Diffusion coefficient from energy and temperature
=================================================

The diffusion coefficient is a quantitative characteristic of the diffusion rate, equal
to the amount of matter passing per unit time through a section of a unit area as a
result of the thermal motion of molecules.

**Notation:**

#. :math:`k_\text{B}` (:code:`k_B`) is :attr:`~symplyphysics.quantities.boltzmann_constant`.

**Conditions:**

#. The material is a solid.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Mass_diffusivity#Solids>`__.

.. py:currentmodule:: symplyphysics.laws.condensed_matter.diffusion_coefficient_from_energy_temperature

.. py:data:: diffusion_coefficient

    :attr:`~symplyphysics.symbols.chemistry.diffusion_coefficient`.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`area/time`


.. py:data:: energy

    Activation :attr:`~symplyphysics.symbols.basic.energy` of the dopant.

Symbol:
    :code:`E_A`

Latex:
    :math:`E_\text{A}`

Dimension:
    :code:`energy`


.. py:data:: maximum_diffusion_coefficient

    Maximum :attr:`~symplyphysics.symbols.chemistry.diffusion_coefficient`, e.g. at infinite temperature.

Symbol:
    :code:`D_0`

Latex:
    :math:`D_{0}`

Dimension:
    :code:`area/time`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature`.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: law

    :code:`D = D_0 * exp(-E_A / (k_B * T))`


    Latex:
        .. math::
            D = D_{0} \exp{\left(- \frac{E_\text{A}}{k_\text{B} T} \right)}