Measuring and Interpreting X-ray Fluorescence from Planetary Surfaces

As part of a comprehensive study of X-ray emission from planetary surfaces and in particular the planet Mercury, we have measured fluorescent radiatio...
0 downloads 0 Views 1MB Size
Download PDF
Anal. Chem. 2008, 80, 8398–8405

Measuring and Interpreting X-ray Fluorescence from Planetary Surfaces Alan Owens,*,† Burkhard Beckhoff,‡ George Fraser,§ Michael Kolbe,‡ Michael Krumrey,‡ Alfonso Mantero,| Michael Mantler,⊥ Anthony Peacock,† Maria-Grazia Pia,| Derek Pullan,§ Uwe G. Schneider,# and Gerhard Ulm‡ Science Payload and Advanced Concepts Office, ESA/ESTEC, 2200AG Noordwijk, The Netherlands, Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany, Department of Physics and Astronomy, Leicester University, Leicester LE1 7RH, U.K., INFN, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy, Technische Universita¨t Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria, and Bruker ¨ stliche Rheinbru¨ckenstrasse 49, 76187 Karlsruhe, Germany AXS, O As part of a comprehensive study of X-ray emission from planetary surfaces and in particular the planet Mercury, we have measured fluorescent radiation from a number of planetary analog rock samples using monochromatized synchrotron radiation provided by the BESSY II electron storage ring. The experiments were carried out using a purpose built X-ray fluorescence (XRF) spectrometer chamberdevelopedbythePhysikalisch-TechnischeBundesanstalt, Germany’s national metrology institute. The XRF instrumentation is absolutely calibrated and allows for reference-free quantitation of rock sample composition, taking into account secondary photon- and electroninduced enhancement effects. The fluorescence data, in turn, have been used to validate a planetary fluorescence simulation tool based on the GEANT4 transport code. This simulation can be used as a mission analysis tool to predict the time-dependent orbital XRF spectral distributions from planetary surfaces throughout the mapping phase. Remote X-ray and γ-ray sensing has played a significant role in the exploration of airless solar system bodies, such as the Moon, Mars, and the large S-class asteroid Eros and has been baselined for surface composition studies of Mercury.1-3 X-rays give information on the composition of the top few micrometers of surface, whereas γ-ray measurements give information on elements located up to 30 cm below the surface. Taken together, it is possible to differentiate between the regolith, soil, dust, and buried components, such as water ice. In principle, remote X-ray chemical analysis of a planetary surface can be achieved in two ways: by detecting X-ray fluorescence (XRF) or particle-induced * To whom correspondence should be addressed. E-mail: [email protected]. Phone: 31-71-565-5326. Fax: 31-71-565-4690. † Science Payload and Advanced Concepts Office, ESA/ESTEC. ‡ Physikalisch-Technische Bundesanstalt. § Leicester University. | INFN. ⊥ Technische Universita¨t Wien. # Bruker AXS. (1) BepiColombo, an Interdisciplinary Cornerstone Mission to the Planet Mercury - system and technology study report, ESA-SCI(2000); 2000; p 1. (2) Clark, P. E.; Trombka, J. I. JGR 1997, 102 (E7), 16361. (3) Brueckner, J.; Masarik, J. Planet. Space Sci. 1997, 45, 39.

8398

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

X-ray emission (PIXE). XRF arises from the solar coronal X-ray flux, which for the inner solar system is sufficient to fluoresce measurable fluxes that can be detected by an orbiting spacecraft even in solar quiescence. PIXE, on the other hand, is significant (and may exceed the XRF signal) only during particle events. Remote γ-ray spectrometry can be used to detect natural γ-ray emission from the transuranic series, K, Th, and U and cosmic ray-induced γ-rays from H, O, Si, and Fe. Chemically, Mercury is the least known of the terrestrial planets, with only the Mariner 10 color difference maps4 to indicate the apparent depletion of surface Fe and Ti relative to the Moon and predominantly radar measurements5 to hint at the presence of water ice and/or sulfur. At present, no clear associations can be drawn between the mapped terrains (intercrater plains, smooth plains, highlands) and geochemical boundaries. Thus, the discussion of the planet’s tectonic and volcanic histories has proceeded largely unconstrained. High-quality compositional data for Mercury are crucial to understanding the evolution of the inner solar system. In particular, the measurement of Al (1.49 keV) X-rays distinguishes between rock classes (anorthosites from basalts) while Mg (1.25 keV) distinguishes within classes (KREEP versus normal basalt). The measurement of Fe provides the key link between measurements by the various energies of electromagnetic radiation as well as PIXE; depth sensitivities differing by 1 order of magnitude and more due to element-dependent energies of the fluorescent radiation as well as excitation modes place constraints on the nature of regolith formation. Both ESA and NASA plan to send spacecraft to Mercury.6,7 NASA’s Messenger mission consists of a single spacecraft that will enter orbit around Mercury after a 5-year cruise phase. ESA’s BepiColombo is currently planned to have two components: the Mercury Planetary Orbiter (MPO) and the Mercury Magnetospheric Orbiter (MMO). Of critical importance to both missions is the in-orbit compositional mapping of the surface using XRF techniques. Whereas the Messenger XRF spectrometer employs (4) Robinson, M. S.; Lucey, P. G. Science 1997, 275, 197. (5) Slade, M. A.; Butler, B. J.; Muhleman, D. O. Science 1992, 258, 635. (6) Grard, R.; Scoon, G.; Coradini, M. Mercury Orbiter-An Interdisciplinary Mission, ESA J. 1994, 18, (No. 3), 197. (7) Solomon, S. C.; McNutt, R. L.; Gold, R. E.; Santo, A. G. MESSENGER: The Rediscovery of Mercury, 30th Annu. Lunar Planet. Sci. Conf., Houston, TX, 1999; p 1410. 10.1021/ac8009627 CCC: $40.75  2008 American Chemical Society Published on Web 10/15/2008

Figure 1. Left: calculated solar X-ray induced emission (quiet Sun and flare conditions) from basalt using a 1-D transport code.10 Curves are given for a variety of solar conditions and illustrate the large variations that can be expected throughout the solar cycle. This is illustrated on the right, where we show the X-ray flux variations measured during the last solar cycle (cycle 23) by the GOES satellite: Note that BepiColombo will begin observations of Mercury just after solar minimum, which, in terms of flux, would be equivalent to the years 1998-2000 of the last solar cycle.

three gas proportional counters with relatively poor energy resolution (∼15% fwhm), the BepiColombo MPO will carry a new high-resolution solid-state spectrometer capable of resolving spectral features at the few percent levelsthe Mercury imaging X-ray spectrometer, or MIXS. Since XRF can only give information on the top few micrometers of the surface, both Messenger and BepiColombo also carry γ-ray and neutron spectrometers to extend compositional studies to depths of ∼30 and ∼100 cm, respectively. Because of the high spectral resolution of the MIXS, we have carried out a series of synchrotron radiation-based experiments to determine to what extent it is possible not only to distinguish between different types of soil and rock samples and ultimately, compositional models for Mercury’s surface, but also to investigate reliable quantitation procedures. The MPO spacecraft will occupy a 2.3-h polar orbit in a fixed inertial frame of perigee 400 km and apogee 1500 km. The orbital plane is perpendicular to the equator, and the pericenter is on the equator opposite to the Sun at perihelion and subsolar at aphelion. The MIXS is nadir pointing. Initially, surface maps of the line ratios of characteristic fluorescent X-rays will be generated. These are valuable analysis tools, especially in the early stages of XRF investigations, since variations of matrix effects due to gross physical and compositional influences are significantly reduced and most of the geometric corrections cancel out. Also, line ratio maps made with respect to a constant-abundance element preserve a direct relationship between the ratio data and abundance data for the variable element. Thus, for example, if preliminary measurements indicate that Mercury most closely resembles a basaltic achondrite, where Si abundances do not vary significantly with subclass, then surface maps of line ratios with respect to Si will be generated. For later analysis, it is expected that compositional data will be directly unfolded from the measured fluorescence spectra using analysis tools validated by these laboratory measurements. Only limited computational facilities will be available on board, and transmission of large amounts of data to the terrestrial ground station is impossible for routine data evaluation due to restricted telemetry. Large codes such as full-scale Monte Carlo software (like GEANT-4) require fast processors and much longer computing times than actual acquisition times of the individual spectra. Its main value is therefore

the study of instrumental design parameters such as optics and detector layout as well as detailed modeling of the simultaneous interaction of particle radiation and photons with the atoms of the investigated material. This is partially true as well for the currently used deterministic fundamental parameter (FP) modeling; however, simplified approaches compatible with the mission’s requirements can be derived by using parametrizations of data obtained from studies by Monte Carlo methods. EXCITATION OF PLANETARY FLUORESCENCE RADIATION A key tool in the analysis and interpretation of planetary XRF data is a quantitative model of the X-ray production at the planetary surface by the highly variable solar X-ray flux. Here, the incident X-ray spectrum was estimated by inverse-square law scaling of the fluxes measured at the Earth. Representative spectra were then calculated for M-, C-, and B-class flares and for the quiescent Sun. The surface of Mercury was assumed to be composed of basalt, since what little data are available suggest that the Mercurian surface is similar to the lunar mare.8 The relative efficiencies for fluorescence from each of the primary excitation processes can then be evaluated. These are as follows: (1) direct excitation by solar X-rays and subsequent relaxation; (2) PIXE by solar flare protons; (3) PIXE following electromagnetic cascades induced by nuclear interactions of protons and other nuclei (principally the galactic cosmic rays). The initial estimation of X-ray production yields was carried out using a combination of a 1-D electron-photon transport code and analytical models.9 The calculations considered a fluorescent medium with a composition (by weight) appropriate for a mare basalt and used source spectra based on current models for solar coronal X-rays, solar-flare protons, and cosmic rays. The simulation was limited to energies of >1 keV, primarily due to the complexities of low-energy electron propagation. The computations were performed for 20 million histories and modeled both photon and electron transport. Discrete line contributions to the spectra were also included. Preliminary results are shown in Figure 1 (left) for (8) McCord, T. B.; Clark, R. N. J. Geophys. Res. 1979, 84, 7664. (9) Truscott, P.; Dyer, C.; Peerless, C.; Basalt X-ray Fluorescent Study, DERA/ CIS/CIS2, 2000.

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

8399

a variety of solar conditions. K-Shell fluorescence is clearly visible from iron (KR and Kβ at 6.4 and 7.1 keV, respectively), titanium (KR and Kβ at 4.5 and 4.9 keV), calcium (KR and Kβ at 3.7 and 4.0 keV), and from silicon, aluminum, and magnesium (KR at 1.74, 1.49, and 1.25 keV). Steps in the spectra are apparent at 1.84, 4.04, and 7.12 keV, corresponding to the K-shell absorption edges of silicon, calcium, and iron, respectively. The spectral resolution of the MIXS detector will be better than 200 eV at 5.9 keV (MnKR), allowing measurement of fluorescent lines as well as backscattered radiation from the same surface region. This information is complemented by an additional spectrometer recording the direct incident photon and proton flux from the Sun. This can be used as a reference input for FP-based X-ray emission calculations. The KR line intensities of the higher Z elements are extremely sensitive to the incident solar X-ray spectrum. During solar flare conditions, the induced line emission from basalt can increase by between 1 and 5 orders of magnitude depending on the species and the class of the solar event. The right-hand graph shown in Figure 1 illustrates the wide range of solar activity encountered during the last cycle. At solar maximum, we may conclude that the Sun will spend most of its time in C/B flare conditions. Within this range, the calculations predict that we can expect Fe KR fluxes to vary by nearly 2 orders of magnitude while those from Mg vary by only a factor of ∼3 9sthe differences in the magnitudes of the fluxes being due to the hardening of the solar spectrum with increasing activity. This clearly demonstrates the importance of measuring the incident solar spectrum accurately and continuously during XRF observations. The contribution from PIXE to the total fluorescence signal was evaluated analytically using proton-stopping powers and ranges derived using the SRIM 2000 package.10 It was found that, on average, the flux induced by flare X-rays was ∼1 order of magnitude greater than proton-induced X-rays for the lighter elements and about the same for the heavier elements. However, the instantaneous PIXE levels can be a lot higher. The contribution of detected X-rays due to the galactic cosmic rays was found to be small, being at worse a factor of 7 below the photon-induced events during solar quiet conditions. Consequently, these fluxes will only be important during observations during the dark part of the orbit. While the above simulations are useful for mission study purposes, the calculated X-ray production yields, both at the planets’ surface and in orbit, are approximate, since they are based on several key assumptions. For example, the calculations are simplified in that they assume an infinite plane geometry, a 1-D transport, and are only valid above 1 keV. The latter is a severe limitation since the X-ray production yields for the L-edges could be potentially much larger than for the K-edges in view of the softness of incident solar X-ray spectrum. The detected fluxes depend on the qualitative and quantitative composition of the rocks. Straightforward evaluation assumes that the rock medium and its constituent components form a homogeneous layer. Additionally, PIXE is handled analytically. To eliminate the shortcomings caused by these simplifications, a new simulation has being written, based on the GEANT4 11,12 code system, which includes the accurate modeling of fluorescent processes, including (10) http://www.srim.org/. (11) Agostinelli, S.; et al. Nucl. Instrum. Methods, A 2003, 506, 250. (12) Allison, J.; et al. IEEE Trans. Nucl. Sci. 2006, 53, 270.

8400

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

Figure 2. Left: schematic view of the four crystal monochromator (FCM) beamline in the PTB laboratory at BESSY II. Right: external view of the XRF chamber at PTB. Monochromatic beam from the FCM enters the chamber on the right and is incident on one of three samples in a conventional 45°-45° arrangement. Here, the fluorescent photons are detected by a Si(Li) detector, whose dewar can be seen upper right.

PIXE, with both particles and photons tracked down to a threshold energy of 250 eV.13 EXPERIMENTAL SECTION In order to validate the simulation and to further refine the code, we have measured the fluorescent radiation from a number of reference materials and simulant soil and rock samples. The latter are standard planetary analogs. The purpose of these measurements is to test the Monte Carlo calculations against real fluorescent spectra measured from actual rocks as well as to provide a library of such spectra for future reference. In addition to Mercury analogs, we also examined several Martian and Lunar analogs for use in future ESA missions. The X-ray measurements were carried out with monochromatized synchrotron radiation at the electron storage ring BESSY II, using the four crystal monochromator (FCM) beamline14 of the Physikalisch-Technische Bundesanstalt (PTB). This beamline is illustrated in Figure 2 (left) and employs four InSb(111) or four Si(111) crystals to produce highly monochromatic X-ray beams, tuneable over the energy range 1.75-10.5 keV, with a typical energy resolution of 1 eV at 10 keV. The FCM is coupled directly to a purpose-built XRF spectrometer chamber (see Figure 2 right) developed by PTB specifically to ensure reference-free X-ray fluorescence analysis.15,16 An internal view of the chamber is shown in Figure 3 (left) and a schematic of its principal components given in Figure 3 (right). The chamber allows the accurate positioning of up to three samples to be investigated with respect to a set of high-purity, precision Al or Cu diaphragms. These do not define the size of the excitation beam but prevent stray light from passing through and define the solid angle of fluorescence radiation detection. X-rays are incident at the center of the sample and the fluorescent photons measured by a lithium drifted silicon energy-dispersive detector. The detection efficiency of this detector has been evaluated using both, calculable undispersed synchrotron radiation and monochromatized radiation, and transfer detectors to a relative uncertainty of less than 2%. Its (13) Chauvie, S.; et al. Geant4 Low Energy Electromagnetic Physics. Conf. Rec. 2004 IEEE Nucl. Sci., Symp. 2004, 3, 1881. (14) Krumrey, M.; Ulm, G. Nucl. Instrum. Methods, A 2001, 467–468, 1175. (15) Beckhoff, B.; Ulm, G. Adv. X-ray Anal. 2001, 44, 349. (16) Kolbe, M.; Beckhoff, B.; Krumrey, M.; Ulm, G. Spectrochim. Acta B 2005, 60, 505.

Figure 3. Left: internal view of the XRF chamber (as in the initial experiments with normal incidence). The beam enters from the upper right and passes through a central diaphragm onto the sample. The lower photograph gives a closer view of the diaphragm and sample holder assemblies. Right: a simplified schematic of the experimental configuration within the chamber (as in later experiments, 45° incident). The highly monochromatic beam from the FCM is collimated and incident on the sample under an angle of 45°. Three samples, each 25 mm in diameter can be held in the sample holder, which can be positioned successively into the beam. The beamline is calibrated in energy by using reference foils. The energy scale of the Si(Li) and a second optional detector can be calibrated by fluorescence radiation of the stainless steel sample holder in an interstitial position. Table 1. Bulk Major Elemental Composition of Test Samples Determined by Wavelength-Dispersive XRFa composition % wt oxide, normalized to 100% sample/ origin weathered basalt (Hawaii) (JSC Mars1 0) basalt (Hawaii) 0) basalt (Madagascar) obsidian (Iceland) anorthosite (South Harris) hematite (Sishen) gabbro (Mount Royal) dolerite (Whin Sill)

SiO2

TiO2

Al2O3

Fe2O3

MnO

MgO

CaO

Na2O

K2 O

P2O5

Mars soil

41.5

3.9

24.7

17.2

0.3

2.3

6.3

1.7

0.7

0.9

Mars Moon Mars Mercury MoonMarsMercury MoonMercury Mars

45.0 39.6 45.0 46.6 5.2 36.8 48.7

2.1 3.3 2.1 0.1 0.1 3.8 2.3

15.1 11.9 15.1 31.9 3.0 10.0 17.0

17.5 18.6 17.5 0.7 91.2 17.5 12.4

0.3 0.2 0.3 0.1 0.0 0.2 0.2

5.1 11.6 5.2 0.4 0.0 14.9 4.5

11.2 9.7 11.2 16.1 0.1 15.4 9.2

2.8 3.0 2.8 3.5 0.1 0.8 3.47

0.46 1.0 0.3 0.3 0.2 0.2 1.5

0.2 0.7 0.8 0.0 0.1 0.1 0.5

analog

a The samples were in the form of pressed pellets. Measurements by Bruker AXS (application lab Karlsruhe) by a (proprietary) standardless method without grain size corrections; no detailed error budgets were provided; however, an indication are the sums of concentrations between 91% and 103% before normalization.

FWHM energy resolution is 130 eV at 5.9 keV, which is close to the Fano limit. The angle at which the detector can view the sample can be varied, as can the angle of X-ray incidence on the sample. In the first set of measurements, the incident beam was normally incident and the fluorescent photons were measured at an angle of 45°; in the second run, a 45°-45° conventional XRF beam geometry was employed. The chamber also has provision to incorporate a second reference detector in an other quadrant. A hole in the sample holder allows the intensity of the direct beam to be directly measured using a calibrated photodiode.16,17 During XRF measurements, a thin photodiode further downstream of the FCM beamline monitors the incident flux on the sample. Before and after each XRF measurement series, this photodiode is calibrated against the Si photodiode behind the XRF chamber, which is an absolute reference detector. If necessary, the XRF chamber can be surrounded by a class-100 clean room to minimize (17) Krumrey, M.; Gerlach, M.; Hoffmann, M.; Mu ¨ ller, P, AIP Conf. Proc. 2007, 879, 1145.

the risk of cross-contamination during sample changes. The system has been tested using carbon and boron reference samples. Total K-edge fluorescence yields of ωK ) (1.11 ± 0.11) × 10-3 and (2.97 ± 0.16) × 10-3 were determined.15 This is to be compared to the accepted values of ωK ) 1.408 × 10-3 and 2.757 × 10-3.18 Likewise the single differential resonant Raman cross sections of Si at the K-edge were determined with relative uncertainties of ∼7%.19 XRF MEASUREMENTS AND RESULTS A total of eight rock samples were initially measured: five mafic igneous rocks, an anorthosite, an obsidian, and a sample of the Fe ore hematite. A survey on the respective sample types is given in Table 1. Wavelength dispersive XRF data were obtained using a Bruker S8 Tiger X-ray fluorescence spectrometer operating a (18) Hubbell, J. H.; et al. J. Phys. Chem. Ref. Data 1994, 23 (2), 339. (19) Mu ¨ ller, M.; Beckhoff, B.; Ulm, G.; Kanngiesser, B. Phys. Rev. A 2006, 74, 012702.

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

8401

rhodium end window X-ray tube powered by a 4-kW generator with up to 160 mA or 60 kV. All major elements are analyzed at 50 kV, 50 mA. Detection limits are 0.01% (0.001% for K2O) yielding precisions of 1% (0.1% for K2O). The quantitation procedure did not take into account for potential particle size effects20 (also known as powder effects), and the deduced concentrations were normalized to 100%. Typically, for this type of quantitation, the sum of the calculated compositions for pressed pellets will lie in the range ∼90-104%, mainly due to these powder effects. The most reliable results are obtained using glass beads where particle size effects are negligible. The basalts were sourced from different geological environments and provinces: namely, the mid-Atlantic ridge (Iceland), Indian Oceanic trench (Madagascar), and the central Pacific hot spot (Big Island, Hawaii). A weathering product of Hawaiian basalt is included as an analog of Martian soil (JSC Mars1).21 Anorthosite has been cited as a potential Mercurian analog based on mid-IR (7.3-13.5 µm) spectroscopy studies of equatorial and low-latitude regions of Mercury. Hematite is included since it has been unambiguously identified at the surface of Mars by the Opportunity and Spirit rovers. Gabbro and dolerite are, respectively, coarse- and fine-grained equivalents of basalt and are included to provide additional variability and provide a possible cross calibration source. The samples were pulverized into a powder and pressmolded into disks of diameter 25 mm and thickness 4 mm and loaded into the sample holder. Five pure reference materials (Al, Si, Ti, Fe, Cu) were also measured separately to directly test the new fluorescence coding in the GEANT4 simulation. In these cases, the simulation was set up to accurately reflect the XRF chamber and included the response function of the Si detector. It was found that the simulations agreed well with the measured spectra. For each sample, fluorescent spectra were recorded by the Si(Li) detector at four different incident photon energies in a conventional 45°-45° beam geometry. The incident photon energies were 9.2 (well above the Cu K-edge); 7 (just below the Fe K-edge), 4 (just below the Ca K-edge), and 2.5 keV (well above the Si K-edge). The latter energies were chosen to ensure that the elements whose edge was just above the energies were not excited, allowing a higher degree of spectral acuity to be achieved in the spectral region immediately below this energy. Additional sets of data were taken to assess the clarity of the microphysics in GEANT4 and specifically to check on coherent, incoherent, and Raman scattering components, by also allowing for measurements in a 90°-45° beam geometry, which enhances scattering contributions. Examples of fluorescent spectra are shown in Figure 4 in which four spectra recorded from an Hawaiian basalt at different excitation energies and two additional spectra of an Icelandic basalt and a Gabbro at the highest incident photon energy of 9.2 keV are compared. In Figure 5, we show a fluorescent spectrum of the Hawaiian basalt sample in which the fluorescent and scattered lines are indexed. The incident beam energy was 9.2 keV. From the figure, it can be seen that nearly all the emission from the sample is in the form of characteristic lines, and the KR and the Kβ lines of (20) Maruyama, Y. K.; Ogawa, T.; Okada, M. Lunar Planet. Sci. 2007, 37, 1186. (21) Allen, C. C.; Morris, R. V.; Lindstrom, D. J.; Lindstrom, M. M.; Lockwood, J. Lunar Planet. Sci. 1998, 28.

8402

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

elements with Z > 20 are clearly resolved. By best-fitting detector response function profiles, fixed in energy but allowing the line intensities to be free parameters, the count rates NXi for each resolved fluorescence line could be determined. The concentrations of the various elements in the sample could then be derived from the count rates as follows. Employing the simplest case to excite fluorescence radiation of an element, the detected count rate NXi of fluorescent radiation of element i at energy EXi,l emitted from the specimen is given by, NXi,l(E0) ) I0(E0)τi(E0)Ci

rXi - 1 1 1 ω f q(EXi,l) sin ψin Xi rXi Xi,l µtot(E0, EXi,l)

where I0 is the photon flux of the incident excitation radiation at energy E0; Ci is the concentration of element i in the sample; q(EXi) is a geometric factor describing the effective areas presented by the source and detector to the sample and includes the detection efficiency as well as the detection solid angle; µtot(E0,EXi) takes into account the (mass) attenuation of incident and fluorescent radiation along their paths inside the sample; ωXi is the fluorescence yield and rXi is the jump ratio of the shell (subshell) Xi; and fXi,l is the probability of emission of line l and τi,Eo is the photoelectric mass absorption by element i for the incident radiation, E0. This equation includes only the direct excitation process of an element in a sample. A very similar quantitation approach22 was recently developed for reference-free total reflection XRF analysis where the most prominent difference is the modification of the exciting radiation by the standing wave field at the surface of a very flat sample, as in the case of a semiconductor wafer surface. In Table 2, we list the derived relative elemental contents for the samples from which we see there is good agreement with the expected concentrations. Note: we have also included indirect (secondary and tertiary) excitation processes 23,24 by fluorescent photons of other elements with higher energies as well as of the same element, cascade effects, and excitation by photoelectrons25 originating inside the sample. Best results with deviations of only a few percent were obtained for medium Z elements, where fundamental parameters 18,26,27 are most reliable and the computational models are accurate for bulk materials as well as for thinfilm structures. The effect of secondary excitation by photoelectrons originating from within the sample increases the measured count rates for fluorescence lines. In particular, the values of the (22) Beckhoff, B.; Fliegauf, R.; Kolbe, M.; Muller, M.; Weser, J.; Ulm, G. Anal. Chem. 2007, 79, 7873. (23) Mantler, M. Adv. X-ray Anal. 2000, 43, 429. (24) Mantler, M.; Willis, J. P.; Lachance, G. R.; Vrebos, B. A. R.; Mauser, K.-E.; Kawahara, N.; Rousseau, R. M.; Brouwer, P. N. Quantitative Analysis. In Handbook of Practical X-Ray Fluorescence Analysis; Beckhoff, B., Kanngiesser, B., Langhoff, N., Wedell, R., Wolff, H. Eds.;Springer: Berlin, 2006, 309. (25) Kawahara, N.; Shoji, T.; Yamada, T.; Kataoka, Y.; Beckhoff, B.; Ulm, G.; Mantler, M. Adv. X-Ray Anal. 2002, 45, 511. (26) Krause, M. O.; Nestor, C. W.; Sparks, C. J.; Ricci, E. X-ray Fluorescence Cross Sections for K and L Rays of the Elements, Oak Ridge National Laboratory, report no. 5399; 1978. (27) Zschornack, G. H. Handbook of X-Ray Data; Springer: New York, 2007. (28) Beckhoff, B.; Kolbe, M.; Hahn, O.; Karydas, A. G.; Zarkadas, C.; Sokaras, D.; Mantler, M. X-Ray Spectrom. 2008, 37, 462.

Figure 4. Fluorescent spectra of materials recorded under different excitation conditions for simultaneous evaluation by the new referencefree FP method (see Table 2 for results). Spectra (1), (2), (3) and (4) are from a Hawaiian basalt which has been excited at four photon energies (2.5, 4.0, 7.0 and 9.2 keV). Spectra (5) and (6) are from two different samples—an icelandic basalt, and a Gabbro—each excited at the highest incident photon energy of 9.2 keV for comparison with (spectrum) (4).

Table 2. Comparison of Compositional Data of Three Rock Samples in the Form of Pressed Pellets Obtained by Conventional Wavelength-Dispersive XRF Data (WD XRF) and a Completely Reference-Free Fundamental Parameter Based XRF (FP XRF) Analysisa composition % wt, normalized to 100% sample/ origin 1/ ‘Hawaiian basalt’ 2/‘Icelandic basalt’ 3/‘gabbro’

technique

SiO2

TiO2

Al2O3

Fe2O3

MnO

MgO

CaO

Na2O

K2O

P2O5

WDXRF FP XRF WDXRF FP XRF WDXRF FP XRF

41.5 46.7 45.0 52.4 36.8 35.6

3.9 3.7 2.1 2.3 3.8 3.8

24.7 20.1 15.1 12.4 10.0 10.9

17.2 16.3 17.5 17.0 17.5 18.0

0.3 0.3 0.3 0.3 0.2 0.2

2.3 3.3 5.2 3.9 14.9 13.8

6.3 6.2 11.2 11.6 15.4 16.2

1.7 1.7 2.8 2.9 0.8 1.0

0.7 0.7 0.3 0.4 0.2 0.2

0.9 1.0 0.2 0.3 0.1 0.4

a The major component compositions (presumed stoichiometry) are given in percentage by weight. The total error budgets are mainly influenced by the reliability of fundamental parameters with estimates between 7% for compounds of heavier elements and 15% for compounds of light elements..28,32 Total Fe calculated as Fe2O3.

major matrix elements silicon and aluminum are influenced by this effect, which cannot yet be fully modeled due to certain limitations in the knowledge of absolute electron interaction cross sections and hence, is only included empirically in the calculation

model based on dedicated investigations of ∼2-µm-thick selfstanding Al and Si foils. The simultaneous processing of the XRF spectra of each rock sample, recorded at different excitation energies, allow for checking of both the energy-dependent Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

8403

Figure 5. Measured fluorescent radiation from a Hawaiian basalt. The incident photon energy was 9.2 keV. The black line is the measured spectrum, and the red smooth line shows the fit with the detector response function used to deduce fluorescence count rates for each resolved fluorescence line.

discrepancies in the fundamental parameters27 and spectral deconvolution problems, thus ensuring a reliable and selfconsistent reference-free quantitation. Estimated Errors in Reference-Free XRF. Truly referencefree XRF requires a completely calibrated experimental setup and depends fundamentally on the accuracy of the involved physical parameters. Earlier studies show that the analytical error, i.e., relative uncertainty, induced by all uncertainties in the geometrical, detection efficiency, and electronic instrument calibration at the PTB beamlines at BESSY II, is of the order of 3%.13,16 The statistical error due to counting statistics varies widely corresponding to concentrations and excitation efficiency of the measured lines; up to several 105 counts were accumulated for the main constituents resulting in errors (standard deviation) of less than 1%. However, in case of less abundant components as well as analysis by L-lines, it may exceed 10%. The largest error contribution arises from the uncertainties in literature data26,27 for fundamental parameters, in particular for the light elements such as aluminum, silicon, and oxygen. Some parameters are directly proportional to the computed counts (such as fluorescence yields or transition probabilities) and may add errors of up to 10-20% and more. These considerations suggest a precautious error estimate of not less than 20% for the individual computed analyte line intensities (higher for oxygen, L-lines, and Kβ-lines). However, for the estimate of the final error in the sample composition, it must be taken into consideration that (a) the sample composition is expected to be given as normalized concentrations while the underlying fundamental parameter computations deliver mass ratios (equivalent to concentration ratios), (b) that the results refer to stoichiometric components rather than single elements, and (c) that for most elements several lines have been measured, allsas far as energetically possiblesunder several experimental conditions (different excitation energies). Thereby the overall analytical result could be greatly improved by building averages. This is supported by results of a comparative study of ceramic materials initiated by the IAEA,28 where the data obtained by the above method compared very wellsin fact, within a few percent of reference data for the main constituents. 8404

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

Figure 6. GEANT4 calculated and measured fluorescence spectrum of the Hawaiian basalt sample for 9.5-keV incident beam energy. The computational setup accounts for secondary excitation by fluorescent radiation but not for multiple scattering of the primary beam (which does not noticeably contribute to fluorescence). While the agreement is good in the center range it is only fair at the low energy side, possibly due to usage of less accurately known fundamental parameters. The discrepancy for the Compton peak is however much larger than expected and requires further research in cooperation with the authors of GEANT4 as well as reviewing the complex application setup.

Altogether the derived results should be within an error limit of less than 15% for Al2O3 and SiO2 and less than 20% for the concentrations of other constituents except traces. The influence of the three main constituents on the mutual ratios of the minor constituents (not their absolute values) was minimized by evaluating them in a second step for the fixed matrix of the three main constituents. More studies of fundamental parameters and comparisons of the evaluation methods with multielemental standard reference materials will be required to improve the reliability of the results. This applies to all evaluation techniques including those by Monte Carlo techniques. It should be noted that uncertainties in fundamental parameters affect also the interpretation of the raw spectra because the deconvolution of overlapping lines is much more successful when the relative line intensities from an element are well-known and can be improved by iterative techniques whereby an analytical evaluation of the data is included at each step. GEANT4 Simulations. While the original GEANT code covered all high-energy processes and interactions from 1 keV to 1 GeV, some low-energy atomic and shell effect processes were based on empirical calculations and therefore approximate. For the work described here, the Low Energy Electro-magnetic (LowE) package was used. It includes specific low-energy models (down to 250 eV) for the description of the electromagnetic interactions of electrons, γ-rays, protons, antiprotons, and ions.29 The microphysics of atomic relaxation processes was developed and incorporated into the Geant4 toolkit. It includes models for the simulation of Auger electron and fluorescence photon emission. The experimental geometry described in the section XRF Measurements and Results was simulated30 using the updated (29) Amako, K.; Guatelli, S.; Ivanchencko, V.; Maire, M.; Mascialino, B.; Murakami, K.; Pandola, L.; Parlati, S.; Pia, M. G.; Piergentili, M.; Sasaki, T.; Urban, L. Nucl. Phys. B (Proc. Suppl.) 2006, 150, 44. (30) Mantero, A.; Bavdaz, M.; Owens, A.; Peacock, A.; Pia, M. G. IEEE Nucl. Sci. Symp. Conf. Rec. 2003, 3, 1527.

GEANT4 toolkit. The code was tested and benchmarked using the Hawaiian basalt sample for which typical elemental contents data are already available.31 In Figure 6, we show a comparison of the measured and GEANT4 calculated spectra from which a good qualitative agreement can be seen. There are however a number of deviations between measurement and simulation. These are marked (A), (B), (C), and (D). The discrepancies A and B around 1.3 and 2.5 keV are most likely caused by incomplete iterations of minor matrix constituents in addition to inaccuracies in the fundamental atomic data, which has been shown by Mantler et al. 24 and Kawahara et al. 25 to be less reliable with both decreasing atomic number and photon energies. The discrepancy at (C) is due to incomplete iterations of transition metal traces. Part of the discrepancy around the Compton peak, (D), is probably due to the fact that multiple elastic and inelastic events were not tracked in the simulation to reduce CPU time. However, in any case, the two data sets are found to be compatible at a confidence level of 95% with respect to the main constituent components.30 CONCLUSIONS We have measured XRF spectra from a number of Mercury, Lunar, and Mars analog rocks which are being used to establish (31) http://volcano.und.edu/vwdocs/vwlessons/activities/r_number8.html. (32) Beckhoff, B. J. Anal. At. Spectrom. 2008, 23, 845.

a library of reference standards for future planetary missions. The data have also been used to test and validate simulation codes based on a reference-free XRF quantitation and the GEANT4 code system. Both codes can be used to accurately predict the spectral distributions of XRF from planetary surfaces and potentially derive elemental compositions from measured spectra. The advantage of a reference-free XRF analysis based on deterministic algorithms over a pure Monte Carlo approach is greatly reduced computing time. However, the advantage of the GEANT4 approach is that the complex (and changing) source/detector geometry during the planetary mapping phase is more easily modeled. The extent to which multiple and alternating excitation sources (for example, involving both varying solar X-ray and energetic proton excitation) can be accommodated in a single reference-free approach remains an ongoing topic for further research, also to be extended well into the soft X-ray range.

Received for review May 9, 2008. Accepted August 20, 2008. AC8009627

Analytical Chemistry, Vol. 80, No. 22, November 15, 2008

8405