Miller indices are a method used in crystallography to describe the orientation of a plane or direction within a crystal lattice. They are represented by three integers (h,k,l) and are used to identify specific lattice planes or directions.
Miller indices are determined by taking the reciprocals of the intercepts of a plane or direction on the crystal lattice and then simplifying the resulting fractions to the smallest set of integers. The resulting numbers represent the values for h, k, and l in the Miller indices notation.
Miller indices are important in crystallography because they provide a standardized way to describe the orientation of crystal planes and directions. They are also used to calculate important properties of crystals, such as density and packing efficiency.
The packing density for an HCP unit cell is 0.74, meaning that 74% of the unit cell volume is occupied by atoms.
The packing density of an HCP unit cell is lower than that of a face-centered cubic (FCC) unit cell, which has a packing density of 0.74. It is also lower than that of a body-centered cubic (BCC) unit cell, which has a packing density of 0.68.