Linear partitioning in binary solutions; a review with a novel partitioning array
Linear partitioning in binary solutions; a review with a novel partitioning array
American Mineralogist (June 2015) 100 (5-6): 1021-1032
- alkali feldspar
- augite
- chain silicates
- clinopyroxene
- crystallization
- equations
- feldspar group
- framework silicates
- gabbros
- graphic methods
- igneous rocks
- melting
- nesosilicates
- olivine
- olivine group
- orthopyroxene
- orthosilicates
- partitioning
- phase equilibria
- pigeonite
- plagioclase
- plutonic rocks
- pyroxene group
- sanidine
- silicates
- solid solution
- solutions
- thermodynamic properties
- troctolite
- binary solutions
Linear partitioning refers to a graphical plot of a partition ratio D < or =1.0 against a composition ratio X (sub 2) given as the mole fraction of a refractory component 2. When this plot is linear from D = 1.0, X (sub 2) = 0.0, its intercept at X (sub 2) = 1.0 is a value on the D scale here identified as the value of the exchange coefficient K (sub D) . The plot is generated from phase compositions 1 and 2 in states L (sub V) or L (sub S) or S (sub 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 identical with D, a identical with K (sub D) , x identical with X (sub 2) , and b = 1 - x identical with 1 - X (sub 2) . In practice, the linearity is tested by regressing values of D against X (sub 2) to find the intercept K (sub 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 (sub 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 (sub 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 (sub 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 (sub 2) (super 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.