Tetrahedral Plots of the Phase Relations for Basalts
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Tetrahedral Plots of the Phase Relations for Basalts1 Sven Maaløe2 and Richard N. Abbott, Jr.3 The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system. KEY WORDS: phase diagrams, basalts, primary magmas.
INTRODUCTION The compositions of primary basaltic magmas are controlled by the phase relations of lherzolite and the way melt accumulation takes place in the mantel. Characterization of the phase relations of lherzolite is therefore fundamental for understanding the genesis of basalts. Phase relations for partial melting of lherzolite involve olivine, orthopyroxene, clinopyroxene and spinel or garnet. Accessory minerals and a fluid phase are significant components at small degrees of melting, but the essential phase relations can be represented by four mineral components. The phase relations for partial melting of lherzolite have been represented by using three components only, or by projections from a selected oxide or mineral composition onto a plane. However, the phase boundaries of four-component systems cannot be represented in projections, because it results in multitude of intersecting curves. The phase relations must be shown in tetrahedrons as shown by Presnall and others (1978). The projected representations have proven useful, as shown amongst others by O’Hara (1968), but a representation using four components makes the phase relations more comprehensive. This is demonstrated in Figure 1a, 1Received
14 January 2004; accepted 28 February 2005.
2Department of Earth Sciences, Allegaten 41, 5007 Bergen, Norway; e-mail: [email protected] 3Department
of Geology, Appalachian State University, Boone, North Carolina; e-mail: abbottrn@
appstate.edu 869 C 2005 International Association for Mathematical Geology 0882-8121/05/1100-0869/1
870
Maaløe and Abbott
Figure 1. (a) A projection of interpolated melt compositions obtained by partial melting of garnet lherzolite at 30 kbar (Kushiro, 1996). The percentages of melt vary from 0 to 25%, and the dots show the positions of the melts at 5% intervals. The projection is from the garnet apex onto the olivine–orthopyroxene–clinopyroxene plane. (b) Projection of these melt compositions from orthopyroxene onto the olivine–clinopyroxene–garnet plane. (c) A tetrahedral plot of the melt compositions.
Tetrahedral Plots of the Phase Relations for Basalts
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which shows the projection of interpolated melt compositions at 30 kba
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