Abstract
Units cells are the basic building block of minerals and all crystalline solids. Students have difficulty comprehending unit cells due to their intangibility and the many ways they are displayed. Assessment suggests student's lack of unit cell understanding persists even after instruction. 63% of the students thought the carbonate unit cell would change shape and 18.5% thought the unit cell would become unstable as cations were substituted for each other. To address this, we combined powder and single crystal X-ray diffraction (PXRD & SCXRD) with 3D printing of carbonate unit cells. Carbonate minerals were chosen because the radius of the 6-fold cation controls the size of the unit cell while the shape remains rhombohedral (trigonal). Students prepared and analyzed 5 different carbonates with PXRD (CaCO (sub 3) , (CaMg)(CO (sub 3) ) (sub 2) , MnCO (sub 3) , MgCO (sub 3) , & FeCO (sub 3) ). They identified the 2theta and calculated the d-spacing of the rhombohedral crystal faces for all 5 carbonates. They then graphically compared the d-spacing and 2theta vs. the 6-fold ionic radii of the cations. Students then prepared 3 carbonate minerals (CaCO (sub 3) , (CaMg)(CO (sub 3) ) (sub 2) , MnCO (sub 3) ) for SCXRD. SCXRD provided the students with the alpha , beta , and gamma , crystallographic axes lengths, space group, crystal system, and volume of the unit cells. Students graphed the a and c axes for each of the carbonate minerals. In combination with the data generated for the carbonate minerals with the PXRD and SCXRD, 3D models for CaCO (sub 3) , (CaMg)(CO (sub 3) ) (sub 2) , and MnCO (sub 3) unit cells were printed using fused deposition modeling. 3D printed models were compared with traditional mineral structural model for carbonates and typical diagrams for carbonates from textbooks. The students physically compared the size and shape of the different 3D printed carbonate unit cells and measured the c-axis in centimeters. They also compared the 3D models to the PXRD and SCXRD data. Assessment after work with the 3D models and XRD data displayed improvement in the student's understanding of the carbonate unit cell. 62% correctly stated the unit cell's size was dependent on the cation, 24% could relate the d-spacing to the cation substitution, only 2 students thought the unit cell would change shape, and only 1 student thought it would become unstable.
