Trace Element Behaviour in Magmatic Systems

Trace Element Behaviour in Magmatic Systems: When the melting of the mantle takes place, the trace elements show a preference either towards the melt phase or the solid (mineral) phase. So elements which prefer the mineral phase are termed as Compatible Elements and elements which prefer the melt phase are termed incompatible, i.e. they are incompatible in the mineral structure and will leave at the first available opportunity. The degree of compatibility and incompatibility of trace elements will vary in their behavior in melts of different composition.
If the trace elements were to be divided on the basis of their charge / size ratio (which is also termed as Field Strength or electrostatic charge per unit surface area of the cation), then the elements can be grouped as HFSE (High Field Strength Elements) and LFSE (Low Field Strength Elements) or better known as LILE (Large Ion Lithophile Elements). HFSE are small highly charged cations and LILE are large cations of small charge. So elements with smaller radius and a relatively low charge tend to be compatible. These include a number of major elements and transition elements. HFS includes all the REEs, Sc, Y, Th, U, Pb, Zr, Hf, Ti, Nb and Ta. LILE includes Cs, Rb, Ba, K and to an extent Sr, divalent Eu and divalent Pb.
Partition Coefficient: The distribution of trace elements between phases may be described by Distribution Coefficient or Partition Coefficient (McIntire, 1963). The Nernest Distribution Coefficient is used extensively of a trace element between a mineral and a melt.
It is defined by: K_d=(C_(element i)^mineral)?(C_(element i)^melt )
Where, Kd is the Nernst Distribution coefficient
C is the concentration of element ‘i’ in ppm or wt%.
Bulk Partition Coefficient: is a partition coefficient calculated for a rock for a specific element from the Nernst Partition Coefficients of the constituent minerals and weighted according to their proportions. It is defined by the expression –
Di = x1 Kd1 + x2 Kd2 + x3 Kd3 + ……….
Where, Di is the bulk partition coefficient for element ‘i’
X1 and Kd1 are the %age proportion of mineral 1 in the rock and the Nernst partition coefficient for element ‘i’ in mineral 1 respectively.
The behaviour of trace elements during evolution of magmas may be considered in terms of their partitioning between crystalline and liquid phases, expressed as the partition coefficient, D. So elements that have D1 (Eg; Ni, Cr) are termed compatible, and these are preferentially retained in the residual solids during partial melting and extracted during crystallizing solids in fractional crystallization.
The preference of an element for a given phase is measured by its partition coefficient (D). It is customary to use trace elements whose partition coefficients are sensitive to the presence or absence of particular phases. For example the REEs exhibit partitioning behavior between garnet and melt and can therefore be useful in determining whether melt generation took place in the presence of that mineral, which in turn has implications for the depth of melting.
MODELS FOR SOLID-MELT PROCESSES:
Batch Melting:
In this model, the melt remains in equilibrium with the solid, until at some point, perhaps when it reaches some critical amount, it is released and moves upward as an independent system. Shaw (1970) derived the following equation to model batch melting:
(C_i^l)?(C_i^o )= 1?(D_i^o ) (1-F)+F

Where; C_i^o= the concentration of the trace element in the original assemblage before melting began, F is the weight fraction of melt produced – melt / (melt + rock).
When Di = 1, there is no fractionation, and the concentration of the trace element is the same in both the liquid and the source. The concentration of a trace element in the liquid varies more as Di deviates progressively from 1.
As F approaches 1, the concentration of every trace element in the liquid must be identical to that in the source rock, because it is essentially all melted.
(C_i^l)?(C_i^o )=1 as F?1
On the other hand, as F approaches zero,
(C_i^l)?(C_i^o )= 1?(D_i^o ) as F?0
Thus, if we know the concentration of a trace element in a magma (CL) derived by a small degree of batch melting, and we know Di we can estimate the concentration of that element in the source region (C0). The closer to unity the value of Dt the larger the range of F .
For very incompatible elements, as Di approaches zero:
(C_i^l)?(C_i^o )= 1?F as D_i^o?0
This implies that if we know the concentration of a very incompatible element in both a magma and the source rock, we can determine the fraction of partial melt produced. This is the way in which trace elements can be used to evaluate melting processes at depth.

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Rayieigh Fractionation
Fractional melting occurs when the melt is constantly extracted from the residue
during the ascent of magma through the earth’s mantle; that is the partial melt is continuously removed from the system as soon as it is formed, so that no reaction with the crystalline residue is possible. For this type of partial melting the bulk composition of the system is continuously changing. The concentration of some element in the residual liquid , C_L, is
C_L/C_O =?F_1?^((D_i-1) ) Rayleigh crystal fractionation
C_L/C_O =1/D_i (1-F_2 )^((1?D_i -1) ) Rayleigh fractional melting
Where;
C_O= concentration of element in the original magma
F_1= fraction of melt remaining after removal of crystals
F_2= fraction of melt produced
Rare Earth Elements
REEs, a group of fourteen elements (Lanthanum to Lutetium) are members of Group III in the periodic table and have very similar chemical and physical properties. Despite this similarity, these elements can be partially fractionated, one from the other, by several petrological and mineralogical processes. The wide variety of types and sizes of the cation co-ordination polyhedra in rock forming minerals provides means for chemical fractionation. It is this phenomenon which has important consequence in geochemistry.
The significant growth of interest in the geochemistry of REEs has come about because of the realization that the observed degree of REE fractionation in a rock or mineral can be a pointer to its genesis, and also because accurate quantitative analysis for the REE, both as a group and individually, is now possible on routine basis even when the elements occur at very low concentration. The application of REE abundances to petrogenetic problems has centered on the evolution of igneous rocks where such processes like partial melting of crustal or mantle materials, fractional crystallization, and/or mixing of magmas are involved. In these studies, the matching of observed REE abundances with those provided by theoretical modeling of petrogenetic processes has helped considerably to restrict the number of possible hypotheses on the genesis of a rock or mineral suite.
The REEs have been divided into two sub-groups: those from La to Sm (i.e. lower atomic numbers and masses) being referred to as light rare earth elements (LREEs) and those from Gd to Lu (higher atomic numbers and masses) are referred to as heavy rare earth elements (HREEs). Very occasionally, the term middle rare earth elements (MREEs) is loosely applied to the elements from Pm to Ho.
In order to graphically compare the REE for different rocks, it is necessary to eliminate the Oddo-Harkins effect, which is the occurrence of higher concentrations for the elements with even atomic numbers as compared to the concentrations for the elements with odd atomic numbers. Thus, concentrations for the individual REE are generally normalized to their abundance in chondrites by dividing the concentration of a given element in the rock by the concentration of the same element in chondritic meteorites. Chondrites have been used because they are primitive solar materials which have been considered the parental material of the Earth (Hanson, 1980). The advantages of this method are that the abundance variation between the REE of odd and even atomic numbers is eliminated and the extent of any fractionation amongst the various REE in the specimen is discernible because there is considered to have been no fractionation between the light and heavy REE in chondrites.
5 Mineral Melts Kd’s for REE
A given mineral will have a characteristic effect on the REE pattern for a melt which allows identification of the influence of that mineral during melting or fractional crystallization; although it may not be possible to calculate the fraction of that mineral in the residue. For most igneous minerals the mineral melt Kd’s in general increase with decreasing temperature and compositional variation from basic intermediate acidic.
In this section individual minerals are considered with respect to how they qualitatively affect the concentration of the REE and the shape of the REE pattern in the melts/ the magnitude of the effect of a mineral is directly related to both the relative abundance of the mineral and the magnitude of the Kd’s. Some typical mineral melt Kd’s for the REEs are as follows (Hanson, 1980) :
Feldspar – the feldspars have low Kd’s for the REE and large positive Eu anomalies. The plagioclase/melt Kd’s for the REE other than Eu are not strongly dependent on temperature or composition (Drake and Weill, 1975). The plagioclase Eu anomaly decreases with increasing fO2 and increasing temperature, but will be significant in almost all known terrestrial igneous systems (Drake 1975). Feldspar has but a minor effect on the REE pattern of the melt, except the large positive Eu anomaly in the Kd pattern will contribute to a negative Eu anomaly in the melt.

Garnet – Garnet has very low Kd’s for the light REE and increasingly larger Kd’s for the HREE; the Kd’s decrease by an order of magnitude from rhyolitic to basaltic systems. The presence of Garnet leads to depletion of the HREE and generally contributes to a positive Eu anomaly in the melt.

Hornblende – the Kd’s for Hornblende show a strong dependence on composition and may be greater than 10 for the MREE in the rhyolitic systems. The presence of Hornblende will lead to a depletion of the MREE, less so the HREE and contribute to a positive Eu anomaly.

Biotite – Biotite generally has low Kd’s for the REE and its presence should have little effect on the REE pattern of the melt.

Perovskite – Perovskite has larger Kd’s for the LREE and MREE than the HREE. The presence of significant Perovskite can lead to depletion or less enrichment of the LREE and MREE relative to the HREE (Irving, 1978).

Zircon – Zircon has very large Kd’s (of the order of 100’s) for the HREE. However, its low abundance (generally less than 0.1%) leads to a minor depletion of the HREE in the melt.
Apatite and Sphene – Apatite and Sphene have similar Kd patterns for the REE with Kd’s greater than one for all of the REE. Their generally low abundance reduces the effect of their large Kd’s. Both Apatite and Sphene lead to enrichment of the LREE and HREE relative to the MREE. The presence of Apatite could contribute to a positive Eu anomaly.