Degenerate reactions may, or may not, pass through an invariant point.Another consequence of these relationships is that a given mineral assemblage is limited to an arc of ≤180 o again, this is because the stability field of a mineral assemblage will be cut off by another reaction (see details about the Morey-Schreinemakers Rule in Zen, 1966).(Metastable curves are sometime plotted as dashed lines but for clarity are usually omitted from phase diagrams.) A reaction is said to be metastable in space where product or reactant minerals or assemblages are unstable. Reaction curves involving n+1 phases cannot pass through an invariant point because crossing other reaction curves means that some of the phases or assemblages become unstable.If degenerate reactions are involved at an invariant point, it may appear that there are too few univariant curves because two or more curves may a) be collinear on opposite sides of the invariant point and thus appear to be the same curve, or b) may be superimposed on top of each other, so a single curve may represent reactions with two or more phases absent). (Degenerate reactions are those that can be described with fewer components than the overall system, see below. Special case:If one (or more) of the reactions are degenerate, the reaction(s) will include fewer than n+1 phases, there will be fewer than n+2 reaction curves, and fewer than n+2 divariant fields.There are n phases stable in each divariant field (F=2) and there are n+2 divariant fields.In the general case, there are n+1 phases involved in each univariant reaction.In the general case, there are n+2 univariant reaction curves that intersect at the invariant point each reaction is represented by a univariant curve.There are n+2 phases related by univariant reactions (F=1) around an invariant point (F=0).(You can vary both P and T, within limits, independently and you will still stay in the field.Ĭorrolaries to the phase rule are that, for an "n" component system (C = n): Fields between reactions have two degrees of freedom.(You are free to change either P or T, but once you do that, the value of the other is fixed at a particular value or you will not stay on the line.) Reaction lines occur over a range of P and T, but the two cannot be varied independently. ![]() (You are NOT free to vary either if you wish to stay at the point.) Invariant points occur at a fixed P and T.An invariant point (where reactions intersect) has 0 degrees of freedom (F=0), a reaction line has 1 degree of freedom (F=1), and a divariant field between reactions has 2 degrees of freedom (F=2).įor a PT diagram, what the phase rule tells us is that: P, F, and C refer to the number of phases present, the degrees of freedom, and the number of system (chemical) components. Start with the phase rule (P + F = C + 2). ![]() ![]() Note that the (Tr)(Cc) reaction is degenerate it involves fewer phases than the others. Analyzing TX diagrams using the Schreinemakers approach is a bit different than analyzing a PT diagram because TX diagrams imply the presence of H 2O and CO 2. As is traditionally done, the reactions have been labeled by putting the "missing" phase(s) in parentheses at the end of the reaction curve. This example of an invariant point in TX space includes reactions involving tremolite, calcite, dolomite, diopside, quartz, CO 2 and H 2O.
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