Crystal Lattice Viewer

A fundamental measure of a crystal structure's efficiency is its Atomic Packing Factor (APF). It's the fraction of volume in a unit cell that is occupied by atoms, treated as hard spheres.

For example, in a Face-Centered Cubic (FCC) lattice, there are 4 whole atoms per unit cell. If the atomic radius is $r$, the cube side length is $a = 2\sqrt{2}r$. The APF calculation yields the famous close-packed value.

Another key concept is the Coordination Number (CN), which is the number of nearest neighbor atoms touching a given atom. This directly influences bonding strength and material properties.

In the simulator, the coordination number is calculated for you. Notice how it jumps from 6 in Simple Cubic, to 8 in BCC, and to 12 in FCC and HCP—the maximum for equal spheres.

Metallurgy & Alloy Design: The crystal structure determines a metal's properties. For instance, FCC metals like aluminum and copper are highly ductile and malleable, making them ideal for wires and sheets. BCC metals like iron at room temperature are stronger but less ductile.

Semiconductor Manufacturing: Silicon crystallizes in the diamond cubic structure, which is based on two interpenetrating FCC lattices. The precise arrangement of atoms is critical for the electronic properties of every computer chip.

Biomaterials & Implants: Titanium and its alloys, which often have an HCP structure (alpha-Ti), are used for bone implants because this structure, along with surface treatments, promotes excellent biocompatibility and bone integration.

Polymer Crystallinity: While polymers are often disordered, regions can form crystalline lamellae with chain-folded structures. Understanding lattice packing helps engineers control the stiffness and melting point of plastic products.

First, please do not take the simplified "atoms as hard balls" model too literally. The spheres displayed by NovaSolver are a convenient representation of the "electron cloud" spread of an atom using a radius. In actual chemical bonding, electrons are shared or orbitals hybridize, which differs from simple geometric contact. For example, the extreme hardness of the diamond structure, despite its low packing density, cannot be explained by this "hard ball" model alone; the directionality of strong covalent bonds is key.

Next, there is a tendency to mistakenly think parameters can be varied independently. In the tool, moving the "nearest neighbor distance" slider changes the atomic radius, and the lattice constant changes accordingly. However, in real materials, the lattice constant is largely determined by the element type and is not something you can freely change. For instance, the lattice constant of pure iron's BCC structure (ferrite) is about 0.286 nm. Adding larger molybdenum atoms here strengthens the material by forcibly "stretching" the lattice. The operation of increasing the BCC radius to create strain in the tool is precisely what helps you understand the concept of solid solution strengthening.

Finally, note that if you focus the "display range" only on the unit cell, you lose sight of the bigger picture. Real materials are "polycrystals" composed of hundreds of millions to trillions of these unit cells gathered together, with the orientation of each crystal grain being random. When evaluating material anisotropy (differences in strength by direction) in CAE, the behavior of this aggregate is simulated. Expanding the display range in the tool to show repeated lattices is the first step in grasping the concept from "single crystal" to "polycrystal".