Abstract
Linear partitioning refers to a graphical plot of a partition ratio D ≤1.0 against a composition ratio X2 given as the mole fraction of a refractory component 2. When this plot is linear from D = 1.0, X2 = 0.0, its intercept at X2 = 1.0 is a value on the D scale here identified as the value of the exchange coefficient KD. The plot is generated from phase compositions 1 and 2 in states LV or LS or SS depending on whether the system is a boiling mixture, a melting equilibrium, or a solid-solid equilibrium. The linear partitioning equation so generated is a mathematical description of a binary solution loop, and it has the form y = ax + b where y ≡ D, a ≡ KD, x ≡ X2, and b = 1 − x ≡ 1 − X2. In practice, the linearity is tested by regressing values of D against X2 to find the intercept KD. If linearity occurs, the system is a binary solution loop; if it does not occur, the system is not a binary loop. Strict linearity is not always observed even in true binary solutions; in such cases the path to KD may be either segmented or moderately curved. Such is the case with the melting equilibria of both plagioclase and olivine, possibly a clue to the non-ideality of solution. Loop width is an inverse function of KD, and can vary with pressure as in the case of plagioclase in troctolites and gabbros. Systems with two loops joined at a common minimum or maximum are called azeotropes and all of them show linear partitioning. Sanidine crystalline solutions form a classic example of such behavior. When the system An-Ab is revisited to repeat the Bowen thermodynamic calculation from the latent heats of fusion with modern data, the array shows a single modest curvature. The monoclinic pyroxene pairs augite and pigeonite form a binary loop; augite-orthopyroxene does not. The olivine compositions of rocks in the Kiglapait intrusion follow a linear partitioning line with KD = 0.26 for data above 50% crystallized (50 PCS). All the rocks below 50 PCS occupy a new trend in the linear partitioning diagram. This trend is anchored at D = 0.0, X2S = 1.0 and runs to the calculated liquid composition at its intercept with the D = 1.0 upper bound. The new trend is an artifact of a nearly constant liquid composition and serves only to show low Fo contents in the range 0–50 PCS.
