A review of the lattice strain and electrostatic effects on trace element partitioning between clinopyroxene and melt: applications to magmatic systems saturated with Tschermak-rich clinopyroxenes

The purpose of this review study is to reappraise in a more comprehensive form the thermodynamic principles behind the partitioning of trace elements between clinopyroxene and melt. The original corollary is that the partitioning energetics controlling the crystal-melt exchange are described by two distinct but complementary contributions: ΔGpartitioning = ΔGstrain + ΔGelectrostatic. ΔGstrain is the excess of strain energy quantifying the elastic response of the crystallographic site to insertion of trace cations with radius different from that of the major cation at the site. ΔGelectrostatic is the excess of electrostatic energy requiring that an electrostatic energy penalty is paid when a trace cation entering the lattice site without strain has charge different from that of the resident cation. Lattice strain and electrostatic parameters for different isovalent groups of cations hosting the same lattice site from literature have been discussed in comparison with new partitioning data measured between Tschermak-rich clinopyroxenes and a primitive phonotephritic melt assimilating variable amounts of carbonate material. Through such a comparatively approach, we illustrate that the type and number of trace cation substitutions are controlled by both charge-balanced and -imbalanced configurations taking place in the structural sites of Tschermak-rich clinopyroxenes. A virtue of this complementary relationship is that the control of melt composition on the partitioning of highly charged cations is almost entirely embodied in the crystal chemistry and structure, as long as these crystallochemical aspects are the direct expression of both ΔGstrain and ΔGelectrostatic. A size mismatch caused by cation substitution is accommodated by elastic strain in the surrounding lattice of clinopyroxene, whereas the charge mismatch is enabled via increasing amounts of charge-balancing Tschermak components, as well as the electrostatic work done on transferring the trace cations from melt to crystallographic sites, and vice versa. The influence of the melt chemistry on highly-charged (3+ and 4+) cation partitioning is greatly subordinate to the lattice strain and electrostatic energies of substitutions, in agreement with the thermodynamic premise that both these energetic quantities represent simple-activity composition models for the crystal phase. The various charge-balanced and -imbalanced configurations change principally with aluminium in tetrahedral coordination and the clinopyroxene volume change produced by heterovalent cation substitutions. In contrast, for low-charged (1+ and 2+) cations, the role of melt chemistry cannot be properly deconvoluted from the structural changes of the crystal lattice. The incorporation of these cations into the clinopyroxene lattice depends on the number of structural sites critically important to accommodating network-modifying cations in the melt structure, implying that the partitioning energetics of monovalent and divalent cations are strictly controlled by both crystal and melt properties. We conclude that the competition between charge-balanced and charge-imbalanced substitutions may selectively change the ability of trace elements to be compatible or incompatible in the clinopyroxene structure, with important ramifications for the modeling of natural igneous processes in crustal magma reservoirs which differentiate under closed- and open-system conditions.