Learn about crystallographic planes, which are imaginary flat surfaces within a crystal lattice, and Miller Indices, a notation system used to describe their orientation in materials science and crystallography.
Have More Questions →
Crystallographic planes are imaginary flat surfaces that pass through a crystal lattice, defined by the periodic arrangement of atoms. These planes are crucial because many material properties and behaviors, such as slip systems in plastic deformation, cleavage, and diffraction patterns, are directly related to the the arrangement and spacing of atoms along these specific planes.
Miller Indices are a symbolic notation, represented as (hkl), used to uniquely identify the orientation of crystallographic planes and directions within a crystal lattice. They are derived from the reciprocals of the fractional intercepts that a plane makes with the crystallographic axes, then cleared to the smallest set of integers. A negative intercept is indicated by a bar over the number.
For a cubic crystal, the (100) plane intersects the x-axis at 1 unit length and runs parallel to the y and z axes (meaning it intercepts at infinity along y and z). Taking the reciprocals (1/1, 1/∞, 1/∞) gives (1, 0, 0). This plane is a fundamental reference in many cubic crystal structures, such as face-centered cubic (FCC) or body-centered cubic (BCC).
Miller Indices are indispensable in materials science and engineering. They help predict preferred growth directions of crystals, understand mechanical deformation mechanisms like twinning and slip, interpret X-ray diffraction patterns for material characterization, and design semiconductor devices where specific crystal orientations are critical for performance.