How Do I Calculate Bulk Modulus from DFT Data for Solid Carbon Dioxide?

Click For Summary
SUMMARY

The discussion focuses on calculating the bulk modulus of solid carbon dioxide using data derived from density functional theory (DFT). The participant has plotted unit cell size against pressure and is advised to fit this data to the Birch–Murnaghan equation of state. An alternative method involves finite differencing the pressure versus volume to derive dP/dV, which can then be used to calculate the bulk modulus using the formula BM = -V(dP/dV). The target bulk modulus value is approximately 350 GPa.

PREREQUISITES
  • Understanding of the Birch–Murnaghan equation of state
  • Familiarity with density functional theory (DFT) calculations
  • Knowledge of finite difference methods in calculus
  • Basic concepts of pressure-volume relationships in solid-state physics
NEXT STEPS
  • Research the Birch–Murnaghan equation of state for solid materials
  • Learn how to perform finite difference calculations for pressure and volume data
  • Explore software tools for DFT calculations, such as Quantum ESPRESSO or VASP
  • Investigate methods for curve fitting experimental data in scientific computing
USEFUL FOR

Researchers in materials science, chemists working with solid-state materials, and anyone involved in computational modeling of bulk properties in solid carbon dioxide.

raovq
Messages
2
Reaction score
0

Homework Statement


I have been asked to calculate the bulk modulus for a carbon dioxide solid from data I have calculated. I have made a quick plot of unit cell size vs pressure (sorry for no labels, unit cell is Y axis as square angstroms, and pressure is in GPa), which looks ok.

http://img406.imageshack.us/img406/1072/screenshotin1.png



Homework Equations


I have been told to fit it to the http://en.wikipedia.org/wiki/Birch–Murnaghan_equation_of_state" but that is where it all falls over (I'm a chemist completely out of my depth).

I have been told I can also "You can finite difference the pressure vs volume at low pressure to get dP/dV and then the BM can be got from BM = - V(dP/dV)", but I am not sure what that actually means.

I'm not fussed which method I use, the room for error on this particular example is acceptable at around 50 GPa (It will tell me if I am even remotely close to having what i want, which is 350 GPa).

The Attempt at a Solution


It seems that most people do it with scripts, but most I have seen rely on preforming their own calculations to get the raw data. As a condition of this project I have to use a specific application, which seems to be the easy part.

Thanks for any advice, I can't seem to make any sense from any papers I have read so far, and it is starting to look a little sad.
 
Last edited by a moderator:
Physics news on Phys.org
An important question is, what is the unit cell's volume given your square-Angstrom values?

If you can get that, then a curve fit will give you dV/dP at any pressure.

Once you have dV/dP, then use your equation to get BM.
 

Similar threads

Graduate Bulk and Slab electronic structure differences
  • · Replies 6 ·
Replies
6
Views
4K
What is the equation for the bulk modulus of a Fermi gas?
  • · Replies 1 ·
Replies
1
Views
7K
Calculating Young's Modulus for a Cylinder with Given Pressure and Bulk Modulus
  • · Replies 2 ·
Replies
2
Views
3K
Calculating total bulk modulus of cylinder, piston and oil
  • · Replies 10 ·
Replies
10
Views
7K
Graduate How to practically perform first-principles calculations on Li-ion batteries?
  • · Replies 0 ·
Replies
0
Views
2K
How can I calculate bulk modulus from an elastic tensor?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad How temperature effects bulk modulus?
  • · Replies 2 ·
Replies
2
Views
10K
How Do I Calculate Actual Frequency from Wind Turbine Simulation Data?
  • · Replies 11 ·
Replies
11
Views
2K
Discerning the Elasticity Modulus of Brittle Cast Iron from Test Data
  • · Replies 3 ·
Replies
3
Views
4K
How Do Carbon Ions Behave in a Tandem Accelerator?
  • · Replies 1 ·
Replies
1
Views
2K