Calculate the Haven's Ratio

[v1kko]

No description provided.

[stefsmeets]

This is essentially the tracer diffusivity of the center of mass of all floating atoms (from the starting point).

[stefsmeets]

Haven ratio is defined as:

$H_R = \frac{D^*}{D_\sigma}$

Tracer diffusion (SimulationMetrics.tracer_diffusivity()):

$D^*=\frac{1}{3}\int_{0}^{\infty}\left \langle \overline{v(0)}\cdot \overline{v(t)} \right \rangle dt$

Ionic conductivity (essentially tracer_diffusivity of center of mass):

$D_\sigma=\frac{1}{3N}\int_{0}^{\infty} \sum_{i,j}^{1...N} \left \langle \overline{v_i(0)}\cdot \overline{v_j(t)} \right \rangle dt$