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    "# Thermal Conductivity\n",
    "\n",
    "Compute phonon linewidth and thermal conductivity of the system with third order phonon interaction coefficients.\n",
    "\n",
    "The code is recently developed and heavily relies on its Fortran counterpart for intense calculations. At the meantime, the new version of the tetrahedron finder `Tetrahedra` is developed along with it to improve processing speed. And the class `AnharmInterp` is developed to handle interaction coefficients. New object oriented `constants` and graph based `unit_conversion` system is also developed to enhance their flexibility and usability.\n",
    "\n",
    "The algorithm involved has been heavily optimized, but some clean-up is necessary to improve the code readability,\n",
    "and also to get rid of some redundant and unused stuff.\n",
    "\n",
    "The equations about phonon linewidth and the RTA approach to the thermal conductivity are described in paper Phys. Rev. B 91, 094306 (2015), that of thermal conductivity through LBTE approach in  Phys. Rev. Lett. 110, 265506 (2013).\n",
    "\n",
    "### Examples:\n",
    "\n",
    "To instantiate the object:\n",
    "\n",
    "``` python\n",
    "cd = Conductivity(\n",
    "    struct=\"../../data/poscar\",\n",
    "    grid=\"11 11 11\",\n",
    "    pgn=\"C1\",\n",
    "    phi2=\"../../data/order2/phi2_444.pkl\",\n",
    "    phi3=\"../../data/order3/phi3_222.pkl\",\n",
    "    epsilon=\"../../data/epsilon.yml\",\n",
    "    q_direction=\"1 0 0\",\n",
    "    )\n",
    "```\n",
    "\n",
    "Then the phonon linewidth of a given q-point can be computed, at a series of temperatures:\n",
    "\n",
    "```python\n",
    "temps = np.linspace(0, 1000, 101)\n",
    "cd.gamma_tetra_at_phonon(q=q, temperature=temps, phonon_cutoff=0.001, units=\"THz\")\n",
    "```\n",
    "\n",
    "or all the grid points:\n",
    "\n",
    "```python\n",
    "cd.gamma_tetra_grid(temperature=temps, units=\"THz\")\n",
    "```\n",
    "\n",
    "or the thermal conductivity:\n",
    "\n",
    "```python\n",
    "cd.thermal_conductivity_RTA(temperature=temps, units=\"THz\") # Relaxation time approaximation\n",
    "cd.thermal_conductivity_LBTE(temperature=temps, units=\"THz\") # Linearized Boltzmann transport equation\n",
    "```"
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    "--- \n",
    "\n",
    "## Container for the phonon interaction data\n",
    "\n",
    "All the relative coefficients of phonon interactions can be accessed using `AnharmInterp` class.\n",
    "\n",
    "``` python\n",
    "ai = AnharmInterp( # Instantiate with second order phonons\n",
    "    struct=\"../../data/poscar\",\n",
    "    grid=\"11 11 11\",\n",
    "    pgn=\"C1\",\n",
    "    phi2=\"../../data/order2/phi2_444.pkl\",\n",
    "    epsilon=\"../../data/epsilon.yml\",\n",
    "    q_direction=\"1 0 0\",\n",
    "    )\n",
    "ai.add_phin( # Add in 3rd order coefficients\n",
    "    phin=\"../../data/order3/phi3_222.pkl\",\n",
    "    order=3,\n",
    "    )\n",
    "```\n",
    "\n",
    "Then dynamic tensors, phonons, group velocities, derivatives of dynamic matrices with respect to q-point,\n",
    "and heat capacities can be calculated.\n",
    "\n",
    "```python\n",
    "ai.get_phonons(kpts, return_eigenvectors=False, units=\"THz\")\n",
    "ai.getDqN(\"1/2 0 0; 1/2 0 0\", order=3)\n",
    "ai.group_velocity(\n",
    "    kpts,\n",
    "    fd=False, # Take the analytic derivative of dynamic matrix (finite difference option is available)\n",
    "    units=\"THz\",\n",
    "    )\n",
    "ai.analytic_derivative_dynamic_matrix(kpts)\n",
    "ai.fd_derivative_dynamic_matrix(\n",
    "    kpts,\n",
    "    amplitute=1.0E-5,\n",
    "    )\n",
    "ai.heat_capacity( # Returns values in the units of eV/K\n",
    "    kpts, \n",
    "    temperature=temps,\n",
    "    )\n",
    "```"
   ]
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