Activity Cite This: J. Chem. Educ. 2019, 96, 1449−1452
pubs.acs.org/jchemeduc
Inquiry-Based Experiment with Powder XRD and FeS2 Crystal: “Discovering” the (400) Peak N. Stojilovic*,†,‡ and D. E. Isaacs† †
Department of Physics and Astronomy and ‡Department of Chemistry, University of WisconsinOshkosh, Oshkosh, Wisconsin 54901, United States
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S Supporting Information *
ABSTRACT: We discuss how a powder X-ray diffraction (XRD) system can be used to probe large pyrite (FeS2) crystals to reveal a peak generally not documented in the literature. The ability to detect this peak is attributed to the use of a large crystal, which gives large signal intensities. This type of experiment provides a research-like experience and gives students the opportunity to deepen their understanding of diffraction orders. In this experiment students are first challenged to be creative and determine how to mount a mineral crystal in a powder XRD system and then practice critical thinking in order to determine the origin of the unknown XRD peak. This experiment may also be generalized to crystals other than pyrite.
KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Inquiry-Based/Discovery Learning, Solid State Chemistry, Student-Centered Learning, X-ray Crystallography
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INTRODUCTION In traditional laboratories students are often instructed on what to measure and how, and thus they do not fully develop problem-solving and critical thinking skills. Many instructors use laboratories to strengthen the concept covered in lectures, but it seems that laboratories are not effective in this role. For example, Wieman and Holmes compared final test results from two large introductory physics courses, one with and one without an associated “traditional” lab component.1 They found no observable effect on the final exam performance on questions involving topics covered in the laboratory. Their findings question the effectiveness of laboratories as a means to increase mastery of the lecture content. The laboratories are more effective when their goal is to teach experimental practices.2 Providing an undergraduate research experience through courses stimulates students’ curiosity3 and improves their conceptual understanding4 and critical thinking skills.5 Crystallography laboratory activities have been successfully incorporated into various experimental chemistry courses for undergraduate students.6−13 In a recent inquiry-based activity, a powder XRD instrument was used to probe an Al2O3 (0001) single crystal, and through the discovery of the origin of the peak doublet, students could learn about X-ray generation, electronic transitions, and spin−orbit coupling.14 In the present activity, the puzzle is not the origin of the doublet but the origin of the higher-order diffraction peak not given in some reference XRD patterns (JCPDS file 42-1340). In this activity students are learning about diffraction orders, relative © 2019 American Chemical Society and Division of Chemical Education, Inc.
peak intensities, missing peaks, and preferred orientation. They are comparing an XRD pattern of a single crystal to that of the powder and try to figure out why an XRD peak visible in the single crystal specimen is absent from the XRD pattern of the pyrite powder. Students generally cannot find the (400) peak in the literature and have to trust their own calculations and arguments. This activity mimics scientific research since it engages students in critical thinking. Pyrite (FeS2), also known as “fool’s gold”, is a mineral with pale brass-yellow appearance and metallic luster. Although it commonly forms cubes, octahedral and pentagonal dodecahedra forms can also be found.15 XRD experiments on pyrite samples are typically done using the powdered mineral; however, in this paper, we will demonstrate how large pyrite cubes found in nature can be probed using a powder XRD system. We will also show how probing bulk pyrite cubes can reveal a higher-order diffraction peak not easily found in the literature. Other minerals or single crystals could be studied using powder XRD systems. This type of activity can easily be expanded and is best suited as an upper-level inquiry-based lab.
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EXPERIMENTAL DETAILS
Pyrite minerals found in nature, with relatively large cubic faces (Figure 1), were studied. In XRD experiments using systems Received: February 3, 2019 Revised: May 29, 2019 Published: June 19, 2019 1449
DOI: 10.1021/acs.jchemed.9b00099 J. Chem. Educ. 2019, 96, 1449−1452
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Activity
primarily designed for powders, the positioning of the crystal (height in particular) is critical.
Figure 2. Powder XRD of a typical cubic FeS2 crystal found in nature. The inset shows the (400) peaks due to Kα1 and Kα2 X-ray lines. The numbers in parentheses are Miller indices, which indicate crystal planes.
Figure 1. Pyrite mineral held by transparent adhesive tape.
In order to probe different cubic faces of various crystals, the samples were directly mounted on transparent adhesive tape with the X-ray beam passing through it. The signal intensity from single crystals is so large that the attenuation effect of the transparent adhesive tape on the XRD pattern is insignificant. Wide and fast scans can be used to reveal the locations of the peak(s), and then narrow high-resolution scans can be used to resolve the doublets. Samples are inexpensive, harmless, and readily available and can often be analyzed without any special sample preparation. Students performing XRD experiments should have prior radiation safety training. Pyrite powders were also probed, and their diffraction patterns were compared to those of pyrite crystals. The powder was prepared after crushing and grinding stacked pyrite crystals with the agate mortar and pestle and was mounted on the standard glass sample holder with 0.2 mm depth.
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EXPERIMENTS AND DISCUSSION Powder XRD instruments are generally used for powdered specimens. Thus, mounting and positioning large crystals for diffraction experiments in a typical powder XRD system requires the students to think creatively, and assigning Miller indices to peaks not reported in the reference XRD patterns requires some critical thinking. The XRD pattern of a cubic face of a natural FeS2 crystal is displayed in Figure 2. When a pentagonal dodecahedron face is probed, the most intense peak corresponds to another set of planes (see Supporting Information). Figure 3 shows an XRD pattern from FeS2 powder. Although the large (200) peak observed from the cubic face of the single crystal is also seen in our FeS2 powder, the second peak (doublet of much lower intensity), displayed in the inset of Figure 2, is barely visible in the powdered sample. Thus, students try to “discover” what it represents by calculating the peak positions corresponding to different diffraction orders and making a direct comparison with the observed peaks. This peak doublet, which reveals the Kα1 and Kα2 splitting, is better resolved at higher values of Bragg’s angles. The positions of possible peaks can be calculated using theory. The expression for finding the interference maxima in
Figure 3. XRD pattern of FeS2 powder. The peak at about 69° present in the single crystal is typically not detectable in the powder.
the case of X-ray diffraction from a crystal is given by Bragg’s law 2d sin θ = nλ
(1)
where d is the spacing between reflecting crystal planes, n is the diffraction order (n = 1, 2, 3, ...), θ is the angle of incidence measured from the face of the crystal, and λ is the wavelength of incident X-rays. The separation of the (hkl) planes (h, k, and l are the Miller indices) is denoted by dhkl for a cubic crystal lattice and is given by 1 h2 + k 2 + l 2 = 2 dhkl a2 1450
(2) DOI: 10.1021/acs.jchemed.9b00099 J. Chem. Educ. 2019, 96, 1449−1452
Journal of Chemical Education
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If all three Miller indices are multiplied by the same integer n (diffraction order), the separation is reduced by that factor and can be calculated using 1 2 dnh , nk , nl
=
2 2 2 (nh)2 + (nk)2 + (nl)2 1 2h + k + l n = = n2 2 2 2 a a dhkl (3)
or dnh . nk , nl =
dhkl n
(4)
In a cubic lattice with lattice constant a, the spacing between reflecting planes is given by eq 2. Therefore, the angles at which the (hkl) planes diffract X-rays are given by sin θ =
h2 + k 2 + l 2 λ 2a
(5)
Since the crystal structure of pyrite is primitive cubic, reflections are allowed for any integer values of h, k, and l. We can predict the reflections that can be observed by determining the possible integer values of the sum of the squares of the Miller indices. Note that the (400) peak is theoretically possible but generally not observable in pyrite samples. The reason is that usually the samples are in the form of powder and the (400) signal intensity is below or at the detection limit. Using a large single crystal, the resulting signal intensities are orders of magnitude greater than those from powdered samples allowing detection of the (400) peak. The doublet profile of the (400) peak can be explained by Kα1 (1.54050 Å) and Kα2 (1.54434 Å) lines whose wavelengths are so close in value that in typical powder XRD patterns they may appear as single peaks. The wavelength of the Cu Kα radiation reported in the literature actually corresponds to (2Kα1 + Kα2)/3 since the Kα1 line is about 2 times larger than that of Kα2.16 Separation between Bragg peaks due to Kα1 and Kα2 radiation increases with diffraction angle θ. The inset in Figure 2 shows how these two X-ray lines can be separated when single crystals are probed using powder XRD systems. Using eq 5, one can solve for the angles corresponding to Kα1 and Kα2 (400) reflections. The calculated separation between these two peaks is 0.19° and matches the measured one shown in Figure 4. The intensity of the (400) peak is more than 100 times smaller than that of the largest peak, and thus the (400) peak is not reported in some reference X-ray diffraction patterns like JCPDS file 42-1340 (see Supporting Information). These reference X-ray diffraction patterns typically have the intensity of the greatest peak assigned a value of 100, and the intensity of the smallest peak is not less than 1. The fact that one cannot find the (400) peak in this reference card index gives students an opportunity to “discover” it via critical thinking. One of the reasons we see the (400) peak is the fact that our XRD pattern of pyrite powder has a somewhat greater relative intensity of the (200) peak compared to other peaks from the reference pattern. This suggests a slightly preferred (nonrandom) orientation of the crystallites in our powder prepared from grinding pyrite cube crystals. Therefore, how powder is prepared can play a role in detecting the (400) reflection. The crystallites should have all possible orientations in finely ground powders. The crystallite shapes within a powder give rise to what is known as a preferred orientation. If peak
Figure 4. Two hour long narrow XRD scan of FeS2 powder. The doublet peak at about 69° not given in the JCPDS file 42-1340 reference card can be detected in the powder prepared from grinding cubic pyrite crystals.
intensities are to be determined by diffraction from powders, it is essential that there is no preferred orientation in the powder since the preferred orientation can produce systematic errors in peak intensities. To successfully complete this inquiry-based experiment, students should know Bragg’s law, be familiar with Miller indices, and be able to calculate the angles of Bragg’s peaks using the theory presented above. Students generally do not demonstrate a deep understanding of the concept of diffraction order, and this type of activity helps them learn about higher diffraction orders through “discovery”. Searching and reading scientific literature (primarily books and articles) should be an integral part of the activity. Since the answer is not trivial, this activity allows students to engage in scientific ways of thinking. They will have to create a hypothesis and determine a way to test it. This experiment is an inquiry-based type of lab activity suited for students taking physical chemistry or advance physics laboratories but can also be given as an independent study. The activity was given to 29 students taking either general physics or independent study. Students either worked on the activity individually or in groups of two. In a four week period, none of the students “discovered” the origin of the “unknown” peak but gained a lot from working on it and exercising critical thinking. A set of questions was then given to students to help them focus on relevant concepts and terms (see the Supporting Information). The lecture on XRD covered relevant sections from Atkins’ Physical Chemistry textbook.17 The university has access to the Journal of Chemical Education and SciFinder. Learning objectives were learning from mistakes (wrong hypothesis), developing critical thinking skills, and deepening understanding of the term diffraction order.
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SUMMARY We discussed an activity which mimics scientific research and in which students can exercise their creativity and critical thinking which are considered essential scientific skills. The fact that the given reference X-ray diffraction pattern of pyrite does not show the (400) peak provides students the 1451
DOI: 10.1021/acs.jchemed.9b00099 J. Chem. Educ. 2019, 96, 1449−1452
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opportunity to “discover” it in the diffractogram of a single crystal using a powder XRD system. Once students mount the sample and observe unexpected results, they may come up with their own experiments to test their hypothesis. The question can be posted in class (physics, chemistry, materials science, etc.) without performing the actual experiment if students are given XRD data and this reference pattern. Students can collect or can be given diffractograms of different crystal faces of the same sample and can repeat experiments on various mineral or crystal samples. They can probe a cubic face and compare it to a pentagonal one or grind the mineral to make a direct comparison with the powder. One advantage of using single crystals in powder XRD systems is the ability to resolve Kα1 and Kα2 lines that typically overlap and form a single peak in XRD analyses of powders. As they investigate the doublet peak profile students can learn about electronic transitions responsible for different X-ray lines. This type of activity could be easily incorporated in physical chemistry or advanced physics laboratories.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.9b00099. Details of the experiment and how this activity can be implemented (PDF, DOCX)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
N. Stojilovic: 0000-0002-1751-6033 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Dr. Eric Hiatt and Dr. Sheri Lense for critical reading of the manuscript and suggestions. We also thank anonymous reviewers for excellent comments. N.S. was supported by UW Oshkosh Grant FDT592.
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REFERENCES
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DOI: 10.1021/acs.jchemed.9b00099 J. Chem. Educ. 2019, 96, 1449−1452
