Statistics – Applications
Scientific paper
Nov 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987gecoa..51.2931l&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 51, Issue 11, pp.2931-2946
Statistics
Applications
110
Scientific paper
The densities of 27 liquids in the system Na 2 O-K 2 O-MgO-MgO-FeO-Fe 2 O 3 -Al 2 O 3 -TiO 2 -SiO 2 have been measured using the double-bob Archimedean technique. These results indicate that multicomponent silicate liquid volumes have a linear dependence on composition with the exception of the TiO 2 component. The equation: was used to derive values of the oxide partial molar volumes ( ) by the method of least squares. Regressions were made separately at 1573, 1673, 1773 and 1873 K (as liquid ferric-ferrous ratios change with temperature) with relative standard errors for each fit of 0.38%, 0.32%, 0.30% and 0.32%, respectively. Derived values by separate least squares regression for each oxide component reproduce the measured dV / dT of the experimental liquids by 20.21% on average. The effects of iron redox state on the density of a variety of natural liquids are demonstrated and at most amount to a variation of 1%. These new data on silicate liquid volumes were used to re-derive oxide partial molar compressibilities, and , at 1 bar from ultrasonic velocity and calorimetric data from the literature. The fits for and at 1673 K have relative standard errors of 3.9% and 1.8%, respectively, which represent substantial improvements over previous fits. Two applications of these volume data are given: firstly, the fusion curve of diopside is calculated up to 95 kbr using an equation of state for liquid volume expressed as: V ( T , P ) = V ( T ) exp - ( T )(1 - bP + cP 2 ) dP (where = K -1 and therefore dK / dP = K ' = - -2 d / dP ); secondly, using a range of K ' appropriate to a komatiite liquid, the pressure-temperature conditions where the density of the liquid equals that of its olivine phenocrysts are calculated.
Carmichael Ian S. E.
Lange Rebecca A.
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