View source for Solution LAB1 diamond bulk modulus


* Back to the previous page: [[Structural and electronic properties of semiconductors and metals #Convergences]]

===Bulk modulus of diamond===

Using the data produced in the previous exercise (total energy as a function of the lattice parameter for a range of ecutwfc values), one can do the following:
* extract etot vs volume for each wfcutfc value into different files;
* fit the data and extract the second derivative in the minimum;
* this can be done using a second (or better higher) order polynomial or other fitting functions (cubic splines, [https://en.wikipedia.org/wiki/Birch–Murnaghan_equation_of_state Murnaghan equation of state], ...)
* Evaluate the bulk modulus taking care of unit conversion to international system (B modulus is given in GPa)
* The above steps are coded in the script <code>./LabQSM/tools/compute_B_modulus.py</code> for convenience


'''Results as a function of the kinetic energy cutoff''' are reported below:

#  ecut [Ry]     B modulus [GPa]
   20         4222.035362534261
   30          545.8276696265291
   40          577.6525328096515
   50          678.313290451693
   60          526.4841165649044
   80          463.3508978235948
  100          471.6781060558174
  120          468.6260793219729
  140          467.798081344509
  160          467.04233495671605

Once again, a cutoff of 60-80 Ry (80 better) seems to be sufficient.
 
A script to automate the calculation can be put together as follows:

  #!/bin/bash
  
  list=`ls results_*_vol.dat`
  fileout=results_BMOD.dat
  
  echo "#  ecut [Ry]     B modulus [GPa]" > $fileout
  
  for file in $list
  do
     filein=$file
     ecut=`echo $file | cut -d "_" -f2 | sed 's/Ry//'`
     bmod=`./compute_B_modulus.py $file | tail -1 | awk '{print $(NF-1)}'`
     echo $ecut $bmod >> $fileout
  done