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Questions on Point Groups Symmetry and other topics in Crystallography

Important Questions on Point Groups Symmetry and other topics in Crystallography


Elements of Crystal Structure:

Q1. What is a lattice? Express a lattice mathematically.

What do you mean by a ‘basis’? How can you combine a lattice with a basis to obtain a crystal structure?


Q2. What are the 3 fundamental translation vectors?

Show with 2 dimensional examples, how the fundamental translation vectors may define either a non-primitive (conventional) unit cell or a primitive unit cell.


Q3. Express mathematically the size (area in 2 dim: & volume in 3 dim) of a unit cell.


Symmetry & point groups:

Q1. What do you mean by symmetry in a crystal lattice?


Q2 (a) What are the different symmetry operations that you find in 2 dimensional lattices?

(b) What are the different symmetry operations that you find in 3 dimensional lattices?


Q3. What is the difference between symmetry operations and symmetry elements?

What are the different point symmetry elements in a 2 dim: lattice?


Q4 What do you mean by a ‘point group’? How many point groups are possible in a 2 dim: and in a 3 dim: crystal lattice? (Use Hermann-Mauguin International symbols)


Q5. What is a Bravais Lattice?

Draw the five 2-dim: Bravais lattices clearly showing the fundamental lattice translation vectors.

What is the difference between a centered rectangular lattice and a simple rectangular lattice?


Q6.How many 3 dim: Bravais lattices are present? How many 3 dim: crystal systems are there? Make a Table having the following columns:


System Bravais lattice Diagram of Conventional unit

Name & Symbol unit cell. Cell characteristics.


Q7. What do you mean by packing fraction? Calculate the packing fraction in a simple cubic , base centered cubic and a face centered cubic structures.

In which structure are the atoms most closely packed?


Q8. What do you mean by ‘coordination number’ in a crystal structure?


Q9.Explain with diagram the Nacl structure and the CsCl structure? What is the structure of diamond?(No need to draw diagram)


Q10. What are Crystal planes? What do the Miller Indices represent?

What do the following indices represent..?

(hkl), {hkl},[hkl] and <hkl>? See Singhal Chapter 1.

Draw the unit cell & the following planes in a simple cubic lattice:

(100), (ī00), (200), (1ī1), (201), (2ī0),(122).


Q11. What do you mean by crystal lattice inter planar spacing (dhkl )? Write the formulae for

dhkl for a orthogonal lattice and a cubic lattice. Also write the formula for the angle between 2 planes in a cubic lattice.


Diffraction of X-Rays by Crystals: Bragg’s Law

Q1. Explain in short how X-rays can be diffracted by a crystal.

A neutron beam can also be used instead of X-rays to study diffraction. Why? (State de Broglies hypothesis of matter waves i.e. wave –particle duality: l=h/p) Already discussed in class.


Q2. Draw a neat diagram and deduce Bragg’s Law for diffraction by a crystal (2d sinq = nl).

Visible light cannot be used to study diffraction by crystals, why?


Important problem:

The Bragg angle for reflection from the (111) planes in Al (fcc) is 19.2 degrees for an X-ray wavelength of l=1.54 Ǻ.


(i)               the length of the cube edge of the unit cell.

(ii)             The interplanar distance for these planes.

Ans 4.04 Ǻ and 2.33 Ǻ.

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Abhijit Poddar