Heat effects of assimilation,crystallization, and vesiculation in magmas

The heat balance for crystal fractionation and assimilation processes is the enthalpy difference between the initial and final states of a system. To order the calculations, the process is viewed as one of assimilation; the heat change for a crystallization process is obtained by changing the signs of the pertinent heat effects. The initial state is a mineral assemblage at T_s and P and an initial magma at T_m and P. The final state is a magma at T_m and P.The net heat change results from: (a) Unmixing of solid solutions, (b) Heating (cooling) each component to its fusion temperature, (c) Fusion of each component, (d) Cooling (heating) of each fused component to the magma temperature, (e) Mixing of each fused component in succession with the melt.The heat required to form a basaltic melt from its equilibrium mineral assemblage is approximately twice that required for a granitic melt. A zero heat balance, with the heat of crystallization from phases with which the magma is saturated supplying the energy for assimilation, necessitates that the mass crystallized be approximately twice that assimilated. The heat effects attendant on release of H₂O from silicic melts depends on the state of the H₂O in the external environment; a low fugacity could cause the magma to cool.The uncertainties in the calculations are estimated at ±10%.