Bulk Modulus from DFT results

In summary, the person has been asked to calculate the bulk modulus for a solid carbon dioxide using data they have calculated. They have plotted unit cell size vs pressure and have been advised to fit it to the Birch-Murnaghan equation of state, but they are unsure how to do so. They have also been told they can use finite difference to get dP/dV and then calculate BM, but they are not sure how to do that either. They are open to using any method and have a margin of error of 50 GPa. They are using a specific application for this project. They are seeking advice and are having difficulty understanding papers they have read. An important factor in this problem is the unit cell's volume given the square-A
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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 [Broken]



Homework Equations


I have been told to fit it to the http://en.wikipedia.org/wiki/Birch–Murnaghan_equation_of_state" [Broken] 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.
 
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  • #2
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.
 

1. What is the bulk modulus?

The bulk modulus is a measure of a material's resistance to compression. It is a fundamental property of materials and is defined as the ratio of stress to strain under uniform compression.

2. How is the bulk modulus calculated from DFT results?

The bulk modulus can be calculated from DFT (density functional theory) results by using the equation: B = -V(dP/dV), where B is the bulk modulus, V is the volume, and dP/dV is the derivative of pressure with respect to volume.

3. What factors affect the accuracy of bulk modulus calculations from DFT?

The accuracy of bulk modulus calculations from DFT results can be affected by several factors, including the choice of exchange-correlation functional, the size of the simulation cell, and the choice of basis set.

4. Can the bulk modulus be used to predict the mechanical properties of materials?

Yes, the bulk modulus can be used to predict the mechanical properties of materials, such as their elasticity, compressibility, and strength. It is an important parameter in understanding and designing new materials for various applications.

5. How can the bulk modulus be experimentally determined?

The bulk modulus can be experimentally determined by subjecting a material to different levels of compression and measuring the resulting stress and strain. This can be done using techniques such as high-pressure X-ray diffraction or Brillouin scattering.

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