If I understand correctly, partition coefficients (concentration in solid / concentration in melt) are usually determined according to the weight percentage of the material involved. However, the density of a mineral can vary depending on the elements present. For example, iron-rich olivine (fayalite) is much denser than magnesium-rich olivine (forsterite). If the partition coefficient is calculated for, say, nickel for the olivine solid solution series, wouldn't it have a lower partition coefficient for fayalite than it would have for forsterite that contains the same amount of nickel because iron is heavier than magnesium? (In the same manner than fayalite contains less silica than forsterite on a weight basis). I'm curious because the literature I've read only report one partition coefficients for olivine, while I feel that the values will vary depending on the Mg/Fe ratio.
Any help would be appreciated.
Element partitioning depends on whole system composition and other intensive variables (P, T, fO2). Kd is a dimensionless number that simply describe how an element enter in a solid structure respect to a liquid phase. Of course a trace element will act as compatible if vicariants a major element in the mineral structure, depending on the physic-chemical conditions. For example, Ni substitute Fe when the system is reduced on contrary, acts as vicariant of Mg in oxydized systems. Hope will be useful.
As the previous contribution already said, the distribution coefficient is dimensionless: (ppm Ni in olivine)/(ppm Ni in silicate melt). P, T, oxygen fugacity, as well as the exact composition of the mineral, and the composition (structure) of the melt determine how 'eager' the element is to partition into the melt or the mineral involved.
Dear Willem,
A detailed discussion of partitioning coefficients is provided by McIntire (1963) who also discusses solid solutions at some length. Indeed, the partitioning coefficient as you have defined it should vary continuously between the two endmembers (and this is not just for reasons of density, but also because changes in melt composition will have an effect on the partitioning coefficient). However, for an ideal solid solution (such as olivine), this variation will be described by a simple relationship such that:
ln k = ln k_b + x*ln(k_a/k_b)
where k is the partitioning coefficient, a and b are the two endmembers of the series, and x is the weight fraction of endmember a (more references for the origin of this equation are provided by McIntire). It might be the case that the difference between k_a and k_b is negligible for olivine - and that this is why they are not discussed separately by different authors. I am unfortunately not familiar with the entire literature on this topic and only answered because I happened to remember McIntire using olivine explicitly as an example. You might wish to search for a paper where partitioning coefficients for both endmembers are actually determined.
I do hope this comment helps, and have attached a PDF copy of McIntire (1963).
Kindest regards,
Max
Thanks a lot everyone, especially for the article Max! I'll take a look at it.
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