TEXTURAL AND MICROANALYSIS OF IGNEOUS ROCKS: TOOLS ...

where R is the gas constant, T is temperature (Kelvin), i is the element of interest,
and XAn is the mole fraction of anorthite. Using equation 3.1, Ginibre et al.
[59] noted that temperatures in the range of 850-1,000 ◦ C had miniscule effect on
calculated melt concentrations for Sr and Ba (within their analytical uncertainty).
Likewise, Bindeman et al. [7] showed that variations of ∼150 ◦ C produce < 10%
differences for particular partition coefficients, which were often within error of
the respective D values.
Blundy and Wood [11] presented an alternative model for quantitative predic-
tion of D values based upon thermodynamic principles and lattice strain theory
(i.e., [15]). Specifically, they noted the dominant roles of cation size, lattice site
size, and elasticity of the lattice site related to cation substitution in minerals.
The elastic response of a lattice site to cation substitution is measured by Young’s
Modulus (E), and the value of E plag is dependent upon plagioclase An content
and the charge of the substituent cation [11, 12]. Equation 3.2 (Equation 2 of
Blundy and Wood [11]) is the basis of their predictive D model that I apply to
plagioclase,
Di = D z+
o
∗ exp
−4πEplagNA
ro
2 (r2 o − r2 1
i ) + 3 (r3 i − r3 o )
RT
(3.2)
where Di of a trace element (i) is a function of the strain compensated partition
coefficient for the divalent (D 2+
0 ) or trivalent (D 3+
0 ) substituent cation, Young’s
Modulus for the plagioclase M lattice site (E plag), NA (Avogadro’s Number), the
radius of the plagioclase M site (ro), the radius of the substituent cation (ri),
the gas constant (R), and crystallization temperature (T). For a more thorough
discussion of this model see Blundy and Wood [11, 12].
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