Thomas C. Chust

<`thomas.chust@uni-bayreuth.de`

>

Temperature field of a convection simulation from Nakagawa et al. [2010]

$$\begin{align*} \nabla\cdot \left(\color{red}{\rho} u\right) &= 0, \\ -\nabla p + \color{red}{\eta} \Delta u + \color{red}{\rho} g &= 0, \\ \color{red}{\rho} T \, \left(\frac{\partial}{\partial {t}} + u\cdot\nabla\right) \color{red}{S} &= \color{red}{k} \, \Delta T + \color{red}{\bar\tau} \, \nabla u + \color{red}{\rho H^*}. \end{align*}$$

Global seismic wave propagation simulation from Schuberth et al. [2012]

$$ \partial_t^2 x = \color{red}{v}^2 \Delta x, \\ \color{red}{v_p} = \sqrt{\frac{\color{red}{\kappa_S} + \frac43\color{red}{\mu}}{\color{red}{\rho}}}, \color{red}{v_s} = \sqrt{\frac{\color{red}{\mu}}{\color{red}{\rho}}}. $$

Category | Properties | Dependencies |
---|---|---|

Thermal | $S, C_p$ | $\leftarrow \partial_T^{1,2} G$ |

Elastic | $V, \rho, \kappa_S, \color{#88f}{\mu}$ | $\leftarrow \partial_{p,T}^{1,2} G$ |

Transport | $k, \eta$ | Not linked to $G$ |

Potentials | $E, A, H, G$ | $\mathrm{d}G = V\,\mathrm{d}p - S\,\mathrm{d}T$ |

Energetic equilibrium between the $\ce{Mg}$- (blue), $\ce{Fe}$- (red) and $\ce{Al}$-endmembers (green) of bridgmanite and post-perovskite in $p, T$ space.

Energetic equilibrium between the $\ce{Mg}$- (blue), $\ce{Fe}$- (red) and $\ce{Al}$-endmembers (green) of bridgmanite and post-perovskite in $p, T$ space.

In order to compute chemical equilibrium between multiple phases with varying composition, we need three more things:

- The Gibbs energy of phases modelled as solid solutions has to be computed.
- The Gibbs energy of aggregates of phases has to be computed.
- An energetically optimal collection of phases has to be chosen at given $p, T$ and bulk composition.

Phase diagram computed for $\ce{FeO-MgO-SiO2}$ composition with $\frac{\ce{Fe}}{\ce{Fe + Mg}} \approx 0.11$ as a function of $p$ and $T$.

Phase diagram computed for $\ce{FeO-MgO-SiO2}$ composition with $\frac{\ce{Fe}}{\ce{Fe + Mg}} \approx 0.11$ as a function of $p$ and $T$.

Phase diagram computed for $\ce{FeO-MgO-SiO2}$ composition with $\frac{\ce{Fe}}{\ce{Fe + Mg}} \approx 0.11$ as a function of $p$ and $T$.

With the addition of more chemical components,

- new phases and their stability fields occur,
- new endmembers are introduced and form mineral solutions whose stability fields generally expand, and/or
- the variance of mineral assemblages increases, resulting in binary or higher-order phase loops which allow the coexistence of phases previously separated by sharp boundaries.

Relative atomic amounts of stable phases for $\ce{FeO-MgO-SiO2}$ composition along the isentrope with a potential temperature of $1600\,\mathrm{K}$.

Relative atomic amounts of stable phases for $\ce{CaO-FeO-MgO-SiO2}$ composition along the isentrope with a potential temperature of $1600\,\mathrm{K}$.

Relative atomic amounts of stable phases for $\ce{FeO-MgO-SiO2}$ composition along the isentrope with a potential temperature of $1600\,\mathrm{K}$.

Relative atomic amounts of stable phases for $\ce{FeO-MgO-Al2O3-SiO2}$ composition along the isentrope with a potential temperature of $1600\,\mathrm{K}$.

Phase diagram for $\ce{Na2O-CaO-FeO-MgO-Al2O3-SiO2}$ composition as a function of $p$ and $T$. Lines indicate phase boundaries for $\ce{MgSiO3}$ (blue), $\ce{FeSiO3}$ (red) and $\ce{Al2O3}$ endmembers (green) of bridgmanite and post-perovskite.

$$
\partial_pT\mid_S = \frac{\alpha V}{C_p} T
$$

Self-consistently computed isentropes for two different pyrolite-based compositions in comparison with the adiabat from Katsura et al. [2010].

- High accuracy of thermo-elastic parameters or good $p, T$ extrapolation behaviour is possible.
- Calibration of phase equilibria may be specific to certain composition ranges.
- Complex phase transitions buffer latent heat effects and result in smoother adiabats.
- Elastic property profiles computed for homogeneous chemical composition or mechanical mixtures are very similar.

- Versatile simulation software for minerals and mantle aggregates.
- Computes thermoelastic properties and chemical equilibrium states.
- Supports multiple widely used equations of state.
- Features an easy-to-use solution model.
- Offers a free, open and extensible implementation.