A first-principles machine-learning force field for heterogeneous ice nucleation on microcline feldspar

The formation of ice in the atmosphere affects precipitation and cloud properties, and plays a key role in the climate of our planet. Although ice can form directly from liquid water under deeply supercooled conditions, the presence of foreign particles can aid ice formation at much warmer temperatures. Over the past decade, experiments have highlighted the remarkable efficiency of feldspar minerals as ice nuclei compared to other particles present in the atmosphere. However, the exact mechanism of ice formation on feldspar surfaces has yet to be fully understood. Here, we develop a first-principles machine-learning model for the potential energy surface aimed at studying ice nucleation at microcline feldspar surfaces. The model is able to reproduce with high-fidelity the energies and forces derived from density-functional theory (DFT) based on the SCAN exchange and correlation functional. Our training set includes configurations of bulk supercooled water, hexagonal and cubic ice, microcline, and fully-hydroxylated feldspar surfaces exposed to a vacuum, liquid water, and ice. We apply the machine-learning force field to study different fully-hydroxylated terminations of the (100), (010), and (001) surfaces of microcline exposed to a vacuum. Our calculations suggest that terminations that do not minimize the number of broken bonds are preferred in a vacuum. We also study the structure of supercooled liquid water in contact with microcline surfaces, and find that water density correlations extend up to around 10 Å from the surfaces. Finally, we show that the force field maintains a high accuracy during the simulation of ice formation at microcline surfaces, even for large systems of around 30 000 atoms. Future work will be directed towards the calculation of nucleation free-energy barriers and rates using the force field developed herein, and understanding the role of different microcline surfaces in ice nucleation.