U-series modeling and the degree of partial melting

For U-series modeling, we have five parameters m (f), M, T, f and X. Since there are two equations (Eqs. (5.44) and (5.74)) to relate these five parameters, we have three independent parameters. Theoretically, we can express Raj Th) and as functions 

The physical significance of melting time has not been well handled before. Equation (5.77) is in fact the definition of melting time. It can be seen from Eq. (5.77) that if / = O, then P = 0 and if / — 1, then T oo. Accordingly, increasing melting time reflects increasing 

Activity ratios in the melt when / before melt extraction starts 

Equations (5.61), (5.62) and (5.63) describe the activity ratios in the extracted melt when / O. In this section we will discuss the behaviors of activity ratios when / O. Since there is no extracted melt when / O, we only study the behaviors in the residual melt. We will first describe the case when / = O (or the initial conditions) and then the case when / O. According to Eq.(5.33), we have 

Substitution of (5.81) into Eq. (5.51) for the initial activity ratio gives rise to 

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