From 2D to 3D: Escher Drawings - Crystallography, Crystal Chemistry, and Crystal "Defects"

Peter Buseck

Arizona State University

This activity is part of the On the Cutting Edge Peer Reviewed Teaching Activities collection. (view details)

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Initial Publication Date: August 19, 2008 | Reviewed: January 19, 2015 (see revision history: 2 events)

Summary

This set of exercises illustrates plane and space groups as well as crystal chemistry and "defects" in crystals. The problems are designed to present the material as puzzles that are visually attractive and intellectually challenging.

Crystallography, Crystal Chemistry, Mineral Analysis, Physical ...(more) | College Lower (13-14), College Upper (15-16)

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Context

Audience

This exercise is designed for a sophomore or junior level required course in mineralogy.

Skills and concepts that students must have mastered

Students should have a basic familiarity with symmetry elements, unit cells (2D and maybe 3D), and have been exposed to the concepts of plane groups.

How the activity is situated in the course

This is a stand-alone exercise.

Goals

Content/concepts goals for this activity

This exercise was designed to increase students' skills in understanding mineral symmetry, unit cells, plane and space groups, crystal chemistry, and "defects" in crystals.

Higher order thinking skills goals for this activity

Other skills goals for this activity

Description of the activity/assignment

This problem set uses Escher drawings as 3-D projections to make analogies to real minerals as well as order/disorder relations to provide examples of features found in real minerals (e.g. superstructures, substitutions, structural defects, and modulated and incommensurate structures).