University:
Massachusetts Institute of Technology
Course:
12.520 | Geodynamics
Academic year:

2023
Views:

321

Pages:

10
Author:

Hartkern721

mineral melt equilibrium common - well studied and of interest is olivine - melt choice of components & way that we want to use reaction are important issues. consider solid - liquid lig & solid both solidus. simply treat the solid like a gas & see what happens- condition of equilibrium M1g2.5i04 = M1g2.5iO4 μFo^melt + RT ln xFo^melt = μFo^melt + RT ln xFo^melt ΔH^melt = μFo^melt - μFo^solid = (H^melt - H^solid)/R if we want to see how this changes with T we differentiate d(μFo^melt - μFo^solid)/dT = ΔH^melt/RT^2 and integrating) assuming that ΔCp is constant (heat of fusion) ln xFo^melt = [(ΔH^melt - ΔH^solid)/R] * (1/T - 1/T0) + ΔCp ln(T/T0) This is melting point lowering equation for solid solution for system Fo - Fa let's see if the thermodynamic model works. we may calculate the phase diagram from 2 equations & the form... 2 ln (Xmg^melt / Xmg^ol) = 1/R * [ΔH^Fo - ΔCp^Fo * T^melt * (1/T - 1/T^melt) + ΔCp^Fo * ln(T/T^melt)] so we need ΔH^Fo = 39,240 J/mol ΔH^ol = 25,010 J/mol ΔH^Fo - ΔCp^Fo = 7,455 J/mol*K^-1 then we use these values for Xmg^melt, Xmg^ol, XFe^melt, XFe^ol at liquidus T's mass balance says... XFe^melt = a(1-b) XFe^ol = b so we can calculate x; solve for the shape of the binary loop in Fo - Fa this suggests that for some system - they are close to ideal but not exactly so. - compare the exptl. diagram with exptl. see problem set - they don't match. why - turns out olivine is a non-ideal solid solution - ask you to use equations for the Geek for Fo-Fa solution in a prob. set. clever thermo approach by choosing components with physical insight - can explain the free energy of mixing. other approaches - Gmixo + Gmixideal Ghioiso and Sack (1995) CMP 119: 197-212. also - MELTS we purge on Toop & Samis model Anionic matrix controls the energy of mixing (2+1) MO - SiO2 Melt consists of a polymerized network of SiO2 where Si and O atoms are tetrahedrally coordinated by oxygen atoms and a continuous network. O - Si - O - Si - O | | - O - O - dissociation: M^2+ - O^2- models discuss the tendency (degree) to which this dissociation occurs. Once the dissociation occurs, it results in the breakup of the SiO2 chains. Equilibrium constant based on the oxygen (ionic) species in the melt. (O^2-)free ion of non-bridging oxygen (MgO)^2+ - (AlO2)^- K = (MgO)^2+ * (AlO2)^- / (MgAlO2)^2+ Toop & Samis chose the square root of the equilibrium constant K' = sqrt(K)