Structure and thermodynamics of defects in Na-feldspar from a neural network potential

The diffusive phase transformations occurring in feldspar, a common mineral in the crust of the Earth, are essential for reconstructing the thermal histories of magmatic and metamorphic rocks. Due to the long timescales over which these transformations proceed, the mechanism responsible for sodium diffusion and its possible anisotropy has remained a topic of debate. To elucidate this defect-controlled process, we have developed a neural network potential (NNP) trained on first-principle calculations of Na-feldspar (albite) and its charged defects. This force field reproduces various experimentally known properties of feldspar, including its lattice parameters and elastic constants as well as heat capacity and DFT-calculated defect formation energies. A new type of dumbbell interstitial defect is found to be most favorable, and its free energy of formation at finite temperature is calculated using thermodynamic integration. The necessity of including electrostatic corrections before training an NNP is demonstrated by predicting more consistent defect formation energies.