Modal Batch Melting

During modal melting, the melting proportion is the same as the mineral source proportion and thus x is constant throughout the melting process x =x q. When K is also constant (K = ), then the bulk partition 

Example. Calculate Ci fC for three elements with bulk partition coefficients of 0.02, 0.10 and 1.5, respectively. From Eq. (1.7) we can make Fig. 1.3 by plotting C /Cq vs. F for the three D values. 

---

Equation (1.16) is the famous non-modal batch melting equation from Shaw (1970). 

Modal Batch Melting Modal BM w/ constant Modal BM w/ linear K Modal BM w/ linear K and linear q ... 

Problem. Demonstrate low-degree (F] )/high-degree (F ) concentration ratio (Q) of the same element decreases with increasing partition coefficients (Dq) during modal batch melting. 

The linear regression method, or slope-intercept method (Zou, 1997), for whole-rock residues can only be applied to modal batch melting. For elements a (highly incompatible) and b (not-so-highly incompatible), their concentrations in the residue during modal batch melting, and, respectively, are given by... 

Alternatively, a linear relationship between l/C and l/Qj, for modal batch melting can also be obtained from Eqs. (7.51) and (7.52) as follows ... 

The basic equations describing the variation in concentration of a trace element in cpx of non-modal batch melting model can be obtained as follows (Johnson et al., 1990) ... 

In contrast to the case for whole rocks, the linear regression method for residual clinopyroxenes can be applied to non-modal batch melting. The basic equation for the variation of a trace element in cpx during non-modal batch melting has been given in Eq. (7.56). We can obtain the following linear relationship from Eq. (7.56) (Zou, 1997) ... 

In the context of non-modal (eutectic) batch melting, the variation in the concentration of a trace element in a whole-rock residue,, is given by Shaw (1970) as... 

Figure 4.36 Chondrite-normalized REE patems calculated for modal batch partial melting of a primitive mantle source with ca 2.IS chondridc concentration of REE and with the mineralogy — V olivine 55 %, orthopyroxene 25 %, cUnopyroxene 11 % and garnet 9 %. Curves are shown...

---