Explore SC, BCC, FCC, and HCP crystal structures in interactive 3D. Adjust lattice constant, rotation, and atom radius to see packing fraction and coordination numbers change in real time.
It's the ratio of atomic volume to unit cell volume, assuming atoms are hard spheres. SC≈52.4%, BCC≈68.0%, FCC=HCP≈74.0%. The remaining space is interstitial volume that can accommodate smaller atoms (like carbon in steel) or contribute to diffusion pathways.
X-ray diffraction (XRD) is the standard method. X-rays scattered by crystal planes satisfy Bragg's law: nλ=2d·sinθ. By measuring diffraction angles θ, the d-spacing and hence lattice constant can be determined with accuracy better than 0.001 Å. Synchrotron XRD achieves even higher precision.
HCP is not one of the 14 Bravais lattices by itself — it is a hexagonal lattice with a two-atom basis. The hexagonal Bravais lattice plus the diatomic basis (one atom at origin, one at 2/3, 1/3, 1/2) forms the HCP structure. This distinction matters in crystallography but not for most engineering applications.
Single-crystal materials (like turbine blades) require anisotropic elastic constants (up to 21 independent stiffness components). HCP metals like titanium need full 5-component elastic tensors. In FEM, crystal plasticity models explicitly track slip systems per grain. Polycrystalline averaging (Taylor/Voigt/Reuss) provides homogenized properties for engineering-scale simulations.
Crystal Lattice Structure Visualizer is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
The simulator is based on the governing equations of Crystal Lattice Structure Visualizer. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Engineering Design: The concepts behind Crystal Lattice Structure Visualizer are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.