Enter the lattice constant and the miller indices h,k, and l into the calculator to determine the interplanar spacing of a cubic lattice.
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Lattice Spacing Formula
The following equation is used to calculate the Lattice Spacing.
dhkl = a / SQRT(h^2+k^2+l^2)
- Where dhkl is the lattice spacing
- a is the lattice constant
- h, k, and l are the miller indices
What is a Lattice Spacing?
The crystal’s interplanar spacing, or lattice spacing, is the shortest distance between planes of atoms in a crystal. A plane is one of the sets of three-dimensional coordinates that lie in a single symmetry direction of the crystal. The planes are related to the faces of a geometric object called a parallelepiped, which has its edges lying in three coordinate planes.
The description and representation of interplane distances may be complicated. They are usually represented as vectors, but they may also be described as scalar quantities such as fractions or ratios.
The smaller the interplanar distances, the closer the planes are, and the more closely packed the atoms are. There are several representations for lattice constants in materials science and crystallography, including vectors, fractions, and gradients.
Interplanar spacing is one of the parameters used to describe crystal structures using stereographic projection in structural chemistry and materials science. Crystals with relatively small interplanar spacings have facilities that are essentially 3-dimensional near their surfaces; these crystals are called close-packed and often have metallic properties.
Those with greater spacings have lower density and form simple cubic structures (such as ionic crystals). Those with greater spacings can develop complex cubic systems (such as diamonds).