
be closely similar, errors arising from this cause are unlikely to be significant in the present context. In such geochemical studies, moreover, great accuracy, as provided by established analytical methods, may not be the essential requirement; rapid detection and estimation of all elements present can be of greater significance and may, indeed, be the ultimate goal of the analysis. Consequently, we have chosen to evaluate the technique via its application to the analysis of aluminosilicates. The conclusions we reach in this paper concerning the viability of X P S as a quantitative analytical tool are not, however, specific to geochemical work, and, following the advent of adequate experimental cross-section data for the heavier elements (24), we expect the range of quantitative applications of the technique to expand substantially.
EXPERIMENTAL All XPS peak intensity ratios were determined using an AEI ES 200A electron spectrometer equipped with an Mg K a x-ray source. The angle between the incident photons and analyzed electrons in this instrument is 90’ and the transmission of its analyzer system increases linearly with photoelectron kinetic energy (23, 32). Polycrystallinesamples were ground to a powder with a mortar and pestle, pressed into pellets of 1 mm thickness in a stainless steel press [using pressures of 10-20tons/in.*(15o(r3000 Kg cm-?] and attached to the (rotatable) probe with stainless steel screws. Contamination of the surface of the pellet originating in the pressing and mounting procedure was then eliminated by the exposure of a fresh surface by abrasion with a clean stainless steel razor blade immediately prior to insertion of the probe into the spectrometer. [The intensity ratios within each spectrum (unlike the absolute intensities) are independent of roughness factors and control of sample grain size and of roughness caused by abrasion is unnecessary.] Single crystal samples of lepidolite, muscovite, and phlogopite were mounted directly onto the probe and cleaved with a clean razor blade immediately before examination. All x-ray photoelectron spectra were recorded after rotation of the probe t o maximize the XPS signal intensity; electrons analyzed then emerged from the sample at 25 f 10’ from the normal to its surface. (This angle is a function of instrument geometry and sample thickness and has no fundamental significance; gross increases in the takeoff angle would however markedly increase the differential attenuation of signals at different kinetic energies arising from contamination of the sample surface, and affect the correction for this effect described in the next section.) After recording a wide scan (cf. Fig.l), and, in the case of most of the mineral specimens, a more detailed examination of the 1100-1250 eV KE region also (cf. Figure 21, the principal peaks were recorded digitally for area measurement. The energy increment used was typically 0.2 or 0.5 eV, and all the relevant peaks were recorded two or (usually) three times in sequence to minimize any long-term fluctuations in the intensity of the spectrum. C (Is) and 0 (Is) spectra were not recorded; these elements (mainly as hydrocarbon and water) are almost always present on the surfaces of air-prepared samples, which consequently cannot be used for the bulk determination of these elements. Background subtraction and peak area determination were carried out by an iterative computer program, assuming the net
-
background at each pout to be proportional to the total integrated peak intensity to higher KE. Although there exists no rigorous physical justification for this procedure, it is realistic in that the background resulting from the inelastic scattering of electrons of any specified primary energy can extend only to lower electron energies. Chemical analyses of the mineral specimens were carried out using essentially standard literature procedures (33). Initial dissolution of the minerals was via sodium hydroxide fusion, following which silicon was determined gravimetrically as quinoline silicomolybdate, aluminum gravimetrically as the &hydroxyquinolate, and magnesium (with calcium, which was negligible in the specimens concerned) volumetrically using EDTA with methyl thymol blue complexone indicator (33). All determinations were carried out in duplicate. D A T A T R E A T M E N T A N D RESULTS The true intensity ratio (i.e., after correction for the linear increase of our analyzer transmission with KE), ZA/Z*, between the XPS peaks from two core levels in a homogeneous polycrystalline solid material A,B, is given by (3, 4, 14):
In this equation, uTA,TB are the total subshell photoionization cross sections, EA,n are the KE's of the ejected photoelectrons, 17is the thickness of any contaminating overlayer present on the surface of the solid and XA,B are the inelastic mean free paths for the ejected photoelectrons in the overlayer. T h e term in E A , g allows reasonably accurately (25) for the variations in peak intensity arising from the increase in photoelectron escape depth with KE in the energy range of interest. The expression in square brackets describes the angular distribution of the photoelectrons, neglecting the small partial randomization induced by elastic scattering (17). 0 is the angle between the incident (unpolarized) photon and ejected electron beams, and P A , B are the appropriate asymmetry parameters, which are functions of both the character of the orbital ionized and of the photoelectron energy. [P-values generally lie between +1 and +2, but can fall, exceptionally, as low as -1 (34).] For closed, spherically-symmetric, shells, intensity ratios within each spectrum are thus functions of the angle between the photon and electron beams but not [for a clean (uncontaminated) sample] cjf the orientation of the sample with respect to these beams (35). Consequently, it is convenient for analytical purposes to combine this angular distribution factor-a constant for a given core level, photon UT, tabulating energy, and experimental geometry-with partial [as opposed to total (angle-integrated)] subshell cross-section ratios for a stated angle; in the present work 0 = 90'. Comparison with calculated total cross-section ratios may be made using the recently reported comprehensive Hartree-Fock calculations of /3 (34) to derive the appropriate angle-resolved cross-section ratios; these calculations could also be used with our experimental cross sections to estimate (via Equation 1) cross-section data appropriate to instruments of other geometries. The exponential factor in Equation 1 is required to take account of the differential attenuation caused by contaminant overlayers on the surface of the sample. Neither parameter in the exponential factor is known a priori, but we may reasonably assume that for the overlayer, as for the sample,
the escape depth varies as the square root of the electron energy. The exponent -Df X then becomes - c l P 5 where c may be treated (24) as an empirical experimental constant for given experimental conditions; we use c = 34.3 in the present work, as determined previously (14). Because this determination was based on a comparison between gas-phase and solid-state data, any residual RE-dependent errors in the solid-state treatment-including, principally, any mean deviation from the assumed square-root energy dependence of the (bulk) mean free path-will also be largely compensated in this factor. Nevertheless, the inevitable uncertainties in the KE-dependent correction terms render it desirable to restrict the application of Equation 1 to a limited KE range; in this work, as in our previous study, we confine our attention principally to the 850-1240 eV region. The exponential term affects individual cross-section determinations (Table I, column 5) by no more than 8% over this range. Inter- and intra-elemental XPS peak intensity ratios for a variety of compounds are tabulated in column 4 of Table I; the cross sections derived from them (via Equation 1)appear in column 5. As in our recent study of the 3p subshell (14), we have applied fitting procedures to the final mean experimental cross section (column 6) both to minimize random fluctuations in the results-cross sections should increase smoothly with increasing BE and atomic number (3, 4, I4)-and to enable interpolations to be made for crom sections which were not measured directly [Be 1s (because of the toxicity of Be) and P 2s and 2p (uncommon in aluminosilicates) in particular]. Again as in our previous work (14), we found that equations of the form
log u = A ( l 0 g BE)'
+ B log BE -1 C
(2)
and
were the least complex needed to fit all the experimental data for each subshell to within about one standard deviation. For the Is shell, the fits were constrained to pass through F 1s = 1.00 (by multiple weighting) since this is our primary reference standard, and in each case the smallest cross-section was double-weighted in Equation :3 t o ensure adequate treatment of small cross sections in the least-squares fitting program. The fitted values from Equations 2 and 3 were always quite close; we list in Table I1 the mean values for all the elements and levels concerned. These values should be essentially independent of the fitting/interpolation scheme used, and we consider them to be accurate to 55%. XPS peak intensity ratios for the mineral specimens are given in Tables I11 and IV (column 3). Atom ratios (columns 4 and 5) were derived from these data and the final crosssection values in Table I1 by substitution into Equation 1. The results of the wet-chemical analyses are shown in column 6 for comparison. DISCUSS ION The fact that the mean standard deviation (Table I, column 6) is less than 5% of the mean experimental cross section for the eleven levels considered constitutes firm justification for the belief that for homogeneous, air-stable solids XPS intensity data can be used to obtain reasonably quantitative analyses. The percentage error may be expected to increase if the level concerned exhibits a low cross section, or if the element in question is only present in low concentration, but Table I clearly implies that on average, for main-group elements, an accuracy of 5% should be attainable. This expectation is fully borne out in Table 111, where an accuracy of 5% is demonstrated both internally (Le., between different core levels of the same element) and against standard chemical ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
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Table I. Cross-Section Determinations from XPS Intensity Dataa
1
Level Li Is
Mg 2s Al 2s
Si 2s
s 2s
c1 2s
K 2s
Na 2p
Mg ZP
A1 2p
Si 2p F Is
2 Reference
4 Area ratio (corr. for stoichiometry)
5b Relative cross section
s 2P N Is s 2P c1 2p s 2P c1 2p c1 2p s 2P N Is Si 2p (q.v.) Si 2p (q.v.) Si 2p (q.v.) Si 2p (q.v.) s 2P s 2P s 2P s 2P s 2P c1 2p c1 2p c1 2p c1 2p c1 2p K 2p K 2P Na 2s N 1s Na 2s c1 2p Na 2s Mg 2s (q.v.) Mg 2s Mg 2s Mg 2s s 2P s 2P A1 2s (q.v.) A1 2s A1 2s K 2~ Na 2s Li I s
0.064 0.129 0.040 0.036 0.334 0.324 0.338 0.390 0.766 0.762 0.829 0.783 0.808 0.502 0.490 0.486 0.478 0.490 0.399 0.389 0.373 0.346 0.437 0.275 0.266 0.545 0.379 0.564 0.125 0.567 0.689 0.664 0.637 0.641 0.426 0.377 1.009 0.941 0.935 0.264 1.785 12.1
0.024
0.027 0.015 0.017 0.136 0.164 0.171 0.165 0.176 0.191 0.208 0.196 0.202 0.251 0.250 0.248 0.245 0.249 0.275 0.263 0.256 0.234 0.363 0.387 0.376 0.063 0.077 0.066 0.058 0.066 0.103 0.099 0.094 0.095 0.171 0.149 0.160 0.149 0.151 0.23 2 0.232 0.96g
6 Mean cross section (SD)
7 Calcd cross section ( p ld
0.021
0.014 (2)
(0.006) 0.157 (0,019) 0.171
0.123
0.199 (0.007)
0.201
0.248 (0.003)
0.293 (2)
0.257 (0.017)
0.347 (2)
0.375 (0.012)
0.458 (2)
0.066 (0.007)
0.041 (0.86)
0.098 (0.004)
0.068 (0.95)
0.156 (0.01)
0.107 (1.03)
(2)
0.160 (2) (2)
0.232
0.159 (1.10)
1.000 (defn) (2)
mean deviation (11values) 0.0087 (4.8% of mean cross section)
The standards employed are S 2p = 0.458, C1 2p = 0.600, and N IS = 0.378, previously determined by gas phase measurements (23),and Na 2s = 0.121 and K 2p = 1.21, determined from these by solid-state measurements ( 1 4 ) similar to those reported here. All values are relative to F Is = 1.00, Cross-section values in column 5 ( c r ) were calculated from the area ratios ( R )in column 4 (which have not been corrected for analyzer transmission) by application of the equation Eref l . u = R . u , ~ . -E - . 1 . 5 exp( 14.3(E-o.5-E,f-a.s)) (la) which is derived directly from Equation 1 by substituting the amendments detailed in the text. All materials [except aluminum 8-hydroxyquinolate, which was prepared by a standard literature method ( 4 0 ) ] were supplied by BDH Ltd., and were o f the highest purity normally available. From Scofield ( 1 6 ) , correcting for the photoelectron angular distribution using the 0-values of Reilman et al. ( 3 4 ) (given in parentheses) where necessary. e Unstable under irradiation. f Showed substantial 0 Is signal due to hydrolysis; interelement ratios therefore not used. g Included to investigate the effectiveness of the contamination term in Equation 1;the uncorrected value is 0.77. See also Table 111. ~
methods of analysis for some dozen different polycrystalline mineral specimens. Bulk quantitative analysis by XPS is clearly practicable. Conversely, however, that the calculated cross-section ratios (Table I, column 7), even after correction for angular distribution effects, differ from our experimental values by amounts ranging from +34% (C12s) to -31% (Si 2p) implies that the presently-available calculated cross sections cannot be used satisfactorily for quantitative analysis. This conclusion conflicts with the suggestion of Carter et al. (17)that Scofield’s calculated cross sections (16) might be used directly t o give acceptable analyses (*lo%). In fact, however, our data 2004
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
~~
~~
support Carter et al.’s own measurements rather than the average of three groups’ data they adduced in support of their contention; five of the eleven ratios they measured also differed from those calculated by 30% or more of the calculated values. Clearly, experimental determinations of relative cross sections for suitable shells of all the elements will be essential to extend the range of applications of XPS in analysis beyond the present restricted canvas. The 5% scatter in the experimental results is probably due to two main causes, one fundamental and one experimental. Shakeup intensities are unlikely to be rigorously constant, and 2-3% variation from this factor seems likely to be inevitable
Table 11. Smoothed Experimental Relative (30sSections (Mg KCY) EleCross Element Level section ment Level Li Be
Is
Ba
Is Is 1s Is Is
Cb Nb
0
F
Naa Mg Al
Si P S c1
Ar K
Is
2s 2s
2s
2s 2s
2s 2s 2s 2s
0.022 0.054c 0.118 0.225 0.384 0.624c 1.000
0.123 0.150 0.174 0.198 0.220c 0.245 0.271 O.31Oc 0.365
Na Mg
A1 Si P S c1 Ar
Ka
Ka Caa
2p 2p 2p 2p 2p 2p 2p 2p
zP
3p 3p
Cross section 0.064 0.102
0.154 0.234 O.32Oc 0.458 0.602 0.83gc 1.21
0.11 0.14
Experimental data from Ref. 14. Experimental data Interpolated value; no experimental data from Ref. 23. used. a
and an ultimate limit on the accuracy of X P S analyses. The experimental factor concerns the measurement of peak areas. Despite the use of a computer program to evaluate these areas, a small subjective element in the identification of the points of commencement and termination of the peaks is impossible to avoid. Moreover, the variability of the backgroundespecially where a number of peaks occur relatively close in K E (cf. Figure 2)-introduces a further element of uncertainty in addition to the fundamental difficulties in background correction referred to earlier (22). It can, for example, happen that the background on the low K E side of a peak is actually lower than on the high KE side; whether in such circumstances one assumes each element of background t o be negatively related to the integral of the peak (this is computationally convenient but physically unrealistic) or adopts a straight-line background can, typically, make up to 2% difference to the derived area. Other changes in the background function assumed could-quite justifiably-produce variations of a similar magnitude, and where peaks even marginally overlap each other much larger errors (515%) are possible. Much of this variability in background is due to a3,a4 satellite peaks which are always present in achromatic Mg (and Al) K a sources a t ca. 13% of the K q 2 intensity. Where an exact coincidence of the a3,a4satellites and a primary peak occurs (e.g., A1 2p(a3,a4)with Na 2 s ( q 2 )in zeolite, Table 111) an approximate correction may readily be applied: more general remedies include the application of digital subtraction procedures (36) or Fourier transform methods (37). It would however undoubtedly be preferable to use a monochromatic x-ray source. Such a source is available for the ES200, but uses A1 K a radiation, as do many other instruments not employing monochromation. The relationship between relative photoionization cross sections for Mg K a and A1 K a radiations thus merits comment. Cross-section ratios calculated in the Hartree-Slater approximation (16) for A1 and Mg K a differ significantly (by up t o about 20% for the shells considered here) over this energy range; we have already remarked that these calculations are not sufficiently accurate in themselves, but the ratio of relative cross sections for the same shell and element may well be much more reliable, the systematic (correlation) errors largely cmcelling. Should this be so, our data could be used t o derive analytically useful A1 K a relative cross sections. It should be remembered in this that B is also energy-dependent; fortunately calculations of the necessary data for both energies
have been reported (34). It would be advisable, nevertheless, before embarking upon any extensive analytical application of such data, to test the underlying assumptions by remeasuring several of the more sensitive cross-section ratios with A1 K a radiation. Occasionally, specific interferences can cause difficulties. Very rarely, two elements each possessing only one peak suitable for quantitative analysis may give rise to coincident primary peaks. We have encountered only one such instance in the present studies, Li Is/Fe 3p; lithium cannot, therefore, be determined in minerals unless iron is shown (chemically or spectroscopically (Fe 2p XPS)) to be absent. Much more subtly, however, the small percentage of Al K a a n d bremsstrahlung radiation normally present in achromatic Mg x-radiation can cause unforeseen problems. This AI K a radiation may arise from an A1 x-ray window (1/2-1%) or from the presence of aluminum in the target itself. Early AEI Mg-targets contain up to 10% aluminum. Mg K a radiation cannot, of itself, excite Mg KLL Auger electrons; but Al K a and bremsstrahlung radiation can. The principal Mg KLL Auger peaks-at -1125 eV and -1171 eV K E (%)-coincide exact,ly with the Mg Ka-excited AI 2s and 2p signals, and consequently quantitative analysis of A1 in Mg-containing minerals (with Mg K a ) is rendered considerably more difficult. Since the 1171-eV Auger peak is -5.8 times more intense than that at 1125 eV, the effect is to make the Al 2p-derived analysis (especially) markedly too high (cf. phlogopite, Table IV). The error can be quantitatively corrected, but a new calibration measurement has to be made (using e.g. MgO) for every new x-ray target. Fortunately, however, this is the only such interference we have encountered, although if substantial quantities of A1 K a (5-10%) are present the possibility of other, more straightforward, interferences should be remembered (e.g. A1 K a 0 1s overlaps Mg K a K 2p). The use of Auger peaks (rather than the photoelectron peaks) for quantitative analysis within the same theoretical model, is tempting when, as for sodium (and magnesium, with A1 K a ) the Auger intensity far exceeds that of the outer-shell P E peaks. However, because the Auger intensity is related to the total number of primary core holes, not to the number produced by the Mg or A1 photons alone, separate calibration is needed for each set of new operating conditions (i.e., each specific target, operating current and voltage). The procedure can nevertheless be valuable; for our present conditions the principal Na KLL Auger peak has an “apparent relative cross section” of 1.2, cf. 0.124 for Na 2s and only 0.063 for Na 2p (Table II), giving considerably enhanced sensitivity. The majority of common elements in these minerals give rise t o a t least one reasonably intense peak free from interferences and suitable for quantitative analysis in the higher KE region of the spectrum (cf. Figure 2), but one important exception is fluorine, especially as this is not the easiest of elements to determine by traditional methods. The F 2s peak (cf. Figure 2) is of limited value for analytical purposes. Many other elements also give rise to bands in this region, and chemical effects on the peak intensity a t such low BE are unlikely always to be negligible. The results of the experiments on lithium fluoride and Greenland cryolite regarding the possibility of estimating fluoride by X P S using the (rather slow) F Is photoelectrons are, however, quite encouraging. As Tables I and I11 show, the contamination correction considerably improves the agreement with the known stoichiometries, while in neither case has the correction proved excessive. These results suggest that provided one is certain (from the size of any contaminant peaks in the spectrum) that the surfaces of the samples are reasonably clean, analysis for F may be undertaken by XPS with an expectation of 10-15% accuracy. ANALYTICAL CHEMISTRY, VQL. 49, NO. 13, NOVEMBER 1977
2005
Table 111. Comparison of XPS and Wet-Chemical Analyses for Selected Polycrystalline Minerals“
1
Mineralb Kaolinite (St. Austell) Kaolinite No. 7 (Bath, S. Car.) Talc (Mo-i-Rona, Norway). Pressed o n KBr backing to aid cohesion Montmorillonite No. 23 (Chambers, Ariz.) Montmorillonite No. 22a (Amory, Miss.) Montmorillonite (Belle Fourche, S. Dak.) [Na-exchanged and sedimented ( 3 1 ) before pressing] Montmorillonite (Belle Fourche, S. Dak.) (Cu-exchanged, intercalated by azobenzene and sedimented directly onto Ag foil sample base.) Laponite B (synthetic)
Laponite XLG (synthetic ) Lepidolite (Brazil) (single crystals pulverized and then pressed)
2 Level Si 2p Si 2s A1 2s A1 2p Si 2p Si 2s AI 2s A1 2p Si 2p Si 2s Mg 2s Mg 2P Si 2p Si 2s Al 2s A1 2p Si 2p Si 2 s A1 2s A1 2p Si 2p Si 2s A1 2s A1 2p Si 2p Si 2s AI 2s A1 2p N Is Si 2p Si 2s
Mg 2s Mg 2P F Is Si 2p Si 2 s Mg 2s Mg 2~ Si 2p Si 2s Al 2s
4 3 5 Derived Mean XPS XPS pk. area ratioC atom ratio atom ratio 1.00
0.81 0.69 0.63 1.00
0.84 0.68 0.65 1.00
0.81 0.35 0.25 1.00
0.77 0.26 0.25 1.00
0.82 0.27 0.27
t 0.90 I OGg5 1.06 I 0.94 0.93 1 1.03 1
1.00
1.00
0.92
0.96 (0.95)
1.00
(1.00)
0.91
(0.89)
1.00
1.00
0.52
0.52
I
1.00
1.00
\
0.36
0.36(0.39)
1.00
1.00
0.37
0.38(0.53)e
1.00
1.00
0.37
0.39( 0.39)
1
1.00
1.00
O0.39 S4l1 0.10 1.00 0.96
0.40 0.10
0.39(0.39)
3
...
...
1.00
1.00
0.56 0.61
0.64 i.0.04
1.00
1.00
0.57
0.61
1.00
1.00
1.02
0.51 0.54
1
0.97 0.35 0.36 l.OO 1.04
1
1
0*37 0.39
1.00
0.77 0.25 0.24 1.00
0.79 0.30 0.28 0.10 1.00
0.76 0.38 0.25 0.76 1.00
0.78 0.38 0.27 1.00
0.82 0.35 0.33 0.22 0.97 0.64
6 Atom ratio 7 from wet % diff., cols. analysisd 5 and 6
0.38 0.99
1 0.55 0.54 t 0.60 0.98 1 0.54 1 0.59 1.04 t 0.48 t 0.49 0.24 o.21 I 0.42
4
2
0
0
3
5
12
7
4 0.46 0.48 A1 2p K 2s 0.22 ... K 2P ... 0.42 F Is 1.00f 1.00 1.00 1.00 Cryolite Na 2s 0.41 (Greenland) A1 2s 0.33f 0.32 (3) 0.34 0.41 A1 2p 2.00f 1.83 4.04 1.83 F Is (9) 1.00 Y Zeolite (1) Si 2p 1.00 1.00 1.08 0.84 Si 2s 0.41 A1 2s 0.52h 0 0.52 0.57 0.50 0.35 AI 2p 0.32 0.578 Na 2 s 0.5Zh 0 0.52 0.5w 0.15 Na 2p 1.00 Si 2p Y Zeolite ( 2 ) 1.00 1.00 0.85 1.09 Si 2s 0.27 A1 2 s 8 0.38h 0.35 0.24 A1 2p 0.22 Na 2s 0.3gh 10 0.34 0.408 0.318 0.092 Na 2p “ Mean internal discrepancy between XPS analyses derived from different, core-levels: 4.8% on 34 comparisons (not all in Table). Mean discrepancy between (average) XPS analyses and wet chemical analyses: 4.9% on 16 comparisons. API/NBS standards, referred t o by number, were supplied by Wards Natural Science Establishment; montmorillonite from Belle Fourche by Volclay Ltd; laponites (synthetic hectorites) by Laporte Ltd; cryolite by BDH Ltd; zeolites of known composition by L. V. C. Rees (London); other specimens were supplied by Bottleys. All specimens were examined as Reproducible to f; 0.01 Uncorrected for analyzer transmission. freshly-abraded pressed disks except where indicated, or better except where indicated. Figures in parentheses are API/NBS data from Ref. 4 1 for the same mineral for comparison; those additionally in italics refer to a standard mineral from the same location. e This specimen was visibly inhomogeneous and our sample evidently differed seriously from the API one: the API-derived formula for the “pure” mineral does, however, correspond to a ratio of 1:0.39. Montmorillonite No. 3 1 showed similar discrepancies, even between the X P S data (Si/Al= 0.52 +- 0.01) and our wet analysis of a separate specimen (Si/Al= 0.40 i 0.005). This mineral has in conse) quence been omitted from the Table. Uncorrected for overlap of A1 2p ( a s p s with From idealized formula Na,AlF,. Na 2s ( c y L 2 ) ; 2s analyses are consequently high, while Na 2p, because of the close proximity of the 0 2s band, gives a low result. Analysis using the Na KLL Auger peak (see text) gave results consistent with the mean value shown (0.54 and 0.36 for zeolites 1 and 2 respectively). From analyses supplied with the zeolites by L. V. C. Rees (Imperial College, London).
0.311
t 1 1 1
Table IV. Comparison of XPS and Wet Chemical Analysis for Selected Single-Crystal Mineral Specimensa 6 3 4 5 Atom ratio 7 1 2 X P S pk. Derived Mean from wet % diff. Mineralb Level area ratio atom ratio atom ratio analysis cols. 6 and 6 Lepidolite (Brazil)
Muscovite (Norway)
Si 2p Si 2s A1 2s A1 2p K 2s K 2P F Is Si 2p Si 2s A1 2s A1 2p K 3P Si 2p Si 2s A1 2s A1 2p K 2P K 3P
1.00
0.82 0.37 0.33 0.28 0.97 0.67
1 0.52 t 0.47 o.28 1 0.26 0.54 1.03
l.OB
0.81 0.62 0.56 0.145
0.82 0.27
1.00
1.00
0.49
0.46
0.27 0.53
...
1.00
1.00
0.83 0.27
0.84
6
. , .
1
1.00 Phlogopite 1.00 1.00 (Norway) 0.76 0.54 0.38 (typical 0.26 52 0.54 0.67c1 0.45 result of 11 examined) 1.12 ... 0.30 0.29 recorded 0.16 on new 0.53 0.89 7 0.83 o.81 0.85 cleavage 0.40 Examined as a Mean internal discrepancy between XPS analyses for single-crystal surfaces: 5.6% on 8 comparisons. A1 2p coincides with Mg KLL Auger causing serious interference (see text): freshly-cleaved single-crystal flakes. correction for this effect gives a 2p-analysis in agreement with the 2s-derived figure.
One further potential source of error-electron diffraction effectashould be briefly discussed. One-KeV electrons have a d e Broglie wavelength of -0.4 A, and diffraction of the outgoing electrons can, in a highly ordered substrate, cause the angular distribution of the electrons to become a function of the rotational orientation of the specimen with respect to the x-ray source and analyzer. Mavima in the intensity of each peak occur as the crystal is rotated; and the angles characterizing these maxima are, predictably, functions of both the crystallographic location of the atom and of the photoelectron energy (39). T h e magnitude of the largest such intensity variations so far reported, however, have still been relatively small [ca. 30% overall, for a 1-KV energy range (39)], and one would not expect serious errors to be induced in the present analytical work, even for the single-crystal data reported in Table IV. T h e internal consistency of these data is in fact only marginally worse than in Table I11 (5.6% cf. 4.8%), suggesting that such effects may usually be neglected in comparison with the other errors. The agreement between the analyses for powdered lepidolite and the single crystal surface is very satisfactory, as is that between the “wet” and X P S analyses for muscovite; clearly these minerals are reasonably homogeneous and cleave in regions of typical composition. Phlogopite however equally clearly does not. The differences between the XPS Si:AI ratio in particular and the wet analysis is far greater than the expected error, and show that this specimen cleaves in regions high in aluminum (and to a lesser extent, low in magnesium). Our investigations into this phenomenon are not yet complete; but it is already certain that this is not an isolated anomaly; eleven cleavages in four specimens (all from the same location) have shown similar effects. T h e structural and chemical implications of these results have not yet been fully evaluated, and further studies are planned. These results do, however, already illustrate the value of X Y S as a quantitative technique for surface analysis.
CONCLUSIONS X P S is capable of providing bulk quantitative analyses of air-stable homogeneous solids, accurate to 5% on average for main-group elements, provided that (i) the use of low-energy (5800 eV) photoelectrons is avoided and (ii) care is taken to
0*31t 1
avoid excessive contamination of the sample Burface. Experimental photoionization cross sections for all levels examined are essential as the presently-available calculations are insufficiently accurate. In its analytical (as in its other) applications, however, the technique is especially valuable in studies of the surface regions of solids.
ACKNOWLEDGMENT We thank the following for samples: L. V. C. Rees for zeolites of known composition, Laporte Industries for the synthetic hectorites, The Steetley Co. (Minerals Division) for the St. Austell kaolinite, and Volclay Ltd. for samples of montmorillonite. LITERATURE CITED (1) K. Siegbahn, C. Nordlirig, A. Fahiman, R. Nwdberg, K. Hamrin, J. Hedman, G.Johansson, T. Bergmark, S. E. Karisson, I. Lindgren, and B. Lindberg, ESCA”, Aimqvist 8 Wikseils, Uppsaia, 1967. (2) C. D.Wagner, Anal. Chem., 44, 1050 (‘1972). (3) V. I. Nefedov, N. P. Sergushin, I. M. Band, and M. B. Trzhaskovskaya, J . Electron Spectrosc., 2, 383 (1973). (4) V. I. Nefedov, N. P. Sergushin, Y. V. Salyn, I. M. Band, and M. 8. Trzhaskovskaya, J . Electron Specfrosc.. 7 , 175 (1975). (5) C. K. Jbgensen and H. Berthou, faraday Discuss. Chem. Soc., 54, 219 (1972). (6) C. K. Jbgensen and H. Berthou, Anal. Chem., 47, 482 (1975). (7) M. Janghorbani, M. Vuili, and K . Starke, Anal. Chem., 47, 2200 (1975). (8) L. J. Briilson and G. P. Ceasar, Surf. S o . , 58 457 (1976). . (9) W. E. Swarz, Jr., and D. M. Hercules, Anal. Chem., 43, 1774 (1971). (10) D. M. Wyatt, J. C. Carver, and D. M. Hercules, Anal. Chem., 47, 1297 (1975). ( 1 1 ) R. C. G. Leckey, Phys. Rev., Sect. A , 13, 1043 (1976). (12) G.M. Bancroft, I. Adams, H. L a m p , and T. K. Sham, Chem. phys. Left., 32, 173 (1975). (13) D. R. Penn, J . Electron Spectrosc., g, 29 (1976). (14) S.Evans, R. G. Pritchard, and J. M. Thomas, J . phvs. C:Soiid State R w s . . 10, 2483 (1977). (15) F. M. Chapman, Jr., and L. L. Lohr, Jr., J . Am. Chem. SOC.,96, 4731 11 974) (16) j. H. Scofield, J. Electron Spectrosc., 8, 129 (1976). (17) W. J. Carter, G. K. Schweitzer, and T. A. Carlson, J. E k t r o n Spectrosc., 5, 827 (1974). (18) J. J. Chang and D C. Langreth, Phys. Rev. B , 8 4638 (1973). (19) C. S.Fadley, J . Electron Spectrosc., 5 , 895 (1974). (20) T. A . Carlson, J. C. Carver, L. J. Saethre, F. G. Santibdnez, and G. A. Vernon, J Electron Spectrosc., 5, 247 (1974). (21) M. Mehta, C. S.Fadley, and P. S.Bagus, Chem. Phys. Len., 37, 454 (1976). (22) R. L. Park, “Chemical Analysis of Sw-faces”, Surface Analysis Techniques for Metallurgical Applications, ASTM STP 596,American Society f w TestJng 8 Materials, Philadelphia. Pa., 1976, p 3. (23) P. Cadman, S.Evans, J. D. Scott, and J. M. Thomas, J. Chem. Soc., faraday Trans. 2 , 71, 1777 (1975).
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
2007
(24) S. Evans, R. G. Pritchard, and J. M. Thomas, unpublished work, Aberystwyth, 1976. (25) C. J. Powell, Surf. Sci., 44, 29 (1974). (26) C. C. Chang, Surf. Sci., 48, 9 (1975). (27) J. M. Morabito, Surf. Sci., 49, 318 (1975). (28) B. A. Joyce and J. H.Neave, Surf. Sci., 34, 401 (1973) and references therein. (29) S. Evans, J. Pielaszek, and J. M. Thomas, Surf. Sci.. 5 5 , 644 (1976) and references therein. (30) S. Evans and J. M. Thomas, Proc. R Soc. London, Ser. A , 353, 103 (1977) (31) G.-Brown, Ed., “The X-ray Identification and Crystal Structures of Clay Minerals” Mineral Society, London, 2nd ed., 1961. (32) A. Barrie and C. R. Brundie, J . Nectron Spectrosc., 5 , 321 (1974). (33) H. Bennett and R. A. Reed, “Chemical Methods of Silicate Analysis”. Academic Press New York, N.Y., 1971. (34) R. F. Reilman. A. Msezane, and S. T. Manson, J . Electron Spectrosc., 8 , 389 (1976).
(35) R. G. Hayes, Chem. Phys. Lett., 38, 463 (1976). (36) J. M. Adams. S. Evans, and J. M. Thomas, J . Phys. C: Solid State Phys., 6, L382 (1973). (37) N. Beatham and A. F. Orchard, J . Nectron Spectrosc., 9, 129 (1976). (38) C. D. Wagner, in “ E m o n Spe&oscopy”, D. A. Shirley, Ed., North Holland, Amsterdam, 1972, p 861. (39) K. Siegbahn, U. Gellus, H. Slegbahn, and E. Olson, Phys. Left. A , 32, 221 (1970). (40) R. Belcher and A. J. Nutten, “Quantitative Inorcwnk Anatysis”, Butterwcnth, London, 2nd ed., 1960, p 86. (41) A.P.I. Research Project 49: Reference Clay Minerals (Columbia University) Preliminarv ReDort No. 8 (1951). (42) I.Adams,’J. M‘. Thomas, and G : M. Bancrofi, Earth Planet. S o .Lett., 16, 429 (1972).
RECEIVEDfor review May 12, 1977. Accepted July 25, 1977. We thank the Science Research Council for fimancid support.
Sample-Loss Mechanism in a Constant-Temperature Graphite Furnace Ray Woodriff,’ Momir Marinkovlc,’ R. A. Howald, and I s a a c Elierer Department of chemistry, Montana State University, Bozeman, Montana 597 15
A constant temperature furnace, used for the study of sample loss, has an advantage of essentially constant temperature over the duration of the observatlon pulse. I n addltlon, because of the enclosed nature of the furnace and the absence of rapld heating of the graphlte tube, the convectlon loss of the sample vapor Is small. I t has been found that one group of elements closely follows a simple dlffuslonal law, whlle for other elements a considerable devlatlon Is observed. Devlatlons are linked to the sample vapor redeposklng In the heater tube for those elements whlch form compounds wlth carbon at elevated temperatures. I n the case of gas phase dlffudon controlled sample loss, a new procedure for expanslon of the useful analytlcal range Is proposed.
Atom liberation from the distribution in a graphite furnace has been recently studied by several workers (1-4). Such studies are important for the interpretation of atomic absorption measurements in these furnaces. I t has been found that reduction by carbon is the probable mechanism for free atom formation for most elements (5-7) a t least a t lower temperatures. Modification of the inside of the graphite tube by reaction with carbide-forming elements has been used to prevent carbide formation by other elements and to improve the limits of detection for these other elements (8-10). Tt is clear t h a t carbide formation and decomposition on the graphite can affect the height and shape of absorption peaks observed in graphite tube furnaces; however, these effects have not been studied previously. In this paper, a simple technique for the study of the diffusion mechanisms for sample loss from graphite furnaces is described. Cases of both simple diffusion and diffusion complicated by carbide formation have been found and interpreted. For the cases of simple diffusional loss, a new procedure for the expansion of the useful analytical range is proposed. ‘Present address, C h e m i s t r y L a b o r a t o r y , B o r i s K i d r i c I n s t i t u t e , Beograd, Yugoslavia.
2008
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
THEORY In a well-designed tube atomizer, the sample loss can be limited to diffusion through the apertures and to diffusion through the porous walls if the heater tube is made of graphite. If the sample loss is controlled by diffusion through the apertures of the tube, and the evaporation time is short compared to the mean residence time of the analyte atoms, the total amount of analyte present in the tube at the time t , M,, is given by the exponential equation:
M,
=
1
M , exp(--), c
la
where a is the length of the graphite tube, M , is the initial weight of analyte, t is the time elapsed after the sample is vaporized, and T, is the time constant for gas diffusion through the apertures, i.e., mean residence time of the analyte atoms in the tube ( 1 1 ) . As discussed in the Appendix, this single term is adequate to represent our measurement on Zn and Cd, since they were made a t time sufficiently long that the material used diffused to the end of the furnace tube. Under such conditions, t >> 0, the concentration in the gas phase is given by (see Appendix):
C, = C ,,
sin ( m / a ) exp(-t/ra)
(2)
Inserting the expression into the differential equation for diffusion (12) gives the relation between 7, and the effective diffusion coefficient for transport in the gas phase, D.
r , = a2/ri2D
(3)
For materials which react with the graphite tube, there are two additional effects to be considered. The first effect is diffusion out through the graphite wall which provides an additiond mechanism for removal of atoms from the furnace tube and can be characterized by a time constant
(4) where b is the wall thickness of the graphite tube and D‘ is an effective diffusion coefficient in graphite. This would give
