# FCC Structure Factor: Exploring Bragg's Diffraction

• I
• Yair Galili
In summary, the conversation discusses treating FCC lattice with a lattice constant of a as a monoatomic lattice and the resulting reciprocal lattice being a BCC with a lattice constant of 2pi/a. It also mentions the structure factor being 1. The conversation then goes on to mention treating FCC lattice with a lattice constant of a as a simple cubic lattice with 4 atoms in each unit cell. The distance between adjacent planes in the reciprocal lattice is calculated to be a/sqrt(h^2+k^2+l^2) and there is confusion about getting the same wavelengths according to Bragg's diffraction. However, it is pointed out that specific values for the lattice spacings show they are actually the same. The suggestion to calculate the first
Yair Galili
I tried to treat FCC lattice with a lattice constant a, as a monoatomic lattice.
The reciprocal lattice is a BCC with a lattice constant 2pi/a.
And the structure factor is 1.
But I can treat FCC lattice with a lattice constant a, as a simple cubic lattice,
with 4 atoms in each unit cell. As one can see in Wikipedia:

Now the distance between adjacent planes in the reciprocal lattice is
as in a simple cubic: a/sqrt(h^2+k^2+l^2),and I cannot see
how I can get the same wavelengths,according to Bragg's diffraction.

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Yair Galili said:
View attachment 203502 I tried to treat FCC lattice with a lattice constant a, as a monoatomic lattice.
The reciprocal lattice is a BCC with a lattice constant 2pi/a.
And the structure factor is 1.
But I can treat FCC lattice with a lattice constant a, as a simple cubic lattice,
with 4 atoms in each unit cell. As one can see in Wikipedia:
View attachment 203503
Now the distance between adjacent planes in the reciprocal lattice is
as in a simple cubic: a/sqrt(h^2+k^2+l^2),and I cannot see
how I can get the same wavelengths,according to Bragg's diffraction.
You did not calculate any specific values for the lattice spacings if you do you'll see they are the same. Try to calculate the first 5 peaks, for example.

## 1. What is the FCC structure factor?

The FCC (face-centered cubic) structure factor is a mathematical representation of the diffraction pattern produced by a crystal with a FCC crystal structure. It is used to analyze the arrangement of atoms in a crystal lattice and determine the spacing between the lattice planes.

## 2. How is the FCC structure factor calculated?

The FCC structure factor is calculated by taking the Fourier transform of the lattice points in the crystal. This involves summing up the contributions from each atom in the crystal and taking into account the phase difference between the scattered waves.

## 3. What is Bragg's law and how does it relate to the FCC structure factor?

Bragg's law is a fundamental principle in X-ray crystallography that relates the angle of incidence of a beam of X-rays to the spacing between crystal planes. The FCC structure factor is used to determine the intensity of the diffraction peaks in a Bragg diffraction pattern, which can then be used to calculate the lattice spacing.

## 4. What insights can be gained from studying the FCC structure factor?

Studying the FCC structure factor can provide valuable information about the arrangement of atoms in a crystal lattice, including the size and spacing of the unit cell, the symmetry of the lattice, and any defects or imperfections present in the crystal. It can also reveal information about the physical and chemical properties of the material.

## 5. How is the FCC structure factor used in practical applications?

The FCC structure factor is used extensively in materials science and engineering to analyze the crystal structure of various materials, including metals, ceramics, and semiconductors. It is also used in X-ray diffraction techniques to identify and characterize unknown crystalline materials. Additionally, it is used in the development and design of new materials with specific properties, such as high strength or electrical conductivity.

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