Condensed matter physics
Crystal structures
Identify lattice sites in SC, BCC, and FCC unit cells, change the lattice constant, and calculate the atomic packing fraction .
Equipment
- Rotatable 3D unit-cell visualization with atoms at lattice sites
- SC, BCC, and FCC selectors and a lattice-constant control
Procedure
Select a unit cell
Switch among SC, BCC, and FCC. Count corner, body-center, and face-center contributions to the effective atoms per cell.
Rotate and resize
Drag the cell to inspect its three-dimensional arrangement, then adjust the lattice constant . The displayed sphere radius follows the contact geometry of each lattice.
Compare packing
Read the effective atom count and packing fraction. SC, BCC, and FCC give approximately 52.4%, 68.0%, and 74.0%, respectively, in the hard-sphere model.
Simulation
Experiment history
In 1912, Max von Laue and his collaborators demonstrated that crystals diffract X-rays, establishing that crystals have regularly spaced internal structure and that X-rays have wave character. In 1913, William Henry Bragg and William Lawrence Bragg used X-ray diffraction to determine crystal structures, including the relation now known as Bragg's law.
Max Born and Theodore von Kármán helped develop the theoretical physics of crystal lattices and lattice vibrations in the early twentieth century. Born's work connected atomic arrangements with the stability and dynamics of solids; the SC, BCC, and FCC hard-sphere cells shown here are idealized geometric models rather than full descriptions of real materials.