LINEAR PARTITIONING IN BINARY SOLUTIONS: A REVIEW WITH A NEW TWIST

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, X = 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 1,2 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, having 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. Loop width is an inverse function of KD, and can vary with pressure as in the case of olivine-saturated plagioclase. 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. Strict linearity is not always observed: the path to KD may be segmented or moderately curved, as with the melting equilibria of both plagioclase and olivine. A repeat of the Bowen thermodynamic calculation for the system An-Ab using modern latent heats of fusion shows an array with a single slight 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, Labrador, form a unified linear partitioning curve to KD = 0.33 for all data above fifty-percent crystallized. All the other rocks except two occupy a new trend in the linear partitioning diagram. This trend is anchored at D = 0.0, X2S = 1.0 and defines the liquid composition at its intercept with the upper bound at D = 1.0. Olivines along this path have reacted to varying degrees by equilibration either with trapped liquid or with exotic evolved magma. Ten out of 36 samples suggest an exotic influence. Seven of these lie at 6 to 13 percent solidified where new liquid injections have previously been inferred. The other three are in doubt from their field relationships to a roof pendant. The new equilibrium crystallization trend is the graphical solution to the liquid composition given the crystal composition and the value of KD.