Grt-Cpx: Beyer, 2015

Garnet–clinopyroxene geobarometer for mantle eclogites. The barometer is based on the incorporation of tetrahedrally coordinated aluminum in clinopyroxene coexisting with garnet.

Details

Article	Beyer C., Frost D.J., Miyajima N. Experimental calibration of a garnet--clinopyroxene geobarometer for mantle eclogites, 2015 [ref]
Collibration	Calibrated using the results of piston cylinder and multi-anvil experiments. Starting materials were hydrous and anhydrous synthetic mixtures of basaltic bulk compositions that yielded homogeneous bimineralic garnet–clinopyroxene phase assemblages. The experimental data set was expanded by employing results from previous experimental studies conducted in eclogitic systems.
Accuracy	±2 kbar
Ranges	1200 °C ≤ T ≤ 1550 °C, 30 kbar ≤ P ≤ 70 kbar
Renew sensors	Kiseeva, et al. (2012), Spandler, et al. (2008), Hammouda, et al. (2009), Klemme, et al. (2002), Green, et al. (2012), Yasuda, et al. (1994), Kessel, et al. (2005), Kogiso and Hirschmann, et al. (2006), Petermann and Hirschmann, et al. (2003), Tsuno and Dasgupta, et al. (2011), Yaxley and Bray, et al. (2004), Konzett, et al. (2008)

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Source

 
source('recalc_grt_nm.r');
source('recalc_px_nm.r');
 
sensors.p.grt_cpx_beyer <- function(Grt, Cpx, Temp, usePFU = FALSE, ...){
 
    presults <- data.frame(Name = paste0(Grt$Name,"-",Cpx$Name));
    
    if(!usePFU){
        Grt <- recalc.grt_nm(Grt);
        Cpx <- recalc.px_nm(Cpx);
    }
    
    T <- Temp+273;
    
    Grt <- selectNames(Grt,c('Fe_pfu', 'Mg_pfu', 'Ca_pfu'));
    Cpx <- selectNames(Cpx,c('Si_pfu', 'Ti_pfu', 'Al_pfu', 'Fe_p2_pfu', 'Fe_p3_pfu', 'Mn_pfu', 'Mg_pfu', 'Ca_pfu', 'Na_pfu'));
    
    #Recalc to 12 ox
    Grt$X_Fe <- Grt$Fe_pfu / (Grt$Fe_pfu + Grt$Mg_pfu + Grt$Ca_pfu);
    Grt$X_Mg <- Grt$Mg_pfu / (Grt$Fe_pfu + Grt$Mg_pfu + Grt$Ca_pfu);
    Grt$X_Ca <- Grt$Ca_pfu / (Grt$Fe_pfu + Grt$Mg_pfu + Grt$Ca_pfu);
 
    Grt$Fe_ox12_pfu <- Grt$X_Fe*3;
    Grt$Mg_ox12_pfu <- Grt$X_Mg*3;
    Grt$Ca_ox12_pfu <- Grt$X_Ca*3;
        
    Cpx$Al_T_pfu <- 2 - Cpx$Si_pfu;
    Cpx$FeMg_M1_pfu <- 1 - (Cpx$Al_pfu-Cpx$Al_T_pfu) - Cpx$Ti_pfu - Cpx$Fe_p3_pfu;
    Cpx$Fe_M1_p2_pfu <- Cpx$Fe_p2_pfu / (Cpx$Fe_p2_pfu + Cpx$Mg_pfu) * Cpx$FeMg_M1_pfu;
    Cpx$Fe_M1_p3_pfu <- Cpx$Fe_p3_pfu;
    Cpx$Mg_M1_pfu <- Cpx$Mg_pfu / (Cpx$Fe_p2_pfu + Cpx$Mg_pfu) * Cpx$FeMg_M1_pfu;
    Cpx$Al_M1_pfu <- Cpx$Al_pfu - Cpx$Al_T_pfu;
    
    Cpx$FeMg_M2_pfu <- (Cpx$Fe_p2_pfu + Cpx$Mg_pfu) - Cpx$FeMg_M1_pfu;
    Cpx$Ca_M2_pfu <- Cpx$Ca_pfu;
    Cpx$Na_M2_pfu <- Cpx$Na_pfu;
    Cpx$Fe_M2_pfu <- Cpx$Fe_p2_pfu / (Cpx$Fe_p2_pfu + Cpx$Mg_pfu) * Cpx$FeMg_M2_pfu;
    Cpx$Mg_M2_pfu <- Cpx$Mg_pfu / (Cpx$Fe_p2_pfu + Cpx$Mg_pfu) * Cpx$FeMg_M2_pfu;
    Cpx$Al_Esk_pfu <- ifelse((Cpx$Al_pfu-Cpx$Na_pfu)-2*(2-Cpx$Si_pfu) < 0, 0.0, (Cpx$Al_pfu-Cpx$Na_pfu)-2*(2-Cpx$Si_pfu));
    Cpx$NaCa_M2_pfu <- Cpx$Na_M2_pfu + Cpx$Ca_M2_pfu;
       
    Grt$W_CaMg <- 21627-5.78*T;
    Grt$W_MgCa <- 9834-5.78*T;
    Grt$W_CaFe <- 873-1.69*T;
    Grt$W_FeCa <- 6773-1.69*T;
    Grt$W_MgFe <- 2117;
    Grt$W_FeMg <- 695;
 
    Grt$Grs_RTg <- 0.5 * Grt$W_CaMg * Grt$X_Mg * (1-Grt$X_Ca+Grt$X_Mg+2*Grt$X_Ca*(Grt$X_Ca-Grt$X_Mg-1)) +
               0.5 * Grt$W_MgCa * Grt$X_Mg * (1-Grt$X_Ca-Grt$X_Mg-2*Grt$X_Ca*(Grt$X_Ca-Grt$X_Mg-1)) +
               0.5 * Grt$W_CaFe * Grt$X_Fe * (1-Grt$X_Ca+Grt$X_Fe+2*Grt$X_Ca*(Grt$X_Ca-Grt$X_Fe-1)) +
               0.5 * Grt$W_FeCa * Grt$X_Fe * (1-Grt$X_Ca-Grt$X_Fe-2*Grt$X_Ca*(Grt$X_Ca-Grt$X_Fe-1)) +
                     Grt$W_MgFe * Grt$X_Mg * Grt$X_Fe*(Grt$X_Mg-Grt$X_Fe-0.5) +
                     Grt$W_FeMg * Grt$X_Fe * Grt$X_Mg*(Grt$X_Fe-Grt$X_Mg-0.5) +
               (((Grt$W_MgCa - Grt$W_CaMg ) + (Grt$W_CaFe - Grt$W_FeCa) + (Grt$W_FeMg - Grt$W_MgFe))/2) * 
               Grt$X_Mg * Grt$X_Fe * (1-2 * Grt$X_Ca);
       
    Grt$Grs_RTln_X3 <- 8.314*T*log(Grt$X_Ca^3);
    Grt$Grs_RTlna_CaAl <- 3*Grt$Grs_RTg + Grt$Grs_RTln_X3;
    
    Grt$Pyr_RTg <- 0.5*Grt$W_MgCa*Grt$X_Ca*(1-Grt$X_Mg+Grt$X_Ca+2*Grt$X_Mg*(Grt$X_Mg-Grt$X_Ca-1))+
               0.5*Grt$W_CaMg*Grt$X_Ca*(1-Grt$X_Mg-Grt$X_Ca-2*Grt$X_Mg*(Grt$X_Mg-Grt$X_Ca-1))+
               0.5*Grt$W_MgFe*Grt$X_Fe*(1-Grt$X_Mg+Grt$X_Fe+2*Grt$X_Mg*(Grt$X_Mg-Grt$X_Fe-1))+
               0.5*Grt$W_FeMg*Grt$X_Fe*(1-Grt$X_Mg-Grt$X_Fe-2*Grt$X_Mg*(Grt$X_Mg-Grt$X_Fe-1))+
                   Grt$W_CaFe*Grt$X_Ca*Grt$X_Fe*(Grt$X_Ca-Grt$X_Fe-0.5)+
                   Grt$W_FeCa*Grt$X_Fe*Grt$X_Ca*(Grt$X_Fe-Grt$X_Ca-0.5)+
               (((Grt$W_MgCa-Grt$W_CaMg)+(Grt$W_CaFe-Grt$W_FeCa)+(Grt$W_FeMg-Grt$W_MgFe))/2)*Grt$X_Ca*Grt$X_Fe*(1-2*Grt$X_Mg);
    
    Grt$Pyr_RTLn_X3Y2 <- 8.314*T*log(Grt$X_Mg^3);
    Grt$Pyr_RTlna_MgAl <-  3*Grt$Pyr_RTg + Grt$Pyr_RTLn_X3Y2;
    
    Cpx$W_MgFe <- 0;
    Cpx$W_MgAl <- 4849;
    Cpx$W_FeAl <- 3573;
 
    Cpx$W_CaNa <- 11567;
    Cpx$W_MgNa <- -35873;
    Cpx$W_FeNa <- 59319;
    Cpx$W_CaMg <- 24920;
    Cpx$W_CaFe <- -49275;
    Cpx$W_FeMg <- 0;
    Cpx$W_AlSi <- 7038;
    
    Cpx$Dio_RTLn_XM1XM2Xtet <- 8.314*T*log(Cpx$Ca_M2_pfu*Cpx$Mg_M1_pfu*(Cpx$Si_pfu/2)^2);
 
    Cpx$Dio_RTLn_M2 <- Cpx$Mg_M2_pfu^2*Cpx$W_CaMg+
                       Cpx$Na_M2_pfu^2*Cpx$W_CaNa+Cpx$Fe_M2_pfu^2*Cpx$W_CaFe+
                       Cpx$Fe_M2_pfu*Cpx$Mg_M2_pfu*(Cpx$W_CaMg+Cpx$W_CaFe-Cpx$W_FeMg)+
                       Cpx$Mg_M2_pfu*Cpx$Na_M2_pfu*(Cpx$W_CaMg+Cpx$W_CaNa-Cpx$W_MgNa)+
                       Cpx$Na_M2_pfu*Cpx$Fe_M2_pfu*(Cpx$W_CaNa+Cpx$W_CaFe-Cpx$W_FeNa);
    
    Cpx$Dio_RTLn_M1 <- Cpx$Al_M1_pfu^2*Cpx$W_MgAl+Cpx$Fe_M1_p2_pfu^2*Cpx$W_MgFe+
                       Cpx$Al_M1_pfu*Cpx$Fe_M1_p2_pfu*(Cpx$W_MgAl+Cpx$W_MgFe-Cpx$W_FeAl);
    
    Cpx$Dio_RTLn_tet <- Cpx$W_AlSi*(Cpx$Al_T_pfu/2)^2;
    
    Cpx$Dio_Recip <-  0-Cpx$Al_M1_pfu*(Cpx$Fe_M2_pfu*(-21000))-
                        Cpx$Fe_M1_p2_pfu*(Cpx$Fe_M2_pfu*(-4680) + Cpx$Mg_M2_pfu*(-5010));
 
    Cpx$Dio_RTLna_CaMgSi <- Cpx$Dio_RTLn_XM1XM2Xtet + Cpx$Dio_RTLn_M2 + Cpx$Dio_RTLn_M1 + Cpx$Dio_RTLn_tet + Cpx$Dio_Recip;
    
    Cpx$CaTs_RTLn_XM1XM2Xtet <- 8.314*T*log(Cpx$Al_M1_pfu*(4*Cpx$Ca_M2_pfu)*(Cpx$Al_T_pfu/2)*(Cpx$Si_pfu/2));
    
    Cpx$CaTs_RTLn_M2 <- Cpx$Dio_RTLn_M2;
    
    Cpx$CaTs_RTLn_M1 <- Cpx$Mg_M1_pfu^2*Cpx$W_MgAl+Cpx$Fe_M1_p2_pfu^2*Cpx$W_FeAl+
                        Cpx$Mg_M1_pfu*Cpx$Fe_M1_p2_pfu*(Cpx$W_MgAl+Cpx$W_FeAl-Cpx$W_MgFe);
    
    Cpx$CaTs_RTLn_tet <- Cpx$W_AlSi*(Cpx$Si_pfu/2)^2;
    
    Cpx$CaTs_Recip <- (1-Cpx$Al_M1_pfu)*(Cpx$Fe_M2_pfu*(-21000))-
                      Cpx$Fe_M1_p2_pfu*(Cpx$Fe_M2_pfu*(-4680)+Cpx$Mg_M2_pfu*(-5010));
    
    Cpx$CaTs_RTLna_CaAlAl <- Cpx$CaTs_RTLn_XM1XM2Xtet + Cpx$CaTs_RTLn_M2 + Cpx$CaTs_RTLn_M1 + 
                             Cpx$CaTs_RTLn_tet + Cpx$CaTs_Recip;
  
    presults$RTLnK <- Cpx$CaTs_RTLna_CaAlAl +Cpx$Dio_RTLna_CaMgSi -1/3*Grt$Pyr_RTlna_MgAl -2/3*Grt$Grs_RTlna_CaAl;
 
    presults$K <- exp(presults$RTLnK/(8.314*T));
    
    presults$dGt <- 16500-23.5*T;
 
    presults$P <- -(presults$dGt+8.314*T*log(presults$K))/(0.719*1000);
    # if NA -> "no Al4 in cpx!"
 
    return(data.frame(Name = presults$Name, T=Temp, P_calc = presults$P));
}
 
sensors.p.grt_cpx_beyer.args <- function() {
    ars <- list();
    ars$minerals = c('Grt','Cpx');
    ars$ranges = c('Temp');
    return(ars);
}
 
sensors.p.grt_cpx_beyer.test <- function() {
 
    grt = data.frame(Name='Grt', Fe_pfu=c(25), Mg_pfu=c(52), Ca_pfu=c(23));
    cpx = data.frame(Name='Cpx', Si_pfu=c(1.962), Al_pfu=c(0.244), Fe_p2_pfu=c(0.09), Mg_pfu=c(0.741), Ca_pfu=c(0.783), Na_pfu=c(0.171));
        
    ret = sensors.p.grt_cpx_beyer(grt, cpx, 1007, usePFU = TRUE);
    print(ret);
}