Kristallplan

Kristallplan, or crystal plane, is a plane within a crystal lattice along which the arrangement of atoms repeats in a regular, periodic way. The term kristallplan is the German equivalent of the English term and is commonly used in crystallography to describe one of the many parallel planes that can be imagined cutting through a crystal.

Each crystal plane is labeled by Miller indices (hkl). These indices describe the plane’s intercepts with the crystal axes: the plane crosses the x, y, and z axes at distances proportional to a/h, b/k, and c/l, where a, b, and c are the lattice parameters. The indices are the reciprocals of these intercepts (scaled to integers). Planes related by crystal symmetry are grouped into families, denoted by braces {hkl}, while a single plane is denoted by parentheses (hkl). The direction perpendicular to a plane is called its normal.

The spacing between parallel crystal planes, denoted d_hkl, depends on the lattice type. For a cubic crystal system, the interplanar spacing is d_hkl = a / sqrt(h^2 + k^2 + l^2). This spacing governs how X-ray, electron, or neutron waves diffract off the planes, a relationship described by Bragg’s law. Crystal planes thus underpin diffraction patterns, lattice indexing, and the interpretation of crystal structures in minerals, metallurgy, and materials science.

In practical use, kristallplan helps researchers describe crystal orientation, identify phases, and relate microscopic structure to macroscopic properties. The concept is foundational in crystallography, solid-state chemistry, and related fields.