How do you calculate Miller indices?

How do you calculate Miller indices?

1.2: Miller Indices (hkl)

  1. Step 1: Identify the intercepts on the x- , y- and z- axes.
  2. Step 2: Specify the intercepts in fractional co-ordinates.
  3. Step 3: Take the reciprocals of the fractional intercepts.
  4. Other Examples.

Why do we need 4 indices to index a hexagonal system?

4-index notation is more important for planes in HCP, in order to distinguish similar planes rotated by 120o. 1. Find the intercepts, r and s, of the plane with any two of the basal plane axes (a1, a2, or a3), as well as the intercept, t, with the c axes. 2.

How many Miller indices are there in hexagonal unit cells?

four indices
In HCP unit cells, crystallographic planes are indicated using four indices which correspond to four axes: three basal axes of the unit cell, a1, a2, and a3 , which are separated by 120º; and the vertical c axis.

How many Miller indices are there in hexagonal unit cell?

Why are there four numbers in a hexagonal unit cell?

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Four numbers are used in order to make the relationship between the indices and the symmetry of the hexagonal lattice more obvious. The hexagonal unit cell, is described with reference to four axes, one along the axis of the hexagonal prism and three (a 1, a 2, a 3) in the base, 120° apart (see Fig. 2.57b).

How are crystallographic planes indicated in HCP unit cells?

In HCP unit cells, crystallographic planes are indicated using four indices which correspond to four axes: three basal axes of the unit cell, a 1 , a 2 , and a 3 , which are separated by 120º; and the vertical c axis.

How do you find the Miller indices of a direction?

The following steps are utilized to determine the Miller indices of a direction: (1) A vector of convenient length is positioned such that it passes through the origin of the co-ordinate system. (2) The length of the vector projection, each on the three axes is determined; these are measured in terms of the unit cell dimensions a, b and c.

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What are Miller-Bravais indices for hexagonal crystal?

Miller-Bravais Indices for Hexagonal Crystal: An alternate indexing system, which has four numbers in each set of indices, is often used for hexagonal crystal. The indices are called Miller-Bravais indices. Four numbers are used in order to make the relationship between the indices and the symmetry of the hexagonal lattice more obvious.