Miller indices were introduced in 1839 as a method to uniquely identify crystallographic planes and directions in a crystal structure. The Miller indices (hkl) are a set of integers that represent the inverse of the intercepts of a plane with the crystallographic axes. There are rules for determining the Miller indices based on these intercepts, such as always reducing fractions to lowest terms. Miller indices allow the orientation of different crystal planes and directions to be precisely defined and compared.

1. Structure of
matter(miller indices)

2. What is matter?
Matter is anything that has weight and takes up space.
This includes the solids, liquids, and gases in our surroundings, as well as inside
our bodies.

3. A structure is an arrangement and organization of interrelated elements in a
material object or system, or the object or system so organized.
What is structure??

4. Crystal???
A crystal is a solid whose atoms are arranged in a "highly ordered" repeating
pattern. These patterns are called crystal systems. If a mineral has its atoms
arranged in one of them, then that mineral is a crystal.

5. Introduction
Miller indices were introduced in 1839 by the British mineralogist William
Hallowes Miller. The method was also historically known as the Millerian system,
and the indices as Millerian.
The orientation of a surface or a crystal plane may be defined by considering
how the plane (or indeed any parallel plane) intersects the main crystallographic
axes of the solid.

6. The application of a set of rules leads to the assignment of the Miller Indices, (hkl); a
set of numbers which quantify the intercepts and thus may be used to uniquely
identify the plane or surface.
The application of a set of rules leads to the assignment of the Miller Indices, (hkl); a
set of numbers which quantify the intercepts and thus may be used to uniquely
identify the plane or surface.

7. Rules for Miller Indices
i. Determine the intercepts (a,b,c) of the plane along the crystallographic axes, in terms of unit
cell dimensions.
ii.Take the reciprocals of the intercepts.
iii.Clear fractions and reduce to lowest terms by multiplying each intercepts by the denominator
of the smallest fraction.
iv. If a plane has negative intercept, the negative number is denoted by a bar above the number.
Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get 1,1,1.

8. vi.If plane is parallel to an axis, its intercept is zero and meets at infinity.
vii. The three indices are enclosed in parenthesis, (hkl). A family of planes is
represented by (hkl).

9. General principles
i.If a Miller index is zero, the plane is parallel to that axis.
ii. The smaller a Miller index, the more nearly parallel the plane is to the axis.
iii.The larger a Miller index, the more nearly perpendicular a plane is to that
axis.
iv. Multiplying or dividing a Miller index by a constant has no effect on the
orientation of the plane
V. When the integers used in the Miller indices contain more than one digit, the
indices must be separated by commas. E.g.: (3,10,13)

10. vi. By changing the signs of all the indices of a plane, we obtain a plane located
at the same distance on the other side of the origin.

14. Family of planes
.Planes that are crystallographically equivalent have the same atomic packing.
• Also, in cubic systems only, planes having the same indices, regardless of order
and sign, are equivalent.

23. Summery
• Crystallographic points, directions and planes are specified in terms of indexing schemes.
• Materials can be single crystals or polycrystalline.
• Material properties generally vary with single crystal orientation (anisotropic), but are generally non
directional (isotropic) in polycrystals with randomly oriented grains.
• Some materials can have more than one crystal

24. Importance of Miller Indices
>In Materials Science it is important to have a notation system for atomic planes
since these planes influence
>Optical properties
>Reactivity
>surface tension
>Dislocations

25. Thank you