Absorption Correction for X-Ray Fluorescence Analysis of Aerosol Loaded Filters F. C. Adams and R. E. Van Grieken Depadment of Chemistry, Antwerp University (U.I.A.), B-26 10 Wilruk, Belgium
A method is described for the evaluation of fluorescence radiation absorption in the analysis of air particulate material collected on depth filters and imperfect screen filters. The total absorption effect Is divided into two components, one due to the particulate itself, and one due to the filter materiai. The flrst effect is calculated after evaluating the mass absorption coefficient by transmission measurements. The second correction is obtained by determinlng experimentally an hypothetlcai equivalent depth defined as the one hypothetical depth from which the particulate material would give rise to the same fllter absorptlon effect as that obtained from the actual distribution. Measurements of the ratio of the fluorescent intensities obtained from the front slde of the filter and from Its back slde allow this hypothetical depth to be calculated. The method is applied to the determination of calcium and sulfur in air pollution dust collected on Whatman and Millipore filters. The determinations of all the factors involved are carried out, and typical values are shown.
ferential thickness d(pz) at a depth pz from the surface can be written as dIA = K I , S C , ( ~ Z )exp[-(p, cosec e, + where p = density; K, proportionality constant dependent on the apparatus; I,, primary beam intensity; p1,p2, mass absorption coefficients of the primary radiation and the fluorescent radiation; 6'1,6'2, angle of incidence of the primary beam and angle of emergence of the fluorescent radiation; and C A ( ~ Z )concentration , of element A at the depth pz. The distribution C A ( ~ Zis )normally unknown. p , ~ ~ , pare z not constant but depend on the filter loading at the depth pz. We assume for the sake of clarity a monoenergetic primary radiation. The total intensity from a filter with thickness pD is IA = KIos ~ o D D c A ( p Z ) e ~ X D z d ( ~ Z )
+
Present concerns about the environmental quality have led to an increased interest in the multielement analysis of airborne particulate matter deposited on a suitable collection filter. One of the methods considered for the routine direct nondestructive determination of a considerable number of elements is X-ray fluorescence analysis (1-27). In the most favorable case, this technique avoids any preliminary treatment of the sample with the advantage of both quick operation and preservation of the unaltered sample for further investigations. However, the general applicability of the method is limited because the spectral response is affected by variations of the sample density and thickness and the interelement effects. On a thin filter, the radiation absorption effects are often negligible for high-2 elements, detected through their K-radiation. For low-2 elements such as silicon, phosphorus, sulfur, chlorine, etc., which are important from a pollution and geochemical point of view, self-absorption effects can be considerable. This paper suggests one way of circumventing the absorption problem for the analysis of air particulate material. The principles used in the proposed correction procedure are sufficiently general to make them applicable for the energy-dispersive and the classical wavelength-dispersive method. Moreover, they can be applied to material collected on different types of filters. Membrane filters, e.g., Millipore, can be approximated as screen filters which collect most of the material at or near the surface. Absorption by the filter material itself is thus relatively low. Cellulose fiber filters, on the other hand, are typical depth filters in which the particulate matter penetrates to some extent, thus giving rise to a higher radiation absorption in the filter which should be taken into account for accurate work.
THEORY The contribution of the characteristic radiation d l of ~ element A from an infinitesimal layer with area S and dif-
where x = p1 cosec 6'1 ~2 cosec 6'2. The mass per unit area M , can be calculated from M = -
IA KIoSt
(3)
where t is the absorption factor t defined as s o ' D c , ( p Z ) e-xDzd(pZ)
t =
ODD
JO
It is a common practice in X-ray spectrometry to use standard samples instead of calculating M from known atomic data. If standards and unknown samples are of different thickness, the measured characteristic radiation of both should be divided by t , implying normalization to infinitely thin samples. From Equation 2, it appears that any attempts to calculate this absorption factor depend on the ).a a priori knowledge of the distribution function C A ( ~ ZIn literature study, Brosset and Akerstrom (9) found neither a theoretical derivation nor an experimental measurement for the concentration of aerosols deposited on a filter by air flow. Moreover, for a given type of filter and sampling system, the properties and size distribution of the particles, as well as atmospheric conditions such as the humidity may influence the distribution. Nevertheless, it can safely be assumed that it is a continuously decreasing function from the front surface to the interior. The integral Equation 2 can only be calculated readily in a few simple cases, namely, for a homogeneous sample which was treated by Leroux and Mahmud (22), a linearly decreasing concentration profile as assumed by Brosset and Akerstrom (9) and an exponential concentration distribution used by Brady and Cahill (27). Idealized Filters. The absorption corrections become particularly simple in the case of the following hypothetical distributions.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
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1)A perfect screen filter on which all the particulate material is collected as a thin layer on the filter substrate. Any absorption of primary and fluorescent radiation occurs in the particulate material itself. It can easily be calculated through Equation 4, provided the mass absorption coefficient and mass of the aerosol material are known, as: 1 - ,-Xq(PD)p
t, =
XP(PD)P
(5 1
+
where xp = plP cosec 81 p 2 , cosec 82; and (pDIp = thickness of the particulate material. The subscript p stands for particulate material. 2) A theoretical depth filter in which the particulate material would only become trapped at one specific depth, pa, below the filter surface. Primary and fluorescent radiation will be subject to absorption by the aerosol material in the same manner as in the first case, Equation 5 . According to Rhodes and Hunter (28), particle size effects are generally negligible for the analysis of aerosols collected on filters. A second correction, however, will have to be made for absorption of primary and fluorescent radiation by the filter material of thickness pa. This latter absorption factor takes the form
particle activation analysis (29), the equivalent monoenergetic radiation introduced by Tertian (30) in X-ray fluorescence analysis, the effective neutron cross-section and neutron flux (31). Estimation of Equivalent Depth. The equivalent depth as defined in Equation 9 is of any practical value only if it can be determined experimentally with a sufficient accuracy. A measurement of the radiation intensity from the front and back side can be applied for a more or less precise determination. Whereas Equation 9 can always be defined, the determination of (paA)f by the measurement of front and back sides is not always reliable. Indeed in the backside geometry one has
&
=
JopD
C ( p D - p z ) e - X f P L d ( p z )E
)]j0 PD
C ( p D - p z ) d ( p z ) (10)
e-Xf[P(D-Q'A withoA'
+
oA.
and
spD
C ( p z )e - X f ( P rd(pz) )
[$]eXP
-
i p D d ( p D- pz)e-Xf(PL)d(p~) e + X f [ P D -P(aA+Q'*) If
The subscript f stands for the filter; xf = plf cosec fI1 + pzf cosec 8 2 ; (pa)fis the absorption thickness of the filter. The total absorption factor t is then
Provided that xp, ( P D ) ~Xf, and (pa)f are known, the absorption correction is easily calculated. xf and xp can be determined conveniently by the usual procedure from transmittance measurements of the radiation through a bare filter with thickness (pD)f and one loaded with particulate material. ( P D ) is~ the particulate material loading of the filter or total suspended particulate material expressed in g cm-2. It is commonly available through weighing of the filter. The only remaining term in Equation 7 is the absorption depth pa. It may be determined by measuring the radiation intensity of the filter from the front side, intensity ZA,and from the backside, intensity ZA'. Indeed:
Equivalent Depth Concept. I t can easily be deduced that the radiation absorption of the depth filter and also of the imperfect screen filter is completely equivalent to that in a hypothetical filter with the absorption effects being described by Equation 5. The depth (pa)f then takes the significance of an hypothetical equivalent depth, Le., the depth at which the absorption by the theoretical depth filter is equivalent to that obtained in the real filter. Thus
The equivalent thickness (paA)f is subscripted for element A because the distribution function C ( p z ) may differ from element to element. The equivalent depth concept introduced here for inhomogeneously distributed material in a filter is similar to that used in other quantitation procedures of analytical chemistry, e.g., the equivalent thickness concept in charged 1768
(11)
To allow the application of the experimental intensity ratio to the determination of U A , it is necessary that UA' = U A . Whether the approximation (PD - p(a* + 0Al)f 2 [ p ( D - 2o,)l, (12) is valid with a sufficient precision in the case of aerosol loaded filters depends on the shape of the unknown distribution function C ( p z ) . It can readily be shown that when C ( p z ) is a monotonically decreasing function, the more rapidly it decreases as a function of pz relative to e - X f ( p * ) f , the closer UA' will equal U A ; hence, the closer the experimentally determined value aexp = '/z ( U A + U A ' ) will equal QA.
To obtain a reasonable estimate of the errors involved, a more or less likely hypothetical distribution function can be selected and then, for various conditions, the errors inherent to the determination of U A by the procedure described can be calculated. Computer calculation was performed for two distributions: (1) an exponentially decreasing one:
(2) a linearly decreasing one:
[I
C(pz) = C ( 0 ) 1
-
v
-pz PD
The error involved in using the experimentally determined equivalent depth was calculated for various values of x and k . It was expressed as the relative difference
The results of the calculation are shown in Figures 1 and 2. The X-values used are consistent with the mass absorption coefficients of the elements from phosphorus upwards. It appears that the results are more accurate for steep aerosol material distributions, Le., large values of k in Equations 13 and 14. For p 5 80 cm2/g, Le., for calcium and all elements with larger atomic mass, the errors on the results of the proposed procedure are negligible, independent of the aerosol material distribution, at least when the analysis is performed through the K-radiation.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
,
l!
I
~ 2 -0 pB(I--m-
L
~~
=!ry&?,g
Figure 1. Relative deviation between experimental estimation and theoretical value of the filter material absorption correction in the case of an exponential concentration distribution C(pz) = C(o) e--kpz
APPARATUS The spparatus for energy-dispersive X-ray measurements consists of a Kevex subsystem 0810, a Siemens Kristalloflex 2 generator, and a Northern NS 720 multichannel analyzer. Sample excitation was performed through the fluorescent K-radiation of a titanium or molybdenum secondary target irradiated with the X-ray spectrum from a tungsten-anode high-power water-cooled tube. Collimators were provided between the secondary target and the sample and between the sample and the detector, both positioned a t a 4 5 O angle with respect to the sample plane. The fluorescence radiation of a central area of 0.8 cm2 was measured. The 30 mm2 X 3 mm Si(Li) detector was mounted in a cryostat with a 0.0025-mm beryllium window. The signal pulses were processed through a F E T pre-amplifier, an X-ray amplifier with base-line restorer and pulse pile-up rejector, and a 4096-channel ADC. Spectrum output facilities consisted of a Teletype writer/puncher and a magnetic tape recorder. The wavelength-disuersive instrument. a Philius PW 1450 modular X-ray spectrometer, can be considered as representative for the sequential crystal spectrometers used under routine analytical conditions. It contained a Philips PW 1140 generator and chromium target tube for X-ray generation and a pentaerythritol dispersive crystal and gas flow proportional counter with a 6-wm polypropylene window for characteristic X-ray detection. Automatic pulse-height selection was based on the sine 0 potentiometer principle. The exciting radiation from a chromium-anode tube operated at 20 kV impinged after filtering upon the sample under a 60" angle, while the fine-entrance Soller slit collimator for the fluorescent radiation was positioned a t 40' vs. the sample plane. The primary radiation spectrum was measured in the energy region from the sulfur absorption edge to the chromium K-radiation, using a pure carbon scatterer. In the region near the sulfur Kab, the polychromatic component was at least four orders of magnitude lower than the maximum chromium Kcu intensity. From the absorption cross section variation in the energy region of interest, it readily appeared then that fluorescence due to the polychromatic component was negligible.
-
RESULTS AND DISCUSSION For depth filters or imperfect screen filters, a correction for the absorption effect of both the filter paper and the particulate material is to be carried out. The following will demonstrate and discuss the applicability of the proposed method, based on the equivalent depth concept. Correction for Filter Paper Absorption. The filter absorption effect from Equation 9 is given by f
- C-XfPfQ f -
= e-Xf(PD)fa/Df
(16)
with (pD)f = pfDf. All the factors in the exponent can be evaluated straightforwardly.
Relative deviation between experimental estimation and theoretical value of the filter material absorption correction in the case of a linear concentration distribution q p z ) = C(o) (1 - (k/pD) P4
Figure 2.
Table I. Average Filter Weight per Unit Area for Some Common Air Filter Types Typical Filter type
Whatman 41,
0 110-mm Millipore AAWP 14200, d 1 4 2 - m m , 0.8-pm pore-size Millipore HAWP 04700, o 47-mm. 0.45-pm pore-size
\ ariabilit.I,
massi area, g / c m 2
(.
2.1
0.00855 0.00436
4.3
0.00569
1.9
1) (pD)f: Filter Paper Mass per Unit Area. Obviously, simple weighing of blank filter papers with known size yields the filter paper mass per unit area. Average (pD)f values, obtained from large numbers of some common filter specimen, are given in Table I. As a measure of the homogeneity within one fabrication batch, the third column lists the average standard deviation on the weights per unit area of specimen from the same batch. 2) xf= pfl cosec 81 i- pfgcosec 8 2 . The angles between the samples and the exciting and detected X-ray beams, O1 and 02, respectively, are known from apparatus construction data. The mass absorption coefficients, pfl and pf2, are found from transmission measurements of exciting and detected X-radiation, respectively, through preweighed blank filter papers. Indeed the characteristic X-ray intensities I and I , from any sample measured with and without a blank filter as an absorber, perpendicularly in the X-ray path between sample and detector, yield mass absorption coefficients through:
The p-values given in Table I1 were obtained by measuring the S-Ka, Ca-Ka and Ti-Ka radiation from a synthetic sample containing S, CaS04, and TiOn, using molybdenum secondary fluorescer excitation. Multiple evaluations of the S - K a mass absorption coefficients, carried out a t different locations of one Whatman 41 and one Millipore AAWP 04700 filter, yielded a -2% standard deviation per determination, not significantly above the uncertainty expected from counting statistics. This points to a homogeneous filter paper composition. The mass absorption coefficient for Cr-Ka was extrapolated from the values measured for Ca-Ka and Ti-Ka.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
1769
1
’:.. .\.... .’
. . . . I .
I i
f M r g y 1 LeV 1
and back side (- - - - -) of a typical loaded Millipore screen filter
Figure 3. X-Ray spectra measured from the front side (--)
Differences between front and back side counts arise from filter absorption effects, and depend on the concentrationand blank contribution of every element
Table 11. Measured Mass Absorption Coefficients for the Filters
Table 111. Relative Equivalent Deposition Depths for Different Typical Filters Average a l D t
Llasr absorption coefficient Filter t y p e
Whatman 41,
S-Ko
294 i 5
~q
and stand. d e v . , in c m 2 / g C2.--Ka
Ti-Ko
73.0 i 0.8 40.7
+ 0.8
Filter type
Loaded Whatman 41, 6 110-mm
d 110-mm
Millipore AAWP
367 i. 5 83.4 i 1.6 44.3
i
0.8
14200, d 1 4 2 - m m : 0 . 8 - p m pore size Millipore HAWP 04700, 369 i 6 83.8 i: 1.0 45.5 i 1.4 d 4 7 - m m : 0.45p m pore size
3 ) alDf: Relative Equivalent Deposition Depth. From Equation 11, it follows that:
As indicated above, the factors (pD)f and Xf can be determined for each filter type and X-ray energy. The relative equivalent deposition depths of all elements in a filter can, hence, be calculated from the ratio zA/zA’ of the X-ray intensities measured from the front and back side of the filter. Table I11 lists average (aeXp/Df)-values found on sets of 5 different Whatman 41 and Millipore AAWP 14200 filters loaded with particulate material. Both the energy-dispersive and wavelength-dispersive X-ray technique were applied to the same samples, using counting times of 1000 and 500 sec, respectively. Figure 3 represents typical energy-dispersion spectra from a typical filter in the normal (A) and reversed (B) position, measured in identical geometries and spectrometric conditions. 1770
Loaded Millipore- AAWP 14200, 6 1 4 2 - m m : 0.8-pm pore-size
X-Ray technique
For S
For C a
Energydispersion Wavelengthdispersion Energydispersion Wavelengthdispersion
0.29
0.11
0.27
0.06
0.10
0.00
0.09
. ..
The aerosol samples had been collected a t several stations in a highly polluted industrial zone close to Ghent, Belgium. The sampling equipment (32) consisted of a carbon-vane rotary pump and a filter-holder assembly in a specially designed shelter. Air filtering was continued for about one day a t a 15-20 m3 hr-’ flow rate. The deposited aerosol mass ranged from 0.1 to 1 mg cm-2. The results for both X-ray techniques, which involve the use of different 81, 8 2 , and p1 factors in Equation 18 appear to be in good agreement with each other. The Millipore membranes representative for screen filters, are expected to collect the aerosol a t their surface, unlike the Whatman cellulose papers. Both for sulfur and calcium, the experimental results point indeed to a significantly deeper deposition in the case of sampling on Whatman. For both filters, sulfur exhibits a much deeper deposition depth than calcium. This can easily be understood from the usual difference in particle size distribution between both elements [e.g., Ref. (33-35)]. In industrial areas like the sampling zone, sulfur is mostly associated with the small particle diameter aerosol component [mass-median diame-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
Table V. Typical Average Aerosol Material Mass Absorption Coefficients
Table IV. Reproducibility of Relative Equivalent Deposition Depth Determinations
\ \ e r a q L rash aasorption
Alerage a l D f 3.-Ra)
\,aluea and stand. de\. per determination Filter type
For S
Whatman 4 1 , 0.33 + 0.01 (0.01)‘ 6 110-mm Millipore AAWP 0.18 = 0.04 (0.01) 14200, o 142m m : 0.8-pm
S-Ka C a-K CY TI-Ka
For C a
0.10
I
0.05 (0.01)
0.00
i
0.02 (0.01)
ioefiicients, a.id stand. d?,
515 201
160
f
+
27 8 6
-
pore-size a ( ) is standard deviation per determination expected from counting statistics.
Table VI. Typical Correction Factors for the Absorption Effect CorrLition i i i t o r -
F2r
ter, e.g., 0.8 pm ( 3 4 ) ] since , it results mainly from anthropogenic sources implying combustion processes and condensation from the vapor phase. This property explains the deep deposition of sulfur in the cellulose fiber material and even its slight penetration into the membrane filter matrix. Calcium, on the other hand, is usually found to be much more weighted towards the large particles. This indicates production by natural or anthropogenic mechanical dispersion sources. Most of the calcium mass is found in the 2-10 wm diameter size fraction [mass median diameter, e.g., 6 pm (34)l. Hence, average collection at or close to the filter surface was to be expected. In order to investigate the reproducibility of the equivalent depth determination and/or the homogeneity of the deposition distribution within large filters, (u/Df)-values were determined by energy-dispersive measurements of the X-ray yield from front and reversed side at six different positions of two representative filters. Results are summarized in Table IV. The absolute experimental errors appear to be small enough not to be reflected significantly in the final absorption correction quality. Correction f o r Aerosol Material Absorption. In order to apply a correction for the particulate matter absorption included in Equation 5, two additional factors have to be determined. 1) ( P D ) ~Aerosol : Deposit Muss p e r Unit Area. The particulate matter load per unit area is routinely obtained by weighing the aerosol filter before and after the sampling step. The well-known hygroscopicity of Whatman cellulose paper can potentially induce serious errors here. Indeed, determining the aerosol mass often boils down to weighing a deposit of 50 mg or less on a 800-mg filter with large surface and hygroscopicity. Therefore, the filters must be equilibrated a t constant relative humidity before weighing. This procedure was first successfully implemented on a routine basis by the Bay Area Air Pollution Control District of San Francisco, Calif., and later by the Institute of Nuclear Sciences, Ghent University, Belgium (34). For the samples studied in this work, (pD)p-valuesranged from 0.1 to 1 mg/cm2. 2 ) xp = ppl cosec 81 + p p l cosec 82. Measurement of the characteristic X-radiation intensities of any sample containing sulfur, calcium, and titanium, both with ( I ) and without ( I o ) a loaded filter as an absorber in the path between sample and detector, gives:
Since all other factors can be evaluated as described above, can easily be calculated. It is obvious that the aerosol mass absorption coefficients depend on the composition of the aerosol material. Hence, they should ideally be deterpp
f
. ( i n im‘/g)
aerosol
For rilter material tf-’
natarial,
Total i o r -
tie- t p - l , from From Filter vpr.
Whatman41:ollO-mm
Millipore AAWP 14200: o 1 4 2 - m m : 0.8-1i.m pore-size
mcnt
S
Ca S Ca
Ei.
.ld-
rcctiunQ,
11
I 1) and CM+is the total metal ion concentration (the symbol C will subsequently be used for total concentration, as opposed to free or equilibrium concentration which will be denoted by the species symbol in brackets); other symbols have the usual meanings. As stated above, Equation 1 holds true for strong interaction only, i.e., only under circumstances where the free product concentration a t the working electrode surface, [Ra-]", is much less than the correspond-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 1 1 , SEPTEMBER 1975
* 1773
