This is possible because all equispaced parallel planes are indicated by the same Miller indices.If the crystal plane being considered passes through the origin so that one or more intercepts are zero, the plane must be moved to an equivalent position in the same unit cell, and the plane must remain parallel to the original plane.Further examples of cubic crystal planes are discussed in the below Example Problem.Thus, the reciprocal intercepts become 6, 3, 2, and the Miller indices are (6 3 2).

Since fractional intercepts are not allowed, these fractional intercepts must be multiplied by 2 to clear the 3/2 fractions.The reciprocals of these intercepts are 3, 3/ 2, 1.The following figure shows three of the most important crystallographic planes of cubic crystal structures. The notation (hkl) is used to indicate Miller indices in a general sense, where h, k, and l are the Miller indices of a cubic crystal plane for the x, y, and z axes, respectively. These whole numbers are the Miller indices of the crystallographic plane and are enclosed in parentheses without the use of commas. Clear fractions and determine the smallest set of whole numbers that are in the same ratio as the intercepts.Form the reciprocals of these intercepts.Determine the intercepts of the plane in terms of the crystallographic x, y, and z axes for a unit cube.Choose a plane that does not pass through the origin at (0, 0, 0).The procedure for determining the Miller indices for a cubic crystal plane is as follows: Procedure for Determining Miller Indices for Cubic Crystal plane The cube edges of the unit cell represent unit lengths, and the intercepts of the lattice planes are measured in terms of these unit lengths. The Miller indices of a crystal plane are defined as the reciprocals of the fractional intercepts (with fractions cleared) that the plane makes with the crystallographic x, y, and z axes of the three nonparallel edges of the cubic unit cell. Miller Indices for Crystallographic planes

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