Crystallography

Trigonometry · Axiom Academy

LESSON Crystallography: Determining Crystal Structure Discover how trigonometry helps scientists determine the 3D structure of crystals and molecules by calculating angles between atomic bonds. The Hidden Geometry of Crystals When you look at a diamond or a snowflake, you're seeing the result of atoms arranged in precise geometric patterns. But how do scientists figure out these patterns? They can't see individual atoms with a regular microscope! Crystallographers use X-ray diffraction to study materials at the atomic level. By measuring how X-rays bounce off atoms, they can calculate the angles between atomic bonds —and these angles reveal the crystal's structure. In this module, you'll explore two fundamental crystal structures found throughout nature and technology: Let's explore these structures interactively and learn the trigonometry behind them! A tetrahedron is a 3D shape with four triangular faces. In chemistry, this is one of the most common molecular geometries—found in methane (CH₄), diamond crystals, and many proteins. Methane (CH₄): One carbon atom at center, four hydrogen atoms at corners Diamond: Each carbon atom bonded to four others in tetrahedral arrangement Silicon crystals: The basis of computer chips and solar cells Amino acids: Carbon centers in proteins often have tetrahedral geometry Try it: Drag the molecule above to rotate it. Notice how the atoms maintain their precise angular relationships! Calculating the Tetrahedral Angle

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