Table 2.

Structural, chemical, and physical properties of constituent elements of oxides for regression models, given as “features” for symbolic regression modeling.

Properties	Description	Unit
$\stackrel{\circledR }{O}$	Molar ratio of oxygen ions to metal ions	—
$M$	Atomic mass	$\mathrm{g}·{\mathrm{mol}}^{-1}$
$Z$	Valence	—
$r_{\mathrm{V}\mathrm{I}}$	Shannon ionic radius with sixfold coordination to oxygen108,109	$Å$
$r$	Shannon ionic radius depending on $n_c$ (see below)108,109	$Å$
$B$	Bulk modulus	$\mathrm{GPa}$
$G$	Shear modulus	$\mathrm{GPa}$
$\rho$	Density	$\mathrm{g}·{\mathrm{cm}}^{-3}$
${\rho }_{\mathrm{m}\mathrm{ol}}$	Molar density, defined as $\rho /M$	$\mathrm{mol}·{\mathrm{cm}}^{-3}$
${\eta }_f$	Ionic filling rate (per unit volume), defined as ${\eta }_f=N_{\mathrm{avo}}{\rho }_{\mathrm{mol}}\left(\frac{4}{3}\pi r_{\mathrm{VI}}^3\right)$ where $N_{\mathrm{avo}}$ is the Avogadro’s constant	—
$n$	Principal quantum number of valence electrons	—
$l$	Azimuthal quantum number of valence electrons	—
$\alpha$	Thermal expansion coefficient (linear not volumetric)	${\mathrm{K}}^{-1}$
$\kappa$	Thermal conductivity	$\mathrm{W}·{\mathrm{m}}^{-1}·{\mathrm{K}}^{-1}$
$\chi -{\chi }_{\mathrm{O}}$	Difference in electronegativity between metal ions and oxygen	—
$\nu$	Poisson’s ratio	—
${\theta }_D$	Debye temperature	$\mathrm{K}$
$n_c$	Coordination number to oxygen ions, which depends on the occupied sites ($A_s$, $B_s$, or $C_s$) in different crystal classes. For example, in perovskite oxides, $n_c$ for $A_s$ and $B_s$ are given as $12$ and $6$, respectively	—
$〈\cdots 〉$	Average over the constituent metal ions	Common to $\cdots$
$\sigma \left(\cdots \right)$	Standard deviation over the constituent metal ions	Common to $\cdots$
$r\left(\cdots \right)$	Skewness over the constituent metal ions	—