A write down the fractional coordinates of all the atoms in

Question

1. The silicon crystal has a cubic lattice as shown below

(a) Write down the fractional coordinates of all the atoms in the unit cell.

(b) Write down the formula for structure factor Fhkl, taking the atomic form factor of silicon as fSi.

(c) On the basis of your equation for Fhkl, derive the rules of systematic absence of diffraction for this structure.

(d) What kind of Bravais lattice does this cubic structure belong to, primitive, body centred, or face centred cubic? Provide an explanation to your answer.

2. What would be the differences in the X-ray diffraction patterns of two powder samples of silicon, the first with crystal size ~1µm, in the other each crystal is a silicon nanoparticle of size ~50 nm? Provide a quantitative description of the differences, as well as an explanation to the origin of such differences.

3. (a) Describe briefly the powder and single crystal x-ray diffraction methods.

(b) Describe the advantages, disadvantages and main applications of each method respectively.

Answer 1

For the following crystal based questions, provide a paper in which you have to respond to the following questions in detail. Q1. The silicon crystal consists of a cubic lattice as illustrated below: a) Illustrate the fractional coordinates of all the atoms in the unit cell. b) Illustrate the formula for structure factor Fhkl, taking atomic form factor of silicon as fSi. c) Base on the equation for Fhkl, derive the rules of systematic absence of diffraction for this structure. d) What type of Bravais lattice does this cubic structure belong to, primitive, body centered or face centered cubic? Give a description to your answer. Q2. Illustrate what would be the differences in the X-ray diffraction patterns of two powder samples of silicon, the Ist with crystal size ~1µm, in other each crystal is a silicon nano-particle of size ~50 nm? Give a quantitative explanation of the differences, and also a description to the origin of these differences.