TOPOLOGIC PROPERTIES OF C-COMPONENT, (C+4) PHASE PETROGENETIC GRIDS WITH APPLICATIONS TO SILICA AND METAMORPHIC ROCKS IN THE GOLD CREEK AREA, GUNNISON COUNTY, COLORADO

Topological properties of c-component, (c + 4)-phase straight-line multisystem nets are examined in the first chapter. These nets differ from (c + 3)-phase nets in the interconnectivity of invariant points and in relationships among nets consistent with a given topology. In (c + 3)-phase nets, each invariant point is connected to every other; in (c + 4)-phase nets each is connected to only (2c + 4). For a given number of components, all (c + 3)-phase nets are derivable from one another by transposition. Nets with (c + 4) phases fall into equivalence classes based on the number of (singly) metastable invariant points; only nets in the same class are related by transposition. The existence of exactly 1320 unary 5-phase nets is demonstrated. It is suggested that in general there are {lcub}(c + 4)!/2{rcub}*{lcub}2('(c+4))-2*(c + 4){rcub} c-component, (c + 4)-phase nets.; Potential phase diagrams for the five-phase system (alpha)-quartz, (beta)-quartz, coesite, cristobalite, tridymite are investigated in the second chapter by examining the constraints imposed on the topology of a phase diagram by reported experimental data. Only three diagrams are consistent with these data. If one assumes that the slope of (alpha) = CO is steeper than that of (beta) = CR, then only one phase diagram is possible. If one accepts the data which suggest that the slope of (beta) = CO is less than that of (beta) = CR, then there are two possible phase diagrams which differ from one another only in the relative stabilities of the metastable phases.; The results of geologic mapping in the Gold Creek area, Gunnison County Colorado, are presented in the third chapter. Many of the parageneses observed in the metamorphic rocks in the Gold Creek area may be modelled in the AlO(,1.5)-MgO-FeO system. The phases modelled here are andalusite, anthophyllite, cordierite, cummingtonite, garnet, gedrite, and staurolite. Although techniques for handling (c + 4)-phase systems are at present inadequate for dealing with the complete system, a six-phase anthophyllite-free petrogenetic grid is presented. The addition of anthophyllite adds only one reaction which may destablize the observed facies. Metamorphic conditions are estimated to have been 450-585(DEGREES)C and 2.0-3.8 kb based on the observed mineral assemblages.(, )...