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kALDo Amorphous silicon tutorial

This notebook can be run on Google Colab.

In Colab, you can enable the GPU acceleration from Edit > Notebook Settings > Accelerator > GPU.

Amorphous silicon tutorial¶

pip install $\kappa$ ALDo¶

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%%capture
! pip install kaldo

Fetch supplyment data remotely¶

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%%capture
# Activate large file transfer in github
! git lfs install --skip-repo --skip-smudge

# Git clone kALDo
! git clone https://github.com/nanotheorygroup/kaldo.git

# Copy si-amorphous structure and force constant files
! cp -r /content/kaldo/kaldo/tests/si-amorphous ./
! rm -rf kaldo sample_data

Thermal transport simulation for Amorphous-Silicon (a-Si)¶

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from kaldo.forceconstants import ForceConstants

# Read amporphous silicon with eskm format
forceconstants = ForceConstants.from_folder(folder='si-amorphous', format='eskm')

Create phonons object¶

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from kaldo.phonons import Phonons

# Create a phonon object
# is_classic flag can be true or false, as
# well as 0 (quantum) or 1 (classic)
phonons = Phonons (forceconstants=forceconstants,
                   is_classic=0,
                   temperature=300,
                   folder='si-amorphous',
                   third_bandwidth=0.5/4.136,
                   broadening_shape='triangle',
                   storage='numpy')

Access and visualize properties calculated during simulations¶

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import matplotlib.pyplot as plt
plt.style.use('seaborn-v0_8')

# Direct access to properties
# calculated during the simulation
frequency = phonons.frequency.flatten(order='C')
bandwidth = phonons.bandwidth.flatten(order='C')

# Plot phonon bandwidth vs frequency
print('\n')
plt.plot(frequency[3:],bandwidth[3:],'.',markersize=10,label= 'broadening shape: ' + str(phonons.broadening_shape))
plt.ylabel('$\Gamma$ (THz)', fontsize=25, fontweight='bold')
plt.xlabel("$\\nu$ (THz)", fontsize=25, fontweight='bold')
plt.ylim([bandwidth.min(), bandwidth.max()])
plt.legend(loc=2,frameon = False)
plt.grid()
plt.show()

phase_space = phonons.phase_space.flatten(order='C')

# Plot phase space vs frequency
print('\n')
plt.figure()
plt.plot(frequency[3:], phase_space[3:], '.', markersize=10)
plt.ylabel ("Phase space", fontsize=25, fontweight='bold')
plt.xlabel("$\\nu$ (THz)", fontsize=25, fontweight='bold')
plt.grid()
plt.show()

Calculate and visualize $\kappa_{per \ mode}$ and $\kappa_{cum}$ ¶

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from kaldo.conductivity import Conductivity
from kaldo.controllers import plotter
import numpy as np

# Compute conductivity with per phonon mode basis using qhgk method
kappa_qhgk_per_mode = np.einsum('maa->m',1/3*Conductivity(phonons=phonons, method='qhgk',n_iterations=20).conductivity)

# Compute cumulative conductivity by frequency with qhgk method
kappa_qhgk_cum_freq = plotter.cumulative_cond_cal(phonons.frequency,Conductivity(phonons=phonons, method='qhgk').conductivity,phonons.n_phonons)

print('\n')

# Visualize the per mode conductivity vs frequency
plt.figure()
plt.plot(frequency[3:],kappa_qhgk_per_mode[3:],'.',label='QHGK',ms=8)
plt.xlabel ("$\\nu$ (THz)", fontsize=25, fontweight='bold')
plt.ylabel(r'$\kappa(W/m/K)$', fontsize=25, fontweight='bold')
plt.legend(loc=1,frameon=False)
plt.grid()
plt.show()

print('\n')

# Visualize the cumulative conductivity vs frequency
plt.figure()
plt.plot(frequency[3:],kappa_qhgk_cum_freq[3:],'.',label='QHGK',ms=8)
plt.xlabel ("$\\nu$ (THz)", fontsize=25, fontweight='bold')
plt.ylabel(r'$\kappa_{cum}(W/m/K)$', fontsize=25, fontweight='bold')
plt.legend(loc=4,frameon=False)
plt.grid()
plt.show()

# Please check out amorphous_silicon_Tersoff_LAMMPS in the example folder for more detail.