Linear partitioning refers to a graphical plot of a partition ratio D ≤1.0 against a composition ratio X 2 given as the mole fraction of a refractory component 2. When this plot is linear from D = 1.0, X 2 = 0.0, its intercept at X 2 = 1.0 is a value on the D scale here identified as the value of the exchange coefficient K D . The plot is generated from phase compositions 1 and 2 in states L V or L S or S S 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 ≡ K D , x ≡ X 2 , and b = 1 − x ≡ 1 − X 2 . In practice, the linearity is tested by regressing values of D against X 2 to find the intercept K D . 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 K D 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 K D , 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 K D = 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, X 2 S = 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.
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