Topochemical Speciation of Intercalated Palladium in Graphite by

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Anal. Chem. 2003, 75, 6576-6585

Topochemical Speciation of Intercalated Palladium in Graphite by Valence Band X-ray Spectrometry in the Electron Microprobe Udo Rohr,† Hugo M. Ortner,*,† and Stephan Weinbruch‡

Institute of Material Science, Department of Chemical Analytics, Darmstadt University of Technology, Petersenstrasse 23, 64287 Darmstadt, Germany, and Institute of Applied Geosciences, Department of Environmental Mineralogy, Darmstadt University of Technology, Schnittspahnstrasse 9, 64287 Darmstadt, Germany

The binding state of palladium was studied within the frame of an investigation on the mechanism of analyte fixation during the pyrolysis step in graphite furnace atomic spectrometry. One approach was the determination of the palladium intercalated in the pyrolytic coating of the graphite tube. Due to the low concentrations of intercalated palladium in the pyrolytic coating, precise determination of the shift of certain X-ray lines was chosen. From several investigated valence state sensitive X-ray transitions, the Pd Lβ2/15 (L3-N4,5) line shift was the one best determinable. The measured line shifts are in the range of -0.14 to 0.71 eV at line widths of 13 eV (fwhm) and a line energy of 3.1729 keV. These very small line shifts were determined by electron probe microanalysis. The detection of the small line shifts was performed with a new methodsby evaluation of the change of the intensity in the flanks of the X-ray line. The measurements yielded the following results: inside the pyrolytic graphite, the palladium is distributed inhomogeneously in the form of clusters or islands and in the form of particles on the surface of the pyrolytic graphite. The differentiation between particles and clusters is a very practical one: as long as a particle can be seen in the SEM we talk of particles. Often, however, Pd is detected in an area on the tube or platform surface without detection of a particle. Hence, it can be assumed that the Pd is present in the form of clusters which might even be intercalated in the uppermost graphite layers. The valence state inside these clusters does not appear to be uniform. It can be interpreted as a mixture of Pd with PdO in the center of the clusters or particles (positive peak shift) and of Pd bound to the graphite (strong negative peak shift). On the basis of these observations, a way is proposed to determine how activated Pd atoms in intercalated Pd domains are forming strong covalent bonds to analytes. These bonds are responsible for the analyte fixation of even very volatile analytes. The demand for information on speciation of elements in solidstate systems is steadily increasing. Knowledge of the binding * Correspondingauthor.Phone: ++49(0)6151166309.E-mail: h.ortner@hrzpub. tu-darmstadt.de. † Department of Chemical Analytics. ‡ Department of Environmental Mineralogy.

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state is necessary to judge the toxicity of environmental pollutants or for understand different processes in technology or science (e.g., corrosion, diffusion, surface treatment, color of glass).1 We wanted to clarify the mechanism of analyte fixation in GFAAS by the palladium modifier. In the presence of palladium salts, normally, volatile elements such as arsenic and lead are retained in the graphite tube during the pyrolysis step with typical temperatures between 400 and 1000 °C. This phenomenon was introduced to routine GFAAS analysis by Welz et al.2 It offered, on one hand, the possibility of GFAAS analysis of volatile elements. On the other hand, it triggered a lot of research activities devoted to understanding the mechanism of analyte retention of the palladium modifier.3-34 (1) Cornelis, R., Crews, H., Caruso, J., Heumann, H., Eds. Handbook of Elemental Speciation: Techniques and Methodology; Wiley: New York, 2003. (2) Welz, B.; Schlemmer, G.; Mudakavi, J. R. J. Anal. At. Spectrom. 1992, 7, 1257-1271. (3) Ortner, H. M.; Bulska, E.; Rohr, U.; Schlemmer, G.; Weinbruch, S.; Welz, B. Spectrochim. Acta, Part B 2002, 57, 1835-1853. (4) Slavin, W.; Carnrick, G. R.; Manning, D. C. Anal. Chem. 1982, 54, 621624. (5) Schlemmer, G.; Welz, B. Spectrochim. Acta, Part B 1986, 41, 1157-1165. (6) Tserovsky, E.; Arpadjan, S.; Karadjova, J. Spectrochim. Acta, Part B 1992, 47, 959-970. (7) Weibust, G.; Langmyhr, F. J.; Thomassen, Y. Anal. Chim. Acta 1981, 128, 23-29. (8) Katsura, T.; Kato, F.; Matsumoto, K. Anal. Sci. 1990, 6, 909-910. (9) Voth-Beach, L. M.; Shrader, D. E. J. Anal. At. Spectrom. 1987, 2, 45-50. (10) Rettberg, T. M.; Beach, L. M. J. Anal. At. Spectrom. 1989, 4, 427-431. (11) Welz, B.; Schlemmer, G.; Mudakavi, J. R. Anal. Chem. 1988, 60, 25672572. (12) Heinrich, H.-J.; Emrich, G.; Schierhorn, E. Selected Papers of the 26th CSI, Tsalev, D. L., Ed., Sofia, July 2-7, 1989; Vol. 7, p 239. (13) Dabeka, R. W. Anal. Chem. 1992, 64, 2419-2424. (14) Eloi, C. C.; Robertson, J. D.; Majidi, V. Anal. Chem. 1995, 67, 335-340. (15) Docekalova, H.; Docekol, B.; Kamarek, J.; Novotny, J. J. Anal. At. Spectrom. 1991, 6, 661-668. (16) Johannessen, J. K.; Gammelgaard, B.; Jons, O.; Hansen, S. H. J. Anal. At. Spectrom. 1993, 8, 999-1004. (17) Krivan, V.; Arpadjan, S. Z. Anal. Chem. 1989, 335, 743-747. (18) Koreckova, J.; Frech, W.; Lundberg, E.; Persson, J.; Cedergen, A. Anal. Chim. Acta 1981, 130, 267-280. (19) Quiao, H.; Jackson, K. W. Spectrochim. Acta, Part B 1991, 46, 1841-1859. (20) Quiao, H.; Mahmood, T. M.; Jackson, K. W. Electrothermal Atomic Absorption Spectrometry, FACS Meeting, September 20-25, 1992, Philadelphia, Lecture No. 231. (21) Majidi, V.; Robertson, J. D. Spectrochim. Acta, Part B 1991, 46, 17231733. (22) Weikang, X. Spectrochim. Acta, Part B 1992, 47, 545-551. (23) Boszai, G.; Welz, B.; Sperling, M. In CAS 5 Colloquium Atomspektrometrische Spurenanalytik; Welz, B., Ed.; Bodenseewerk Perkin-Elmer GmbH, Ueberlingen, 1989; pp 235-245. 10.1021/ac034527g CCC: $25.00

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One goal of our investigations was to obtain more information about the binding state of analytes and modifier constituents during the important steps of GFAAS, namely, the drying step and the pyrolysis step. Previous investigations by EPMA and SIMS showed that palladium is distributed in the upper 10 µm of the graphite platform inhomogeneously in form of clusters inside the pyrolytic coating of the graphite tube.35,36 The respective palladium concentration lies in a range of 0.5% (m/m) down to the ppm level as compared to an absolute mass of Pd introduced into the graphite tube of ∼10 µg. Hence, the choice of a sufficiently sensitive method for the determination of the binding state was important. Other commonly used instrumental methods such as XRD, AES, EXAFS, or ESCA are not sensitive enough. Some of these methods (AES, ESCA) also exhibit an excellent depth resolution of the order of several nanometers. This is, however, a disadvantage here since the investigated phenomena take place in the upper 10 µm of a graphite platform or tube as described above. Since Pd like many other species is well known to form intercalation compounds with graphite, special attention was given to this phenomenon.37 The shift of X-ray lines was used by other scientists for identification of the valence state (e.g., of C, Al, S, and of the 3d transition metals).38-43 In general, the shift of X-ray lines is small (∼1-3 eV) as compared to the peak width (∼40 eV) and it decreases with rising atomic number. The element with the highest atomic number investigated was zinc.43 Hence, a new method of evaluation had to be developed for the determination of the expected very small shifts of palladium. This method is based on the fact that a peak shift leads to pronounced change of intensity in the flanks of the peak. This method was first applied by Hoefer et al. to the FeLR/FeLβ (FeL3-M4,5/FeL2,3-M4,5) line shift (24) Styris, D. L.; Prell, L. J.; Redfield, D. A.; Holcombe, J. A.; Bars, D. A.; Majidi, V. Anal. Chem. 1991, 63, 508-517. (25) Styris, D. L.; Redfield, D. A. Spectrochim. Acta Rev. 1993, 15, 71-123. (26) Byrne, J. P.; Lamoureux, M. M.; Chakrabarti, C. L.; Ly, T., Gre´goire, D. C. J. Anal. At. Spectrom. 1993, 8, 599-609. (27) Teague-Nishimura, J. E.; Tominaga, T.; Katsura, T.; Matsumoto, K. Anal. Chem. 1987, 59, 1647-1651. (28) Wendl, W.; Mu ¨ ller-Vogt, G. In CAS 4 Colloqium Atomspektrometrische Spurenanalytik; Welz, B., Ed.; Bodenseewerk Perkin-Elmer GmbH, Ueberlingen, 1987; pp 153-166. (29) Gong, B.; Li, H.; Ochiai, T.; Zheng, L. T.; Matsumoto, K. Anal. Sci. 1993, 9, 723-726. (30) Yang, P.-y.; Ni, Z.-m.; Zhuang, Z.-x.; Xu, F.-c.; Jiang, A.-b. J. Anal. At. Spectrom. 1992, 7, 515-519. (31) Shan, X.-Q.; Wang, D.-X. Anal. Chim. Acta 1985, 173, 315-319. (32) Mahmood, T. M.; Quiao, H.; Jackson, K. W. J. Anal. At. Spectrom. 1995, 10, 43-47. (33) Quiao, H.; Jackson, K. W. Spectrochim. Acta B 1992, 47, 1267-1276. (34) Sturgeon, R. E.; Chakrabarti, C. L. Anal. Chem. 1976, 48, 1792-1807. (35) Rohr, U. Ph.D. Thesis, Technical University of Darmstadt, 1996. (36) Bulska, E.; Thybusch, B.; Ortner, H. M. Spectrochim. Acta, Part B 2001, 56, 363-373. (37) Bulska, E.; Thybusch, B.; Ortner, H. M. Spectrochim. Acta, Part B 2000, 55, 491-499. (38) Goldstein, J. I.; Newbury, D. E.; Echlin, P.; Joy, D. C.; Fiori, C.; Lifshin, E. Scanning Electron Microscopy and X-Ray Microanalysis; Plenum Press: New York, 1981; pp 441-442. (39) Potts, P. J. A Handbook of Silicate Rock Analysis, Blackie and Son Ltd., Glasgow, 1992, 233, 356-357. (40) Sachs, L. Angewandte Statistik, 7th ed.; Springer-Verlag: Berlin, 1992; p 358. (41) Willard, H. H.; Merrit, L. L.; Dean, J. A.; Settle, F. A. Instrumental Methods of Analysis, 7th ed.; Wadsworth Inc.: Belmont, CA 94002, 1988; pp 345346. (42) Fischer, D. W. J. Appl. Phys. 1965, 36 (6), 2048-2053. (43) Hoefer, H. E.; Brey, G. P.; Schulz-Dobrick, B.; Oberhaensli, R. Eur. J. Mineral. 1994, 6, 407-418.

Figure 1. Conventional methods for the determination of the peak shift of X-ray fluorescence lines.

problem for the determination of Fe II and Fe III.43 The commonly used methods applied to an unsymmetrical peak are depicted in Figure 1. Due to the relatively large dispersion of the X-ray crystals, the peak appears broad and the determination of the peak maximum becomes uncertain. The tangent method (cross point of the two tangents at the peak flanks) and the center of gravity method (peak area is divided in two equal sections) also show uncertainties mainly due to a peak shape dependency. Hence, these methods are insufficient for the precise determination of the peak maximum and for the small peak shifts of palladium. EXPERIMENTAL SECTION Instrumentation. (1) EPMA. All measurements were performed with a Cameca SX50 electron probe microanalyzer (Cameca, Paris, France). The instrument was equipped with an energydispersive Si(Li) detector (Princeton Gamma-Tech, Princeton, NJ) and with four WDX spectrometers, three vertically and one horizontally mounted (for the evaluation of rough surfaces).44 Various software packages from Cameca and PGT were used, for example, the IMIX software for standardless EDXRF analysis.45 It calculates relative pure element intensities, using peak ratios rather than absolute integrals. It automatically subtracts the background, deconvolutes overlays, calculates relative K ratios, and normalizes them, computes the interelement correction factors (ZAF) and then calculates the concentrations. For more sensitive and accurate quantitative EDXRF measurements, the Cameca software program QuantiView46 with external reference standards and the PAP correction procedure was used.47 The latter is similar to the ZAF algorithm but applies a more realistic model for the calculation of the depth distribution of primary electrons. (2) GFAAS. The preparation of the graphite tubes was performed with a Perkin-Elmer 2380 spectrometer equipped with an HGA 500 and an AS40 (Perkin-Elmer, Rodgau-Juegesheim, Germany). (44) Camebax SX50, company brochure of Cameca, Paris, France, 1988. (45) IMIX, Integrated Microanalyzer for Imaging and X-ray, Software Manual of Princeton Gamma-Tech, Release 6. (46) Program QuantiView, Reference guide Version 3.0, Cameca, Paris, France, 1993. (47) Pouchou, J. L.; Pichoir, F. In Electron Probe Quantitation; Heinrich, K. F. J., Newbury, D. E., Eds.; Plenum Press: New York 1991; pp 31-75.

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(3) XRD. The type of the prepared graphite intercalation compounds was characterized with an X-ray diffractometer D500 (Siemens, Berlin, Germany). Palladium Reference Compounds. Reference compounds were necessary for identification of the valence state of the unknown Pd compound. The following reference compounds were used and their preparation was carried out in the following way: (1) Pd Metal. A sheet of Pd metal (99.99% (m/m); Aldrich, Steinheim, Germany) was used as standard reference material. (2) PdO. Palladium oxide was prepared by evaporating a Pd(NO3)2 solution (Merck, Darmstadt, Germany) and drying the residue at 200 °C.48,49 Analysis of the resulting palladium oxide powder by EPMA with the program QuantiView46 yielded the following results: c(Pd) ) 85.0% (m/m) and oxygen 15% (m/m) (theoretical values: 86.9% (m/m) Pd and 13.1% (m/m) O). Other elements were not detectable. There was no sample charging observable under the electron bombardment of the EPMA measurements. (3) Pd/Cu Alloy. Appropriate amounts of Cu and Pd powder (each 99.99% (m/m); Merck) were molten in a quartz vial under argon. The metal regulus was embedded in a conductive resin and polished. The composition was controlled by standardless EDXRF analysis in the EPMA:46 15.33% (m/m) Pd; 84.67% (m/ m) Cu. (4) PdCl2 Graphite Intercalation Compound. Synthesis of the graphite intercalation compound was performed according to Croft’s procedure50 and the general guidelines of Ruedorff:51 A total of 380 mg of PdCl2 (anhydrous; Merck) and 103 mg of graphite powder (Teroson, Heidelberg, Germany; washed with HCl/HF solution and dried) or 356 mg of PdCl2 and 108 mg of ground pyrographite were mixed and kept under chlorine gas for 15 h at 350 °C. The excess of PdCl2 was removed by washing the mixture twice with 40 mL of 0.25 M hydrochloric acid at 60 °C. The residue was washed again with 20 mL of water and dried at 120 °C. The products of this synthesis were characterized by EPMA and XRD because of the potential problems involved in the preparation of the GIC (e.g., decomposition during washing). The results of the quantitative analysis by EPMA are shown in Table 1. According to Croft,50 up to 58% (m/m) PdCl2 can be intercalated in graphite (stage 2 intercalation compound; layer sequence C/C/metal; C/C/metal; etc.). The result of the quantitative analysis (∼38% (m/m) PdCl2) can be interpreted as a GIC with lower content of PdCl2 than a stage 2 GIC. The nonstoichiometry regarding the chlorine was also noticed by other authors.51 The prepared PdCl2 pyrographite intercalation compound exhibits the lowest content of intercalated PdCl2 (∼2% (m/m)). The X-ray diffraction diagram shows two peaks at 3.33 and 19.54 Å. The former can be interpreted as the spaces of the (001) planes in graphite (described value in the literature 3.35 Å).52 The latter is interpreted as one PdCl2 layer in GIC plus three graphite layers leading to an intercalation compound (10 Å according to ref 49). (48) Gmelin: Handbuch der Anorganischen Chemie: Palladium, 8th ed.; Verlag Chemie: Berlin, 1942; pp 260-270, 335-336. (49) Gmelin: Handbook of Inorganic Chemistry, Pd, Supplement Volume B2 Compounds, 8th ed.; Springer-Verlag: Berlin, 1989; Vol. 6, p 78. (50) Croft, R. C. Aust. J. Chem. 1956, 9, 184-193. (51) Ruedorff, W. Adv. Inorg. Chem. Radiochem. 1959, 1, 224-266. (52) Weast, R. C., Ed. Handbook of Chemistry and Physics, 51st ed.; The Chemical Rubber Co.: Cleveland, OH, 1970-1971; pp E147-E148.

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Table 1. Quantitative Analysis Results of the PdCl2-Graphite Intercalation Compound by EPMAa PdCl2/graphite average (n ) 10) std dev molar ratio

PdCl2/pyrographite

Pd

Cl

PdCl2

Pd

Cl

PdCl2

22.71 2.52 1.00

17.97 1.92 2.38

38

1.04 0.59 1.00

0.77 0.46 2.22

1.7

a Analytical conditions: 15 kV; 30 nA; horizontal spectrometer; PET; Cl KR; Pd LR; acquisition time (peak) 60 s; acquisition time (background) 60 s for Pd and Cl; scanned area 40 × 40 µm; reference standards, palladium metal and potassium chloride; evaluation, QuantiView software with PAP correction procedure;46 the concentration of carbon was calculated as the difference to 100%; the influence of rough surface was neglected due to the use of the horizontally mounted spectrometer. Data are % (m/m).

Hence, the prepared PdCl2-GIC is a stage 3 intercalation compound with a layer sequence C/C/C/PdCl2, C/C/C/PdCl2, etc. Preparation of Samples with Unknown Valence State. For the investigation of the mechanism of the Pd modifier in GFAAS, respective experiments were conducted as follows: Graphite tubes with a mounted pyrographite platform were used. Ten microliters of modifier solution (c(Pd) ) 1500 mg/L; c(HNO3) ) 0.1 mol/L, or (c(Pd) ) 1500 mg/L; c(Mg(NO3)2) ) 1000 mg/L; c(HNO3) ) 0.1 mol/L) and 20 µL of sample solution (c ) 40 mg of As(V), Se(IV), and Te(IV)/L in 0.1 M HNO3) were injected by the autosampler onto the platform and the furnace program was started. The furnace program was interrupted after the drying step (120 °C) or after the pyrolysis step (1300 °C). The platforms were then taken out of the tube and fixed on a holder for EPMA measurements. Preliminary Tests. (1) Due to the expected small peak shifts, the reproducibility of angle adjustment of the used horizontal spectrometer of the electron microprobe was checked. Five spectra of the Pd LR (L3-M4,5) line were acquired and the peak maximums were determined by the tangent method shown in Figure 1. The reproducibility obtained for the Pd LR (L3-M4,5) line (49 903 × 10-5 ( 2 × 10-5 sin θ; n ) 5) was found to be acceptable and much better than that of other spectrometers.39 The angle adjustment, that is, the crystal rocking on the Rowland circle, is (in order to overcome mechanical clearance) controlled by a bar code-photocell system that provides the high reproducibility. This is a special feature of the Cameca SX 50 instrument without which the here-described experiments would not have been feasible. Further investigations have shown that the method of finding the peak position is also contributing to the uncertainty. Peak maximum method and center of gravity method are less accurate than the flank intensity method due to a rather flat-topped peak and uncertainty of count rate at the outer peak wings, respectively. The reproducibility of angle adjustment performed with the flank intensity method for the Pd Lβ2/15 (L3-N4,5) line results in 44 680 × 10-5 ( 0.4 × 10-5 sin θ; n ) 6. This equals ∼0.03 eV. (2) No shift was found for the Lγ1 (L2-N5) line (line positions of PdO and Pd metal were compared). (3) For the Pd and PdO, the line shifts of the Lβ2/15 (L3-N4,5) and the Lβ7 (L3-O1) line, were ∼4 × 10-5 sin θ. The observed shifts exhibited insufficient significance (standard deviation, (36) × 10-5 sin θ), because they were determined by the tangent

Figure 2. Orbital energy level diagram and X-ray lines for a Pd atom. Compiled from refs. 39 and 48). Transitions to the M shell are not completely presented. Inclined arrows indicate bonding-sensitive transitions. The labeling of the transitions was carried out according to IUPAC with energies in keV: (a) maximum occupation of the energy level; (b) designation of the energy level: resulting from the combination of the electron spin and of the orbital momentum mentioned in column c.

method. Hence, another method had to be found for a more precise determination of such small peak shifts. (4) No peak shifts were observed for the Lβ3 (L1-M3) and Lβ4 (L1-M2) lines. This fact confirms the considerations from the orbital energy level diagram depicted in Figure 2 and discussed below. (5) The intensity ratio of the Pd LR (L3-M4,5) line to binding sensitive lines is LR:Lβ2/15:Lβ7:Lγ1 (L3-M4,5):(L3-N4,5):(L3-O1):(L2N5) ) 1:0.09:0.024:0.045. Consequently, the Pd Lβ2/15 (L3-N4,5) was chosen, because its sensitivity to changes in the binding state is 4 times higher than that of the Lβ7 (L3-O1) line. Measurement of Peak Shift and Evaluation. On each sample and the reference material, three to five sites were measured by EPMA under the following conditions: 15 kV; 100150 nA, horizontal spectrometer, scanned area 6 × 4 µm

(magnification 20000×); PET crystal, acquisition time 300-999 s for each position on the peak. Wavelength scanning was performed in the step scan mode with a minimum step size of 1 × 10-5 sin θ - units. The target peak positions of the Pd Lβ2/15 (L3N4,5) line were for IL 44 590 × 10-5 sin θ, for IR 44 724 × 10-5 sin θ, for BGR 44 000 × 10-5 sin θ, and for BGL 45 000 × 10-5 sin θ. The measurements were performed automatically in the sequence IL, BGL, IR, and BGR with the instrument program QuantiView.46 Because four quantities (IL, IR, BGL′, BGR′) are necessary to calculate the background-corrected ratio of the flank intensities, a rough calculation for the propagation of error was made. To achieve precise results with a relative error of less than 1%, the ratio of background to flank intensity measurements must be g2. A minimum of 5000 counts must be acquired for each quantity Analytical Chemistry, Vol. 75, No. 23, December 1, 2003

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measured. The results for each site of the material were averaged and the difference was calculated accordingly as described under principles. Statistical significance of the measured δ values was checked by application of the t-test according to Sachs.40,42 Calibration of the X-ray Spectrometer. Due to extremely small shifts of the Pd Lβ2/15 (L3-N4,5) line, an accurate calibration of the sin θ scale is important. For this purpose, a two-step spectrometer calibration was applied. First the routine calibration of the spectrometer with the PET crystal on the Fe KR line (KL2,3) (standard, andradite) was performed. Then the second step, the fine calibration, was performed with palladium metal as standard. For this purpose, the initially assumed line positions of the Pd-Lβ2/15 (L3-N4,5) line (IL 44 590 × 10-5 sin θ; IR 44 724 × 10-5 sin θ; BGR 44 000 × 10-5 sin θ; BGL 45 000 × 10-5) were incremented until a flank intensity ratio of 1.000 ( e0.05 was reached. By these measurements it is assured that the Pd Lβ2/15 (L3-N4,5) line is always centered between the positions of the acquisition. All line shifts were then determined relative to the exactly determined flank intensity ratio of 1.000 ( e0.05 from above. These data indicate that the micromechanic system of sinθ adjustment of the SX50 is one of the most exactly working among all EPMA instrumentation available. Decomposition Phenomena during Electron Beam Excitation. The determination of the ratio of the flank intensities of PdCl2 was not possible because the substance decomposed under the electron bombardment. The PdCl2 GIC was checked for decomposition, too. However, under conditions of the measurement, no decomposition occurred within 2400 s (Cl KR (K-L2,3) and Pd Lβ2/15 (L3-N4,5) intensities were constant). All other substrates showed no decomposition under the conditions used for electron beam excitation. Additional Chemical Experiments. PdO was prepared by evaporating Pd(NO3)2 solution and drying the residue at 120 °C. A solubility test showed that a few milligrams of this PdO are dissolved completely in 5 mL of 6 M hydrochloric acid at 60 °C within 3 min. With the following experiment the elution of a few micrograms of Pd from the doped platform was tested. Ten microlites of Pd/ Mg and Pd modifier solution, respectively, plus 20 µL of 0.1 M HNO3 were injected onto a platform mounted in the graphite tube. The temperature program of the GFAAS was started and stopped after the drying step. The platform was taken out of the graphite tube and extracted in a test tube with 5 mL of 6 M hydrochloric acid for 31 h at 60 °C. Afterward, the concentrations of palladium and magnesium in the extract were determined (Pd via GFAAS and Mg via flame-AAS). For the blank determination, a platform spiked with 20 µL of 0.1 M HNO3 was treated in the same way as described above. Three replicates were performed for each experimental setting. The results are shown in Table 2. RESULTS AND DISCUSSION Choice of Suitable X-ray Line. The choice of the suitable X-ray line results from the orbital energy level diagram shown in Figure 2. The electron configuration of the 4d and 5s orbitals is altered by a change of the valence state of palladium. Hence, only those X-ray lines are influenced that result from transitions of the (O I), (N V), and (N IV) energy levels. These are the Kβ4 (KN4,5), Lβ2/15 (L3-N4,5), Lβ7 (L3-O1), Lγ1 (L2-N5), Mγ (M3-N5), and further M lines. The Kβ4 (K-N4,5) line and the M lines are not 6580

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Table 2. Results of the Elution of Pd and Mg from the Pyrographite Platforma

modifier

eluted mass of Pd (µg)

recovery Pd (%)

Pd/Mg Pd

13.48 ( 0.45 12.93 ( 0.15

84.2 ( 2.8 80.8 ( 1.0

eluted mass of Mg(NO3)2 (µg)

recovery Mg(NO3)2 (%)

10.67 ( 1.37

106.7 ( 13

a Analytical conditions: Pd, λ ) 247.6 nm; slit 0.7 nm; GFAAS, pyrolysis temperature 600 °C; atomization temperature 2500 °C; Mg, λ ) 285.2 nm; slit 0.7 nm; flame-AAS, C2H2/air, 1-2/8 l/min. Amounts injected onto the platform: 15 µg of Pd (as nitrate) and 10 µg of Mg(NO3)2.

Table 3. Conversion Table between the Conventional Siegbahn Notation and the New IUPAC Notation53 for the X-ray Fluorescence Diagram Lines of Figure 2 and Supplemented According to the Application Siegbahn

IUPAC

Siegbahn

IUPAC

Siegbahn

IUPAC

KR2 KR1 Kβ3 Kβ1 Kβ5 Kβ2 Lι LR2 LR1

K-L2 K-L3 K-M2 K-M3 K-M4,5 K-N2,3 L3-M1 L3-M4 L3-M5

Lβ6 Lβ2/15 Lβ7 Lη Lβ1 Lγ5 Lγ1 Lβ4 Lβ3

L3-N1 L3-N 4,5 L3-O1 L2-M1 L2-M4 L2-N1 L2-N5 L1-M2 L1-M3

Lβ9 Lγ2/3 Lβ10 MII-MIV MII-NI MII -NIV MI-NII,III Mξ Mγ

L1-M5 L1-N 2,3 L1-M4 M2-M4 M2-N1 M2-N4 M1-N2,3 M 4,5-N2,3 M3-N5

suitable due to low fluorescence intensities. The low intensity is a result of the low excitation efficiency by the electron beam of the EPMA and a strong absorbance of the generated fluorescence radiation of low energy (M lines!) in the sample. Hence, the L lines mentioned above were preferred for this investigation. It is realized by the authors that the International Union of Pure and Applied Chemistry (IUPAC) has suggested an alternative nomenclature system for X-ray lines based on edge designation.53 This system is referred to here as the IUPAC notation. Table 3 gives an overview of the conventional X-ray line notation by Siegbahn and the new IUPAC notation for the lines depicted in Figure 2. Expected Shift and Choice of Measurement Conditions. The expected shift of the X-ray lines can roughly be estimated from the energy difference of the standard compound and the unknown compound divided by the number of bonding electron pairs. For example, the expected shift of the valence state sensitive X-ray line is in the case Pd/PdO (∆HB0(PdO)/2) ≈ 0.44 eV. With this energy difference, it is possible to estimate the expected line shift by the modified and subtracted Bragg equations:

∆sin θ ) sin θ2 - sin θ1 )

(

)

nhc 1 1 2d E2 E1

(1)

This equation shows that it is better to use a higher diffraction order and a crystal with a small lattice spacing (if there is any choice) in order to observe a high difference of the Bragg angle. The valence state sensitive Pd L lines can only be measured with a PET crystal (2d ) 8.742 × 10-10 m). With the expected energy (53) Jenkins, R.; Maune, R.; Robin, J. H.; Senemand, C. Pure Appl. Chem. 1991, 63, 736-746.

Figure 3. Principle of the determination of a peak shift from intensity changes in the peak flanks. Solid line: peak of a standard reference compound. Broken line: peak shifted to the right of an unknown compound. Figure 5. Measured changes of the ratio of the flank intensities 5000-250 000 counts were acquired for each position on the peak. The horizontal bars depict (1 s standard deviation.

of the peak, respectively; BGL′ and BGR′ are the interpolated background intensities of the left and right peak flanks. The peak shift is measured relative to a reference compound. For palladium measurements, the palladium metal was used as reference. With the definition of δ for the change of the ratio of the flank intensities Figure 4. Background correction of the intensities of the peak flanks.

difference of the X-ray lines of 0.44 eV, the expected shift of the X-ray line amounts to ∼6 × 10-5 sin θ in the case of Pd/PdO (fwhm 180 × 10-5 sin θ). Principle of the Determination of a Peak Shift from the Change of the Intensity Ratio of the Peak Flanks. The flank intensity ratio of a symmetrical peak is measured in the same distance to the left and to the right from the peak maximum: IL/ IR ) 1. If there is a peak shift to the right, the flank intensity ratio is altered to IL′/IR′ < 1, cf. Figure 3. The measured flank intensities must be corrected for increasing or decreasing background across the measured width of the peak as shown in Figure 4. The background intensities in the peak flanks (BGL′, BGR′) cannot be measured directly. Hence, they must be calculated by linear interpolation from the background intensities (BGL, BGR), which are measured outside of the peak. The background intensity (Bremsstrahlung) is produced by a physical process different from the X-ray fluorescence radiation. It is not known whether the amount of Bremsstrahlung is dependent on the valence state. To avoid the measurement of the superposition of two physical processes it is recommended to subtract the background intensity. The background corrected ratio of the flank intensities R is calculated as follows:

R ) (TIL - BGL′)/(TIR - BGR′)

(2)

TIL and TIR are the total intensities of the left and the right flanks

δ ) RReference - RSample we obtain δ > 0 for a shift to the right and δ < 0 for a shift to the left of the peak. According to the definition, a shift to the left is a shift to higher sin θ values. The synergetic influences of the intensity changes in the peak flanks result in an enhancement of the quantity of δ. Hence, the change of the ratio of the flank intensities is a very sensitive measure for a peak shift. Results of Peak Shift Measurements. The results of the measured changes of the ratio of the flank intensities of palladium compounds and the respective graphite platforms are shown in Figure 5 and Table 4. The palladium oxide exhibits a positive line shift. The Pd/Cu alloy and the palladium GIC show negative peak shifts just as the doped graphite platforms. All graphite platforms doped with palladium and magnesium exhibit a change of the ratio of the flank intensities in the negative direction. Palladium present in particles on top of graphite surfaces exhibits less negative changes of the ratio of the flank intensities (δ ) -0.06 to - 0.16) as compared to the palladium intercalated into the graphite platform (δ ) -0.15 to - 0.27). The point of the interruption of an analysis cycle is exerting no significant influence on the shift of the Pd Lβ2/15(L3-N4,5) line (drying step or pyrolysis step). Due to the measurement uncertainties the significance of the differences of the δ values was tested in order to verify the statements, Table 5. The results of the statistical test show in general a high statistical significance for a line shift depending on the valence state of palladium. Almost all measured values of Analytical Chemistry, Vol. 75, No. 23, December 1, 2003

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Table 4. Results of Statistical Testing of the δ Values δ value

standard deviation

no. of sites measured

0 0.125 -0.106 -0.212 -0.300

0.0102 0.0355 0.0211 0.0060 0.0860

5 5 5 5 5

samples investigated and/or particles on platforms

δ value

standard deviation

no. of sites measured

Pd modifier; after drying step; particle Pd modifier; after drying step; platform Pd modifier; after pyrolysis step; platform Pd/Mg modifier; after drying step; platform Pd/Mg modifier; after drying step; particle Pd/Mg modifier; after pyrolysis step; particle Pd/Mg modifier; after pyrolysis step; platform

-0.070 -0.155 -0.158 -0.272 -0.161 -0.063 -0.244

0.0178 0.0280 0.0673 0.0695 0.0835 0.0150 0.0841

4 5 4 5 5 5 3

reference compounds Pd PdO Pd/Cu alloy PdCl2/graphite PdCl2/pyrographite

Table 5. Results of the Statistical Tests hypothesis tested difference from reference

shift on platform higher than shift on particle drying step vs pyrolysis step

tabulated t value ˆt(5,5;0.05) ) 2.78 ˆt(5,5;0.05) ) 2.78 ˆt(5,5;0.05) ) 2.78 ˆt(5,5;0.05) ) 2.78 ˆt(5,5;0.05) ) 2.57 ˆt(5,5;0.05) ) 2.78 ˆt(3,4;0.05) ) 3.18 ˆt(5,5;0.05) ) 2.78 ˆt(5,5;0.05) ) 2.78 ˆt(5,5;0.05) ) 2.78 ˆt(5,3;0.05) ) 2.30 ˆt(16,14;0.05) ) 2.05 ˆt(4,4;0.05) ) 2.45 ˆt(5,5;0.05) ) 2.31 ˆt(5,3;0.05) ) 2.45

calcd t value 7.19 6.53 8.40 6.82 7.96 6.30 5.44 8.75 4.31 1.51 6.46 3.40 0.93 2.07 0.49

the inspected sites on the platforms and reference compounds are different from the reference compound (except for one, the probability of difference was only 80%). Checking for Variations of Peak Shape. There is also the possibility that the measured change of the intensity ratio of the peak flanks is generated by a change of the peak shape and not by a peak shift. Both phenomena could occur due to a change of the valence state. A possible change in peak shape was checked in the following way: the spectra of the Pd Lβ2/15 (L3-N4,5) lines of Pd, PdO, Pd/Cu alloy, PdCl2, and the PdCl2 GIC were acquired. The spectra were smoothed by use of a three-point plus a fivepoint moving average filter, normalized to the same peak height and background corrected. A change of the peak shape was calculated relative to the spectrum of Pd metal. Applying a spread sheet program, the spectra of PdO, Pd/Cu alloy, PdCl2, and the PdCl2 GIC were shifted to coincide with the spectrum of the Pd metal. The remaining differences of the intensity in the peak flanks were calculated as change of intensity ratio of peak flanks as described above. These changes of the intensity ratio of the peak flanks due to changes of the peak shape are as follows: for PdO 4.5, for Pd/Cu alloy 33, for PdCl2 33, for PdCl2 GIC 11, and for the Pd-doped graphite platforms 10% of the total change of the intensity ratio of the peak flanks (shift + shape alteration). Hence, the measured variation of the change in the intensity ratio of the peak flanks is mainly due to the peak shift. The relation of the change of the intensity ratio of the peak flanks and the peak shift can be achieved by an imaginary shift of the Pd-Lβ2/15 (L3-N4,5) 6582

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difference

tested data

yes yes yes yes yes yes yes yes yes no yes yes no no no

Pd vs PdO Pd vs Pd/Cu alloy Pd vs PdCl2/graphite Pd vs PdCl2/pyrographite Pd vs Pd modifier; after drying step; particle Pd vs Pd modifier; after drying step; platform Pd vs Pd modifier; after pyrolysis step; platform Pd vs Pd/Mg modifier; after drying step; platform Pd vs Pd/Mg modifier; after drying step; particle Pd vs Pd/Mg modifier; after pyrolysis step; particle Pd vs Pd/Mg modifier; after pyrolysis step; platform all platform data vs all particle data Pd modifier platform drying step vs pyrolysis step Pd/Mg modifier particle drying step vs pyrolysis step Pd/Mg modifier platform drying step vs pyrolysis step

peak as demonstrated in Figure 6a. Figure 6b shows the results of the calculation of the respective δ values. From this imaginary experiment it follows that a change of the intensity ratio of the peak flanks of 0.1 corresponds to a peak shift of 4 × 10-5 sin θ unit (cf. Figure 6b). A conversion of all measured δ values in sin θ peak shifts was not performed because the measured δ values are not only peak shifts. Bonding State of Pd in the Doped Graphite Platforms. The negative peak shift of the Pd-doped graphite platforms was surprising. Hence, other Pd compounds such as the Pd/Cu alloy and the Pd GIC were investigated. The way of synthesis and the bonding state of these reference compounds is well known.54-56 It is supposed that the kind of bonding of intercalated Pd in the graphite platforms is similar to that in the Pd/Cu alloy and Pd GIC. For a better understanding, the bonding state of the reference compounds is briefly described. A still more detailed discussion is found elsewhere.3 PdO. This is a compound with polar covalent bonds. Pd is coordinated quadratically and oxygen tetrahedrally.48 The bonding with (4 × O2-)1/4 leads to dsp2 hybridization and to not completely filled 5p orbitals. (54) Wiberg, N. Holleman-Wiberg, Lehrbuch der Anorganischen Chemie; Walter de Gruyter: Berlin, 1985; p 991. (55) Smith, D. J.; Fischer, R. M.; Freeman, L. A. J. Catal. 1981, 72, 51-65. (56) Gmelin: Handbook of Inorganic Chemistry, Platinum, Supplement Volume A1 Technology, 8th ed.; Springer-Verlag: Berlin, 1986; pp 227-231.

Figure 6. (a) Deriving the relation between change of flank intensity ratios and peak shift: line shift ) sin θIL1 - sin θIL2) sin θIL2 - sin θIL3) sin θIR1 - sin θIR2) sin θIR2 - sin θIR3. δ1 ) (IL1/IR1) - (IL1/IR1) ) 0. δ2 ) (IL1/IR1) - (IL2/IR2). δ3 ) (IL1/IR1) - (IL3/IR3). (b) Results of the derivation of (a): relation of δ values with peak shifts.

Pd. The electron configuration of Pd in the metallic state is [Kr]4d9 5s1. This has been confirmed by the measured paramagnetism.54 Pd/Cu Alloy. Due to the introduction of palladium into copper, the dissociation of Pd (Pd h Pd+ + e-) is suppressed by the high concentration of the electron gas of copper. This is again confirmed by measurements of the paramagnetism.49 Hence, the electron configuration of Pd dissolved in Cu is [Kr] 4d10 5s0. The PdCl2 Graphite Intercalation Compound and Other Graphite Intercalation Compounds. In the case of the PdCl2 GIC, it is assumed that a donor-acceptor bonding exists between Pd and graphite. The occupied π orbitals of graphite overlap with suitable unoccupied orbitals of Pd and form bondings of the σ-, π-, and δ-type. For the back-bonding, the occupied d orbitals of Pd overlap with the antibonding pπ* orbitals of graphite.51,56,57 The back-bonding causes a partial decrease of electron density of the metal atom. The interaction between the intercalated metal atoms and the carbon atoms of the graphite lattice was found not only for intercalated metal compounds but also for intercalated metals.58-60 This interaction is described by Shuvaev et al. in the following (57) Elschenbroich, Ch.; Salzer, A. Organometallchemie, 1st ed.; TeubnerVerlag: Stuttgart, 1988; pp 366-438.

way: “The bonding between Fe and graphite is like in ferrocene. Additionally, there are intermetallic bondings between the atoms inside the cluster.” A qualitative comparison of the reference compounds shows that in the series of PdO, Pd, Pd/Cu alloy, and PdCl2 GIC the electron density of the Pd atom is increasing. This is indicated by an increasing shift to the left of the Pd Lβ2/15 (L3-N4,5) line. This shift to the left of the Pd Lβ2/15 (L3-N4,5) line of the palladium-doped graphite platforms and the PdCl2 GIC reference compounds is not totally identical with regard to the Pd Lβ2/15 (L3-N4,5)-line shift: (1) because the PdCl2 GIC and the Pd modifier GIC are not completely identical compounds and (2) since there is besides the Pd bonded to graphite, Pd inside the clusters that is not bound to graphite. Due to the excitation volume of several cubic micrometers, the average Pd Lβ2/15 (L3-N4,5) line position was measured with a high RSD. This might be due to an average of the various binding states concerned: the Pd bonded to graphite, to oxygen, and to Pd in the metal state. Conclusions for the Description of the Valence State of Pd. The presence of the Pd modifier in the graphite platform can be described as follows: (1) Between the layers of the graphite lattice, PdO and Pd exist as agglomerated clusters of several micrometers in diameter which exhibit a height of 10-20 Å (which is the layer distance of the graphite lattice in Pd-GIC).49 (2) Chemical bonds exist between the π electrons of the graphite layers and the coordinative, unsaturated Pd atoms at the outer boundaries of the clusters. (3) Inside the clusters, metallic bonds exist between the palladium atoms and further polarized covalent bonds between the Pd and oxygen atoms. (4) In this case, palladium has 8 or 10 valence electrons of its own in the presence of PdO or PdO clusters, respectively, plus 2, 4, or 6 electrons from bonds to the neighboring atoms in the cluster. Consequently, the missing electrons required to reach the noble gas electron configuration are contributed by the π-electron system of the graphite. Chemical Experiments. The recovery of Pd injected onto the platform after hydrochloric acid elution is ∼80% (cf. Table 2). These results are independent of the presence of magnesium. Hence, the missing portion of Pd is bound to the graphite in a state that is not soluble in hydrochloric acid. The applied elution time is sufficient to dissolve palladium oxide on and in the graphite platform according to preliminary experiments. Even if Pd is dissolved in a depth of 10 µm and a diffusion transport occurs, the elution time is sufficient. The time necessary for pure diffusion transport of Pd from a depth of 10 µm into the solution can be estimated by the “average Einstein shift”:

t ) x2/2D

(3)

Depending on the applied diffusion coefficients, the time for the (58) Shuvaev, A. T.; Kondakov, V. A.; Uvarov, V. N.; Khal’maier, K.; Lapkina, N. D.; Postnikow, V. A.; Novikov, Yu. N.; Vol’pin, M. E. Zh. Strukt. Khim. 1979, 20 (4), 736-738. (59) Shuvaev, A. T.; Khel’mer, B. Yu.; Lyubeznova, T. A.; Kraizman, V. L.; Mirmil’shtein, A. S.; Kvacheva, L. D.; Novikov, Yu. N.; Vol’pin, M. E. Izv. Akad. Nauk SSSR, Ser. Fiz. 1985, 49 (8), 1471-1475. (60) Shuvaev, A. T.; Helmer, B. Yu.; Lyubeznova, T. A.; Kraizmann, V. L.; Mirmil’stein, A. S.; Kvacheva, L. D.; Novikov, Yu. N.; Vol’pin, M. E. J. Phys. (Paris) 1989, 50, 1145-1151.

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process ranges between 0.05 and 5000 s. A diffusion coefficient of 10-9 m2 s-1 was assumed for the diffusion in liquids and a D value of 10-14 m2 s-1 for the diffusion in solids. The penetration depth of palladium into the graphite of ∼10 µm is known from ESMA and SIMS experiments.35 In contrast to Pd, the recovery for magnesium in the eluate was nearly 100%. This is a further hint that an interaction of the graphite with the Pd has occurred. For all possible magnesium compounds (MgO, Mg(OH)2, Mg(NO3)2, Mg2O(NO3)2), it can be stated that they are all easily soluble under the applied experimental conditions (warm 6 M hydrochloric acid)).61 The experimental results of the Pd elution from the platform after the drying step with hydrochloric acid support the results of the EPMA investigations. Palladium exists in two states after the drying step: in a state that is soluble in hydrochloric acid and in a state that is insoluble in hydrochloric acid. The hydrochloric acid soluble state is the PdO of the clusters and particles. The hydrochloric acid insoluble state is the Pd bound to the graphite. It is well known from transition metal carbon bondings in sandwich complexes such as Fe(C5H5)2 and Ni(C5H5)2 that these are resistant to the attack of aqueous nonoxidizing acids.62,63 The experiments of the peak shift measurements and the additional elution experiments indicate that the bonding between Pd and graphite is already formed during the drying step and does not change during the pyrolysis step. The small shift to the left of the Pd Lβ2/15 (L3-N4,5) line found for Pd particles on top of the platform (not intercalated) is rather consistent with the left shift of the Pd intercalated into the graphite. However, one must keep in mind that by scanning with the electron beam across a particle there is an essential overlap between the metallic Pd and the intercalated Pd at the edges of the particles. Analyte Fixation by Bonding to Activated Pd Atoms in Analogy to Metal-Organic Compounds. So far the experimental evidence of the intercalation of the Pd modifier has been described. We can unfortunately only speculate about the subsequent analyte retention mechanism because we have no experimental possibility of studying the bonding of subnanogram amounts of analytes with all the instrumental possibilities of todays’ impressive range of methods of analysis on solid-state systems. Although this mechanism of bonding has been elucidated in detail by us earlier, a short repetition seems appropriate for the sake of completeness of the description of this most important phenomenon of analyte fixation up to the atomization step.3 There is an interaction between the π-electron system of the graphite lattice on the surface of a lattice plane with the coordinatively unsaturated Pd atoms on the outer surface of a Pd cluster adjacent to the graphite lattice. The electrons missing to noble gas configuration for these Pd atoms are, therefore, taken over from the π-electron system of the graphite. This causes an elevated electron density for these Pd atoms which are, therefore, activated for an interac(61) Gmelin: Handbuch der Anorganischen Chemie: Magnesium Teil B, Lieferung 4, 8th ed.; Verlag Chemie, Berlin, 1939; pp 82-85. (62) Gmelin: Handbuch der Anorganischen Chemie, Erga ¨ nzungswerk Board 14 Eisen-Organische Verbindungen, Teil A Ferrocen I; Springer-Verlag: Berlin, 1974; p 114. (63) Gmelin: Handbuch der Anorganischen Chemie, Erga ¨ nzungswerk Board 17, Nickel-Organische Verbindungen; Springer-Verlag: Berlin, 1974; pp 204205.

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tion with, for example, As(OH)3, to function as electron donors. A double covalent bond between the Pd atom and the As(OH)3 is thus formed. It should be emphasized that only the Pd atoms on the phase boundary Pd cluster/graphite are activated. This double bond is not destroyed by a temperature rise to pyrolysis temperature and despite the ongoing reduction of the PdO under the conditions of pyrolysis. By the strong bonding of the analyte to the Pd its mobility at pyrolysis temperature is suppressed. It should also be stressed that the activated domain of the Pd modifier is the subsurface region to a depth of ∼10 µm, that is, the volume of the open porosity with adjacent domains between the graphite layers of the pyrographite structure. CONCLUSIONS According to quantitative analysis of the Pd particles on the platforms of the GFAAS graphite tubes with the electron microprobe, the presence of the following compounds was expected:35 PdO after the drying step; Pd after the pyrolysis step. Hence, δ values between 0 and 0.12 should occur. The investigations of the binding state with the described method leads to completely new information about the interaction of the Pd modifier with the analytes. Intercalation of the Pd modifier turned out to be the central phenomenon for the fixation of even rather volatile analytes. This intercalation takes place already during the drying step at 120 °C, and it is conserved during the pyrolysis step. The intercalation was experimentally confirmed by the precision measurement of the peak shift of a proper bonding-sensitive X-ray line, the Pd Lβ2/ 15 (L3-N4,5) line with the electron microprobe. For this purpose, a special procedure of the determination of the change of the intensity ratio of the peak flanks had to be developed and respective peak shift measurements have never been carried out for elements above Zn in the periodic system. This was indeed only possible due to the very high reproducibility of the sine θ measurements with the Cameca SX 50 electron microprobe. A series of reference compounds was also prepared in order to see how the observed peak shifts are related to the bonding situation of the Pd intercalation compound and the prepared compounds. The proposed mechanism of analyte fixation by the intercalated Pd contributes essentially to a better understanding of the role of the most popular Pd modifier in GFAAS. GLOSSARY AA

atomic absorption spectrometry

AES

Auger electron spectrometry

BGL, BGR

background intensities of the left and right peak flank

BGL′, BGR′

interpolated background intensity of the left and right peak flanks (cf. Figure 4)

c

speed of light

d

lattice spacing

D

coefficient of diffusion

∆H0B

standard heat of formation

E1, E2

energy of the X-ray lines of compounds 1 and 2

EDXRF

energy-dispersive X-ray fluorescence (spectrometry)

ESCA

electron spectrometry for chemical analysis

EPMA

electron probe microanalysis

EXAFS

extended X-ray absorption fine structure

t

fwhm

full width at half-maximum

GFAAS

graphite furnace atomic absorption spectrometry

ˆt (N1, N2, T value according to the number of measurements and 0.05) a probability of 95%

GIC

graphite intercalation compound

TIL, TIR

h

Planck constant

total intensity of the left and right flanks of the peak, respectively

IL, IR

intensity of the left and right peak flanks (cf. Figure 3)

x

path length of diffusion

XRD

X-ray diffraction

time

n

diffraction order

N 1, N 2

number of measurements for data set 1 or data set 2

P

statistical probability

ACKNOWLEDGMENT

PET

pentaerythritol crystal

R

background-corrected ratio of the flank intensities

The authors thank Dr. A. Moeller for performing the XRD measurements.

RSD

relative standard deviation

SIMS

secondary ion mass spectrometry

sin θ1, sin θ2

sines of the Bragg angle of the valence state sensitive X-ray lines of compounds 1 and 2

Received for review May 19, 2003. Accepted July 30, 2003. AC034527G

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