Miller indices are an important tool in materials science. They help to describe crystal structures in an easy way. By using Miller indices, scientists and engineers can look closely at materials on an atomic level.
Miller indices are three numbers written as (hkl). These numbers show the angle of a crystal plane in relation to a crystal's structure. Each number is based on how the crystal plane intersects with the axes of the crystal.
Miller indices also work for crystal directions. Directions are noted using square brackets, like [uvw]. Here, u, v, and w represent the parts of the direction along the axes.
Different crystal systems use Miller indices in various ways. Some of these systems include cubic, tetragonal, hexagonal, orthorhombic, monoclinic, and triclinic.
Characteristics: These crystals have equal sides and angles of 90 degrees between them. Common examples are table salt and diamond.
How Miller Indices Work: In cubic crystals, Miller indices match directly to the planes and directions. For example, the (100) plane cuts the x-axis at one unit while continuing infinitely along the y and z axes.
Characteristics: Tetragonal crystals have two sides that are equal and a third side that is different, all with right angles. Tetragonal zirconia is a good example.
How Miller Indices Work: In this system, Miller indices still apply, but take into account the longer axis. For example, the (001) plane is flat across the a-b plane and goes straight up along the c-axis.
Characteristics: Hexagonal crystals have four axes. Three of them are equal in length and meet at angles of 120 degrees. The fourth axis goes straight up. Graphite is an example.
How Miller Indices Work: In hexagonal crystals, we use something called Miller-Bravais indices, shown as (hkln). The first three numbers show the base
Miller indices are an important tool in materials science. They help to describe crystal structures in an easy way. By using Miller indices, scientists and engineers can look closely at materials on an atomic level.
Miller indices are three numbers written as (hkl). These numbers show the angle of a crystal plane in relation to a crystal's structure. Each number is based on how the crystal plane intersects with the axes of the crystal.
Miller indices also work for crystal directions. Directions are noted using square brackets, like [uvw]. Here, u, v, and w represent the parts of the direction along the axes.
Different crystal systems use Miller indices in various ways. Some of these systems include cubic, tetragonal, hexagonal, orthorhombic, monoclinic, and triclinic.
Characteristics: These crystals have equal sides and angles of 90 degrees between them. Common examples are table salt and diamond.
How Miller Indices Work: In cubic crystals, Miller indices match directly to the planes and directions. For example, the (100) plane cuts the x-axis at one unit while continuing infinitely along the y and z axes.
Characteristics: Tetragonal crystals have two sides that are equal and a third side that is different, all with right angles. Tetragonal zirconia is a good example.
How Miller Indices Work: In this system, Miller indices still apply, but take into account the longer axis. For example, the (001) plane is flat across the a-b plane and goes straight up along the c-axis.
Characteristics: Hexagonal crystals have four axes. Three of them are equal in length and meet at angles of 120 degrees. The fourth axis goes straight up. Graphite is an example.
How Miller Indices Work: In hexagonal crystals, we use something called Miller-Bravais indices, shown as (hkln). The first three numbers show the base