UTILIZING X-RAY INSTRUMENTATION COMBINED WITH 3D PRINTING TO INCREASE STUDENT'S CONCEPTUALIZATION AND UNDERSTANDING OF UNIT CELLS
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Summary
3D printing in the geosciences has been occurring for more than a decade (e.g., Hasiuk, 2014). It can be an easy and effective method to help teach landforms, fossils, porosity, and other areas of the geosciences (Hasiuk et al., 2017; Horowitz and Schultz, 2018; Ishutov et al., 2018; Ziegler et al., 2020). In mineralogy, most 3D printing student engagements have involved the 3D printing of crystal structures to replace traditional wooden block crystal models, as well as studies on crystal symmetry and point groups (e.g., Casas and Estop, 2015 and Hasiuk, 2017). This lab-based activity utilizes 3D printing of carbonate mineral unit cells to help students better understand and conceptualize unit cells. This lab-based activity would normally involve single crystal x-ray diffraction (SCXRD) of carbonate minerals which have a simple cationic substitutional solid solution. However, access to a SCXRD instrument is not required as 3D shape files for three different carbonate unit cells are provided by the authors of this activity.
We chose the carbonate minerals calcite (CaCO3), dolomite (CaMg[CO3]2), siderite (FeCO3), and rhodochrosite (MnCO3), because although Ca-Mg substitution is limited at lower temperatures, the crystal structure of the carbonate unit cell remains rhombohedral (trigonal) while the crystal axes change in length. Additionally, the changes in length are directionally proportional to the ionic radius of the major cations in each carbonate mineral. This allows for a direct relationship to exist between the size of the carbonate unit cell and the size of the major cation – i.e., the larger the cation the larger the carbonate unit cell, the smaller the cation the smaller the carbonate unit cell. This makes it easy to observe and measure unit cell changes after scaling them for 3D printing.
Students crush a carbonate mineral sample to the size appropriate for SCXRD measurements (normally 1 mm in length). Different carbonate minerals (e.g., calcite, dolomite, etc..) are given to different groups to prepare. The unit cells are measured with the SCXRD, and the data is investigated by the students with the free software program Mercury (available from the Cambridge Crystallographic Data Centre [CCDC]). The software program Mercury allows for the SCXRD unit cell data to be saved as either a color (VRML) or monochrome (STL) file for 3D printing. Please see Chen et al. (2014) for more information on using the software program Mercury for printing crystal structures. The 3D printed unit cells can then be compared to each other through physical investigation (e.g., measurements of the c-axis, relationships of the atomic bonds).
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Context
Audience
This unit cell activity is designed for an undergraduate-level student. It is best suited for a mineralogy course, crystallography courses, or an earth materials course. However, with slight modification to increase the depth of learning and expectations from the students, an instructor could use this activity in a graduate-level mineralogy, crystallography, or earth materials course.
Additionally, with modification of the mineral names for compounds (e.g., calcite rephrased to calcium carbonate; or siderite rephrased as iron carbonate) this activity could be well suited for any course which studies unit cells. For example, an inorganic chemistry course, a chemistry-orientated crystallography course, any instrumentation course which uses x-rays, or a materials course could all use this activity.
Skills and concepts that students must have mastered
In a geology course, students should have been exposed to carbonate minerals either through lecture or better yet through lab. They should also be familiar with the concept of atomic substitution in a mineral formula, in our example they need to have a basic understanding of the carbonate minerals, limited and complete solid solutions, the unit cell, the three crystallographic axes, the crystal systems, and the Bravais lattices. It would be helpful if Pauling's rules of crystal chemistry had also been covered, but not critical. All the crystallography can be at the introductory level. The students do not need to have a deep understanding of crystallography to benefit from this activity. We normally conduct this activity later in the semester after these concepts have been covered.
In non-geology courses, content leading up to the basic understanding of a unit cell needs to be known. Atomic substitution and solid solutions would also be very helpful in non-geology courses. This is because in the carbonate system, the size of the unit cell is directly related to the size of the major cation in the carbonate compound (mineral). As the ionic radius of the cation gets smaller, the carbonate unit cell will get smaller.
How the activity is situated in the course
This 3D printing unit cell lab is conducted by the class over several lab meetings. In the first meeting, the students are asked to identify the carbonate mineral based on its basic physical properties. In this first lab they also crushed the sample using pestle and mortar to prepare the carbonate minerals for SCXRD analysis. The students are instructed to crush the samples into exceedingly small fragment, close to 1 or 2 mm in length. Be careful to tell the students not to pulverize the samples.
In the second lab the students are instructed to use MinDat.org to identify the chemical formula, crystal system, and unit cell parameters of their carbonate mineral. The same information can be accurately obtained from the book "Rock-Forming Minerals, Volume 5B: Non-Silicates" by Chang et al. (1996) or similar. The students then make the SCXRD mounts under the guidance of the professor(s) and analyze the carbonate minerals with the SCXRD. This may take several tries depending on the quality of the crystal separates the students created during lab work. Often the minerals separated by the students tend to be too large and the unit cell displays the size expected for a twin. This is why we look up the information before analysis. Allow time for several analyses of each mineral. If there is still class time left after analysis, the students can complete the lab by filling in their measured data for the different carbonate minerals and comparing them to the "expected" data from the MinDat.org website. If not, this can be done during the next lab.
The data analyzed are then interpreted with the software program Mercury. Mercury allows for the SCXRD unit cell data to be manipulated and saved as either a color (VRML) or monochrome (STL) file for 3D printing. In Mercury, we found that displaying the carbonate mineral unit cells as "packing", with a "spacefill" style, color by "element", and the "show cell axis" to be an effective method for student understanding and 3D printing. By clicking "display, then "styles", then "spacefill" setting, we found that setting the atom size of "non-metals" at 0.38, "metals" at 0.54, and "bond radius (angstroms)" at 0.15, created a visually appealing unit cell which also 3D printed well. See Chen et al. (2014) for more information on 3D printing with the Mercury software program.
The files were then transferred over to Bambu Studio, the slicing software utilized to process the STL files. Each model was printed on a Bambu Labs X1C 3D printer. The files were scaled up to ensure printing success as well as general readability. A layer height of 0.20mm was used to keep printing times down but provided sufficient quality for the print. Other settings include 20% infill in a gyroid pattern and grid-like supports to ensure proper printing of pieces not in contact with the bed. Each print was done in white Elegoo PLA. Once printing was completed, supports were removed and minor post-processing was completed. It took between 22 and 24 hours to print our 3D models.
In the third and final lab the students analyze the data generated by the SCXRD and well as visual observations from the 3D printed carbonate unit cells. Students use unit cell parameters to compare crystal systems, crystallographic angles, and unit cell dimensions. By combining numerical data with 3D printed models, the lab explores how cation size influences unit cell dimensions, shape, and overall structure. The assignment ultimately asks students to interpret how substituting different cations affects the geometry and properties of carbonate mineral unit cells.
Goals
Content/concepts goals for this activity
The goal of this teaching activity is to help the students better understand unit cells through 3D printing. Unit cells are normally intangible and therefore very abstract and confusing to undergraduate students. By 3D printing a SCXRD measured unit cell students can have a tangible structure which they can study, measure, and learn from. Therefore, making an intangible unit cell "real", and improving student learning.
Higher order thinking skills goals for this activity
Using 3D-printed unit cells of carbonate minerals to have undergraduate geology majors measure and compare unit cell structures promotes several higher-order thinking skills, particularly analysis, evaluation, and spatial reasoning. This activity converts abstract crystallographic ideas into physical, measurable models, helping students better visualize and interpret complex structural relationships while making comparisons between carbonate minerals.
Skills goals for this activity
Students could potentially develop 3D printing skills.
Description and Teaching Materials
This 3D printing unit cell lab spans several meetings. In the first lab, students identify a carbonate mineral using physical properties and prepare it for SCXRD by carefully crushing it into ~1–2 mm fragments (without pulverizing).
In the second lab, students use Mindat.org or literature sources (e.g., Rock-Forming Minerals, Vol. 5B) to determine the mineral's chemical formula, crystal system, and unit cell parameters. They then mount and analyze samples using SCXRD, often requiring multiple attempts due to crystal size or twinning issues. If time allows, students compare measured data to expected values; otherwise, this is completed in the next lab.
SCXRD data are processed using Mercury software to visualize and export unit cells for 3D printing. Effective settings include "packing" display, "spacefill" style, color by element, and visible cell axes, with adjusted atom and bond sizes for optimal printing.
In the final lab, students analyze SCXRD results alongside 3D-printed models. They compare unit cell parameters and examine how cation size influences unit cell dimensions, geometry, and overall structure, ultimately interpreting how cation substitution affects carbonate mineral properties.
Mercury is free software used for structural visualization and analysis. Using this software, you can convert the single crystal x-ray diffractometer data into a file which you can print in 3D.
https://www.ccdc.cam.ac.uk/solutions/software/free-mercury/
SCXRD labs and key (Microsoft Word bytes May27 26)
Carbonate shape files (Zip Archive 6kB May27 26)
Carbonate 3D print files (Zip Archive 11.9MB May27 26)
Teaching Notes and Tips
Due to the cost, university required x-ray training, and operation complexity of the single crystal x-ray diffractometer (SCXRD) instrument, undergraduate students are not allowed to be primary users. The students prepare the sample by crushing a larger hand sample in a pestle and mortar and extracting several mm-size grains. The students then make the mount for the SCXRD and place the mount into the instrument. A faculty member has already started the SCXRD and aged up the x-ray tube to operating conditions. The student then can help the faculty member enter in required data, such as mineral formula, but the faculty member normally must center the crystal to save time. The student is then allowed to start the analysis through instrument operation software. The faculty member exports the collected data from the instrument software, and the students can then use the Mercury structural visualization software to work with the data as part of a lab under the instructor's guidance.
The Mercury structural visualization software is not difficult to use but requires some prior exposure by the faculty member before using this free structural visualization software in class with students. We recommend allowing time between SCXRD data collection and the class for the faculty member to work with the data using Mercury.
The Mercury structural visualization software can translate and export files into 3D printable files (*.stl or *.vrml). We processed the 3D printable file with the PrusaSlicer slicing software. The 3D printing of the carbonate (calcite, dolomite, and rhodochrosite) was done by a staff member with extensive knowledge of 3D printing. Even with this experience, this was time intensive and required trial and error with layer heights, thickness, and placement of supports. We also needed trial runs using different settings in the Mercury structural visualization software. The first attempt in 3D printing was done with a single calcite structure (CaCO3) as a ball and stick model. This created a 3D printed structure which was too flimsy and weak. We then used a space filled model and modified the space filled settings, so the atom size (times van der Waals radius) was 0.3 for non-metals, 0.54 for metals, and the bond radius was 0.22. This created strong 3D printed structures which were still easy to see all atoms, their relationships, and the bonds. Trial, error, time, and most importantly expertise with 3D printing is suggested. The 3D models we generated took 22 to 24 hours to print, and they are only 19 to about 20.1 cm tall.
Mercury is free software used for structural visualization and analysis. Using this software, you can convert the single crystal x-ray diffractometer data into a file which you can print in 3D.
https://www.ccdc.cam.ac.uk/solutions/software/free-mercury/
Assessment
All labs were graded as part of the class's lab grade. Additionally, we utilized the Creative Exercises of Lewis et al. (2012) to assess the students learning of the unit cell concepts and the impact of the 3D printed unit cells. This consisted of a simple prompt given as a pre-test early in the semester, before the labs involving x-rays but after lectures covering both atomic substitution and unit cells. The same Creative Exercise prompt was given to the students on the last day of class, after all labs related to the x-rays analysis and the printing and study of the carbonate unit cells. See below for the simple Creative Exercise prompt:
We will be investigating five different carbonate minerals, calcite, dolomite, magnesite, rhodochrosite, and siderite, using x-rays over several labs this semester. Each of these minerals have a rhombohedral unit cell. These carbonate minerals have different two-plus cations in their octahedral coordination site.
What do you think will happen to the unit cells of these carbonate minerals as one cation is substituted for another?
On the pre-test many students thought the unit cell would change its shape after cation substitution even though they were told all unit cells are rhombohedral. They also thought the unit cell would become unstable and possible deconstruct. The students demonstrated greater understanding of carbonate unit cells and how atomic substitutions can change the size of a unit cell on the post-test. Most of the students correctly stated the carbonate unit cell size was dependent on the size of the cation. Only two students still thought the unit cell would change shape, and only one student still thought the unit cell would become unstable.
References and Resources
Resources:
A SERC X-ray Diffraction website which can be used to enhance this activity or provide background information for the students: Dutrow, B.L., and Clark, C.M., X-ray Powder Diffraction (XRD): SERC Nontechnology in STEM Instruments and Analytical Methods Common to Nano: serc.carleton.edu/207663
A SERC Single-crystal X-ray Diffraction website which can be used to enhance this activity or provide background information for the students: Clark, C.M., and Dutrow, B.L., Single-crystal X-ray Diffraction: SERC Nontechnology in STEM Instruments and Analytical Methods Common to Nano: serc.carleton.edu/207675
Mindat can be utilized by students and faculty to look up expected unit cell dimensions/volume, space group, formula, and other crystallographic parameters of the minerals you are considering to investigate with the students: https://www.mindat.org/
References:
Casas, L., and Estop, E., 2015, Virtual and printed 3D models for teaching crystal symmetry and point groups: Journal of Chemical Education, v. 92, p. 1338–1343.
Chang, L. L. Y., Howie, R. A., and Zussman, J., 1996, Rock-Forming Minerals, Volume 5B: Non-Silicates: Sulphates, Carbonates, Phosphates and Halides (2nd ed.): London, Geological Society of London, 383 p.
Chen, T-H., Lee, S., Flood, A.H., and Miljanić, O. Š., 2014, How to print a crystal structure model in 3D: CrystEngComm, v. 16, p. 5488–5493.
Hasiuk, F.J., 2014, Making things geological: 3-D printing in the geosciences: GSA Today, v. 24, p. 28–29.
Hasiuk, F.J., Harding, C., Renner, A.R., and Winer, E., 2017, TouchTerrain: A simple web-tool for creating 3D-printable topographic models: Computers and Geosciences, v. 109, p. 25–31.
Horowitz, S.S., Schultz, P.H., 2014, Printing space: using 3D printing of digital terrain models in geosciences education and research: Journal of Geoscience Education, v. 62, p. 138–145.
Ishutov, S., Dawn, J.T., Zhang, S., et al., 2018, Three-dimensional printing for geoscience: fundamental research, education, and applications for the petroleum industry: AAPG Bulletin, v. 102, p. 1–26.
Lewis, S.E., Shaw, J.L., and Freeman, K.A., 2010, Creative exercises in general chemistry: A student-centered assessment: Journal of College Science Teaching, v. 40, p. 48–53.
Ziegler, M.J., Perez, V.J., Pirlo, J., Narducci, R.E., Moran, S.M., Selba, M.C., Hastings, A.K., Vargas-Vergara, C., Antonenko, P.D., and MacFadden, B.J., 2020, Applications of 3D Paleontological Data at the Florida Museum of Natural History: Frontiers in Earth Science, v. 8, 600696.