Models as an Aid to Courses in Crystallography and Mineralogy K. T. Bradyl Department of Chemical Technology, The Papua New Guinea Unl versity of Technology, P.O. Box 793, Lae, Papua, New Guinea Much of the theory associated with crystallography and the behavior of crystals in transmitted lightmicroscopy is difficult to teach to undergraduate students. In part, this is due to the wide gap in competence which exists between an experienced microscopist interpreting an image, compared to the imuressions eained bv a beainner takine.a first look down the microscope. Some of the uroblem, however, lies in the interpretation of the image in teims of the complex theory of transmitted light microscouv, which itself is a marriage of optics, wave theory, and c r y s ~ l o g r a p h y . The value of microscopy has in recent years been neglected in traditional chemistry teaching. No doubt the determination of crystal structure by X-ray diffraction is more specific, but also it is more expensive, time consuming, and often outside the scope of many chemistry courses. Yet structure determinations are imnortant: different allotrovic forms and compounds with differing stoichiometry have significantly different properties, uses, and processing techniques. While it is easy to differentiate diamond from graphite, it is not a simule matter to differentiate calcite from araeonite, pyrite from pyrrhotite, or hornite from chalcopyriteby chemical methods, uarticularlv when they are present in a composite
heavv. tinned comer wire "normals" to each face were soldered in makes an ideal base. In use the students are asked to produce acardboard replica of the
crystal (also in plate 1) and label each plane with the appropriate Miller indices. They then produce a stereographic projection of the crystal, using the large model (which is not labelled) as a guide. (b) Optical lndicatrix Models for Isotropic and Anisotropic
Minerals
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Present address: Metallurgy Department, Ballarat C.A.E., Ballarat, Victoria, Australia.
material. ...-. . ..-. .
Transmitted light microscopy can be used for this purpose, and of course there are other numerous applications in forensic science, organic chemistry, and biochemistry where microscooic identification is of naramount i m ~ o r t a n c e -I n teaching crystallography and mineralogy to students undertaking Bachelor of Chemical Technology courses a t the University of Technology in Papua New Guinea, a series of models was found to assist areatlv. student comprehension in the subject. Specific Models and Their Applications Three simple models are presented in the following paragraphs with some explanation as to their application. They would he easily constructed by any competent technician and their application to similar courses a t other institutions would he almost universal. (a) Stereographic Projection Model This model is shown in Plate 1.It consists of a cubic crystal made from 26 e ealvanized iron. such that the cube. the rhombdodecahedron Figure 1. Stereographic projection model showing a cubic crystal with rhombdodecahedron and octahedron faces developed.
36
Journal of Chemical Education
Figure 2. Models of the optical indicatrix of isometric, Uniaxial and Biaxial Crystals. Figure 3. Model showing the effectof an anisotropic crystal between crossed polars. slotted so that they fit together. In the case of the Biaxial model, the two circular wave fronts corresponding to the two opticaxes are put into the model each as four, quarter circles. A measuringcylinder base makes a suitable stand. Their use is universal in explaining the division of transmitted light into ordinarv and extraord~narv in mineral crvstals. Thev are . ravs " primarily used for lectures and explanations in practical sessions.
analyzer. The polarizer and the analyzer must, of course, be crossed. The resultant resolution of the two waves (with a phase difference) is shown hy using a wave rather than an amplitude notation, since this enables the ~ h a s difference e to be seen readily. Once aeain wire is used
(c) Anisotropic Minerals Under Crossed Polars
anisotropic crystal under crossed polars, including extinction, polarization colors (birefringence) and the effect of rotating the mierascope stage. The model is based on sketches in the text by Read2 and mare particularly an a diagram in a booklet used by Bougainville Copper Ltd. for training purpose^.^
shown in Plate 3. The model consists of a solid steel base into which is fitted a segmented brass rod which represents a ray of light. A circle of wire which supports a radiating array of wires is located near the base of the model. This is meant to represent ordinary light vibrating in all directions normal to the direction of propagation. A disc of Perspexm, suitably marked to indicate the direction of allowable vibration, is next in the sequence, and this represents the polarizer. The amplitude of the allowable vibration directionafter the palarization in one plane is then shown as wires soldered through the brass rod. The anisotropic crystal is represented by a Perspexa rectangle with the allowable vibration directions o and e marked on it. The subseauent vibrations in two lanes allowed hv the anisotrooie
Concluding Remarks T h e models orovide a link between t h e definite a n d t h e abstract which is very useful i n getting t h e message across. T h i s is t r u e of all teachine models and. of course. is t h e reason t h e y a r e used. I n u n d e r d e v e l o ~ e dcountries thev are esoeciallv useful since they help t o bridge t h e technology gap and enabG all students to start from a common concept. F r o m t h e r e on, however, it is, as always, u p t o t h e skill of t h e teacher.
Read, H. H., "Rlrtley's Elements of Mineralogy," 26th Edition, Thos. Murphy & Co., London, 1974. Clark, C., "Mineralogy Manual," Bougainville Copper Ltd.
Volume 60
Number 1
January 1983
37
