Title: Stability
analysis of invariant points using Euler spheres, with an application
to FMAS granulites
Author(s): Kletetschka
G, Stout JH
Source: JOURNAL
OF METAMORPHIC GEOLOGY 17 (4): 435-448 JUL 1999
Document Type: Article
Language: English
Abstract: Alternative
assignment of invariant point stabilities in a possible P-T phase
diagram is given by a family of grids that derives from a form of the
Euler equation. Invariant points are represented by great circles that
divide the surface of a sphere (the Euler sphere) into polygonal
regions that correspond to the number of potential solutions or grids
in n-component systems with n+3 non-degenerate phases. A particular
invariant point is stable in all grids on one side of the great circle
and metastable on the other. The advantage of this representation is
the ease and efficiency by which all grids consistent with experimental
and theoretical constraints can be identified. The method is well
suited for systems of n+3 phases in which the thermochemical data
necessary for direct calculation of the phase diagram is either
uncertain or non-existent for one or more of the phases. The mass
balance equations among the n+3 phases of interest define the Euler
sphere for any particular system. There is a unique Euler sphere for
unary systems, and another for binary systems. Ternary and quaternary
systems have four and 11 different types of Euler spheres,
respectively. In the ternary case with six phases, the 16
non-degenerate chemographies belong to four groups that are associated
with the four Euler spheres. An analysis of those groups shows a close
relationship between the topologies of the chemographies and the
topologies of the grids represented on the Euler sphere. Euler spheres
for degenerate chemographies are characterized by a smaller number of
spherical polygons. A useful application of the Euler sphere concept is
the systematic derivation of possible FMAS petrogenetic grids from
subsystem constraints. Assumption of just one stable invariant point in
each of MAS and FAS systems is consistent with seven FMAS grids
involving cordierite, garnet, hypersthene, quartz, sapphirine,
sillimanite and spinel.
Author Keywords: Euler
spheres; FMAS granulites; invariant points; petrogenetic grids
KeyWords Plus: RELATIONS
INVOLVING CORDIERITE; CONSISTENT THERMODYNAMIC DATA; SYSTEMS; MINERALS;
GARNET; PHASES
Addresses: Kletetschka
G (reprint author), Univ Minnesota, Dept Geol & Geophys, 108
Pillsbury Hall, Minneapolis, MN 55455 USA
Univ Minnesota, Dept Geol & Geophys, Minneapolis, MN 55455 USA
Publisher: BLACKWELL
SCIENCE INC, 350 MAIN ST, MALDEN, MA 02148 USA
Subject Category: GEOLOGY
IDS Number: 225VK
ISSN: 0263-4929