Energy properties to maintain thickness interface

[vovannikov]

The parameters of the free energy depent on the values of the surface $\gammas$ and grain boundary $\gamma{gb}$ energies and the diffuse interface thickness $\delta$ as follows:

\begin{align}
A &= \dfrac{(12\gamma_s - 7\gamma_{gb})}{\delta} \\
B &= \dfrac{\gamma_{gb}}{\delta} \\
\kappa_c &= \dfrac{3}{4} \delta (2\gamma_s - \gamma_{gb}) \\
\kappa_p &= \dfrac{3}{4} \delta \gamma_{gb}
\end{align}

If $\gammas = 1.8$ and $\gamma{gb} = 0.6$, then these are the properties for the energy function for the interface thickness to be at least the predefined $\delta_{\min}$ value:

$\delta_{\min} = 0.5$:

"EnergyAbstract": {
    "A": "34.8",
    "B": "1.2",
    "KappaC": "1.125",
    "KappaP": "0.225"
},

$\delta_{\min} = 1.0$:

"EnergyAbstract": {
    "A": "17.4",
    "B": "0.6",
    "KappaC": "2.25",
    "KappaP": "0.5"
},

$\delta_{\min} = 2.0$:

"EnergyAbstract": {
    "A": "8.7",
    "B": "0.3",
    "KappaC": "4.5",
    "KappaP": "0.9"
},

$\delta_{\min} = 3.0$:

"EnergyAbstract": {
    "A": "5.8",
    "B": "0.2",
    "KappaC": "6.75",
    "KappaP": "1.35"
},

$\delta_{\min} = 4.0$:

"EnergyAbstract": {
    "A": "4.35",
    "B": "0.15",
    "KappaC": "9.0",
    "KappaP": "1.79"
},

[vovannikov]

Another important remark. The formulas above are based on some limit case analysis for flat interfaces which does not hold for us of course. For this reason the formuls provide the lower assessment. In reality normally the interface thickness is larger. Therefore you should set InterfaceWidth twice larger accroding to my experience. For instance if the parameters for $\delta_{\min} = 2.0$ are used, the it is better to set InterfaceWidth = 4.

@peterrum, you can try to use the settings for $\delta{\min} = 2.0$ or $\delta{\min} =3.0$ for the 49 particles case, do not forget that these values should also be in sync with the initial interface thickness as described above.