Behaviors of trace elements and relationships between the compositions of solid phase and melt during fractional crystallization

Given r_i =f _i(F) andK _i = g_i(F), wherer _i is the mineral mass fraction in an instantaneous solid phase,K _i the partition coefficient, andf _i(F) andg _i(F) respectively the continuous, sectionally smooth functions of solidification degreeF, we have: $$C^1 = frac{{C_0 }}{{1 - F}} cdot exp left( { - int_0^F {frac{{Sigma fi(F) cdot g_i (F)}}{{1 - F}} cdot dF} } right)and bar C^s = frac{{C_o }}{F}left[ {1 - (1 - F) cdot frac{{C^1 }}{{C^0 }}} right]$$ Also presented in this paper are other equations describing the compositional changes of solid and liquid phases in magmatic processes (partial melting). The following understanding is attained based on the application of these equations to the Hushan pluton of Mt. Taishan in the west of Shandong Province. 1) For granitoids changes in rock-forming minerals may not be taken into consideration in theoretical modelling of REE distribution, but accessory minerals rich in REE, especially those highly rich in some REE must be taken into account. 2) In the case of well differentiated granitoids, it can be assumed thatFε [0,1] may exert only little influence on the calculations. 3) In practice the (La / Sm)-La diagram should be applied with care.