The Effect of DFT and DFT + U Calculations on the Crystal Structure of the Diopside (CaMgSi2O6)–Hedenbergite (CaFeSi2O6) Solid Solution Series

Diopside–hedenbergite solid solution is the most common clinopyroxene end-member combination in mafic and ultramafic igneous rocks. The crystal structure variety caused by Mg-Fe isomorphous substitution can indicate geological processes such as Mg-Fe isotope fractionation. To explore the effect of Hubbard U correction and Fe content on iron-bearing clinopyroxene structures, we employed GGA and GGA + U to study the lattice constants, unit-cell volume, and average Fe-O bond length of the diopside–hedenbergite solid solution series. On the whole, the results by GGA + U are the increase in lattice constant a (from 9.910 Å to 10.030 Å) and volume (from 456.656 Å3 to 464.640 Å3), the decrease in β angle (from 106.121°to 105.320°), and a slight variation in the lattice constant b (from 9.007 Å to 9.010 Å) with increasing Fe content, which is a better match with the experiment than those by GGA. The average Fe-O bond lengths and polyhedral volumes calculated by GGA and GGA + U both increase with increasing Fe content. The Hubbard U correction significantly affects the lattice constants and unite-cell volume at medium-high Fe content (Fe/(Ca+ Mg + Fe) > 2/8), the Fe-O bond at low Fe content (Fe/(Ca+ Mg + Fe) < 1/8), the bond angle variance, distortion index and quadratic elongation at relatively medium Fe content (1/8 ≤ Fe/(Ca+ Mg + Fe) ≤ 5/16). This study verifies the effectiveness of U-value correction on iron-bearing clinopyroxene and provides a theoretical basis for understanding its structural evolution.