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Problem 4A unit cell of diamond structure belongs to the cubic crystal system and containseight atoms of the same type. Their positions are as follows:(0.0.0) 140 0112'2111 3 3 1 3 13 1444) 4 (4 '4'44'4'4Compute the structure factors Fl and Fhkl

Question

A unit cell of diamond structure belongs to the cubic crystal system and contains eight atoms of the same type. Their positions are as follows: (0,0,0), (.5,.5,0), (.5,0,.5), (0,.5,.5),(.25,.25,25), (.75,.75,.25), (.75,.25,.75), (.25,.75,.75). Compute the structure factors Fhkl and |F|^2.

Problem 4
A unit cell of diamond structure belongs to the cubic crystal system and contains
eight atoms of the same type. Their positions are as follows:
(0.0.0) 140 011
2'2
111 3 3 1 3 13 1
444) 4 (
4 '4'4
4'4'4
Compute the structure factors Fl and F
hkl
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Problem 4 A unit cell of diamond structure belongs to the cubic crystal system and contains eight atoms of the same type. Their positions are as follows: (0.0.0) 140 011 2'2 111 3 3 1 3 13 1 444) 4 ( 4 '4'4 4'4'4 Compute the structure factors Fl and F hkl

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Step 1

For the understanding of the solid state ,we need to have some knowledge about the structure and the forces that hold the structure in the molecule together, therefore the structure of the crystals is determined by using the technique known as X-ray crystallography. This technique relies on the principal that the distance between the atoms in a crystal have the same order as that of the wavelength used in the X-rays. Note that, here the crystal is acting as a three dimensional diffraction grating for the beam of the X-rays used in the crystallography.

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Step 2

Crystalline solids are mainly characterized by regular and repeating pattern of its constituent particles. If this three dimensional arrangement of the constituent particles in a crystal is to be represented diagrammatically, each particle will be depicted as a point, giving rise to an arrangement known as crystal lattice. A part of the crystal lattice is shown in the diagram below:

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Step 3

There are about 14 possible three dimensional lattice known as Bravais lattice. A unit cell refers to the smallest portion of the crystal lattice which when repeated in different leads to the formation of entire crystal lattice. They are mainly divided into two categories:

  1. Primitive unit cell- If the constituent particles are present only at the corners of the unit cell ,then such type of cell is known as primitive unit cell.
  2. Centred unit cells- If in the unit cell one or more constituent particles at positions other than corners than ,such type of unit cells are referred to as centred unit ce...
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