Consider the system built up of the four components—Ca°, MgO, Apart from their polymorphic modifications the number of possible minerals constituted of these oxides or their combinations approximate 20. The phase rule simply states that the maximum number of phases found together is limited at equilibrium, but gives no information as to the particular mineral associations. In the case before us, the maximum number is four. This system is of great importance in metamorphic petrology, for the group of sediments rang ing from pure shales to limestones is largely constituted of these four oxides. A study of the hornfelses derived from shale-limestone sediments shows that a number of well defined assemblages can be recognized as constantly re curring types. Pure shales give rise t o andalusite-cordierite hornfelses, certain marls to di opside-plagioclase hornfelses, etc.
Apart from the alkali minerals, orthoclase, albite and biotite, limefree shale hornfelses have the composition andalusite-cordierite-quartz, a three phase assemblage built up of three components (MgO, If now, to this system lime is added, a fourth phase enters, namely, anorthite, and we have the combination andalusite-anorthite-cordierite quartz. By successive increments of lime a series of mineralogical combinations can be derived which correspond to the hornfelses formed from the continuous shale-limestone series of sediments. As first recognized from the aureoles of the Devonian intrusions of the Oslo region, these mineral assemblages are as follows, quartz and orthoclase being possible phases in all :— I. Andalusite cordierite albite (biotite) 2. Andalusite cordierite plagioclase (biotite) 3. Andalusite cordierite plagioclase (biotite) 4. Andalusite cordierite plagioclase (biotite) enstatite 5. Andalusite cordierite plagioclase (biotite) enstatite 6. Andalusite cordierite plagioclase (biotite) enstatite, diopside 7. Andalusite cordierite plagioclase (biotite) enstatite, diopside 8. Andalusite cordierite plagioclase (biotite) enstatite, diopside grossular 9. Andalusite cordierite plagioclase (biotite) enstatite, diopside grossular 10. Andalusite cordierite plagioclase (biotite) enstatite, diopside grossular wollastonite.
The composition of these assemblages may be represented in a triangular diagram. Such a diagram (fig. i) represents the quartz bearing hornfelses of the f our component system lime-mag nesia-alumina-silica. Each of the classes is represented by the numerals within or on the sides of the triangles, any point representing a mineral assem blage composed of the minerals represented at the apices of the individual triangles. In a
similar way fig. 2 represents, the three-phase mineral assem blages of the three-component system Mg0 — The various associations are char acteristic of thermally altered sediments, periclase-spinel-forsterite, of metamorphosed dolomites and the remainder (with the ex ception of the assemblage forsterite-enstatite-spinel) of argilla ceous sediments, those rich in enstatite corresponding to magnesia rich types, those rich in corundum or spinel to silica-poor types. The dotted area represents the bulk compositions of shales whose constituent minerals are indicated by the points for quartz, kaolin and chlorite. The foregoing assemblages are characteristic of the highest grades of thermal metamorphism and are presumably those stable at the highest temperatures to which the rocks are subjected. Other components such as H20, Cl, B, F, intro duce new phases such as biotite, orthoclase, and albite among argillaceous sediments, scapolite, vesuvianite, chondrodite and axinite among carbonate rocks. That we are able to study at ordinary temperatures such systems formed at high temperatures, naturally implies that a great lag effect accompanies the cooling of the rock. Reactions of adjustment to the conditions of lower temperature are, however, by no means altogether absent. The process of retrograde metamorphism is known as diaphthoresis. In contact aureoles it is commonly seen in the conversion of diopside or augite to tremolite or hornblende and the formation of epidote or clinozoisite from anorthite. Hornfelses bearing amphibole in place of pyroxene are also commonly met with in the outer portions of contact aureoles. Clearly, here the amphibole is developed under the conditions of lower temperature. On the other hand, certain assemblages are characteristic of the highest temperatures. They are commonly met with as inclusions or xenoliths in the igneous mass itself or at the immediate con tact. Mullite appears in place of sillimanite as in buchites, sanidine in place of orthoclase tridymite, or cristobalite in place of quartz, and the combination wollastonite-anorthite in place of grossular garnet. Such high temperature assemblages are known as pyrometamorphic rocks. An intense metasomatic action often accompanies the formation of such rocks. They are typi cally represented in the xenolithic assemblages of volcanic centres such as the Eifel, Vesuvius, etc.