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6
doc/changelog.rst
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@ -3,6 +3,12 @@
Change Log
==========
Feb-9-2017: version 1.11.9
---------------------------
- This version works coupled with phonopy-1.11.8 or later.
- CRYSTAL code interface is implemented by Antti J. Karttunen.
Dec-14-2016: version 1.11.7
------------------------------

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doc/command-options.rst
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@ -1,7 +1,7 @@
.. _command_options:
List of command options (setting tags)
=======================================
Command options and setting tags
=================================
Command-user-interface of phono3py is operated with a variety of
command options. Here those command options are explained.
@ -48,12 +48,14 @@ Calculator interface
``--pwscf``: PWSCF (Quantum espresso) interface
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The default calculator interface is VASP code like input files. But as
an option, PWSCF interface is used with this option.
Using this option, PWSCF interface is invoked.
See the detail at :ref:`pwscf_interface`.
::
``--crystal``: CRYSTAL interface
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% phono3py --pwscf -c Si.in ...
Using this option, CRYSTAL interface is invoked.
See the detail at :ref:`crystal_interface`.
Force constants
----------------
@ -531,7 +533,7 @@ http://atztogo.github.io/phonopy/setting-tags.html#q-direction .
(Setting tag: ``WRITE_GAMMA``, ``.TRUE.`` or ``.FALSE.``)
Imaginary parts of self energy at harmonic phonon frequencies
:math:`\Gamma_\lambda(\omega_\lambda) = 1/2\tau_\lambda` are written
:math:`\Gamma_\lambda(\omega_\lambda)` are written
into file in hdf5 format. The result is written into
``kappa-mxxx-dx-gx(-sx).hdf5`` or ``kappa-mxxx-dx-gx-bx(-sx).hdf5`` with
``--bi`` option. With ``--sigma`` option, ``-sx`` is inserted in front
@ -543,7 +545,7 @@ of ``.hdf5``.
(Setting tag: ``READ_GAMMA``, ``.TRUE.`` or ``.FALSE.``)
Imaginary parts of self energy at harmonic phonon frequencies
:math:`\Gamma_\lambda(\omega_\lambda) = 1/2\tau_\lambda`
:math:`\Gamma_\lambda(\omega_\lambda)`
are read from ``kappa`` file in hdf5 format. Initially the usual
result file of ``kappa-mxxx-dx(-sx).hdf5`` is searched. Unless it is
found, it tries to read ``kappa`` file for each grid point,
@ -565,15 +567,15 @@ this is large data.
In the output file in hdf5, following keys are used to extract the
detailed information.
====================================== =====================================================================================================================
gamma_detail for ``--ise`` (temperature, sampling frequency point, symmetry reduced set of triplets at a grid point, band1, band2, band3) in THz
gamma_detail for ``--lw`` and ``--br`` (temperature, symmetry reduced set of triplets at a grid point, band1, band2, band3) in THz
====================================== =============================================================================================================================================
gamma_detail for ``--ise`` (temperature, sampling frequency point, symmetry reduced set of triplets at a grid point, band1, band2, band3) in THz (without :math:`2\pi`)
gamma_detail for ``--lw`` and ``--br`` (temperature, symmetry reduced set of triplets at a grid point, band1, band2, band3) in THz (without :math:`2\pi`)
mesh Numbers of sampling mesh along reciprocal axes.
frequency_point for ``--ise`` Sampling frequency points in THz, i.e., :math:`\omega` in :math:`\Gamma_\lambda(\omega)`
frequency_point for ``--ise`` Sampling frequency points in THz (without :math:`2\pi`), i.e., :math:`\omega` in :math:`\Gamma_\lambda(\omega)`
temperature (temperature,), Temperatures in K
triplet (symmetry reduced set of triplets at a grid point, 3), Triplets are given by the grid point indices (see below).
weight (symmetry reduced set of triplets at a grid point,), Weight of each triplet to imaginary part of self energy
====================================== =====================================================================================================================
====================================== =============================================================================================================================================
Q-points corresponding to grid point indices are calculated from
grid addresses and sampling mesh numbers given in
@ -629,7 +631,8 @@ symmetrization, the values must be equivalent between them.
Imaginary part of self energy :math:`\Gamma_\lambda(\omega)` is
calculated with respect to :math:`\omega`. The output is written to
``gammas-mxxxx-gx(-sx)-tx-bx.dat`` in THz (without :math:`2\pi`).
``gammas-mxxxx-gx(-sx)-tx-bx.dat`` in THz (without :math:`2\pi`) with
respect to frequency in THz (without :math:`2\pi`).
::
@ -661,9 +664,11 @@ respect to temperature. The output is written to
(Setting tag: ``JOINT_DOS``, ``.TRUE.`` or ``.FALSE.``)
Two classes of joint density of states (JDOS) are calculated. The
result is written into ``jdos-mxxxxxx-gx(-sx).dat`` in THz (without
:math:`2\pi`). The first column is the frequency, and the second and
third columns are the values given as follows, respectively,
result is written into ``jdos-mxxxxxx-gx(-sx).dat`` in
:math:`\text{THz}^{-1}` (without :math:`(2\pi)^{-1}`) with
respect to frequency in THz (without :math:`2\pi`). The first
column is the frequency, and the second and third columns are the
values given as follows, respectively,
.. math::
@ -681,10 +686,12 @@ third columns are the values given as follows, respectively,
--nac --jdos --ga="0 0 0 8 8 8"
When temperatures are specified, two classes of weighted JDOS are
calculated. The result is written into ``jdos-mxxxxxx-gx(-sx)-txxx.dat``,
where ``txxx`` shows the temperature. The first column is the
frequency, and the second and third columns are the values given as
follows, respectively,
calculated. The result is written into
``jdos-mxxxxxx-gx(-sx)-txxx.dat`` in :math:`\text{THz}^{-1}` (without
:math:`(2\pi)^{-1}`) with respect to frequency in THz
(without :math:`2\pi`). In the file name, ``txxx`` shows the
temperature. The first column is the frequency, and the second and
third columns are the values given as follows, respectively,
.. math::

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doc/conf.py
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@ -49,9 +49,9 @@ copyright = u'2015, Atsushi Togo'
# built documents.
#
# The short X.Y version.
version = '1.11.7'
version = '1.11.9'
# The full version, including alpha/beta/rc tags.
release = '1.11.7'
release = '1.11.9'
# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.

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doc/hdf5_howto.rst Normal file
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@ -0,0 +1,297 @@
.. _hdf5_howto:
How to read the results stored in hdf5 files
=============================================
.. contents::
:depth: 3
:local:
How to use HDF5 python library
-------------------------------
It is assumed that ``python-h5py`` is installed on the computer you
interactively use. In the following, how to see the contents of
``.hdf5`` files in the interactive mode of Python. Usually for running
interactive python, ``ipython`` is recommended to use but not the
plain python. In the following example, an MgO result of thermal
conductivity calculation is loaded and thermal conductivity tensor at
300 K is watched.
::
In [1]: import h5py
In [2]: f = h5py.File("kappa-m111111.hdf5")
In [3]: f.keys()
Out[3]:
[u'frequency',
u'gamma',
u'group_velocity',
u'gv_by_gv',
u'heat_capacity',
u'kappa',
u'kappa_unit_conversion',
u'mesh',
u'mode_kappa',
u'qpoint',
u'temperature',
u'weight']
In [4]: f['kappa'].shape
Out[4]: (101, 6)
In [5]: f['kappa'][:]
Out[5]:
array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.86834069e+03, 5.86834069e+03, 5.86834069e+03,
1.20936823e-15, 0.00000000e+00, -2.05720313e-15],
[ 1.37552313e+03, 1.37552313e+03, 1.37552313e+03,
2.81132320e-16, 0.00000000e+00, -5.00076366e-16],
...,
[ 6.56974871e+00, 6.56974871e+00, 6.56974871e+00,
1.76632276e-18, 0.00000000e+00, -2.30450472e-18],
[ 6.50316555e+00, 6.50316555e+00, 6.50316555e+00,
1.74843437e-18, 0.00000000e+00, -2.28116103e-18],
[ 6.43792061e+00, 6.43792061e+00, 6.43792061e+00,
1.73090513e-18, 0.00000000e+00, -2.25828616e-18]])
In [6]: f['temperature'][:]
Out[6]:
array([ 0., 10., 20., 30., 40., 50., 60., 70.,
80., 90., 100., 110., 120., 130., 140., 150.,
160., 170., 180., 190., 200., 210., 220., 230.,
240., 250., 260., 270., 280., 290., 300., 310.,
320., 330., 340., 350., 360., 370., 380., 390.,
400., 410., 420., 430., 440., 450., 460., 470.,
480., 490., 500., 510., 520., 530., 540., 550.,
560., 570., 580., 590., 600., 610., 620., 630.,
640., 650., 660., 670., 680., 690., 700., 710.,
720., 730., 740., 750., 760., 770., 780., 790.,
800., 810., 820., 830., 840., 850., 860., 870.,
880., 890., 900., 910., 920., 930., 940., 950.,
960., 970., 980., 990., 1000.])
In [7]: f['kappa'][30]
Out[7]:
array([ 2.18146513e+01, 2.18146513e+01, 2.18146513e+01,
5.84389577e-18, 0.00000000e+00, -7.63278476e-18])
In [8]: g = f['gamma'][30]
In [9]: import numpy as np
In [10]: g = np.where(g > 0, g, -1)
In [11]: lifetime = np.where(g > 0, 1.0 / (2 * 2 * np.pi * g), 0)
.. _kappa_hdf5_file:
Details of ``kappa-*.hdf5`` file
---------------------------------
Files name, e.g. ``kappa-m323220.hdf5``, is determined by some
specific options. ``mxxx``, show the numbers of sampling
mesh. ``sxxx`` and ``gxxx`` appear optionally. ``sxxx`` gives the
smearing width in the smearing method for Brillouin zone integration
for phonon lifetime, and ``gxxx`` denotes the grid number. Using the
command option of ``-o``, the file name can be modified slightly. For
example ``-o nac`` gives ``kappa-m323220.nac.hdf5`` to
memorize the option ``--nac`` was used.
Currently ``kappa-*.hdf5`` file (not for the specific grid points)
contains the properties shown below.
mesh
^^^^^
(Versions 1.10.11 or later)
The numbers of mesh points for reciprocal space sampling along
reciprocal axes, :math:`a^*, b^*, c^*`
frequency
^^^^^^^^^^
Phonon frequencies. The physical unit is THz, where THz
is in the ordinal frequency not the angular frequency.
The array shape is (irreducible q-point, phonon band).
gamma
^^^^^^
Imaginary part of self energy. The physical unit is THz, where THz
is in the ordinal frequency not the angular frequency.
The array shape for all grid-points (irreducible q-points) is
(temperature, irreducible q-point, phonon band).
The array shape for a specific grid-point is
(temperature, phonon band).
Phonon lifetime (:math:`\tau_\lambda=1/2\Gamma_\lambda(\omega_\lambda)`) may
be estimated from ``gamma``. :math:`2\pi` has to be multiplied with
``gamma`` values in the hdf5 file to convert the unit of ordinal
frequency to angular frequency. Zeros in ``gamma`` values mean that
those elements were not calculated such as for three acoustic modes at
:math:`\Gamma` point. The below is the copy-and-paste from the
previous section to show how to obtain phonon lifetime in pico
second::
In [8]: g = f['gamma'][30]
In [9]: import numpy as np
In [10]: g = np.where(g > 0, g, -1)
In [11]: lifetime = np.where(g > 0, 1.0 / (2 * 2 * np.pi * g), 0)
gamma_isotope
^^^^^^^^^^^^^^
Isotope scattering of :math:`1/2\tau^\mathrm{iso}_\lambda`.
The physical unit is same as that of gamma.
The array shape is same as that of frequency.
group_velocity
^^^^^^^^^^^^^^^
Phonon group velocity, :math:`\nabla_\mathbf{q}\omega_\lambda`. The
physical unit is :math:`\text{THz}\cdot\text{\AA}`, where THz
is in the ordinal frequency not the angular frequency.
The array shape is (irreducible q-point, phonon band, 3 = Cartesian coordinates).
heat_capacity
^^^^^^^^^^^^^^
Mode-heat-capacity defined by
.. math::
C_\lambda = k_\mathrm{B}
\left(\frac{\hbar\omega_\lambda}{k_\mathrm{B} T} \right)^2
\frac{\exp(\hbar\omega_\lambda/k_\mathrm{B}
T)}{[\exp(\hbar\omega_\lambda/k_\mathrm{B} T)-1]^2}.
The physical unit is eV/K.
The array shape is (temperature, irreducible q-point, phonon band).
.. _output_kappa:
kappa
^^^^^^
Thermal conductivity tensor. The physical unit is W/m-K.
The array shape is (temperature, 6 = (xx, yy, zz, yz, xz, xy)).
.. _output_mode_kappa:
mode-kappa
^^^^^^^^^^^
Thermal conductivity tensors at k-stars (:math:`{}^*\mathbf{k}`):
.. math::
\sum_{\mathbf{q} \in {}^*\mathbf{k}} \kappa_{\mathbf{q}j}.
The sum of this over :math:`{}^*\mathbf{k}` corresponding to
irreducible q-points gives :math:`\kappa` (:ref:`output_kappa`).
The physical unit is W/m-K. Each tensor element is the sum of tensor
elements on the members of :math:`{}^*\mathbf{k}`, i.e., symmetrically
equivalent q-points by crystallographic point group and time reversal
symmetry.
The array shape is (temperature, irreducible q-point, phonon band, 6 =
(xx, yy, zz, yz, xz, xy)).
gv_by_gv
^^^^^^^^^
Outer products of group velocities for k-stars
(:math:`{}^*\mathbf{k}`) for each irreducible q-point and phonon band
(:math:`j`):
.. math::
\sum_{\mathbf{q} \in {}^*\mathbf{k}} \mathbf{v}_{\mathbf{q}j} \otimes
\mathbf{v}_{\mathbf{q}j}.
The physical unit is
:math:`\text{THz}^2\cdot\text{\AA}^2`, where THz is in the
ordinal frequency not the angular frequency.
The array shape is (irreducible q-point, phonon band, 6 = (xx, yy, zz,
yz, xz, xy)).
q-point
^^^^^^^^
Irreducible q-points in reduced coordinates.
The array shape is (irreducible q-point, 3 = reduced
coordinates in reciprocal space).
temperature
^^^^^^^^^^^^
Temperatures where thermal conductivities are calculated. The physical
unit is K.
weight
^^^^^^^
Weights corresponding to irreducible q-points. Sum of weights equals to
the number of mesh grid points.
ave_pp
^^^^^^^
Averaged phonon-phonon interaction in :math:`\text{eV}^2`,
:math:`P_{\mathbf{q}j}`:
.. math::
P_{\mathbf{q}j} = \frac{1}{(3n_\mathrm{a})^2} \sum_{\lambda'\lambda''}
|\Phi_{\lambda\lambda'\lambda''}|^2.
This is not going to be calculated in the RTA thermal coductivity
calculation mode by default. To calculate this, ``--full_pp`` option
has to be specified (see :ref:`full_pp_option`).
kappa_unit_conversion
^^^^^^^^^^^^^^^^^^^^^^
This is used to convert the physical unit of lattice thermal
conductivity made of ``heat_capacity``, ``group_velocity``, and
``gamma``, to W/m-K. In the single mode relaxation time (SMRT) method,
a mode contribution to the lattice thermal conductivity is given by
.. math::
\kappa_\lambda = \frac{1}{NV_0} C_\lambda \mathbf{v}_\lambda \otimes
\mathbf{v}_\lambda \tau_\lambda^{\mathrm{SMRT}}.
For example of some single mode, :math:`\kappa_{\lambda,{xx}}` is calculated by::
kappa_unit_conversion / weight.sum() * heat_capacity[30, 2, 0] *
group_velocity[2, 0, 0] ** 2 / (2 * gamma[30, 2, 0])
where :math:`1/V_0` is included in ``kappa_unit_conversion``.
Similary mode-kappa (defined at :ref:`output_mode_kappa`) is
calculated by::
kappa_unit_conversion / weight.sum() * heat_capacity[30, 2, 0] *
gv_by_gv[2, 0] / (2 * gamma[30, 2, 0])

10
doc/index.rst
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@ -15,10 +15,6 @@ The theoretical background is summarized in the paper found at
http://dx.doi.org/10.1103/PhysRevB.91.094306 or the draft in arxiv at
http://arxiv.org/abs/1501.00691 .
:ref:`Interfaces to calculators <calculator_interfaces>` for VASP,
pwscf, and CRYSTAL are built-in.
Documentation
=============
@ -27,12 +23,10 @@ Documentation
install
examples
interfaces
vasp
pwscf
crystal
Interfaces to calculators (VASP, pwscf, CRYSTAL) <interfaces>
command-options
output-files
hdf5_howto
tips
auxiliary-tools
citation

270
doc/output-files.rst
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@ -90,273 +90,3 @@ Joint densities of states are stored in Thz. See :ref:`jdos_option`.
Linewidths (FWHM) at temperatures are stored in THz. See :ref:`lw_option`.
How to read the results stored in hdf5 files
-----------------------------------------------
How to use HDF5 python library
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
It is assumed that ``python-h5py`` is installed on the computer you
interactively use. In the following, how to see the contents of
``.hdf5`` files in the interactive mode of Python. Usually for running
interactive python, ``ipython`` is recommended to use but not the
plain python. In the following example, an MgO result of thermal
conductivity calculation is loaded and thermal conductivity tensor at
300 K is watched.
::
In [1]: import h5py
In [2]: f = h5py.File("kappa-m111111.hdf5")
In [3]: f.keys()
Out[3]:
[u'frequency',
u'gamma',
u'group_velocity',
u'gv_by_gv',
u'heat_capacity',
u'kappa',
u'kappa_unit_conversion',
u'mesh',
u'mode_kappa',
u'qpoint',
u'temperature',
u'weight']
In [4]: f['kappa'].shape
Out[4]: (101, 6)
In [5]: f['kappa'][:]
Out[5]:
array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.86834069e+03, 5.86834069e+03, 5.86834069e+03,
1.20936823e-15, 0.00000000e+00, -2.05720313e-15],
[ 1.37552313e+03, 1.37552313e+03, 1.37552313e+03,
2.81132320e-16, 0.00000000e+00, -5.00076366e-16],
...,
[ 6.56974871e+00, 6.56974871e+00, 6.56974871e+00,
1.76632276e-18, 0.00000000e+00, -2.30450472e-18],
[ 6.50316555e+00, 6.50316555e+00, 6.50316555e+00,
1.74843437e-18, 0.00000000e+00, -2.28116103e-18],
[ 6.43792061e+00, 6.43792061e+00, 6.43792061e+00,
1.73090513e-18, 0.00000000e+00, -2.25828616e-18]])
In [6]: f['temperature'][:]
Out[6]:
array([ 0., 10., 20., 30., 40., 50., 60., 70.,
80., 90., 100., 110., 120., 130., 140., 150.,
160., 170., 180., 190., 200., 210., 220., 230.,
240., 250., 260., 270., 280., 290., 300., 310.,
320., 330., 340., 350., 360., 370., 380., 390.,
400., 410., 420., 430., 440., 450., 460., 470.,
480., 490., 500., 510., 520., 530., 540., 550.,
560., 570., 580., 590., 600., 610., 620., 630.,
640., 650., 660., 670., 680., 690., 700., 710.,
720., 730., 740., 750., 760., 770., 780., 790.,
800., 810., 820., 830., 840., 850., 860., 870.,
880., 890., 900., 910., 920., 930., 940., 950.,
960., 970., 980., 990., 1000.])
In [7]: f['kappa'][30]
Out[7]:
array([ 2.18146513e+01, 2.18146513e+01, 2.18146513e+01,
5.84389577e-18, 0.00000000e+00, -7.63278476e-18])
.. _kappa_hdf5_file:
Details of ``kappa-*.hdf5`` file
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Files name, e.g. ``kappa-m323220.hdf5``, is determined by some
specific options. ``mxxx``, show the numbers of sampling
mesh. ``sxxx`` and ``gxxx`` appear optionally. ``sxxx`` gives the
smearing width in the smearing method for Brillouin zone integration
for phonon lifetime, and ``gxxx`` denotes the grid number. Using the
command option of ``-o``, the file name can be modified slightly. For
example ``-o nac`` gives ``kappa-m323220.nac.hdf5`` to
memorize the option ``--nac`` was used.
Currently ``kappa-*.hdf5`` file (not for the specific grid points)
contains the properties shown below.
mesh
~~~~
(Versions 1.10.11 or later)
The numbers of mesh points for reciprocal space sampling along
reciprocal axes, :math:`a^*, b^*, c^*`
frequency
~~~~~~~~~
Phonon frequencies. The physical unit is THz, where THz
is in the ordinal frequency not the angular frequency.
The array shape is (irreducible q-point, phonon band).
gamma
~~~~~
Imaginary part of self energy. The physical unit is THz, where THz
is in the ordinal frequency not the angular frequency.
The array shape for all grid-points (irreducible q-points) is
(temperature, irreducible q-point, phonon band).
The array shape for a specific grid-point is
(temperature, phonon band).
This is read when ``--read_gamma`` option is specified.
gamma_isotope
~~~~~~~~~~~~~~
Isotope scattering of :math:`1/2\tau^\mathrm{iso}_\lambda`.
The physical unit is same as that of gamma.
The array shape is same as that of frequency.
This is NOT read even when ``--read_gamma`` option is specified.
group_velocity
~~~~~~~~~~~~~~
Phonon group velocity, :math:`\nabla_\mathbf{q}\omega_\lambda`. The
physical unit is :math:`\text{THz}\cdot\text{\AA}`, where THz
is in the ordinal frequency not the angular frequency.
The array shape is (irreducible q-point, phonon band, 3 = Cartesian coordinates).
heat_capacity
~~~~~~~~~~~~~
Mode-heat-capacity defined by
.. math::
C_\lambda = k_\mathrm{B}
\left(\frac{\hbar\omega_\lambda}{k_\mathrm{B} T} \right)^2
\frac{\exp(\hbar\omega_\lambda/k_\mathrm{B}
T)}{[\exp(\hbar\omega_\lambda/k_\mathrm{B} T)-1]^2}.
The physical unit is eV/K.
The array shape is (temperature, irreducible q-point, phonon band).
.. _output_kappa:
kappa
~~~~~
Thermal conductivity tensor. The physical unit is W/m-K.
The array shape is (temperature, 6 = (xx, yy, zz, yz, xz, xy)).
.. _output_mode_kappa:
mode-kappa
~~~~~~~~~~
Thermal conductivity tensors at k-stars (:math:`{}^*\mathbf{k}`):
.. math::
\sum_{\mathbf{q} \in {}^*\mathbf{k}} \kappa_{\mathbf{q}j}.
The sum of this over :math:`{}^*\mathbf{k}` corresponding to
irreducible q-points gives :math:`\kappa` (:ref:`output_kappa`).
The physical unit is W/m-K. Each tensor element is the sum of tensor
elements on the members of :math:`{}^*\mathbf{k}`, i.e., symmetrically
equivalent q-points by crystallographic point group and time reversal
symmetry.
The array shape is (temperature, irreducible q-point, phonon band, 6 =
(xx, yy, zz, yz, xz, xy)).
gv_by_gv
~~~~~~~~~
Outer products of group velocities for k-stars
(:math:`{}^*\mathbf{k}`) for each irreducible q-point and phonon band
(:math:`j`):
.. math::
\sum_{\mathbf{q} \in {}^*\mathbf{k}} \mathbf{v}_{\mathbf{q}j} \otimes
\mathbf{v}_{\mathbf{q}j}.
The physical unit is
:math:`\text{THz}^2\cdot\text{\AA}^2`, where THz is in the
ordinal frequency not the angular frequency.
The array shape is (irreducible q-point, phonon band, 6 = (xx, yy, zz,
yz, xz, xy)).
q-point
~~~~~~~
Irreducible q-points in reduced coordinates.
The array shape is (irreducible q-point, 3 = reduced
coordinates in reciprocal space).
temperature
~~~~~~~~~~~
Temperatures where thermal conductivities are calculated. The physical
unit is K.
weight
~~~~~~
Weights corresponding to irreducible q-points. Sum of weights equals to
the number of (coarse) mesh grid points.
ave_pp
~~~~~~~
Averaged phonon-phonon interaction in :math:`\text{eV}^2`,
:math:`P_{\mathbf{q}j}`:
.. math::
P_{\mathbf{q}j} = \frac{1}{(3n_\mathrm{a})^2} \sum_{\lambda'\lambda''}
|\Phi_{\lambda\lambda'\lambda''}|^2.
This is not going to be calculated in the RTA thermal coductivity
calculation mode by default. To calculate this, ``--full_pp`` option
has to be specified (see :ref:`full_pp_option`).
kappa_unit_conversion
~~~~~~~~~~~~~~~~~~~~~~
This is used to convert the physical unit of lattice thermal
conductivity made of ``heat_capacity``, ``group_velocity``, and
``gamma``, to W/m-K. In the single mode relaxation time (SMRT) method,
a mode contribution to the lattice thermal conductivity is given by
.. math::
\kappa_\lambda = \frac{1}{NV_0} C_\lambda \mathbf{v}_\lambda \otimes
\mathbf{v}_\lambda \tau_\lambda^{\mathrm{SMRT}}.
For example of some single mode, :math:`\kappa_{\lambda,{xx}}` is calculated by::
kappa_unit_conversion / weight.sum() * heat_capacity[30, 2, 0] *
group_velocity[2, 0, 0] ** 2 / (2 * gamma[30, 2, 0])
where :math:`1/V_0` is included in ``kappa_unit_conversion``.
Similary mode-kappa (defined at :ref:`output_mode_kappa`) is
calculated by::
kappa_unit_conversion / weight.sum() * heat_capacity[30, 2, 0] *
gv_by_gv[2, 0] / (2 * gamma[30, 2, 0])