Powder Diffraction Simulated by a Polycrystalline Film of Spherical

In the Classroom edited by

JCE DigiDemos: Tested Demonstrations

Ed Vitz

Powder Diffraction Simulated by a Polycrystalline Film of Spherical Colloids submitted by:

Kutztown University Kutztown, PA 19530

W

Dean J. Campbell* Department of Chemistry and Biochemistry, Bradley University, Peoria, IL 61625; *[email protected] Younan Xia Department of Chemistry, University of Washington, Seattle, WA 98195

checked by:

George C. Lisensky Department of Chemistry, Beloit College, Beloit, WI 53511

This article describes demonstrations of powder X-ray diffraction (PXRD) using a laser and spherical colloids. Although several optical diffraction experiments are known, the majority of these experiments are designed to demonstrate diffraction from single crystals. Diffraction of electromagnetic radiation such as visible light or X-rays from a single crystal projects a pattern of spots that is highly dependent on the orientation of the sample. The optical diffraction experiments are all based on repeating arrays of small features that scatter light. Examples of these types of structures include: • Holes drilled in metal plates and printed, photographic, or imprinted transparent substrates (1–8) (Even halftone dots generated by a laser jet printer on a transparency can be used.) • Fabric and metal meshes (3, 9), including sample holder grids for transmission electron microscopy • Phonograph records (3), computer memory chips (10), compact disks (11), and the arrays of pixels in cathode ray tube and liquid crystal display screens

shown in Figure 1. Specifically, concepts covered by these demonstrations include crystallization and self-assembly, close-packing crystal structures, diffraction, as well as microand nanostructured materials. This demonstration is most suitable for an undergraduate physical chemistry or materials chemistry setting, though the procedure is sufficiently simple that it could also be used at the introductory chemistry level for undergraduates or high school students. Spherical colloids in suspension can aggregate to form long-range ordered (crystalline) structures. When films of these crystals are grown on a flat substrate, these spherical colloids tend to be arranged in a face-centered cubic crystal structure with the (111) planes of these crystals oriented parallel to the substrate surface (15, 16). These are the largest and most well-defined planes in the film. If needed, thin films of colloids may readily be prepared to contain only one or two planes of spheres (Figure 2A). If the spheres are of the proper size, diffraction patterns can be produced by shining

• Light bulb filaments (5) and bird feathers (3) • Dried colloidal crystal films (12)

In contrast, diffraction from a polycrystalline material such as a powder produces many overlapping diffraction patterns to project a pattern of concentric rings. Though much spatial information and resolution is lost, the technique of powder diffraction does not depend on knowing the orientation of a specific crystal—the sample contains many crystals in all possible orientations. Powder diffractometers are less expensive and less sophisticated than single-crystal diffractometers, and some colleges and universities only have the powder variant. Short of some way of spinning a single crystal optical diffraction demonstration in a light beam (proposed at a workshop several years ago), there are relatively few demonstrations simulating powder diffraction resulting from a polycrystalline sample. A couple of demonstrations used transparent photographed hand-drilled or computergenerated arrays (2, 5). Another used a suspension of colloidal particles (13). Finally, yet another article described how a similar suspension of colloidal particles could be used to produce Kossel lines (14). The present article describes how dried films of spherical colloids on a transparent substrate can produce concentric ring-shaped powder diffraction patterns like the one 1638

Journal of Chemical Education

•

Figure 1. Optical diffraction of a diode laser beam produced by a polycrystalline film of spherical colloids with 10 µm diameters. (Inset) Plot of light intensity of the rings as a function of distance from the center of the pattern. The plot also indicates the set of planes that produces each peak in light intensity.

Vol. 83 No. 11 November 2006

•

www.JCE.DivCHED.org

In the Classroom

a laser beam through the film in a direction perpendicular to the substrate surface and therefore the (111) planes on that surface. Each of these (111) planes consists of spheres in a hexagonal packing arrangement. As light waves are scattered from the spheres, they interfere with each other constructively and destructively to produce a diffraction pattern—an array of bright spots of light. A single plane can produce a diffraction pattern that is itself a hexagonal pattern of spots rotated by 30⬚ from the original orientation of the plane (6). A single crystalline film would also produce a hexagonal diffraction pattern. A laser shining through a polycrystalline colloidal film passes through multiple (111) planes with different orientations. The multiple diffraction patterns that result can overlap to produce a pattern of arcs or concentric rings, as shown in Figure 2B. Preparations for the most basic demonstration can be extraordinarily easy. Simply smear a couple drops of aqueous suspension of spherical colloids across a glass slide. As the suspension dries, colloidal particles form a film of (111) crystallites with varying thickness. The slide with the dried film can be held in front of a laser beam and moved around until the brightest, sharpest pattern of diffraction rings is projected. A film that is too thick will prevent the laser from

passing through the film, but too few spheres will also yield a weak diffraction pattern. The diffraction pattern in Figure 1 appears to have been produced by essentially a single polycrystalline (111) layer of spheres. More details of this demonstration and more sophisticated variations are provided below. Hazards Direct eye exposure to laser radiation should be avoided. Cut glass can have sharp edges. Potassium hydroxide is caustic. Poly(dimethylsiloxane) precursor (PDMS) and many of the solvents used in these experiments are skin irritants. Use of gloves and forceps will not only protect hands from reagents but will also protect clean glass surfaces from fingerprints. Working with solvents in a hood to minimize inhalation is recommended. Avoid inhalation of the dried colloidal particles. Demonstrations Suspensions of spherical colloids may be obtained by synthetic methods (17) or by purchasing the spheres from suppliers. Student synthesis of spherical colloids is a good laboratory exercise, but assessment of size monodispersity of the colloids typically relies on more advanced equipment such as scanning or transmission electron microscopy. Commercial suppliers of spherical colloids include Polysciences, Inc. (Warrington, PA), Duke Scientific Corporation (Palo Alto, CA), Bangs Laboratories, Inc. (Fishers, IN), Seradyn (Indianapolis, IN), and Sigma-Aldrich, Inc. (St. Louis, MO).1 Many types of spheres are available. Some things to consider when purchasing colloidal spheres are as follows: • Size: The recommended polystyrene sphere diameters are in the range of 2–10 µm. Keep in mind that there are various methods for measuring the sphere diameter that do not always agree. For example, a colloidal suspension of spheres was measured by the supplier using a quasi-elastic light scattering method, yielding an average measured diameter of 226 nm. These same spheres measured 155 nm by transmission electron microscopy, 180 nm by scanning electron microscopy, and 184 nm based on photonic band gap measurements of crystals of the spheres. • Monodispersity: The more uniform the sphere size, the fewer the packing defects in the crystal.

Figure 2. (A) Scanning electron microscope image of (111) layers of spheres used to produce Figure 1. The boundary of one of the crystallites is indicated by black lines. A unit cell for the planar crystallite would be a parallelogram formed by the centers of four neighboring spheres. (B) Diagram of some of the first seven rings of the diffraction pattern and the spots from the single crystal pattern that can be effectively rotated to produce them. Note that the diagram represents all the spots as being equally distant from their nearest neighbors. In the real light diffraction pattern, the spots more distant from the center of the pattern have increased spacing from neighboring spots, both due to the sine function in the Fraunhofer equation and due to the fact that not all spots on a flat projection surface are equidistant from the sample.

www.JCE.DivCHED.org

•

• Concentration: The colloidal crystals grown for use in this demonstration were produced from suspensions that were used as purchased. These were about 3–10% solids by weight. • Composition: Polystyrene spheres are relatively inexpensive and adequate for the experiments described in this article. They are more susceptible to attack by a wider variety of solvents, such as toluene and benzene, than cross-linked polystyrene or silica spheres. Additionally, if the refractive index of the spheres is too close to that of the surrounding medium, the spheres will not scatter light effectively and the colloidal crystal will “disappear”. For example, this can happen when silica spheres are immersed in poly(dimethylsiloxane).


•


1639

In the Classroom

In this work, diode laser pointers (< 5 mW, 650–660 nm) and a small He–Ne laser (4 mW, 633 nm) were sufficient for the demonstrations. Often more rings are visible in a dark room than in a well-lit environment. It was also found that larger beam width is typically better for making ringshaped patterns. Narrower beams access fewer crystallites and can occasionally produce an array of spots from a single crystallite. If both beam sizes are available in a classroom, a single sample can be used to reinforce the relationship between single crystal and powder diffraction patterns. If necessary, film quality can be improved if the glass substrate is made more hydrophilic. If the surface is too hydrophobic, the aqueous suspensions will simply bead up on the surface of the substrate and not easily allow a flat film to form. Two approaches are recommended. One is to ultrasonicate the substrate in a series of cleaning solvents, such as nanopure water, acetone, and isopropanol, followed by a brief exposure to air plasma in a plasma cleaner, and finally to rinse again with nanopure water and blowing the sample dry under a stream of air. A less costly method is to soak the substrate for about an hour in a base bath2 formed by saturating 95%–100% ethanol with potassium hydroxide (18). After soaking, the sample is rinsed with copious quantities of deionized water and blown dry with a stream of air. Another variation on this demonstration is to infill the void spaces between the spheres with PDMS precursor and then to cure it into an elastomer. When the cured polymer is lifted away from the substrate, the spheres it contains can be used to produce distortable diffraction patterns. Figure 3 provides a schematic for this method, which requires some additional reagents. The colloidal crystal film is again grown by water evaporation from an aqueous colloidal suspension on a glass substrate. After the film is dry, cover the film with a diluted PDMS precursor. The form of PDMS used is SYLGARD 184 Silicone Elastomer, produced by the Dow Corning Corporation. This polymer kit has been used for other educational experiments and demonstrations, as well as for conventional research (7, 19, 20). The product information for SYLGARD 184 can be found on the Internet (21). The polymer is available as a two-component kit of “base” and “curing agent”. Upon mixing, the PDMS oligomers cross-link into a network

as silicon hydride functional groups catalytically reduce vinyl groups. The oxidative addition reaction leaves no byproducts to cloud the polymer, and the cured material is optically transparent in the visible region. The PDMS, as provided in this kit, is too viscous to effectively penetrate between the spherical colloids; therefore it must be diluted with a less viscous solvent that will not dissolve the spheres themselves. A light silicone oil such as DMS-T00 (0.65 cSt, from Gelest, Morrisville, PA) works well, as do hexanes. The ratio of curing agent to base to solvent should be approximately 2:10:10 by mass. The sample should be covered by the well-mixed PDMS mixture overnight. The solvent evaporates from the mixture during this time period, so a fume hood is recommended. Gloves and goggles should also be worn to minimize contact with silicones and solvents. After curing overnight, the sample should be placed in a drying oven at 50–60 ⬚C for an hour to ensure curing is complete. Then the PDMS can be carefully peeled away from the glass substrate as a flexible polymer slab. At times some of the spheres are left behind on the glass surface, but this is not a problem. Occasionally the PDMS adheres so well to the glass substrate that it will tend to fail mechanically. In this case, rather than peeling the polymer away, immerse the slab with glass substrate into hexane. Often the PDMS slab will slip away from the glass as it swells in solvent. The slab will return to its original size upon drying. A single PDMS slab can be used to illustrate the reciprocal lattice effect (3, 7): larger spacing in the crystal results in smaller diffraction pattern spacing. If the slab is gently stretched in a direction perpendicular to the incident laser beam, the projected circular diffraction rings will contract along the same direction into ellipses. As noted above, PDMS can reversibly absorb various solvents such as hexane and swell, increasing the distance between the centers of the colloidal particles. As the spacing between the particles increases, the rings of their diffraction patterns contract. Based on diffraction measurements, PDMS samples containing approximately 2 µm spheres reversibly swelled to about 140% their original size when exposed to hexanes. These same spheres in PDMS still remaining on the glass plate did not exhibit any measurable change in the diffraction pattern upon exposure to hexanes. This indicates that the PDMS was restricted from swelling by contact with the glass in at least the direction parallel to the (111) planes. The free PDMS slabs tend to be more fragile (and often more slippery) when swollen with solvent, so they must be handled with a little care. Stretching a solvent-swollen slab is NOT recommended. Drying a solvent-swollen sample too quickly can result in stress-cracking of the polymer (19a), so heating the swollen polymer to dry it or using very volatile solvents to swell the polymer is also not recommended. Calculations

Figure 3. Schematic for producing a PDMS-infilled colloidal crystal film.

1640


•

In a powder diffraction experiment, an X-ray beam impinges on a polycrystalline sample to produce a diffraction pattern of concentric rings. A detector moves through the scattered X-ray rings to measure the angles between the path of the incident rays and the path of the constructively scattered rays that form each ring. The Bragg law of diffraction


•

www.JCE.DivCHED.org

In the Classroom

is used to convert these angle measurements to spacing between planes in the three-dimensional crystals (22). The diffraction pattern produced by the (111) planar arrays in the colloidal films can be used to calculate the sphere diameter. To do so, the pattern of rings can be projected on a flat surface that is perpendicular to the incident path of the laser beam. To extend the analogy between the optical diffraction demonstration and real powder X-ray diffraction, digital photographs of the optical diffraction pattern can be analyzed by graphics software to produce a light intensity plot of a section through the diffraction pattern.3 The inset of Figure 1 shows a light intensity plot for a section through the concentric rings in the same figure. This plot, with each diffraction ring corresponding to a light intensity peak, is very similar to the data produced in real powder X-ray diffraction, in which X-ray intensity is plotted as a function of detector angle. The equation used for this flat film demonstration with two-dimensional (111) planar arrays is based on the Fraunhofer law of diffraction (6), n λ = d sin φ

where n is the diffraction order; λ is the wavelength of the incident and diffracted light; d is the spacing between parallel rows of spheres; and φ is the angle between the path of the incident light and the path of constructively scattered light. φ can be calculated by the following relationship (6): X L where X is the distance between the 0th order central diffraction spot and the spot or ring of interest in the projected diffraction pattern and L is the distance between the sample film and the central diffraction spot of the projected pattern Figures 1 and 2 illustrate the relationships between the structure of the (111) planar arrays and the observed ring diffraction pattern they produce. Figure 2A shows multiple crystallites in a single layer of spheres; the dark lines mark the borders of a single crystallite. Each hexagonal plane of spheres in a crystallite has its own two-dimensional symmetry and corresponding Miller indices. Since the third Miller index l = 0 at all times in these two-dimensional systems, it will be set aside for the sake of simplicity. The innermost diffraction ring in the patterns corresponds to the spacing between the (10) planes in the layer. The diameter of the spheres is 2兾√3 times this spacing. The second ring corresponds to the (11) planes in this hexagonal, planar system. The diameter of the spheres is twice this spacing. The third ring corresponds to the second-order diffraction spacing between the (10) planes in the hexagonal, planar structure, or alternatively, the spacing between the (20) planes. The diameter of the spheres is still 2兾√3 times the spacing produced by using n = 2 in the Fraunhofer equation. The Miller indices for the first seven rings are provided in Figure 1. Though it is relatively simple to think about these films as single hexagonal planes, they could still be considered to be (111) planes in larger three-dimensional crystals. Extending the hexagonal system to a face-centered cubic structure converts (10) planes to (4兾3 2兾3 2兾3) planes. If this structure were perfect, Bragg diffraction spots that result from these planes, referred to as 1兾3{422} reflections, would actutan φ =

www.JCE.DivCHED.org

•

ally be forbidden (23). However, these polycrystalline, nonuniform films are far from perfect three-dimensional structures. On the other hand, the hexagonal (11) planes convert to (220) planes in the face-centered cubic structure. Reflections from these planes are indeed permitted by Bragg diffraction (22, 23). Measurements were made on the first three rings of the diffraction patterns of colloidal films on glass slides using a He–Ne laser and measurements to the nearest millimeter. Spheres labeled by the supplier as having average diameters of 3.0 µm yielded 3.0 µm diameters based on the first two rings and a 3.1 µm diameter based on the third ring. Spheres labeled by the supplier as having average diameters of 2.134 µm yielded 2.1 µm diameters based on all three rings. There does appear to be a slight increase in calculated sphere diameter as the ring number increases. Also, many times the outer rings were more diffuse than the inner rings, making their measurement more difficult. Colloidal Crystals and the Classroom Many connections can be made in the classroom between diffraction from repeating microstructures and topics in chemistry, physics, geology, and biology. Natural opals contain colloidal crystals—tiny spheres of SiO2 that collectively diffract light to produce flashes of color, referred to as the “fire” in the opal (24). Iris agates also exhibit iridescence, but this is due to closely spaced layers of minerals rather than spheres (25).4 Some animals produce colors from interference of light by physical structures, rather than from pigments alone. Peacocks (25), the sea mouse (actually a worm) (27), and several species of butterflies (28, 29) exhibit this sort of structural color. Some structures in butterfly scales resemble face-centered cubic crystals of spheres of air surrounded by a cuticle matrix (28, 29), a structure referred to as an inverse opal (30–32). Figure 4 shows a scanning electron microscopy image of a different type of structural color feature. Tiny repeating features along the scale ridges of the Morpho peleides butterfly cause light interference (28), producing blue flashes of color perceived by the human eye and also an intense reflection in the ultraviolet region. Many insects can see ultraviolet light. Colloidal crystals capable of manipulating light, referred to as photonic crystals, are being studied for a number of optical applications (15–17, 20, 29–32). Materials scientists have looked to some of the natural structures mentioned above for inspiration in designing their own structures.

Figure 4. A scanning electron microscope image of a scale from a Morpho peleides butterfly.


•


1641

In the Classroom

Acknowledgments DJC would like to acknowledge the Bradley University Sherry Endowment for Collaborative Student–Faculty Projects in Liberal Arts and Sciences for supplies. We would also like to thank Sarah Moore for the donation of the Morpho specimen from the Pacific Science Center, Seattle, WA; and Unyong Jeong for assistance with the Scion Image software. YX has been supported in part by a Career Award from the NSF (DMR-9983893) and a fellowship from the David and Lucile Packard Foundation. Work was performed in part at the University of Washington Nanotech User Facility (NTUF), a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported by the NSF. W

Supplemental Material

A spreadsheet for calculating the diameter of the spherical colloids from the first three rings of the diffraction pattern is available in this issue of JCE Online. Notes 1. Some colloidal sphere samples that gave excellent diffraction patterns were 10 µm Polymer Microsphere Size Standard from Duke Scientific Corporation (catalog number 4210A; 15 mL of suspension costs $270.00); 4.50 µm Polybead Polystyrene Microspheres from Polysciences, Inc. (product number 17135-5; 5 mL of suspension costs $74.75); and 2.00 µm Polybead Polystyrene Microspheres from Polysciences, Inc. (product number 1981415; 15 mL of suspension costs $63.00). The final sample mentioned was also one of the least expensive in our possession. Prices are from March, 2005. 2. This mixture is very corrosive! Wear heavy gloves, goggles, and a lab coat or apron for protection. Our base bath solutions turned brown after a few days, but this did not significantly reduce the effectiveness of the solutions. 3. To produce the plot shown as the inset of Figure 1, the digital photograph was converted by Corel Photo-Paint Version 8.232 to its negative and then to grayscale. The resulting image was then opened in Scion Image–Release Beta 4.02, which is available for free download from: http://www.scioncorp.com/frames/ fr_download_now.htm (accessed Jul 2006). A narrow section of the image was selected and processed using the “Plot Profile” option. 4. Shining a He–Ne laser through a thin section of iris agate produced a diffraction pattern that appeared as a series of parallel stripes. Based on the distances between these stripes and other measurements of the diffraction pattern, the spacing between the bands of the agate was 3.7 µm.

Literature Cited 1. (a) Bragg, W. L. Nature 1939, 143, 678. (b) Bragg, W. L. Nature 1942, 149, 470–471. (c) Bragg, L. Nature 1944, 154, 69–72. 2. Meyer-Arendt, J. R.; Wood, J. K. Am. J. Phys. 1961, 29, 341– 344. 3. Slabaugh, W. H.; Smith, D. J. Chem. Educ. 1974, 51, 207– 208, and references therein. 4. Brisse, F.; Sundararjan, P. R. J. Chem. Educ. 1975, 52, 414–415.

1642


•

5. Welberry, T. R.; Thomas, J. M. Chem. in Britain 1989, 25, 383–388. 6. (a) Lisensky, G. C.; Kelly, T. F.; Neu, D. R.; Ellis, A. B. J. Chem. Educ. 1991, 68, 91–96. (b) Ellis, A. B.; Geselbracht, M. J.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R. Teaching General Chemistry: A Materials Science Companion; Oxford University Press, 1993; Chapter 4 and Experiment 4. 7. Campbell, D. J.; Beckman, K. J.; Calderon, C. E.; Doolan, P. W.; Ottosen, R. M.; Ellis, A. B.; Lisensky, G. C. J. Chem. Educ. 1999, 75, 537–541. 8. Lisensky, G. C.; Lucas, A. A.; Nordell, K. J.; Jackelin, A.-M. L.; Condren, S. M.; Tobe, R. H.; Ellis, A. B. DNA Optical Transform Kit; Shanks, K. M., Ed.; Institute for Chemical Education: Madison, WI, 1999. 9. Bettis, C.; Lyons, E. J.; Brooks, D. W. J. Chem. Educ. 1996, 73, 839. 10. Klier, K.; Taylor, J. A. J. Chem. Educ. 1991, 68, 155–157. 11. Tellinghuisen, J. J. Chem. Educ. 2002, 79, 703–704. 12. Abrams, N. M.; Schaak, R. E. J. Chem. Educ. 2005, 82, 450– 452. 13. Segschneider, C.; Versmold, H. J. Chem. Educ. 1990, 67, 967–970. 14. Spencer, B. H.; Zare, R. N. J. Chem. Educ. 1991, 68, 97–100. 15. Lu, Y.; Yin, Y.; Gates, B.; Xia, Y. Langmuir 2001, 17, 6344– 6350. 16. Fudouzi, H. J. Colloid Interface Sci. 2004, 275, 277–283. 17. Santamaria, F. G. Photonic Crystals Based on Silica Microspheres. Ph.D. Thesis, Universidad Autonoma de Madrid, Madrid, Spain, 2003. 18. Chen, K.; Herr, B. R.; Singewald, E. T.; Mirkin, C. A. Langmuir 1992, 8, 2585–2587. 19. (a) Campbell, D. J.; Rupe, S. B. J. Chem. Educ. 2000, 77, 876–877. (b) Campbell, D. J.; Olson, J. A.; Calderon, C. E.; Doolan; P. W.; Mengelt, E. A.; Ellis, A. B.; Lisensky, G. C. J. Chem. Educ. 1999, 76, 1205. 20. (a) Fudouzi, H.; Xia, Y. Adv. Mater. 2003, 15, 892–896. (b) Fudouzi, H.; Xia, Y. Langmuir 2003, 19, 9653–9660. 21. Dow Corning Home Page. http://www.dowcorning.com (accessed Jul 2006). 22. Atkins, P. W. Physical Chemistry, 3rd ed.; W. H. Freeman and Company: New York, 1986; Chapter 23. 23. Germain, V.; Li, J.; Ingert, D.; Wang, Z. L.; Pileni, M. P. J. Phys. Chem. 2003, 107, 8717–8720. 24. Sanders, J. V. Acta Crystallogr., Sect. A 1968, 24, 427–434. 25. Jones, F. T. Am. Mineral. 1952, 37, 578–587. 26. Zi, J.; Yu, X.; Li, Y.; Hu, X.; Xu, C.; Wang, X.; Liu, X.; Fu, R. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 12576–12578. 27. McPhedran, R. C.; Nicorovici, N. A.; McKenzie; D. R.; Botten; L. C.; Parker, A. R.; Rouse, G. W. Aust. J. Chem. 2001, 54, 241–244. 28. Ghiradella, H. Appl. Optics 1991, 30, 3492–3500. 29. Yablonovitch, E. Sci. Am. 2001, Dec, 47–55. 30. Campbell, D. J.; Freidinger, E. R.; Querns, M. K.; Swanson, S. L.; Ellis, A. B.; Kuech, T. F.; Socie, B. A.; Payne, A.; Condren, S. M.; Lisensky, G. C.; Rasmussen, R. Exploring the Nanoworld with LEGO Bricks; book available online at http:// mrsec.wisc.edu/edetc/LEGO/index.html (accessed Jul 2006). 31. Schroden, R. C.; Al-Daous, M.; Blanford, C. F.; Stein, A.; Chem. Mater. 2002, 14, 3305–3315. 32. Velev, O. D.; Kaler, E. W. Adv. Mater. 2000, 12, 531–543.


•

www.JCE.DivCHED.org

Powder Diffraction Simulated by a Polycrystalline Film of Spherical

Recommend Documents