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
Introduction
The crystal structure of clinopyroxene consists of three distinct polyhedra in which metal cations with small ionic radii are surrounded by larger oxygen anions to develop VI-, VIII- and IV-fold coordinated M1-, M2- and T-sites, respectively. The smaller M1 are almost regular octahedral, M2 sites are larger and more distorted 6- or 8-fold sites. During magma generation and polybaric-polythermal evolution, the most common exchange equilibria in clinopyroxene involve jadeite (Jd; NaAlSi2O6), diopside (Di; CaMgSi2O6), hedenbergite (Hd; CaFeSi2O6), enstatite (En; Mg2Si2O6), ferrosilite (Fs; Fe2Si2O6), and Tschermak (Ts) components expressed as the sum of Ca-Tschermak (CaTs, CaAl2SiO6), CaFe-Tschermak (CaFeTs, CaFeSiAlO6), CaTi-Tschermak (CaTiTs, CaTiAl2O6) and CaCr-Tschermak (CaCrTs, CaCrAlSiO6). These exchange reactions principally control the partitioning of trace elements between clinopyroxene and melt, whose magnitude can be parameterized by the properties (charge Zi and ionic radius ri) of the trace cation of interest (i), the bulk composition (mineral/melt chemistry) of the system and the conditions (pressure P and temperature T) at which clinopyroxene grows (e.g., Blundy and Wood, 2003; Gaetani, 2004; Huang et al., 2006; Mollo et al., 2016; Sun and Liang, 2012, Sun and Liang, 2013; Ubide et al., 2019; Wood and Blundy, 1997, Wood and Blundy, 2001, Wood and Blundy, 2002; Yao et al., 2012). From a thermodynamic point of view, the simple definition of partition coefficient (Di) refers to the equilibrium constant (Ki) of the cation exchange reaction between clinopyroxene and melt, assuming that the ratio between activity compositions of clinopyroxene (acpx) and melt (amelt) are roughly equal to their mole fractions (Lee et al., 2007; Van Orman et al., 2002; Wood and Blundy, 1997). For simplicity, the Nernst partition coefficient [Di = (I)cpx / (I)melt; I is the cation concentration on a weight basis] is generally adopted in petrological and geochemical studies investigating and modeling magmatic processes.
Owing to its abundance in igneous systems, clinopyroxene is one of the most important mineral controlling the composition of magmas in terms of light, mid and heavy rare earth elements (LREE, MREE+Y, and HREE, respectively), high field strength elements (HFSE), and transition elements (TE), as long as these trace cations are greatly incorporated into the clinopyroxene crystal lattice (e.g., Mollo et al., 2018). The entry of highly charged cations into the M1- and M2-sites is generally controlled by local charge balance mechanisms in which TAl replaces for Si in T-site or, alternatively, Na replaces for Ca in M2-site. The role played by TAl and Na, as charge-balancing cations, is to enhance the stability of different local configurations into the clinopyroxene structure, such as REE + YMgAlSiO6 [where REE + Y substitutes for simplicity the crystallochemical notation (REE, Y)], CaTiAl2O6, CaCrAlSiO6, and CaMgNbAlO6 for the Si ↔ TAl substitution or, alternatively, Na0.5REE + Y0.5MgSi2O6, Na0.5REE + Y0.5Al2SiO6, NaTiAlSiO6, and NaNbAl2O6 for the Ca ↔ Na substitution (Bédard, 2014; Bennett et al., 2004; Blundy et al., 1998; Blundy and Wood, 2003; Forsythe et al., 1994; Francis and Minarik, 2008; Gaetani and Grove, 1995; Hart and Dunn, 1993; Hill et al., 2000; Ray et al., 1983; Lundstrom et al., 1994, Lundstrom et al., 1998; Marks et al., 2004; Mollo et al., 2020; Schosnig and Hoffer, 1998; Skulski et al., 1994; Tuff and Gibson, 2007; Wood and Blundy, 1997, Wood and Blundy, 2001; Wood and Trigila, 2001; Scarlato et al., 2014; Sun and Liang, 2012, Sun and Liang, 2014). In a more recent trace element partitioning study by Beard et al. (2019), it is confirmed that both aluminium and trivalent iron in tetrahedral coordination are strong predictors of REE + Y at the M2-site. While the substitution [Na] → [Ca] is not statistically significant for the correlation of various clinopyroxene compositional parameters with lattice strain terms, Ti in M1-site has been recognized as a much stronger predictor for REE + Y incorporation than Na in M2-site (Beard et al., 2019).
In the conventional coupled substitution [M2Ca, TSi] ↔ [M2REE + Y, TAl], the entry of REE + Y onto M2-site accounts for the formation of the hypothetical REE + YMgAlSiO6 end-member, in concert with the achievement of charge-neutral local configurations as TAl increases to compensate the mismatch between 2+ (Ca) and 3+ (REE + Y) charges (Fig. 1). Although the crystal structure of clinopyroxene is characterized by complete AlSi disorder, the probability of trace cations to enter a locally charge-balanced site increases with TAl and formation of Al-O-Al linkages in the short-range structural arrangement of the lattice (Blundy and Wood, 2003; Hawthorne, 2016; Wood, 1976; Wood and Blundy, 1997). This is indirectly corroborated by the study of Wood (1976) showing that the activity-composition relationships of Ts-rich clinopyroxenes are fairly close to a short-range ordering of tetrahedral SiAl. If Löwenstein's principle of Al-O-Al avoidance is locally violated in the crystal structure (Löwenstein, 1954), the incorporation of REE + Y in Ts-rich clinopyroxenes increases because the valence of charge-balancing cations in adjacent sites (next nearest-neighbor sites) changes to produce a statistical proportion of M2-sites in which the local charge of the central cation is 3+ rather than 2+ (Blundy and Wood, 2003; Wood and Blundy, 2001).
It is worth noting that a key issue with the use of a traditional charge-neutral approach is the inability to account for the incorporation of heterovalent trace cations in crystal sites of imbalanced charges (Fig. 1). Any insertion of a trace element of different charge from the major cation hosted in a crystal site carries an electrostatic energy penalty (Blundy and Wood, 2003; Hill et al., 2011; Wood and Blundy, 2001). Therefore, a certain degree of electrostatic work is done when REE + Y substitutes for Ca in M2-sites of charge 0, −1, and − 3 rather than −2 (the negative sign refers to the effective charge on an empty structural site). These electrostatic effects provide a means to incorporate highly charged cations via slightly charge-imbalanced configurations that do not require complete Al occupancy of T-sites. In other words, if a fully charge-balanced substitution for REE + Y has no electrostatic energy penalty and is merely related to lattice strain effects, a charge-imbalanced configuration accounts for the electrostatic work of substitution but avoids Al-O-Al linkages for the REE + Y incorporation (Fig. 1). As previously documented by Wood and Blundy (2001), there is a clear competition between charge-balanced and charge-imbalanced substitutions in controlling the partitioning of trace elements between clinopyroxene and melt (Fig. 1). The extent to which one substitution mechanism dominates over the other is related to the balance between the statistical probability of encountering different structural arrangements in the lattice site (i.e., the clinopyroxene chemistry) and the statistical probability of finding low charge mismatch sites for which the electrostatic energy penalty is a price worth paying (i.e., the electrostatic work of substitution). To distinguish between these rival controls, we have reappraised experimentally the effects of charge-balanced and -imbalanced configurations on the partitioning of highly-charged cations between clinopyroxene and melt. The focal role played by the bulk system (crystal + melt) composition on the lattice strain and electrostatic energies has been illustrated by comparing previous DREE+Y, DHFSE, and DTE from literature with new partitioning data measured between Ts-rich clinopyroxenes and a primitive melt assimilating variable amounts of carbonate material, as it is observed in several natural magmatic systems open to crustal contamination (e.g., Gaeta et al., 2009 and references therein). The overall data set has been critically discussed on a thermodynamic basis in which the magnitude of Di is related to the minimization of the different energies of cation substitutions (Blundy and Wood, 2003; Wood and Blundy, 1997, Wood and Blundy, 2001). We found that crystal configurations carry an energy penalty for accommodating a trace cation with Zi and ri different from the host lattice site, as the total number of Al cations increases in Ts-rich clinopyroxenes. This thermodynamic description for the energetics of crystal-melt exchange makes possible to identify and quantify the physicochemical parameters that describe the overall variance of trace elements in melts saturated with Ts-rich clinopyroxene phenocrysts, thus offering new perspectives for the modeling of natural igneous processes.
Section snippets
Theoretical aspects of the lattice strain and electrostatic energies
By re-evaluating thermodynamic theory of Brice (1975) on the growth of strained crystals, Blundy and Wood (1994) illustrated that partitioning energetics can be rationalized in two thermodynamic quantities: 1) the free energy of fusion (ΔGfusion = RTlnKi where R is the universal gas constant and T is absolute temperature) for the melting (or fusion) reaction of a fictive trace element component (e.g., REE + YMgAlSiO6) with the same stoichiometry as the major element component (e.g., diopside)
Tschermak-rich clinopyroxenes from desilicated, carbonate-contaminated melts
Regarding major element compositional variations, trace elements are much more effective recorders of closed-system (i.e., fractional crystallization) and open-system (i.e., magma mixing and crustal assimilation) phenomena, since their low concentrations in crystals and melts vary significantly. The assimilation of carbonate by magmas is an important open-system process influencing the geochemical signature of many crustal magmatic systems (Baker and Black, 1980; Barnes et al., 2003, Barnes et
Experiments and analyses
Approximately 50 g of the phonotephritic rock was reduced to a homogeneous powder in a ball mill and ground so as to pass through a #200 mesh sieve. Using undoped natural rock for the experiments ensures obeyance of Henry's Law (e.g., Green et al., 2000). The powder was melted to ensure homogeneity of the final starting material at the HP-HT Laboratory of Experimental Volcanology and Geophysics of the Istituto Nazionale di Geofisica e Vulcanologia (INGV), Rome, Italy. A crucible containing the
Phase relations and attainment of equilibrium
The phase assemblage is characterized by clinopyroxene and glass irrespective of temperature and carbonate assimilation (Table 1S). CaCO3-free charges do not contain fluid bubbles in agreement with the solubility of H2O measured by Behrens et al. (2009) for the phonotephritic composition. In contrast, the addition of 5, 10 and 20 wt% CaCO3 leads to fluid-present conditions (Table 1S) and coalescence of large bubbles at the periphery of the experimental capsule. The degree of clinopyroxene
Lattice strain modeling
Through a Levenberg–Marquardt-type, non-linear least-squares fitting routine, we have derived by Eq. 1 the best-fit values of D0, r0 and E for the partitioning of monovalent, divalent, and trivalent cations in M2-site. These isovalent cations form at least five groups in our analytical data set, making possible to minimize the uncertainty of the fit (Table 4S). An example fit parabola is displayed in Fig. 7 for partitioning data from undoped (0 wt% CaCO3) and doped (20 wt% CaCO3) experiments
Concluding remarks
The partitioning of trace elements between clinopyroxene and melt has been reappraised from an experimental and theoretical point of view in terms of both elastic strain and electrostatic energies of substitutions. Through a quantitative thermodynamic approach, we illustrate that heterovalent cation substitutions are controlled by complementary charge-balanced and -imbalanced configurations in the lattice site. In accordance with the energetics of trace element partitioning, we draw the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
We are grateful to Manuela Nazzari and Marcel Guillong for assistance during microprobe and laser ablation analyses, respectively. The Alexander von Humboldt foundation senior research grant to F. Vetere is also acknowledged. C. D. Beard and an anonymous reviewer are thanked for their helpful review of the manuscript. We also acknowledge A. Gomez-Tuena for his editorial guide.
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