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Taking Bragg’s Law to a Higher Cognitive Level: Using Sketches to Assess Misconceptions of X-ray Diffraction Orders
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DOI：10.1021/acs.jchemed.5c01304.png)
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Abstract
En 中文
Undergraduate textbooks covering X-ray diffraction and Bragg’s Law typically show diagrams with only one diffraction order. As a result, students often incorrectly visualize X-ray diffraction orders as beams scattered from different crystalline planes rather than beams scattered at distinct angles. I argue that this misconception arises because the labels for crystalline planes, beams, and diffraction orders all share the same integers (1, 2, ...) and because students typically do not analyze the diagrams carefully. Solving Bragg’s Law problems is straightforward and typically does not produce learning at higher cognitive levels. In contrast, sketching different diffraction orders in real space demands a higher level of cognitive skill and is the main theme of my article. This task serves to assess students’ understanding and identify those students who can translate the Bragg’s Law formula into the physical process in real space. Here, I highlight common student misconceptions and propose hint-based questioning to help students apply critical theoretical concepts. When students see and think about an X-ray diffraction pattern with multiple orders, they experience an “aha!” moment and begin to correctly visualize these beams. I find that showing students a real XRD pattern with diffraction orders is more effective in helping them visualize the physical process than drilling Bragg’s Law problems.
Keywords:
Diffraction
Kinetic parameters
Order
Students
X-rays
Upper-Division Undergraduate
Analytical Chemistry
Physical Chemistry
Inquiry-Based/Discovery Learning
Laboratory Equipment/Apparatus
X-ray Crystallography
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