Dear QE users,
I want to plot the optical properties of a crystal. I'm working with ultrasoft pps, so the only option I found to obtain it was to calculate these properties using the Turbo-Lanczos package in QE. I got two files, the plot_S.dat, and plot_chi.dat.
If I understood it right, the plot_S.dat can be used to plot the absorption spectrum. In the plot_chi.dat, the program created a matrix with Real and Imaginary parts of the dielectric constant, as follows:
\hbar \omega(eV) Re(chi) (e^2*a_0^2/eV) Im(chi) (e^2*a_0^2/eV)
chi_1_1= 0.0000E+00 0.251513E+02 -.00000E+00
chi_2_1= 0.0000E+00 0.289682E-01 -.00000E+00
chi_3_1= 0.0000E+00 -.627424E+01 0.0000E+00
chi_1_2= 0.0000E+00 0.287160E-01 -.00000E+00
chi_2_2= 0.0000E+00 0.316761E+02 -.00000E+00
chi_3_2= 0.0000E+00 -.136008E-01 0.00000E+00
chi_1_3= 0.0000E+00 -.627868E+01 0.00000E+00
chi_2_3= 0.0000E+00 -.1321167E-01 0.00000E+00
chi_3_3= 0.0000E+00 0.250771+02 -.00000E+00
chi_1_1= 0.10000E-01 0.251513E+02 0.908418E-03
......
How can I use this data to plot the real and imaginary parts of the dielectric constant, and the absorption in the directions [001], [010], [100]?
Thanks for your help!
Dear friend José Xavier Lima Neto
To plot the real and imaginary parts of the dielectric constant, and the absorption in different directions, you can follow these steps:
1. Open the plot_chi.dat file and extract the values for the real and imaginary parts of the dielectric constant (chi) for each frequency and direction. You can use a text editor or a scripting language like Python to read and extract the data from the file.
2. Use the extracted data to plot the real and imaginary parts of chi as a function of frequency for each direction. You can use a plotting library like Matplotlib in Python or Gnuplot to create the plots.
3. To plot the absorption, you can use the following formula:
alpha = 2 * omega * Im(chi) / (3 * epsilon_0 * c * n)
where omega is the angular frequency, Im(chi) is the imaginary part of the dielectric constant, epsilon_0 is the vacuum permittivity, c is the speed of light, and n is the refractive index. You can calculate the absorption coefficient (alpha) for each direction and frequency using this formula.
4. Use the calculated absorption coefficients to plot the absorption as a function of frequency for each direction.
Note that the directions [001], [010], [100] correspond to the crystallographic axes of the crystal. You may need to rotate your crystal to align it with these directions before performing the calculations.
Here are some references that may help you:
1. S. Adachi, "Optical Constants of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information," Springer, 2015.
2. J. M. Ziman, "Principles of the Theory of Solids," Cambridge University Press, 1972.
3. Matplotlib documentation: https://matplotlib.org/stable/index.html
4. Gnuplot documentation: http://www.gnuplot.info/documentation.html
Dear Kaushik Shandilya
Thank you for your answer.
It's a 3x3 matrix. How can I organize these data to plot the directions? Is it to take all the chi 1_1, 1_2, etc?
You said: "You may need to rotate your crystal to align it with these directions before performing the calculations." How can I do this?
Dear friend José Xavier Lima Neto
To plot the dielectric function in different directions, you can extract the relevant elements from the matrix. For example, if you want to plot the dielectric function in the [001] direction, you would need to extract the elements chi_3_3, chi_3_1, and chi_3_2, which correspond to the xx, xy, and xz components of the dielectric function. Similarly, for the [010] direction, you would need to extract the elements chi_2_2, chi_2_1, and chi_2_3, which correspond to the yy, yx, and yz components of the dielectric function, and for the [100] direction, you would need to extract the elements chi_1_1, chi_1_2, and chi_1_3, which correspond to the zz, zx, and zy components of the dielectric function.
To rotate your crystal, you can use the 'cell_parameters' keyword in the input file for the Lanczos/Xpectrum calculations. You can specify the orientation of your crystal by changing the lattice vectors. For example, to rotate your crystal so that the [001] direction is aligned with the z-axis, you can set the lattice vectors as follows:
cell_parameters
1.0
a1 a2 0.0
a3 b1 b2
0.0 0.0 c
/
where a1, a2, a3, b1, b2, and c are the lattice parameters of your crystal. By adjusting these parameters, you can align your crystal with any desired direction. Once you have rotated your crystal, you can perform the Lanczos/Xpectrum calculations as before to obtain the dielectric function in the desired direction.
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