Correction to: Scientific Reports https://doi.org/10.1038/s41598-025-07258-1, published online 1 July 2025

The original version of this Article contained errors.

Equation 12 was incorrectly given as:

$$\begin{array}{*{20}c} {\rho_{i}^{Fe} = \mathop \sum \limits_{j = 1,j \ne i}^{{N_{Fe} }} \left( {a^{Fe} /r_{ij} } \right)^{{m^{Fe} }} + \rho_{i}^{Fe} } \\ \end{array}$$

The correct Eq. 12 appears below.

$$\rho_{{i_{Fe} }} = \mathop \sum \limits_{{j_{Fe} \ne i_{Fe} }} \left( {a^{Fe} /r_{{i_{Fe} j_{Fe} }} } \right)^{{m^{Fe} }} + \mathop \sum \limits_{{j_{O} }} \left( {a^{FeO} /r_{{i_{Fe} j_{O} }} } \right)^{{m^{FeO} }}$$
(12)

In addition, Eq. 13 was incorrectly given as:

$$\begin{array}{*{20}c} {\rho_{i}^{O} = \mathop \sum \limits_{j = 1,j \ne i}^{{N_{O} }} \left( {a^{O} /r_{ij} } \right)^{{m^{O} }} + \rho_{i}^{FeO} } \\ \end{array}$$

The correct Eq. 13 appears below.

$$\rho_{{i_{O} }} = \mathop \sum \limits_{{j_{O} \ne i_{O} }} \left( {a^{O} /r_{{i_{O} j_{O} }} } \right)^{{ m^{O} }} + \mathop \sum \limits_{{j_{Fe} }} \left( {a^{FeO} /r_{{i_{O} j_{Fe} }} } \right)^{{m^{FeO} }}$$
(13)

Finally, Eq. 14 has been removed from the Article.

$$\begin{array}{*{20}c} {\rho_{i}^{FeO} = \mathop \sum \limits_{j = 1,j \ne i}^{{N_{O} }} \left( {a^{FeO} /r_{ij} } \right)^{{m^{FeO} }} } \\ \end{array}$$

The original Article has been corrected.