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Goniometry of Direct Lattice Vectors Supporting Students' Comprehension of Crystallographic Core Concepts and Demonstrating Image-Based Nanocrystallography

  • P. Moeck (a1), K. Padmanabhan (a2), W. Qin (a3) and P. Fraundorf (a4)


We are of the opinion that students of an introductory materials science and engineering course should gain a thorough understanding of crystallographic core concepts by applying them quasi-experimentally in computer simulation sessions that run parallel to the lectures. Software simulations of goniometry of direct lattice vectors in a transmission electron microscope (TEM) will serve two purposes at once: to introduce students to practical aspects of electron microscopy and support their comprehension of crystallographic core concepts. We use the programming software Matlab and Java (Jmol applets) on a PC platform for the creation of software simulations that demonstrate this methodology and complement already existing software simulations. The newly created software is used in classroom demonstrations of an introductory materials science and engineering course at Portland State University and will become freely accessible over the internet. This software will also support and promote image-based nanocrystallography in TEM.



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[1] Wuensch, B., Journal of Chemical Education 65, 494 (1988).
[2] Allen, S.M. and Thomas, E.L., The Structure of Materials (John Wiley & Sons, 1999).
[3] Barrett, C.S., Structure of Metals, Crystallographic Methods, Principles, and Data (McGraw- Hill, 1943).
[5] Fraundorf, P.B. and Pongkrapan, N., Proc. 2004 Microscopy and Microanalysis Meeting of the Microscopy Society of America, Savannah (Georgia), August 1-5, 2004.
[6] and
[7] Callister, W.D. Jr., Mat. Res. Soc. Symp. 760E, JJ6.1.1 (2003) and W.D. Callister Jr., Fundamentals of Materials Science and Engineering: An Integrated Approach (John Wiley & Sons, 2005).
[8] Cahn, R.W., MRS Bulletin, July 2003, 468.
[9] Cahn, R.W., The Coming of Materials Science (Pergamon 2001).
[10] Schaffer, J.P., Saxena, A., Antolovich, S.D., Sanders, T.H., and Warner, S., The Science and Design of Engineering Materials (McGraw-Hill, 1999).
[11] Fraundorf, P., Ultramicroscopy 22, 225 (1987).
[12] Qin, W. and Fraundorf, P.B., Ultramicroscopy 94, 245 (2003).
[13] Möck, P., German patents DE 4037346 A1 and DD 301839 A7, priority date: 21 November, 1989.
[14] Since the intersection of the goniometer axes (tilt-rotation center) does not coincide with the center of the Si model crystal in the thinnest region of the disk in Figs. 3a,b, there are projection effects that need to be taken into account in measurements of the spacings of crystallographic planes. Alternatively, one may try to adjust the tilt-rotation center to the correct specimen “height” and “lateral position of interest” – just as one would do in a real TEM. Nevertheless, the crystallography of Si is reasonably well revealed by this matching pair of two-dimensional projections. The length markers in Figs. 1c, 2a, and 2b are adjusted to the size of the buckyball, which was at the tilt-rotation center when these images were captured. Note also that the point-to-point resolution of the simulated TEM is superb as the so called “Si dumbbells”, i.e. the {400} lattice spacings which are in reality only 0.136 nm wide, are clearly revealed in Fig. 3a.
[15] Johari, O. and Thomas, G., The stereographic projection and its application (Wiley, 1969).
[16] Hake, R.R., Am. J. Phys. 66, 64 (1998);∼sdi/ajpv3i.pdf


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