Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

S.E. Delong


A trace element fractionation model originally designed to relate plutonic rocks containing a trapped glass component to a complementary volcanic rock suite was applied to olivine and opaque-oxide gabbroic xenoliths from the summit cone of Mauna Kea, Hawaii.
The mathematical model which is based on the Rayleigh Fractionation Law was extended to include the various phases present in these two groups of gabbros and was generalized to treat multiple trace elements, in this case four. These results were incorporated in a new FORTRAN program using the interval-bisection method to greatly improve the convergence time in the numerical solutions.
Calculated results of the model include the concentrations of four trace elements - Cr, Zr, Ni and Sr - in the glass phase; the weight fractions of all phases in the gabbro; the fraction of the liquid that remained in the magma chamber when some of it was trapped; and the starting compositions for Ni and Sr in the initial liquid before fractional crystallization. The choice of partition coefficients and trace element starting compositions appears to be crucial for the model results, as indicated by sensitivity calculations.
To test the model results, the glass phase in the xenoliths was analyzed for trace elements by electron microprobe. A comparison between the analyses and the values calculated by the model suggests two different possibilities for the large amount of Zr and Sr accumulating in the glass phase: Highly evolved glass might not be a true trapped liquid phase but rather was injected from the hawaiitic host during ascent to the surface. However, tiny patches of cognate melt might possibly also lead to an amplification in the amount of incompatible trace elements. A definitive solution could not be obtained by use of the model.


Eberle, U., 1990. Application of a trace element fractionation model to cumulate gabbroic xenoliths of Mauna Kea, Hawaii. Unpublished MSc. thesis, State University of New York at Albany. 99 pp., +ix
University at Albany Science Library call number: SCIENCE Oversize (*) QE 40 Z899 1990 E34