Apatite Thermodynamic Model

Instruction:

This model can be used to calculate the abundances of water in silicate melts using concentrations of volatiles (F, Cl, H₂O) in apatite, and the equations for the exchange coefficients (K_D) for OH-Cl, OH-F, and Cl-F proposed by:

Li W. and Costa F. (2020). A thermodynamic model for F-Cl-OH partitioning between silicate melts and apatite including non-ideal mixing with application to constraining melt volatile budgets. Geochimica et Cosmochimica Acta 269, 203-222. DOI: 10.1016/j.gca.2019.10.035

[Updates: functions in this webpage are included in a python package called "pyAp" at Github (github.com/alexweiranli/pyAp) since February 2022. There's also an excel version that can be requested from Alex (Weiran Li) at: wl413@cam.ac.uk]

1. Calculating chemical formula of apatite:

Required:

CaO wt. %
P₂O₅ wt. %
F wt. %
Cl wt. %

Optional:

H₂O^* wt. %
CO₂ wt. %
SO₃ wt. %

Optional:

SiO₂ wt. %
Na₂O wt. %
MgO wt. %
Al₂O₃ wt. %
MnO wt. %
FeO wt. %
Ce₂O₃ wt. %
SrO wt. %
BaO wt. %

^*If H₂O in apatite was not directly measured, leave this box empty, so that our model will calculate it based on stoichiometry, assuming that only F, Cl and OH occupy the anion site.

Chemical formula: Ca₁₀(PO₄)₆X₂
(Using 26 Oxygen)

Ca (a.p.f.u)0
P (a.p.f.u)0
F (a.p.f.u)0
Cl (a.p.f.u)0

Mole Fraction

X_F0
X_Cl0
X_OH0
X_OH(calc)^**0

^**Calculated based on stoichimeotry (e.g Deer et al., 1992)

2. Calculating exchange coefficients and volatile ratios in melt using known temperature

Temperature ^oC

Exchange coefficients

K_D(OH-Cl)0
K_D(OH-F)0
K_D(Cl-F)0

Activity coefficients

_γ(OH)_Ap0
_γ(F)_Ap0
_γ(Cl)_Ap0

Calculated volatile ratios in melt using apatite:

Mole OH/Cl0
Mole OH/F0
Mole Cl/F0

3. Calculating H₂O in melt using known melt Cl and/or F concentrations

Fill in at least one box below:

Cl in melt ppm
F in melt ppm

Dacitic-rhyolitic magma^†
Basaltic magma^††

H₂O calculated using Cl0 wt. % (Error: ± 30-40%)

H₂O calculated using F0 wt. % (Error: ± 30-40%)

Water speciation models from Zhang et al. (1997) ^† and Lesne et al. (2010) ^††