Economical Laue x-ray diffraction using photographic film and orientation of single crystals Free

Laue x-ray diffraction (LXD) has been used for over 100 years to investigate the crystal structure of single-crystalline solids.¹ It is an especially useful tool for orienting single crystals for measurements of physical properties along specific crystallographic directions. LXD is also an excellent topic for advanced educational laboratories in physics and materials science. It can provide a forum for the discussion of electronic transitions within atoms, bremsstrahlung, the photoelectric effect, the penetration of electromagnetic radiation into matter, Bragg diffraction, strain within solids, twinning, crystallographic symmetries, and aspects of group theory.

Early imaging systems utilized photographic films. Since the 1960s, the standard was a 4 in. × 5 in. Polaroid Type 57 instant film (3000 ISO), a film packet that integrated the film and a pod of chemical developer enclosed in a wrapper.² It was designed for use with the Polaroid XR-7 Land Diffraction Cassette, a camera with a light-sealed frame and a mechanism for exposing and developing the film. After inserting the film packet, a metal bar at the film’s base was gripped by the camera’s mechanism so that partial withdrawal of the wrapper left the film inside of the camera. An exposure lever was then flipped, which pressed the unexposed film close to an x-ray-sensitive fluorescent screen. After x-ray exposure, the exposure lever was moved back to its original position, the wrapper was lowered to cover the exposed film, and then another lever was flipped, releasing the film’s metal bar while moving rollers tightly against the film packet. As the film packet was withdrawn from the camera, the rollers spread the chemical developer from the pod over the exposed film. After waiting a few moments, the developed film could be removed from the packet. Polaroid discontinued the manufacture of Type 57 film in 2008. Fujifilm FP-3000B temporarily served as a substitute. Although not fully compatible with the Polaroid XR-7, the film could be loaded and developed in a darkroom, and it possessed the correct film speed; it was discontinued in 2013.

The loss of a suitable instant film has made it impossible to keep many LXD units in service. Investment in a solid-state or wire-based detection system is a possibility, but the cost can be prohibitive, especially if the LXD system only experiences occasional use. In our own laboratory, we attempted to image the fluorescent screen in a darkened environment onto a digital astronomy camera with a Peltier-cooled CCD imaging chip. Unfortunately, the light intensity at the screen was insufficient for production of an image, even with exposures of more than 15 min. Eventually, a CCD detector specifically designed for LXD was obtained, but its performance was poor for some of the layered, micaceous-like, single crystals we investigated and for compounds with light elements that scatter x rays poorly. These issues led us to search for a solution using photographic films.

In this report, we describe the use of a 400 ISO silver halide sheet film with the polaroid land diffraction cassette. The exposed film is push processed during development so that it effectively behaves as a 3200 ISO film. The image quality surpasses that of the instant films because the grain size of the 400 ISO film is smaller. It routinely provides excellent images for any of the compounds we have tested. The film loading, exposure, development, and digitizing of the data are described. Data analysis is conducted with readily available freeware. Our method is a low-cost approach to bring LXD to laboratories with existing equipment that is currently idle due to the absence of a suitable instant film. Educators may find this information useful for advanced physics, chemistry, or engineering laboratories. Possible experiments for such laboratories are recommended. Low-cost surplus x-ray generators suitable for LXD experiments may be available on eBay or elsewhere for those who wish to introduce this technique into their laboratories. In addition, many x-ray diffraction units have multiple x-ray ports. LXD can be added to an unused port without disturbing the measurement equipment on the other ports.

The back-reflection method³ is the main focus of this Tutorial. Here, the film is placed between the x-ray source and the sample. The x-ray beam passes through the film before diffracting from the crystal’s surface. The back-reflection method produces diffraction spots arranged on hyperbolas or straight lines, depending on the single crystal’s orientation with regard to the incident beam intersecting the plane of the film. Since the x rays diffract from the surface layers of the sample, the sample size and shape are not important and no special preparation is generally required, although the sample surface should be clean and smooth.

In the transmission method,³ the film is positioned behind the sample so that the diffraction pattern on the film is due to a beam that diffracts as it passes through the sample. This method produces diffraction spots arranged in ellipses, hyperbolas, parabolas, and straight lines on the film, depending on the single crystal’s orientation with regard to the incident beam. In this method, the sample must be very thin in order for the x rays to pass through, and it must possess sufficiently low absorption. In general, μt < 1, where μ and t are the mass absorption coefficient and the thickness of the sample, respectively. Using tabulated values^4,5 for μ, we find that for photon energies around 30 keV, samples thicknesses must typically be on the order of 0.1 mm. This makes them fragile for an educational laboratory setting and often too thin for further investigation of their physical properties.

In orienting a single crystal, the goal is to shape the crystal so that the orientation of each face with regard to the crystal’s principal axes is known. This requires the use of a goniometer, a device on which the crystal can be mounted and then rotated about the spherical angles, α and β, while maintaining the sample’s diffraction surface fixed at the center of the spherical coordinate system. We mount our samples using Crystalbond 509, a thermoplastic adhesive⁶ that melts at 74 °C, binds when cooled, and is easily removed with a razor blade or acetone. If the sample contains naturally occurring facets, they can be used to speed the crystal-orienting process. Crystal facets are flat faces on crystals that grow slower than neighboring regions. They are macroscopic representations of crystallographic planes whose Miller indices are typically of order less than four,⁷ but they may not necessarily be associated with principal crystallographic directions. However, aligning the crystal such that a facet is perpendicular to the beam, or so that the beam bisects a corner formed by two adjacent facets, can yield diffraction patterns that are more easily identified. This can reduce the number of Laue exposures required to orient a crystal. If the sample does not contain naturally occurring facets, one may mount the sample to the goniometer along a cleavage plane, if one exists. If this is not the case, the next best approach is to mount the sample along an axis suggested by the sample’s natural morphology, such as the growth direction.

With the sample mounted, it must be positioned so that its front face is at the center of the goniometer sphere’s center. This is done with the help of a small viewing hole built into the goniometer. The goniometer is then placed (see Fig. 1) in front of the film at a distance that must be measured and recorded for data analysis purposes. Generally, a small rod of known length, approximately 20–30 mm, can serve as a convenient means of measuring the distance between the crystal’s surface and the camera. Later, an additional ∼10 mm must be added to this to account for the film’s displacement from the outside edge of the camera.

The discontinued instant film was replaced with Ilford HP5 Plus 400 Fast Black and White Professional Film,⁸ where 400 denotes the ISO. Normally, 400 ISO is insufficient to capture light from the fluorescent screen using standard developing times. Therefore, push processing was employed, which overdevelops the film such that it mimics film with an ISO of 3200. This method is often implemented by photographers when the lighting conditions are poor. Ilford HP5 Plus is available in a variety of sizes. The 5 in. × 7 in. sheet size was used, which was cut into 3.5 in. × 5 in. sheets using a paper cutter or scissors in absolute darkness. A sleeve was made from plain white office paper for inserting and removing the film from the camera. This was done by folding and trimming the paper to create a sleeve with approximate dimensions of 8 in. × 4 in. Both of the long sides were sealed with a fold and tape. One of the short sides was similarly sealed, while the other was left as an opening through which the film could be inserted. A razor blade was then used to cut out a window. The window is cut through only one side of the sleeve since x rays can easily penetrate through the paper. However, the window serves to give an unobstructed view between the film and the fluorescent screen. It must be slightly smaller than the dimensions of the film to keep the film in place and allow it to be withdrawn from the camera by pulling on the sleeve. Testing insertion and removal of the sleeve without the film is recommended, and it may be helpful to remove the dark screen (held with four screws) from the camera to test the sleeve as it is inserted and removed. In a darkroom, the film is loaded into the sleeve with the light-sensitive emulsion (concave side) toward the window. The sleeve is then loaded into the Laue camera with the window toward the fluorescent screen (away from the sample). After moving the expose lever to expose, which presses the film against the fluorescent screen, the camera is ready for exposure. After the x-ray exposure is complete, the film and the camera are taken to a darkroom. If a darkroom is not available, one can be made from blackout curtains. The film is removed from the camera for developing and marked so that its orientation relative to the sample is known. Cutting a corner from the film with scissors is a good method.

In the darkroom, the exposed film is developed using a series of solutions contained in six trays. In order, the trays contain Ilfotec HC developer, water, Ilford Ilfostop, water, Ilford Rapid Fixer, and the final water rinse. Opaque plastic food containers are used as trays to minimize the cost. The HC developer solution may age quicker with exposure to diffuse light, so a container made of dark plastic is best.

To observe the dim pattern captured by the film, push processing is required. This over-develops the film to the desired ISO by increasing the amount of time the film spends in the developer tray. Push processing increases the contrast and grain seen in photos. Higher contrast is a welcome consequence for Laue diffraction patterns since the diffraction spots are more easily seen. Increased grain is not an issue since the grain size in the 400 ISO film is below the resolution of the diffraction pattern. As an example, if ISO 400 film was used in a camera with an f/stop set for ISO 1600, then the film would be underexposed by two f/stops (400 → 800 → 1600). This would require a +2 push when developing. The Laue camera is assumed to have a hypothetical nonadjustable f/stop set for the ISO 3200 film. The ISO 400 film must undergo a +3 push to become equivalent to the ISO 3200 film. A +3 push corresponds to keeping the film in the developer for a total of 11 min with a developer/water ratio of 1/15 (see Table I). The developer is followed by a water rinse to clear away the majority of the developer solution (∼20 s). This rinse is followed by the stop tray where the film soaks for 10 s to neutralize the remaining developer. Ilford suggests to continue directly to the fixer after this step, but a water rinse was inserted here to reduce contamination between the trays. After this optional water rinse, the film should stay in the fixer for 2–5 min. At this point, a green safety light may be turned on. An image should have appeared after the stop tray (third tray) and will continue to develop into a more resolved image in the fixer. After about 2 min, the fixer will dissolve the unexposed emulsion and reveal a final image of the diffraction pattern in the form of dark spots while the background is left transparent. A final water rinse to eliminate the fixer completes the developing process. The photo is allowed to dry before digitizing the image with a scanner and a computer.

After developing, the photo should reveal a two-dimensional diffraction pattern. An example is shown in Fig. 2. In Laue diffraction, reflections from individual planes of a zone (planes that are parallel to one line, called the zone axis) all lie on the surface of an imaginary cone whose axis is the zone axis.³ When the reflected cone is intersected by the film, the diffraction spots appear along hyperbolas or straight lines, depending upon the crystal’s orientation with regard to the incident x-ray beam. Primary axes will occur at the intersection of many of these hyperbolas (or straight lines), which will appear as a spot on the film that is darker than those surrounding it. The diffraction pattern on the film is a small portion of the Ewald sphere³ whose surface patterns are strongly angular dependent. The pattern arrangement depends highly on the crystallographic axis along which the incident x-ray beam traveled. Therefore, the primary axes correlate with a specific arrangement of diffraction spots, which can be most easily identified using data analysis software programs. For this work, QLaue was used.⁹ It simulates back-reflection Laue diffraction images and can be downloaded for free from the Internet. The acquired Laue image is scanned and uploaded to QLaue. Prior to analyzing the data, the crystallographic parameters for the sample must be entered into QLaue so that an accurate pattern can be generated by the software. These parameters are usually available in the scientific literature. The sample-to-film distance d must also be entered into QLaue (see Sec. III). Tables II–IV in the  Appendix provide parameters for three compounds that can be purchased inexpensively as single crystals.^10–12 Each has a different crystal structure, and each is well suited for advanced educational laboratory exercises in physics or materials science.

Laue diffraction also provides information regarding the quality of the single crystal. Diffraction spots that are smeared might signify that the crystal has undergone a plastic deformation such as bending, twisting, or other types of cold working. This affects some regions of the crystal relative to others,³ leading to non-spherical diffraction spots. Twinning of single crystals is also possible, which alters the obtained Laue patterns depending upon the symmetry under which the twins form.^3,13,14

Once the primary axis is identified using QLaue, the goniometer is adjusted so that the axis is parallel to the incident x-ray beam, and the sample can then be shaped in situ on the goniometer to create a plane perpendicular to the oriented axis. This is done by screwing two plastic extensions of equal length to the goniometer and extending the sample, via the mounting piston, so that the plastic extensions and the sample make contact with a perpendicular plane. After securing the mounting piston, the three points formed by the sample and the plastic extensions lie in a plane that is perpendicular to the horizontal (see Fig. 3). The sample and the two plastic extensions are then placed on a flat glass plate, and the sample is gently sanded with fine-grain sandpaper (400 or finer grit) that is taped to the glass. Once that surface is prepared, the crystal can be removed, rotated by 180°, and remounted. Then, the goniometer is reset to the angles 0 and 0. A Laue exposure to make certain that the orientation is correct can then be taken, any adjustments can be made, and this side of the crystal can be sanded flat too. The result is two parallel, oriented faces. The accuracy of the crystallographic orientation is generally ±1°. The crystal can then be oriented in other directions, if required. Using this method, it is possible to shape the crystal into a parallelepiped with each face perpendicular to a determined crystallographic direction.

The lack of a suitable instant film and the cost of modern imaging systems have left many Laue x-ray diffraction systems inactive. A cost-effective solution that produces high-quality data is the adaptation of the Polaroid XR-7 Land Diffraction Cassette camera for use with a black and white film that is push processed. A brief description of how to determine the crystallographic orientation of a single crystal is provided. In addition, a method for preparing the oriented samples such that a planar surface is perpendicular to the oriented axis is described. Oriented single crystals can be used for further experiments that test for possible anisotropy in physical properties such as the electrical resistivity, magnetic susceptibility, thermal expansion, or stress/strain studies. The content in this Tutorial may prove beneficial for educational and research laboratories.

The authors thank K. J. McClellan for introducing us to the technique of preparing oriented crystals in situ using the type of goniometer shown in Fig. 3. Work at Montana State University was conducted with financial support from the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. DE-SC0016156.

The following tables contain crystallographic parameters of three common and affordable crystals: pyrite, zircon orthosilicate, and olivine. The crystal structures are cubic, tetragonal, and orthorhombic, respectively, which make them good candidates for advanced educational laboratories. Single crystals of each are readily available for purchase.