Lithium Pyroxene Formation Threshold Predicted by Data-Driven Global Bond Valence

The bond valence (BV) method is a semiempirical description of bonding in ionic crystal structures based on Pauling’s second rule, the electrostatic valence principle. However, calculated (unitless) BV bond strengths are often uncorrelated with measured bond energies because conventional BV descriptors, R0 and B, are exquisitely sensitive to the structures and methods used for training. In this work, we show that global bond graph optimization of pyroxene-type compounds enables the prediction of their absolute formation energies. Furthermore, a threshold of -2.31 volts/atom of formation potential - the derivative of formation energy with respect to the standard deviation of the valence - is shown to delineate ambient-pressure from high-pressure phases for this class of structures. Experiments confirm that high pressures are required to form α spodumene, a major mineral resource for lithium production, despite its thermodynamic stability under ambient conditions. All known α-spodumene-type clinopyroxene structures containing lithium, comprising 16 types of cation-anion pairs, exhibited two irreducible BV parameters. We show that R0, which is unique to each structure, is the covalent bond radius and is nearly equal to the observed bond length when the coordination number equals the cation formal charge, such as in BO3 and SiO4 polyhedra. We derive a new parameter β and show that it depends on the formal charge, coordination number, and electron spin, capturing the effects of electronic interactions in ionic bonds. Our findings elucidate the physical underpinnings of valence in minerals and its role in defining thermochemical properties by extending Pauling’s second rule.