def physical_mode(self):
"""Calculate physical modes. Non physical modes are the first 3 modes of q=(0, 0, 0) and, if defined, all the
modes outside the frequency range min_frequency and max_frequency.
Returns
-------
physical_mode : np array
(n_k_points, n_modes) bool
"""
q_points = self._reciprocal_grid.unitary_grid(is_wrapping=False)
physical_mode = np.zeros((self.n_k_points, self.n_modes),
dtype=np.bool)
for ik in range(len(q_points)):
q_point = q_points[ik]
phonon = HarmonicWithQ(
q_point=q_point,
second=self.forceconstants.second,
distance_threshold=self.forceconstants.distance_threshold,
folder=self.folder,
storage=self.storage,
is_nw=self.is_nw,
is_unfolding=self.is_unfolding)
physical_mode[ik] = phonon.physical_mode
if self.min_frequency is not None:
physical_mode[self.frequency < self.min_frequency] = False
if self.max_frequency is not None:
physical_mode[self.frequency > self.max_frequency] = False
return physical_mode
def _eigensystem(self):
"""Calculate the eigensystems, for each k point in k_points.
Returns
-------
_eigensystem : np.array(n_k_points, n_unit_cell * 3, n_unit_cell * 3 + 1)
eigensystem is calculated for each k point, the three dimensional array
records the eigenvalues in the last column of the last dimension.
If the system is not amorphous, these values are stored as complex numbers.
"""
q_points = self._reciprocal_grid.unitary_grid(is_wrapping=False)
shape = (self.n_k_points, self.n_modes + 1, self.n_modes)
log_size(shape, name='eigensystem', type=np.complex)
eigensystem = np.zeros(shape, dtype=np.complex)
for ik in range(len(q_points)):
q_point = q_points[ik]
phonon = HarmonicWithQ(
q_point=q_point,
second=self.forceconstants.second,
distance_threshold=self.forceconstants.distance_threshold,
folder=self.folder,
storage=self.storage,
is_nw=self.is_nw,
is_unfolding=self.is_unfolding)
eigensystem[ik] = phonon._eigensystem
return eigensystem
def participation_ratio(self):
"""Calculates the participation ratio of each normal mode. Participation ratio's
represent the fraction of atoms that are displaced meaning a value of 1 corresponds
to translation. Defined by equations in DOI: 10.1103/PhysRevB.53.11469
Returns
-------
participation_ratio : np array
(n_k_points, n_modes) atomic participation
"""
q_points = self._reciprocal_grid.unitary_grid(is_wrapping=False)
participation_ratio = np.zeros((self.n_k_points, self.n_modes))
for ik in range(len(q_points)):
q_point = q_points[ik]
phonon = HarmonicWithQ(
q_point=q_point,
second=self.forceconstants.second,
distance_threshold=self.forceconstants.distance_threshold,
folder=self.folder,
storage=self.storage,
is_nw=self.is_nw,
is_unfolding=self.is_unfolding)
participation_ratio[ik] = phonon.participation_ratio
return participation_ratio
def velocity(self):
"""Calculates the velocity using Hellmann-Feynman theorem.
Returns
-------
velocity : np array
(n_k_points, n_unit_cell * 3, 3) velocity in 100m/s or A/ps
"""
q_points = self._reciprocal_grid.unitary_grid(is_wrapping=False)
velocity = np.zeros((self.n_k_points, self.n_modes, 3))
for ik in range(len(q_points)):
q_point = q_points[ik]
phonon = HarmonicWithQ(q_point=q_point,
second=self.forceconstants.second,
distance_threshold=self.forceconstants.distance_threshold,
folder=self.folder,
storage=self.storage,
is_unfolding=self.is_unfolding)
velocity[ik] = phonon.velocity
return velocity
def frequency(self):
"""Calculate phonons frequency
Returns
-------
frequency : np array
(n_k_points, n_modes) frequency in THz
"""
q_points = self._reciprocal_grid.unitary_grid(is_wrapping=False)
frequency = np.zeros((self.n_k_points, self.n_modes))
for ik in range(len(q_points)):
q_point = q_points[ik]
phonon = HarmonicWithQ(q_point=q_point,
second=self.forceconstants.second,
distance_threshold=self.forceconstants.distance_threshold,
folder=self.folder,
storage=self.storage,
is_unfolding=self.is_unfolding)
frequency[ik] = phonon.frequency
return frequency
def participation_ratio(self):
"""Calculate phonons participation ratio. A value of 1 corresponds to translation.
Returns
-------
participation_ratio : np array
(n_k_points, n_modes) atomic participation
"""
q_points = self._reciprocal_grid.unitary_grid(is_wrapping=False)
participation_ratio = np.zeros((self.n_k_points, self.n_modes))
for ik in range(len(q_points)):
q_point = q_points[ik]
phonon = HarmonicWithQ(
q_point=q_point,
second=self.forceconstants.second,
distance_threshold=self.forceconstants.distance_threshold,
folder=self.folder,
storage=self.storage,
is_nw=self.is_nw,
is_unfolding=self.is_unfolding)
participation_ratio[ik] = phonon.participation_ratio
return participation_ratio
def plot_dispersion(phonons,
n_k_points=300,
is_showing=True,
symprec=1e-3,
is_nw=None,
with_velocity=True,
color='b',
is_unfolding=False):
atoms = phonons.atoms
if is_nw is None and phonons.is_nw:
is_nw = phonons.is_nw
if is_nw:
q = np.linspace(0, 0.5, n_k_points)
k_list = np.zeros((n_k_points, 3))
k_list[:, 0] = q
k_list[:, 2] = q
Q = [0, 0.5]
point_names = ['$\\Gamma$', 'X']
else:
try:
k_list, Q, point_names = create_k_and_symmetry_space(
atoms, n_k_points=n_k_points, symprec=symprec)
q = np.linspace(0, 1, k_list.shape[0])
except seekpath.hpkot.SymmetryDetectionError as err:
print(err)
q = np.linspace(0, 0.5, n_k_points)
k_list = np.zeros((n_k_points, 3))
k_list[:, 0] = q
k_list[:, 2] = q
Q = [0, 0.5]
point_names = ['$\\Gamma$', 'X']
freqs_plot = []
vel_plot = []
vel_norm = []
for q_point in k_list:
phonon = HarmonicWithQ(
q_point,
phonons.forceconstants.second,
distance_threshold=phonons.forceconstants.distance_threshold,
storage='memory',
is_unfolding=is_unfolding)
freqs_plot.append(phonon.frequency.flatten())
if with_velocity:
val_value = phonon.velocity[0]
vel_plot.append(val_value)
vel_norm.append(np.linalg.norm(val_value, axis=-1))
freqs_plot = np.array(freqs_plot)
if with_velocity:
vel_plot = np.array(vel_plot)
vel_norm = np.array(vel_norm)
fig1, ax1 = plt.subplots()
plt.tick_params(axis='both', which='minor', labelsize=16)
plt.ylabel("$\\nu$ (THz)", fontsize=16)
plt.xlabel('$q$', fontsize=16)
plt.tick_params(axis='both', which='major', labelsize=16)
plt.xticks(Q, point_names)
plt.xlim(q[0], q[-1])
if color is not None:
plt.plot(q, freqs_plot, '.', color=color, linewidth=4, markersize=4)
else:
plt.plot(q, freqs_plot, '.', linewidth=4, markersize=4)
plt.grid()
plt.ylim(freqs_plot.min(), freqs_plot.max() * 1.05)
folder = get_folder_from_label(phonons, base_folder=DEFAULT_FOLDER)
if not os.path.exists(folder):
os.makedirs(folder)
plt.subplots_adjust(left=0.1, right=0.9, top=0.9, bottom=0.1)
fig1.savefig(folder + '/' + 'dispersion' + '.png')
np.savetxt(folder + '/' + 'q', q)
np.savetxt(folder + '/' + 'dispersion', freqs_plot)
if is_showing:
plt.show()
else:
plt.close()
if with_velocity:
for alpha in range(3):
np.savetxt(folder + '/' + 'velocity_' + str(alpha),
vel_plot[:, :, alpha])
fig2, ax2 = plt.subplots()
plt.ylabel('$|v|(\AA/ps)$', fontsize=16)
plt.xlabel('$q$', fontsize=16)
plt.tick_params(axis='both', which='major', labelsize=16)
plt.tick_params(axis='both', which='minor', labelsize=20)
plt.xticks(Q, point_names)
plt.xlim(q[0], q[-1])
if color is not None:
plt.plot(q,
vel_norm[:, :],
'.',
linewidth=4,
markersize=4,
color=color)
else:
plt.plot(q, vel_norm[:, :], '.', linewidth=4, markersize=4)
plt.grid()
plt.tick_params(axis='both', which='major', labelsize=16)
fig2.savefig(folder + '/' + 'velocity.png')
np.savetxt(folder + '/' + 'velocity_norm', vel_norm)
if is_showing:
plt.show()
else:
plt.close()