| rtSaturation {GCDkit} | R Documentation | 
Calculates rutile saturation temperatures for the observed major-element data and Ti concentrations. Also returns Ti saturation levels for the given major-element compositions and assumed magma temperature.
rtSaturation(cats=milli,T=0,P=0,Ti=filterOut(WR,"Ti",1))
| cats | numeric matrix; whole-rock data recast to millications | 
| T | assumed temperature of the magma in °C | 
| P | assumed pressure in kbar, Ryerson & Watson (1987) model only | 
| Ti | numeric vector with Ti concentrations in ppm | 
Ryerson & Watson (1987) have first formulated rutile saturation model for melts ranging in composition from basalt to rhyodacite. The distribution of TiO2 between rutile and liquid was given as:
DTiO2 = exp(-3.16+9373/T+0.026*P-0.152*FM)
where 'T' is the absolute temperature (K) of the magma, 'P' pressure (kbar) 
and 'FM' is a melt composition parameter:
FM = 1/Si*(Na+K+2(Ca+Mg+Fe))/Al
.
The Ti saturation level then would be:
Ti.sat.RW = 599342.9/DTiO2 (ppm)
In turn, when the rutile saturation was reached, the magma temperature (in °C) can be calculated as:
TRt.sat.C.RW<-9373/(3.16+ln(100/TiO2)-0.026*P+0.152*FM)-273.15
The Ti solubility in rutile-saturated hydrous siliceous melts was revisited by Hayden & Watson (2007). According to these authors, it can be expressed as:
Ti.sat.HW = 10^(7.95 - 5305/T + 0.124 FM) (ppm)
where 'T' is the absolute temperature (K) of the magma, and 'FM' 
is the melt composition parameter defined above.
The temperature (in °C) for rutile-saturated magma can be calculated as:
TRt.sat.C.HW = 5305/(7.95 -log(Ti) + 0.124 FM) - 273.15
Using these formulae, the function 'rtSaturation' calculates the rutile 
saturation levels, Ti activities and rutile saturation temperatures following
both models. 
The formulation of Ryerson & Watson (1987) may be more suitable for basic rocks, whereas the more recent model of Hayden & Watson (2007) seems to be appropriate for siliceous magmas. Please note also that the latter does not take into account effects of pressure (having been calibrated at 1 GPa; Hayden & Watson 2007).
Returns a matrix 'results' with the following columns:
| FM | melt composition parameter | 
| Ti | observed Ti concentrations | 
| Ti.sat.RW | saturation levels of Ti for assumed temperature, Ryerson & Watson (1987) | 
| aTi.RW | activity of Ti (ratio of Ti/Ti.sat), Ryerson & Watson (1987) | 
| TRt.sat.C.RW | rutile saturation temperatures in °C, Ryerson & Watson (1987) | 
| Ti.sat.HW | saturation levels of Ti for assumed temperature, Hayden & Watson (2007) | 
| aTi.HW | activity of Ti (ratio of Ti/Ti.sat), Hayden & Watson (2007) | 
| TRt.sat.C.HW | rutile saturation temperatures in °C, Hayden & Watson (2007) | 
Saturation.r
Vojtěch Janoušek, vojtech.janousek@geology.cz
Ryerson FJ, Watson EB (1987) Rutile saturation in magmas; implications for Ti-Nb-Ta depletion in island-arc basalts. Earth Planet Sci Lett 86: 225-239 doi: 10.1016/0012-821X(87)90223-8
Hayden LA, Watson EB (2007) Rutile saturation in hydrous siliceous melts and its bearing on Ti-thermometry of quartz and zircon. Earth Planet Sci Lett 258: 561-568 doi: 10.1016/j.epsl.2007.04.020
    sampleDataset("sazava")
    rtSaturation(T=800,P=3)