Magma mixing is a common petrogenetic process occurring in mid-oceanic ridge, oceanic island and island arc petrotectonic environments. An exploratory model was developed and used to investigate fundamental principles underlying magma hybridization. Unlike many geochemical models that satisfy mass balance only, the Toy model is a rigorous thermodynamic model which satisfies energy conservation as well as major, minor, trace and isotopic conservation expressions. Magma hybridization is defined as two or more disparate magmas, each in internal equilibrium, being mixed thoroughly enough to achieve thermodynamic equilibrium. The phase diagram used in this model is that of an isobaric binary eutectic system with no crystalline solution and zero enthalpy of mixing, similar to the model 'basalt' system CaMgSi2O6-CaAl2Si2O8. There are three possible phases in this system that can coexist in different proportions: alpha crystals, beta crystals or melt.

The two components of the system are A and B with alpha phase pure component A and beta phase pure component B. There are five possible phase assemblages in this system: L, alpha+L, beta+L, Le+alpha+beta or alpha+beta, where L denotes melt and Le denotes eutectic melt. Eight thermodynamic parameters define the phase diagram including the melting temperature of each pure phase, distinct liquid and solid isobaric heat capacities, the enthalpy of fusion of pure alpha and beta crystals and the eutectic temperature and eutectic composition. Five initial mixing conditions are required to define a magma hybridization outcome involving the mixing of two distinct magmas (M and R) to form a H&barbelow;ybrid magma (H): the initial temperatures and bulk compositions of resident M&barbelow;agma (M) and R&barbelow;echarge magma (R) and the mass fraction (fo) of M in the M+R mixture. The enthalpy of H magma is calculated based upon either an adiabatic or diabatic assumption.

The model is also capable of simulating partial melting of a mixture of subsolidus sources through the addition of enthalpy to the subsolidus source. Once the thermodynamic calculations are completed and the phase assemblages pre- and post-hybridization are known, trace element and isotope mass balances are performed. Hence the result of any Recharge hybridization (R-hybridization) or Recharge Fractional Crystallization (RFC-hybridization) process gives complete thermodynamic characterization of the final state consonant with energy and mass conservation. Several applications are presented as examples. In several cases the Magma Chamber Simulator (Bohrson et al., 2013) is used to verify the applicability of the model. A Monte Carlo (MC) method is used to study the statistics of possible outcomes given a range of initial condition values.

Statistical analysis of the MC realizations revealed that 44% of the outcomes were three-phase invariant point outcomes, illuminating a thermodynamic invariant point 'attractor' effect that may be relevant to crystallization (and partial melting) in the upper mantle and crust. Ten to twenty per cent of MC realizations exhibited a thermal anomaly such that the final temperature of hybridized magma was less than the initial temperature of both M and R magmas. This thermal anomaly phenomenon was verified using the Magma Chamber Simulator (MCS) and revealed a ∼0.8 degree drop in H temperature for every percent increase in the crystal content of M magma when R magma is entirely molten. Investigation of the reaction of sub-solidus or mushy stoped blocks with M magma showed that when the mass of M is much greater than the mass of stoped blocks (common condition), the final temperature of H was more strongly dependent on the stoped block mineral mode than its temperature.

Investigations into phase change systematics revealed that cessation of precipitation of the saturation phase of M occurred even when the mixing ratio (mass ratio of M to R) was large. Extensive trace element experimentation was conducted. Results showed that serial isobaric FC-R-FC hybridization can produce trace element signatures consistent with clinopyroxene crystallization in an equilibrium basalt with only glass + plagioclase phenocrysts present, offering an alternative explanation of the 'pyroxene paradox' of MORB petrogenesis. Some results showed that despite significantly elevated concentrations of trace elements in an incoming R melt, H melt may exhibit essentially no enrichment outside the range of measurement. Further experimentation resulted in a 'Dilution Effect' where a trace element concentration in the melt phase of H was lower than in both initial magmas M and R.

This occurs when the enthalpy of the mixed system is high enough that fusion of pre-existing crystals in M and/or R creates a sparsely phyric H magma. Results showed that under diabatic conditions the trace element concentrations in H melt could lie outside the range of values in M and R melts due to partitioning effects associated with fractional crystallization. Modeling trace element ratios during serial recharge showed that the bulk composition of each H fell on a mixing hyperbola defined by M and R, as expected, but that the melt phase of H did not necessarily define a hyperbola from which the original components M and R could be constrained unless the trace element ratios used to form the ratio-ratio coordinates had equal partition coefficients, always the case when isotope ratio - isotope ratio diagrams are considered.

MCS R-hybridization simulation data analyzed in major oxide ratio-ratio space were used to explore the ramifications of fractional crystallization and subsequent crystal separation on two related hybrid magma H's differing only in their M to R mixing ratio. The results confirm the issue set forth in the 'pyroxene paradox' of MORB petrogenesis, where sparsely-phyric or aphyric basalts can contain glass that exhibits trace element trends indicative of specific phenocryst crystallization, even though that phenocryst is not present modally in the sampled lavas. Results from serial application of the binary eutectic model illustrate some possible physical and trace element and isotopic geochemical trends arising from the processes associated with a shallow crustal magma chamber undergoing magma mixing via recharge, fractional crystallization associated with heat loss to wallrock, assimilation of subsolidus hydrothermally altered mafic wallrock, and periodic eruption (RFCAE).

The results show that the most incompatible elements are enriched in the melt of the RFCAE chamber even though the additions to the chamber (recharge and wallrock assimilation) were not particularly enriched relative to the initial magma. This result suggests a possible alternative process for producing enriched eruptive products (e.g., E-MORB) that does not invoke mixing of enriched subsolidus sources coupled to variable extents of partial melting of the mixed source and subsequent unmodified ascent and eruption. Although the Toy model is simple, it is not simplistic: it does provide insight into a variety of petrogenetic mechanisms.