No, just leave it as it is. You should do only two things. 1) Inversion of the coordinates. 2) Multiplication by the LCM of the denominators.( In case a denominator is [itex]\infty[/itex], just ignore it!).TheRedDevil18 said:Do I have to somehow shift it so that it lies inside the cube ?
Miller Indices are a system of notation used in crystallography to represent the orientation of crystal planes and directions within a crystal lattice. They were developed by British mineralogist William Hallowes Miller in the 19th century.
To calculate Miller Indices for a crystal plane, you first determine the intercepts (i.e. the points where the plane crosses each axis) and take the reciprocal of each intercept. Then, these reciprocals are reduced to the smallest set of integers, which become the Miller Indices. For directions, the process is similar but uses the intercepts along the direction instead of a plane.
Miller Indices are important because they provide a standardized way to describe the orientation of crystal planes and directions. This is crucial for understanding the properties and behavior of crystals, which are widely used in many fields such as materials science, geology, and chemistry.
Miller Indices are written within parentheses, with the numbers separated by commas. If a direction has a negative intercept, it is denoted with a bar above the number. For example, the Miller Indices for a plane with intercepts of 2 along the x-axis, 3 along the y-axis, and 4 along the z-axis would be written as (2,3,4). The Miller Indices for a direction with intercepts of 1 along the x-axis, -2 along the y-axis, and 3 along the z-axis would be written as (1,-2,3).
The Miller Indices notation provides a concise and unambiguous way to describe crystal planes and directions. It also allows for easy comparison and identification of similar crystal structures. Additionally, Miller Indices can be used to predict the physical and chemical properties of crystals, as they are closely tied to the arrangement of atoms within the crystal lattice.