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Question bank - Bravais Lattice, Miller indices, Bragg's Law

See the attached file.

1. We know that face centered lattice in cubic and orthorhombic (FCC & FCO) system are listed in Bravais lattice system but face centered tetragonal (FCT) is not listed, why?
2. Draw the plane with miller indices (122) in the unit cell of cubic lattice having lattice parameter 'a'. Find its distances from the parallel plane through the origin.
3. Find the miler indices of plane which makes intercept of 2 on a-axis and 3 on b-axis and is parallel to c-axis.
4. Find the miller indices of plan that makes intercepts on a, b and c axis equal to 4 A, 2 A and 3 A in the orthorhombic crystal with a : b : c = 2 : 4 : 3.
5. The Bragg angle for reflection from (110) plane is 20.2 degree. Find the wavelength of X-ray. (lattice parameter of the crystal is 3.15 A).


Solution Preview


1. Let us consider two face centered tetragonal (FCT) lattice as shown in the above figure. Now join the top face centered atom with the bottom face centered atom, again join them with the shared corner atoms of both crystals as shown by the dashed line. This new lattice, formed by dashed lines and shared face (side), is also tetragonal with body centered arrangement of atoms. On 3-Dimensional repetition of this body centered tetragonal (BCT) lattice we get the same structure as from the given FCT lattice. In crystallography when any crystal can be explained by two lattice types we define it with the simple one and here body centered ...

Solution Summary

Step-by-step method is explained to find the solution, illustrated with suitable diagrams/figures. Also terms of equations are explained. On going through these solutions student will learn to find miller indices, crystal parameter and would understand the use of Bragg's law. Attached MS world file contains 641 words and two figures.