LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
Chemical Environment Effects on Kβ/Kr Intensity Ratio: An X-ray Fluorescence Experiment on Periodic Trends Chaney R. Durham, Jeffery M. Chase, Delana A. Nivens, William H. Baird, and Clifford W. Padgett* Department of Chemistry and Physics, Armstrong Atlantic State University, Savannah, Georgia 31419, United States
bS Supporting Information ABSTRACT: X-ray fluorescence (XRF) data from an energydispersive XRF instrument were used to investigate the chlorine KR and Kβ peaks in several group 1 salts. The ratio of the peak intensity is sensitive to the local chemical environment of the chlorine atoms studied in this experiment and it shows a periodic trend for these salts. KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Laboratory Instruction, Hands-On Learning/Manipulatives, Fluorescence Spectroscopy, Atomic Properties/Structure, Qualitative Analysis, Quantum Chemistry
-ray fluorescence (XRF) is a powerful qualitative technique (and is semiquantitative in many applications) able to detect most of the elements on the periodic table. Generally it is used to determine which atoms are present in a sample and not in what chemical environments the elements are found. Although XRF spectroscopy is a widely used analytical technique in industrial quality control, forensics, art, and materials analysis,1,2 it has been slow to enter the undergraduate curriculum. Recently, the advent of better detectors and field-portable instruments opened up a wider range of onsite analysis.3-6 In addition, low-cost X-ray analyzers have allowed this technique to be accessible to undergraduate students.7-11 In this article, we demonstrate a novel physical chemistry experiment using this instrument. XRF is a common surface-analysis technique fully described elsewhere.12 Typically XRF is used to determine the elemental composition of a sample by probing the electronic structure of the atoms in the sample. The KR line results from a 2p electron filling a 1s vacancy and the Kβ line results from a 3p electron filling a 1s vacancy. For atoms whose Kβ line results from valence electrons, chemical environment can influence both the location of the Kβ peak and the transition probability for the Kβ line. Although direct measurement of the peak position can yield information about the chemical environment, with energy-dispersive instruments such shifts in energy are at or below the resolution of the instrument. This makes a direct measurement of the shift impossible on instruments that are likely to be found in an undergraduate laboratory. However, a measurement of the area ratio of Kβ/KR can be used to examine the local chemical environment even with a relatively low-resolution instrument. Several articles have shown that this ratio is affected by the
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Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
oxidation state and more generally the chemical environment around the atom.13,14 The area of these peaks can be measured and their ratios calculated to give the student access to extra information about a sample, beyond the identity of the elements present. This experiment naturally leads into discussion of the origin of these lines and why their intensity ratios would change based on the local chemical environment. This offers an excellent opportunity to introduce ideas from quantum mechanics, specifically electronic selection rules for atoms, and perturbation theory to explain what is observed. Moreover, because of the low resolution of most undergraduate laboratory XRF instrumentation, students will have to deconvolute the chlorine Kβ, KR peaks and the Ar KR peak (an atmospheric contaminate) using a nonlinear solver to fit the overlapping peaks of the spectrum. The complexity and use of various topics makes this experiment an excellent choice for a formal report in an upper-level class such as physical chemistry.
’ EXPERIMENTAL SECTION The following experiment was performed using a μEDX-1200 energy-dispersive X-ray spectrometer from Shimadzu. This instrument uses a focused 50 W X-ray beam generated from a rhodium target, with a liquid nitrogen cooled lithium-drifted silicon array detector. Students were given a sample of each of the following group 1 metal chlorides, LiCl, NaCl, KCl, RbCl, and CsCl, and asked to Published: March 10, 2011 819
dx.doi.org/10.1021/ed100695v | J. Chem. Educ. 2011, 88, 819–821
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Table 1. Student Sample XRF Data for Chlorine Generated from NaCl Line
a
Peak Location/KeV
fwhm/eVa
Intensity/(cps/μA)
Cl KR
2.630
∼100
0.0353
Cl Kβ
2.822
∼100
0.0038
Full width at half-maximum.
determine the Kβ/KR ratio. Samples were ground, dried, and run in a one-step scan program. The scan was run for 30 min of X-ray integration time at intervals of 5 eV from 0 to 20 keV. The data were not smoothed and no background subtraction was performed. Total scan time was 2.5 h. LiCl was run under mineral oil to slow its deliquescing.
’ THEORY The transition probability for radiative (fluorescence) transitions can be used to calculate the ratio of Kβ/KR by using the radiative transition rate W for each line.15
Figure 1. Sample XRF spectrum of NaCl: x denotes the experimental points and the solid lines are Gaussian fits. Note Argon KR peak is from atmospheric background.
2 3Z 4 RðΔEij Þ ^ Ψ W ¼ μ Ψ dτ i z j 3 p3 c2 In the equation, ΔEij is the difference in the binding energy of the two states i and j, c is the speed of light, p is Planck’s constant divided by 2π, and R is the fine structure constant. In the transitional dipole moment integral above, the z in μz is the direction of the electric field vector of the Kβ or KR photon. The Kβ/KR ratio is the ratio of the two radiative transition rates, and because the constants cancel, this ratio only depends upon the energy difference ratio and the transitional dipole moment integral ratios. The Kβ/KR ratio for the hydrogen atom can be calculated by the students as a “simple” example of the theory (see the Supporting Information). For hydrogen, the ratio is approximately 0.27. Although this is a greatly simplified calculation, it shows the essence of the quantum mechanics involved. This idealized calculation assumes the hydrogen atom is completely isolated; however, in a compound, the hydrogen atoms would not be isolated. Although we cannot analytically treat the effect of the neighboring atoms on our hydrogen atom, we can gain some insight by assuming that their effect on our solution to the Schr€odinger wave equation for the hydrogen atom is minimal. Thus, we add a small piece to the Hamiltonian to correct for this perturbation. To determine the periodic trend observed in the alkali halides, a system was examined consisting of two point charges symmetrically placed in line with our hydrogen atom at the center. Although this system is difficult for an undergraduate to solve, we can explore this idea by using the linear combination of atomic orbitals approximation. In this case, bringing charges near the hydrogen atom from opposite sides along the z direction should polarize the p orbital on the hydrogen atom. Thus, we can rewrite the ψ3pz as a linear combination of orbitals ψ0 3pz = c1ψ3pz þ c2ψ4pz, other orbitals such as 4s and 3d do not contribute owing to their symmetry. Using these approximations, the Kβ/KR ratio for a hydrogen atom with point charges nearby can be calculated (see the Supporting Information). For the unperturbed hydrogen atom, students are guided through a calculation that shows that Kγ < Kβ < KR. This suggests that the contributions of higher orbitals to a perturbed ψ0 3pz would lead to a lower Kβ so that the Kβ/KR
Figure 2. Chlorine Kβ/KR ratio for group 1 metal chlorides. Error bars represent one standard deviation unit. Data represent 6 replicate measurements by students. *LiCl is a deliquescent material and its deviation is discussed in the Supporting Information.
ratio would decrease with increasing external charge or greater proximity of that charge to the hydrogen atom.
’ DATA ANALYSIS AND RESULTS Students imported their data (Table 1) into Excel and fit the Kβ and KR peaks to a Gaussian curve using the solver feature of Excel (an example fit spectrum is shown in Figure 1). From the fitted peaks, the students calculated the Kβ/KR ratio. Students then calculated, by hand or using mathematical software such as Mathematica (commercial) or Maxima (free), the direction of the change in the ratio of Kβ/KR and checked to see if their data matched the theoretical trends (see Figure 2). ’ CONCLUSIONS Students used an energy-dispersive XRF instrument to probe the electronic structure of chlorine in various chemical environments. Although such an instrument cannot directly measure the chemical shifts in energy because of insufficient resolution, information about the surrounding chemical environment can be obtained by examining the peak area ratios for KR and Kβ peaks. This experiment allows students to gain a better 820
dx.doi.org/10.1021/ed100695v |J. Chem. Educ. 2011, 88, 819–821
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understanding of how XRF works and the link between quantum mechanics and spectroscopy by using an approximate calculation to interpret the periodic trend in the Kβ/KR area ratio for alkali chlorides. Quantum mechanics calculations predict that the Kβ/ KR area ratio for alkali chlorides will increase as one moves down the group, which is observed experimentally (see Figure 2) for NaCl to CsCl. The deliquescence of LiCl shields the lithium charge from the chloride ion, increasing its Kβ/KR area ratio in an exception to the trend. Although the calculations are only a rough approximation, they can be performed by undergraduate physical chemistry students either by hand or with the assistance of computer software.
’ ASSOCIATED CONTENT
bS
Supporting Information Direction for the students; notes for the instructor. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: cliff
[email protected].
’ ACKNOWLEDGMENT Support for this work was provided by the National Science Foundation’s Course, Curriculum, and Laboratory Improvement (CCLI) program under Award No. DUE-0736706. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. ’ REFERENCES (1) Jenkins, R.Chemical Analysis. In X-ray Fluorescence Spectrometry, 2nd ed.; Winefordner, J. D., Ed.; John Wiley and Sons: New York, 1999; p152. (2) Tertian, R.; Claisse, F. Principles of Quantitative X-ray Fluorescence Analysis; Heyden: London, 1982. (3) Palmer, R. T.; Jacobs, R.; Baker, P. E.; Fergusion, K.; Webber, S. J. Agric. Food Chem. 2009, 57, 2605–2613. (4) Carr, R.; Zhang, C.; Moles, N.; Harder, M. Environ. Geochem. Health 2008, 30, 45–52. (5) Jang, M. Environ. Geochem. Health 2010, 32, 207–216. (6) Vanhoof, C.; Corthouts, V.; Tirez, K. J. Environ. Monit. 2004, 6, 344–350. (7) Bills, J. M.; Brier, K. S.; Danko, L. G.; Kristine, F. J.; Turco, S. J.; Zimmerman, K. S.; Divelbiss, P. M.; Tackett, S. L. J. Chem. Educ. 1972, 49, 715–716. (8) Mucci, J. F.; Stearns, R. L. J. Chem. Educ. 1975, 52, 750–752. (9) Anzelmo, J. A.; Lindsay, J. R. J. Chem. Educ. 1987, 64, A181–A185. (10) Anzelmo, J. A.; Lindsay, J. R. J. Chem. Educ. 1987, 64, A200–A204. (11) Bachofer, S. J. J. Chem. Educ. 2008, 85, 980–982. (12) Feldman, L. C.; Mayer, J. W. Fundamentals of Surface and Thin Film Analysis; Prentice-Hall: EngleWood Cliffs, NJ, 1986; p 233. (13) Perino, E.; Deluigi, M. T.; Olsina, R.; Riveros, J. A. X-Ray Spectrom. 2002, 31, 115–119. (14) Kulshreshtha, S. K.; Wagh, D. N.; Bajpei, H. N. X-Ray Spectrom. 2005, 34, 200–202. (15) Muoyama, T. Spectrochim. Acta,Part B 2004, 59, 1107–1115. 821
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