Alkali exchange between the A site of hornblende and a coexisting melt may be described by the following reaction:
The equilibrium constant of this reaction is:
where XK and XNa are mole fractions of K20 and Na20 in the hornblende and melt.

The value of this distribution coefficient has been calculated for 24 coexisting hornblende-melt pairs produced by partial melting of three basalts at PH2o ≃ Ptotal, = 5 kbar, under controlled oxygen fugacity, at temperatures ranging from 700 to 1045°C. In calculating the observed distribution coefficient (KD), values used for XK and XNa were the cation proportions of K and Na per 23 oxygens for hornblende, and moles of K and Na per 100 g of melt. When plotted against reciprocal temperature, KD shows a strong positive temperature-dependence, describable by the equation In KD = (−4258/T) + 3.25.

The anticipated effects on KD of varying pressure and water activity, at constant temperature, are small. The exchange is not affected by variations of Na2O and K2O in the bulk composition or in the melt. The distribution coefficient is affected by changes in composition of the hornblende insofar as the changes affect the size of the A site, but this effect can be calibrated by taking into account variations in the cell volume of the hornblende.

Accordingly, this exchange reaction would seem to be a possible geothermometer for appropriate samples. Given the alkali contents of hornblende and a coexisting melt, and the cell volume of the hornblende, the temperature at which they equilibrated is determinable to approximately ±50°C.

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