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Atsushi Togo
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@ -190,7 +190,8 @@ convergence.
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^^^^^^^^^
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Outer product of group velocities :math:`\mathbf{v}_\lambda \otimes
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\mathbf{v}_\lambda` (in THz^2 x Angstrom^2)
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\mathbf{v}_\lambda` divided by primitive cell volume (in :math:`\text{THz}^2 /
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\text{Angstrom}`)
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``--average``
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^^^^^^^^^^^^^^
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@ -233,12 +234,12 @@ Modal heat capacity :math:`C_\lambda` (in eV/K)
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^^^^^^^^^^^^^^
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Absolute value of group velocity :math:`|\mathbf{v}_\lambda|` (in
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THz x Angstrom)
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:math:`\text{THz}\cdot\text{Angstrom}`)
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``--pqj``
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^^^^^^^^^^^^^^
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Averaged phonon-phonon interaction :math:`P_{\mathbf{q}j}` (in eV^2)
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Averaged phonon-phonon interaction :math:`P_{\mathbf{q}j}` (in :math:`\text{eV}^2`)
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.. _auxiliary_tools_kdeplot:
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@ -165,6 +165,8 @@ html_theme_options = {
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# Choose Bootstrap version.
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# Values: "3" (default) or "2" (in quotes)
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'bootstrap_version': "3",
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'nosidebar': "true",
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}
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@ -19,12 +19,12 @@ conductivity calculation is loaded and thermal conductivity tensor at
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300 K is watched.
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::
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In [1]: import h5py
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In [2]: f = h5py.File("kappa-m111111.hdf5")
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In [3]: list(f)
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Out[3]:
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[u'frequency',
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@ -39,10 +39,10 @@ conductivity calculation is loaded and thermal conductivity tensor at
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u'qpoint',
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u'temperature',
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u'weight']
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In [4]: f['kappa'].shape
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Out[4]: (101, 6)
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In [5]: f['kappa'][:]
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Out[5]:
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array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
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@ -58,7 +58,7 @@ conductivity calculation is loaded and thermal conductivity tensor at
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1.74843437e-18, 0.00000000e+00, -2.28116103e-18],
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[ 6.43792061e+00, 6.43792061e+00, 6.43792061e+00,
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1.73090513e-18, 0.00000000e+00, -2.25828616e-18]])
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In [6]: f['temperature'][:]
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Out[6]:
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array([ 0., 10., 20., 30., 40., 50., 60., 70.,
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@ -74,16 +74,16 @@ conductivity calculation is loaded and thermal conductivity tensor at
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800., 810., 820., 830., 840., 850., 860., 870.,
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880., 890., 900., 910., 920., 930., 940., 950.,
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960., 970., 980., 990., 1000.])
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In [7]: f['kappa'][30]
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Out[7]:
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array([ 2.18146513e+01, 2.18146513e+01, 2.18146513e+01,
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5.84389577e-18, 0.00000000e+00, -7.63278476e-18])
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In [8]: g = f['gamma'][30]
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In [9]: import numpy as np
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In [10]: g = np.where(g > 0, g, -1)
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In [11]: lifetime = np.where(g > 0, 1.0 / (2 * 2 * np.pi * g), 0)
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@ -111,7 +111,7 @@ mesh
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(Versions 1.10.11 or later)
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The numbers of mesh points for reciprocal space sampling along
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reciprocal axes, :math:`a^*, b^*, c^*`
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reciprocal axes, :math:`a^*, b^*, c^*`
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frequency
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^^^^^^^^^^
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@ -130,7 +130,7 @@ is in the ordinal frequency not the angular frequency.
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The array shape for all grid-points (irreducible q-points) is
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(temperature, irreducible q-point, phonon band).
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The array shape for a specific grid-point is
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The array shape for a specific grid-point is
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(temperature, phonon band).
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Phonon lifetime (:math:`\tau_\lambda=1/2\Gamma_\lambda(\omega_\lambda)`) may
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@ -143,9 +143,9 @@ previous section to show how to obtain phonon lifetime in pico
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second::
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In [8]: g = f['gamma'][30]
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In [9]: import numpy as np
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In [10]: g = np.where(g > 0, g, -1)
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In [11]: lifetime = np.where(g > 0, 1.0 / (2 * 2 * np.pi * g), 0)
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@ -163,7 +163,7 @@ group_velocity
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^^^^^^^^^^^^^^^
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Phonon group velocity, :math:`\nabla_\mathbf{q}\omega_\lambda`. The
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physical unit is :math:`\text{THz}\cdot\text{\AA}`, where THz
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physical unit is :math:`\text{THz}\cdot\text{Angstrom}`, where THz
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is in the ordinal frequency not the angular frequency.
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The array shape is (irreducible q-point, phonon band, 3 = Cartesian coordinates).
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@ -228,7 +228,7 @@ Outer products of group velocities for k-stars
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\mathbf{v}_{\mathbf{q}j}.
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The physical unit is
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:math:`\text{THz}^2\cdot\text{\AA}^2`, where THz is in the
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:math:`\text{THz}^2\cdot\text{Angstrom}^2`, where THz is in the
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ordinal frequency not the angular frequency.
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The array shape is (irreducible q-point, phonon band, 6 = (xx, yy, zz,
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@ -293,5 +293,3 @@ calculated by::
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kappa_unit_conversion / weight.sum() * heat_capacity[30, 2, 0] *
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gv_by_gv[2, 0] / (2 * gamma[30, 2, 0])
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@ -38,12 +38,12 @@ unit systems used for the calculators are summarized below.
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Abinit | au (bohr) eV/Angstrom au
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``FORCES_FC2`` and ``disp_fc2.yaml`` have the same physical units as
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``FORCES_FC3`` and ``disp_fc3.yaml``, respectively.
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``FORCES_FC3`` and ``disp_fc3.yaml``, respectively.
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Always (irrespective of calculator interface) the physical units of
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2nd and 3rd order force constants that are to be stored in
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``fc2.hdf5`` and ``fc3.hdf5`` are ``eV/Angstrom^2`` and
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``eV/Angstrom^3``, respectively.
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``fc2.hdf5`` and ``fc3.hdf5`` are :math:`\text{eV}/\text{Angstrom}^2` and
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:math:`\text{eV}/\text{Angstrom}^3`, respectively.
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.. _default_unit_cell_file_name_for_calculator:
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@ -51,8 +51,8 @@ Default unit cell file name
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Default unit cell file names are also changed according to the calculators::
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VASP | POSCAR
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VASP | POSCAR
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Pwscf | unitcell.in
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CRYSTAL | crystal.o
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Abinit | unitcell.in
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@ -70,4 +70,3 @@ Default displacement distances created by ``-d`` option without
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Pwscf | 0.06 au (bohr)
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CRYSTAL | 0.03 Angstrom
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Abinit | 0.06 au (bohr)
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@ -55,7 +55,7 @@ See the detail at :ref:`kappa_hdf5_file`.
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^^^^^^^^^^^^^
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Third order force constants (in real space) are stored in
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:math:`\mathrm{eV}/\mathrm{\AA}^3`.
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:math:`\mathrm{eV}/\text{Angstrom}^3`.
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In phono3py, this is stored in the numpy array ``dtype='double'`` and
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``order='C'`` in the shape of::
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@ -93,7 +93,7 @@ e.g., the face centring,
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0 & \frac{{1}}{2} & \frac{{1}}{2} \\
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\frac{{1}}{2} & 0 & \frac{{1}}{2} \\
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\frac{{1}}{2} & \frac{{1}}{2} & 0
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\end{pmatrix} =
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\end{pmatrix} =
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(\mathbf{a}_\text{s}, \mathbf{b}_\text{s}, \mathbf{c}_\text{s})
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\begin{pmatrix}
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0 & \frac{{1}}{4} & \frac{{1}}{4} \\
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@ -104,12 +104,12 @@ e.g., the face centring,
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So what you have to set is ``--pa="0 1/4 1/4 1/4 0 1/4 1/4 1/4 0"``.
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.. _fc2_hdf5_file:
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``fc2.hdf5``
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^^^^^^^^^^^^^
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Second order force constants are stored in
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:math:`\mathrm{eV}/\mathrm{\AA}^3`.
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:math:`\mathrm{eV}/\text{Angstrom}^2`.
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In phono3py, this is stored in the numpy array ``dtype='double'`` and
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``order='C'`` in the shape of::
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@ -133,13 +133,13 @@ Q-point triplet contributions to imaginary parts of self energies at
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phonon frequencies (half linewidths) are stored in THz. See
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:ref:`write_detailed_gamma_option`.
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Simple text file
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Simple text file
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-----------------
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``gammas-*.dat``
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^^^^^^^^^^^^^^^^^
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Imaginary parts of self energies with respect to frequency
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Imaginary parts of self energies with respect to frequency
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:math:`\Gamma_\lambda(\omega)` are stored in THz. See :ref:`ise_option`.
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``jdos-*.dat``
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@ -149,5 +149,3 @@ Joint densities of states are stored in Thz. See :ref:`jdos_option`.
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``linewidth-*.dat``
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^^^^^^^^^^^^^^^^^^^^
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@ -101,7 +101,7 @@ Displacement distance of atoms
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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The phono3py default displacement distance is 0.03
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:math:`\text{\AA}`. In some cases, accurate result may not be obtained
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:math:`\text{Angstrom}`. In some cases, accurate result may not be obtained
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due to the numerical noise of the force calculator. Usually increasing
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the displacement distance by the :ref:`amplitude option
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<amplitude_option>` reduces the numerical noise, but as its drawback
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@ -441,6 +441,8 @@ if __name__ == '__main__':
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mesh,
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ir_grid_points,
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grid_address)
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# gv x gv is divied by primitive cell volume.
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unit_conversion = primitive.get_volume()
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mode_prop = gv_sum2.reshape((1,) + gv_sum2.shape) / unit_conversion
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else:
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@ -451,7 +453,7 @@ if __name__ == '__main__':
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frequencies = f['frequency'][:]
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conditions = frequencies > 0
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if not conditions.all():
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if conditions.sum() > 3:
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sys.stderr.write("# Imaginary frequencies are found. "
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"They are set to be zero.\n")
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frequencies = np.where(conditions, frequencies, 0)
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