Sage-Tips

What are the Miller indices of crystal planes which cut through the crystal axis at 3 by 2 A to B and 1 C?

Hence, the Miller indices are (122).

What will be the Miller indices of a plane having intercepts along three coordinate axes 3a 2b 2c?

The use and definition of these Miller indices are shown in fig Page 3 Figure, This plane intercepts the a, b, c axes at 3a, 2b, 2c. The reciprocals of these numbers are ,1/3, 1/2, 1/2. The smallest three integers having the same ratio are 2, 3, 3, and thus the Miller indices of the plane are (233).

How do you find the Miller indices of a crystal plane?

The procedure is most easily illustrated using an example so we will first consider the following surface/plane:

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.

What are the Miller indices of crystal planes which cut through the crystal axes at?

Planes which cut through the crystal axes at. Hence, the miller indices are (111). Hence, the miler indices are (122).

How many total symmetry axes are present in the cubic crystal system?

13 Axes of symmetry – 3 are C4 or tetrad axis passing through centre of opposite faces.

What are crystal planes and Miller indices?

Crystal planes come from the structures known as crystal lattices. The planes intersect with each other and make 3D shapes that have six faces. These crystal planes define the crystal structure by making axes visible and are the means by which we can calculate the Miller Indices.

What do you understand by Miller indices of a crystal plane?

Miller indices, group of three numbers that indicates the orientation of a plane or set of parallel planes of atoms in a crystal. In the hexagonal system, which has four crystallographic axes, a similar scheme of four Bravais-Miller indices is used.

What is crystal plane in crystal system?

Crystal planes are defined as some imaginary planes inside a crystal in which large concentration of atoms are present. Inside the crystal, there exists certain directions along which large concentration of atoms exists. These directions are called crystal directions.

What are Miller Indices and how are they determined?

Miller indices are used to specify directions and planes. These directions and planes could be in lattices or in crystals. The number of indices will match with the dimension of the lattice or the crystal. E.g. in 1D there will be 1 index and 2D there will be two indices etc.

What are the Miller indices of a crystal plane?

This set is called Miller indices of the plane (hkl). For example, if the plane intercepts x, y, and z in points 1, 3, and 1, the index of this plane will be (313). The orientation of a crystal plane is determined by three points in the plane, provided they are not collinear.

What must be acertained when drawing crystallographic axes?

The first thing that must be acertained are the fractional intercepts that the plane/face makes with the crystallographic axes. In other words, how far along the unit cell lengths does the plane intersect the axis. In the figure above , the plane intercepts each axis at exact one unit length.

How do you find the miller index of the plane?

1/z) and reduce this set to a similar one having the smallest integers by multiplying by a common factor. This set is called Miller indices of the plane (hkl). For example, if the plane intercepts x, y, and z in points 1, 3, and 1, the index of this plane will be (313).

What is the intercept to the b axis of a plane?

In this case the plane intercepts the a axis at one unit length and also the c axis at one unit length. The plane however, never intersects the b axis. In other words, it can be said that the intercept to the b axis is infinity. The intercepts are then designated as 1,infinity,1. The reciprocals are then 1/1, 1/infinity, 1/1.