FAQs on Crystal Structure - 4 (Miller Indices for Crystallographic Points and Directions)

Question 1

1. What are Miller indices in crystallography?

Accepted Answer

Miller indices in crystallography are a system of notation used to describe crystallographic planes, directions, and points in a crystal lattice. They are represented by three integers [hkl], where h, k, and l represent the intercepts of the plane or direction with the crystallographic axes. These indices are used to identify and classify different crystal structures.

Question 2

2. How are Miller indices for crystallographic planes determined?

Accepted Answer

To determine the Miller indices for crystallographic planes, one must first find the intercepts of the plane with the crystallographic axes. The reciprocals of these intercepts are then multiplied by a common factor to obtain integers, which are represented as [hkl]. If the plane is parallel to an axis, the intercept is considered infinite, and its reciprocal is denoted as zero.

Question 3

3. How are Miller indices for crystallographic directions determined?

Accepted Answer

Miller indices for crystallographic directions are determined by finding the direction vector of the desired direction. The direction vector is then expressed in terms of the crystallographic axes. The reciprocals of the direction vector components are multiplied by a common factor to obtain integers, which are represented as [hkl].

Question 4

4. How are Miller indices used to identify crystal structures?

Accepted Answer

Miller indices are used to identify crystal structures by comparing the ratios of the indices with known crystal structures. Each crystal structure has a unique set of Miller indices for its planes and directions. By determining the Miller indices of a crystallographic plane or direction, one can match it with the known crystal structures and identify the type of lattice present.

Question 5

5. Can Miller indices be negative?

Accepted Answer

No, Miller indices cannot be negative. In the Miller index notation, negative signs are not used. If a plane or direction intercepts an axis in the negative direction, it is represented by placing a bar (-) above the corresponding index. This indicates that the intercept is negative and is used to distinguish it from positive intercepts.

Crystal Structure - 4 (Miller Indices for Crystallographic Points and Directions)

Solid State Physics for GATE

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