This paper proposes the concept of concurrent fractional and equilibrium crystallisation (CFEC) in a multi-phase magmatic system in light of experimental results on diffusivities of elements and other species in minerals and melts. A group of equations are presented to describe how the concentrations of an element or isotope change in fractionated solid, equilibrated solid, melt, liquid, and gas phases, as well as in magma, as a function of distribution coefficients and mass fractions during the CFEC process. CFEC model is a generalised and unified formulation that is valid, not only for pure fractional crystallisation (FC) and perfect equilibrium crystallisation (EC) singly, as two of its limiting end-member cases, but also for the geologically more important process of concurrent fractional and equilibrium crystallisation. The concept that both fractional and equilibrium crystallisation can operate concurrently in a magmatic system, for a given element, among different minerals, and even within different-sized crystal grains of the very same mineral phase, is of fundamental importance in deepening our current understanding of magmatic differentiation processes. CFEC probably occurs more frequently in the natural world than either pure fractional or perfect equilibrium crystallisation alone, as a result of the interplay of varying diffusivities of elements under diverse physicochemical conditions, different residence time and growth rates of mineral phases in magmas, and varying grain sizes within each phase and among different phases. The marked systematic variations in trace element concentrations in the melts of the Bishop Tuff have long been perplexing and difficult to reconcile with existing models of differentiation. CFEC, which is able to better explain the scatter trends in a systematic way than fractional crystallisation, is considered to be the cause.

根据Green et al(1986)提出的三元长石温压计公式,以长石三元固溶体和矿物相平衡为基础,通过热力学推导,建立了联立方程法和迭代法两种计算三元长石温度的方法.根据联立求解可获得TAb-Or、TOr-An、TAb-An三个温度值,迭代法求解可获得TAb、TOr、TAn三个温度值.因此,一个样品可计算出6个温度数据.选择粤西地区有代表性的18个花岗岩体,按混合岩建造→深熔花岗岩建造→岩浆建造南岭系列花岗岩→岩浆建造长江系列花岗岩的顺序,进行三元长石法的温度计算,所得到的相应各建造和系列花岗岩的上限温度为755℃→766℃→865℃→970℃;下限温度为664℃→665℃→775℃→814℃,亦即上下限温度都逐渐升高,其规律性与地质和地球化学研究结果完全一致,体现了三元长石地质温度计的可靠性和准确性.

The solubility of both β-whitlockite and α-whitlockite has been experimentally determined between 1200 and 1400°C at 1 atm using a wide range of natural rocks and synthetic mixtures as starting materials. The solubility of both phases depends strongly on melt composition, decreasing systematically with increasing silica content and aluminosity. Experiments also show that α-whitlockite contains much more Na (0.5–6.3 wt.% Na2O) than β-whitlockite (<0.5 wt.% Na2O). Lunar low- and high-Ti mare basalts are far below the saturation limit of whitlockite and need 90–99% fractionation of olivine, pyroxene, plagioclase, and ilmenite to precipitate whitlockite, whereas KREEP basalts need less but at least 80–95% fractionation. It is shown here that both lunar mafic and felsic immiscible melts, the former enriched in Fe, REE, P, U, and Th, and the latter in Si and K, are undersaturated in whitlockite, and further fractionation of fayalite, ilmenite, plagioclase, and K-feldspar is required to reach the saturation limit. Thus, lunar whitlockite must have crystallised from highly fractionated residual melts. Lunar whitlockite, which is low in Na (0.09–0.49 wt.% Na2O), crystallised originally as β-whitlockite from low-temperature residual melts. In contrast, meteoritic whitlockite contains more Na (0.5–3.3 wt.% Na2O and therefore, had formed initially as α-whitlockite at higher temperatures and transformed into β-whitlockite upon cooling. It is proposed that the interior of the Martian mantle and crust was enriched in volatiles in its early history (4.6–1.3 Ga), but has become essentially dry and very depleted in water and halogens at least since the last 180 Ma. Calculations show that the Earth’s crust and mantle as a whole contains only 5% of the total P of the Earth, and the remaining 95% is stored in the core. In contrast, the crust and mantle of Mars are much more enriched in P and contain as much as 43% of the Martian total P budget, with the remaining 57% being distributed in the relatively smaller Martian core. This difference in the distribution of P among planetary shells must have resulted from a more oxidising environment during the accretion and early evolution of Mars compared to the more reducing conditions under which Earth formed.

Major, minor, and trace element abundances in apatites from various I- and S-type (igneous and sedimentary) granites of the Lachlan Fold Belt have been determined using electron microprobe and laser ablation inductively coupled plasma mass spectrometer. The results show that apatite can accommodate many minor and trace elements, whose concentrations and ratios are relatively sensitive to factors controlling many of the fundamental differences between I- and S-type granites. Apatites from S-type granites generally have higher F but lower Cl contents than those from I-type granites, which is ascribed mainly to the loss of Cl during the weathering processes forming the source rocks of S-type granites, although fractional crystallisation can cause significant enrichment in F as well. High Mn and Fe contents in apatites from S-type granites, and high S and As abundances in apatites from mafic I-type granites, result from different oxygen fugacities and degrees of Al saturation (or aluminosity) between metaluminous mafic I-type magmas and peraluminous S-type and felsic I-type magmas. There are systematic and distinctive differences in absolute rare-earth element (REE) abundances, REE distribution patterns, and element ratios (e.g., La/Y, Sm/Nd, etc.) between apatites from different types of granite. The strong Eu depletion that characterises apatites from S- and felsic I-type granites is interpreted here to be a result of the uniqueness of crystal chemistry of apatite and high Eu2+/Eu3+ ratios in S-type and felsic I-type magmas, which are more reduced and peraluminous than mafic I-type magmas. Strong REE (La to Eu) and Th enrichment in apatites from mafic I-type granites and marked Nd depletion in apatites from most S-type and felsic I-type granites are caused by the precipitation and fractionation of monazite in the parental magmas of the latter rocks. Substitution mechanisms are responsible for high Na in apatites from S-type and felsic I-type granites, and for high Si in apatites from mafic I-type granites, and may also have important effects on REE partitioning between apatite and melt. Thus, apatite chemistry can be used as an excellent indicator of granite petrogenesis. The results have important implications for identifying different types of granite and are potentially significant for determining the provenance of sedimentary rocks.

Many crystalline solids have multiple nonequivalent sites among which different atoms show substitutional long-range order-disorder phenomena. The order-disorder kinetics of an atom among any n nonequivalent sites in a crystal can be described by the equationx(i)=c(il)+(j=2)Sigma(n) c(ij)(t)e(lambda jt)where x, is the site occupancy of the atom at site s(i), n is the number of nonequivalent sites, lambda(j)(lambda(j)=0) is constant at a given temperature, pressure, and total composition of the crystal, and c(ij)(t) is constant or polynomial in t. Four theorems governing a multi-site order-disorder process have been proved, requiring that lambda(j) must be either zero (only lambda(l)=0), a negative real number, or a complex-valued quantity with the real part being a nonpositive number. The kinetic model becomes constrained and naturally complies with crystal-chemical conditions when the mole number per formula unit is chosen as the unit of all site-occupancy variables, or site multiplicities are explicitly incorporated into the model. When the mole fraction is directly used as the unit, the model becomes unconstrained, but it is a valid treatment that is as equally applicable to the multi-site order-disorder kinetics as the constrained model.

Mueller's model has been widely applied to modeling kinetic experimental data on the ordering-disordering of cations between two nonequivalent sites. This model is valid only for pure or nearly pure binary systems. For ordering-disordering involving three or more cations (multiple cation or multi-cation) between two sites, Mueller's methodology, which is based on a two-cation exchange reaction, yields no explicit general solution. On the basis of a single-cation exchange reaction, we present an alternative kinetic model for multi-cation ordering-disordering in minerals with two nonequivalent sites. This model is not only suitable for binary systems but is also valid for multi-cation ordering-disordering at two nonequivalent sites. In addition, two kinetic coefficients for each individual cation can be easily obtained using nonlinear parameterization. A comparison of reported experimental data with theoretical calculations has shown that our model can fit both binary and multi-cation ordering-disordering very well and can also explain and predict many kinetic features observed in experiments.

A kinetic model for describing the site occupancies of a cation at three nonequivalent sites in minerals has been presented as follows xi = ci0 + ci1eλ2t + ci2eλ2t (i = 1, 2, 3), where xi is the site occupancy of a given cation at site si, and ci0 (>0), ci1, ci2, λ1 and λ2 are constants at a given temperature and composition of the mineral. The two lemmas concerning three-site ordering-disordering indicate that λ1 and λ2 are either negative or complex-valued, and that they guarantee the convergence of the site occupancies with increasing time. The conditions for extrema have been given in the paper. The greatest difference between two-site and three-site order-disorder processes is that two-site ordering-disordering only occurs as either a monotonously increasing function or a monotonously decreasing function of time at a given initial total composition and temperature, while three-site order-disorder kinetics may have local minima or maxima.

It is proposed that hydrous ultramafic and mafic rocks can originate from the hydration of water-depleted mafic magmas by coexisting water-enriched silicic magmas. This would cause hornblende and biotite to directly crystallise from the hydrated melts, while hydration reactions would result in widespread replacement of existing anhydrous mafic minerals (Ol, Opx and Cpx) by hornblende and biotite. Chemical and mineralogical zonation in ultramafic/mafic-silicic intrusive complexes can thus result from three closely related processes: magma mixing, hydration reactions and fractional crystallisation (MHFC). Although not all hydrous ultramafic/mafic rocks are formed by this mechanism, the MHFC hypothesis may give an alternative explanation for the origin of hydrous ultramafic/mafic rocks in those complexes where mixing of a water-depleted mafic magma and a water-enriched silicic magma can be demonstrated. Evidence supporting this hypothesis includes: (1) contact relations; (2) net-veining and mutual intrusions of coexisting mafic and silicic magmas; (3) quenched mafic enclaves; (4) skeletal growth and branching of hornblende, plagioclase, titanite and acicular apatite indicative of quenching of a high-temperature mafic magma against a relatively low-temperature silicic magma; (5) synplutonic hydrous mafic composite dykes; (6) comb layering and orbicular structure; (7) regular concentration of hydrous ultramafic and hydrous mafic rocks along the contact zones between a water-depleted mafic magma and a water-enriched silicic magma; (8) strong zonation of these complexes; (9) coexistence of magmatic hornblende and biotite with those formed by hydration reactions of anhydrous mafic minerals; (10) similar isotopic and geological ages for different rocks ranging from ultramafic to silicic within these complexes; (11) Sm/Nd, Rb/Sr and O isotopes indicating that different rocks within these complexes are derived from varying degrees of mixing of a mantle-derived mafic magma with a crust-derived silicic magma. All these observations can be consistently explained by the proposed MHFC model.

An attempt has been made to give an insight into the genesis of enclaves in granites by mathematicallyquantitative methods.After some deduction,the quantitative models of trace elements for the geneticallydifferent enclaves have been established,including those for restites,segregation schlierens,enclavesformed out of solidified margins,and enclaves derived from the mixing of different magmas.These modelshave been tested and proven to be valid and reliable.The conclusions inferred from these quantitativemodels are consistent with field observations and petrological,mineralogical and geochemical evidence.