Murnaghan equation for lattice parameters?

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Discussion Overview

The discussion revolves around methods for determining the lattice constant (a) for boron nitride (BN) using computational techniques, specifically through the application of the Murnaghan equation and related methods in the ABINIT software. Participants explore various approaches to calculate the total energy at different lattice constants and the implications of these methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests calculating the total energy for different values of a and selecting the minimum energy value as a method to determine the lattice constant.
  • Another participant outlines three methods for determining the lattice constant:
    • Running multiple self-consistent calculations at different values of a, which may lack accuracy if not enough calculations are performed.
    • Fitting the results to the Birch-Murnaghan equation for a more reliable lattice constant and additional information like bulk modulus.
    • Using codes that can minimize energy by varying atomic coordinates and simulation cell volume in a single calculation, though this requires careful consideration of volume changes.
  • A participant expresses a preference for the second method, citing its ease and the additional information it provides.
  • Another participant notes that there is no implementation of the Murnaghan equation in ABINIT and requests references for the discussed methods.
  • A later reply mentions that while Birch-Murnaghan may not be readily implemented, curve fitting can be performed on simulation results.
  • One participant confirms that ABINIT can perform the third method mentioned, referencing specific variables that can be adjusted.

Areas of Agreement / Disagreement

Participants present multiple competing views on the best method to determine the lattice constant, with no consensus reached on a single preferred approach. There is acknowledgment of the limitations and considerations for each method discussed.

Contextual Notes

Participants highlight the potential inaccuracies in methods that rely on limited calculations and the need for careful handling of simulation parameters when minimizing energy. There is also mention of the lack of direct implementation of certain equations in ABINIT, which may affect the choice of methods.

Who May Find This Useful

This discussion may be useful for researchers and students working on computational materials science, particularly those interested in lattice parameter determination and the application of the Murnaghan equation in simulations.

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Murnaghan equation for lattice parameters?

Hi everybody...
I'm trying to determine lattice constant (a) for BN by calculating the total energy for different values of a using ABINIT, then chose the one which correspond the minimum value of energy, Is this convenient way to determine a ??

thanks...
with regards
 
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To get the lattice constant of a presumably cubic material, hence the only degree of freedom is "a" , one has variety of options.

1- Running multiple self-consistent calculations at different values of "a" ( Values of "a" that sufficiently bracket the experimental lattice constant" and choose the one that minimizes the energy. This method is not very accurate as you may miss a lot of if you do not run enough calculations.

2- Performing multiple self-consistent calculations and then fitting to Birch-Murnghan equation, form which you can obtain a more reliable lattice constant compared to method 1.

3- Some codes can minimize the energy by varying the atomic coordinates and the simulation cell volume and shape. So, in a single (slightly expensive) calculation you can obtain the lattice constant. However, since volume of the simulation cell vary, special care must be taken.


To me the second method is easy to perform and gives also more information such as the bulk modulus. Furthermore you can use the fitted Birch-Murnghan equation in computing the pressure, enthalpy, etc...
 


Useful nucleus said:
To get the lattice constant of a presumably cubic material, hence the only degree of freedom is "a" , one has variety of options.

1- Running multiple self-consistent calculations at different values of "a" ( Values of "a" that sufficiently bracket the experimental lattice constant" and choose the one that minimizes the energy. This method is not very accurate as you may miss a lot of if you do not run enough calculations.

2- Performing multiple self-consistent calculations and then fitting to Birch-Murnghan equation, form which you can obtain a more reliable lattice constant compared to method 1.

3- Some codes can minimize the energy by varying the atomic coordinates and the simulation cell volume and shape. So, in a single (slightly expensive) calculation you can obtain the lattice constant. However, since volume of the simulation cell vary, special care must be taken.


To me the second method is easy to perform and gives also more information such as the bulk modulus. Furthermore you can use the fitted Birch-Murnghan equation in computing the pressure, enthalpy, etc...
Thanks Mr. useful nucleus..
There is no implementation for Murnghan equation in ABINIT, anyway, could you please recommend me a reference about any three above ways
thanks a lot and best regards
 


I would not expect any code to have Birch-Murnghan readily implemented for the user. However, if you now how to perform curve fitting , it is an easy task to fit your simulation results.

A good introductory reference for such calculations is:
Density functional theory:a practical introduction by David S. Sholl, Janice A. Steckel
You may consult Chapter 2 &3

Another resource would be MIT Open course ware ; in particular the lab sessions of course 3.320

http://ocw.mit.edu/courses/material...eling-of-materials-sma-5107-spring-2005/labs/
 


Abinit does do Useful nucleus's solution #3. Look at the variables ionmov, optcell, ecutsm and dilatmx.
 


Thanks dears a lot
 

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