# Radial Distribution Function for HCP and FCC lattices

• thepopasmurf
In summary, the conversation discussed the need for images showing the difference between the radial distribution functions for hcp and fcc lattices. It was suggested to adapt a spreadsheet used for predicting diffractogram peaks for simple lattices to save time and effort. The ideal ratio c/a was mentioned, but it was noted that no real metal has this ideal ratio. The possibility of using cobalt as a reference was also brought up.
thepopasmurf
I was wondering, does anyone have any images that show the difference between the radial distribution functions for hcp and fcc lattices? I would be useful for reference purposes.

thepopasmurf said:
I was wondering, does anyone have any images that show the difference between the radial distribution functions for hcp and fcc lattices? I would be useful for reference purposes.
With the ideal ratio c/a, surely no difference.
But no real metal has this ideal ratio when hexagonal. Maybe cobalt ?
So as many histograms as metals - and alloys...

Maybe you can adapt the speadsheet I made for predicting the diffractogram peaks for any simple lattice, here for chlorite :
http://deonto-ethics.org/resources/chlorite.xls
The main adaptation you have to do is to use the direct metric tensor, rather than the reciprocal metric tensor.
It will save you hours and hours of work.

Last edited by a moderator:

## 1. What is the Radial Distribution Function (RDF) for HCP and FCC lattices?

The Radial Distribution Function is a mathematical function that describes the probability of finding a particle at a certain distance from a central particle in a crystal lattice. For HCP and FCC lattices, the RDF is used to determine the arrangement of atoms and their average distances from each other.

## 2. How is the Radial Distribution Function calculated?

The RDF is calculated by dividing the number of particles found in a spherical shell at a given distance by the volume of that shell. This calculation is repeated for multiple distances, creating a graph that shows the probability of finding a particle at different distances from the central particle.

## 3. What information can be obtained from the Radial Distribution Function for HCP and FCC lattices?

The RDF can provide information about the average distance between particles in the lattice, the coordination number (the number of nearest neighbors), and the degree of order in the lattice. It can also reveal any changes in the structure or organization of the lattice due to external factors like temperature or pressure.

## 4. How does the Radial Distribution Function differ between HCP and FCC lattices?

The RDF for HCP and FCC lattices will have different shapes and peaks due to their different arrangements of atoms. In HCP lattices, there will be a peak at the nearest neighbor distance and additional peaks at longer distances due to the hexagonal symmetry. In FCC lattices, there will be a peak at the nearest neighbor distance and additional peaks at shorter and longer distances due to the cubic symmetry.

## 5. Can the Radial Distribution Function be used to identify different crystal lattices?

Yes, the RDF can be used to identify different crystal lattices based on their unique patterns and peaks. However, it is important to note that other factors such as lattice constant and atomic arrangements must also be considered for accurate identification.

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