demo/lambda.R

In CHNOSZ: Thermodynamic Calculations and Diagrams for Geochemistry

# CHNOSZ/demo/lambda.R
# Plot effects of lambda transition in quartz
# After Berman 1988 Figs. 1 and 2
library(CHNOSZ)

opar <- par(no.readonly = TRUE)
layout(matrix(c(1, 4:2, 1, 7:5), nrow = 4), heights = c(0.7, 3, 3, 3))
# Plot title first
par(mar = c(0, 0, 0, 0))
plot.new()
text(0.5, 0.5, "Effects of lambda transition in quartz, after Berman (1988) Figs. 1 and 2", cex = 1.8)
par(mar = c(4, 4.5, 1, 0.5), cex = 0.8)

TC <- 0:1200
T <- convert(TC, "K")

labplot <- function(x) label.plot(x, xfrac = 0.9, yfrac = 0.1, paren = TRUE)
Cplab <- axis.label("Cp")
Vlab <- axis.label("V")
Tlab <- axis.label("T")

# Calculate properties at 1 kbar with and without transition
Qz_1bar <- Berman("quartz", T = T)
Qz_1bar_notrans <- Berman("quartz", T = T, calc.transition = FALSE)

## Fig. 1a: volume
plot(TC, Qz_1bar$V, type = "l", xlab = Tlab, ylab = Vlab, ylim = c(22.5, 24))
# FIXME: Why don't we get the curvature his plot for V shows?
# Should it be in the v4 parameter (but it's zero)??
## Add data points digitized from Fig. 3B of Helgeson et al., 1978
## and Fig. 1a of Berman, 1988
skinner <- list(T = c(550, 560, 570, 580, 590), V = c(23.44, 23.48, 23.54, 23.72, 23.72))
robie <- list(T = 575, V = 23.72)
ghioroso <- list(T = c(0, 100, 200, 300, 400, 500, 575, 575, 675, 775, 875, 975),
                 V = c(22.7, 22.77, 22.85, 22.94, 23.1, 23.3, 23.5, 23.71, 23.69, 23.69, 23.71, 23.73))
points(skinner$T, skinner$V, pch = 19)
points(robie$T, robie$V)
points(ghioroso$T, ghioroso$V, pch = 0)

## Calculate finite difference derivative of dGlambda/dP  =  Vlambda between 1 and 1.001 bar
Glambda_1bar <- Qz_1bar_notrans$G - Qz_1bar$G
Qz_1.001bar <- Berman("quartz", T = T, P = 1.001)
Qz_1.001bar_notrans <- Berman("quartz", T = T, P = 1.001, calc.transition = FALSE)
Glambda_1.001bar <- Qz_1.001bar_notrans$G - Qz_1.001bar$G
dGlambdadP <- (Glambda_1.001bar - Glambda_1bar) / 0.001
# We're using Joules, so multiply by ten to get cm^3
Vlambda <- -10 * dGlambdadP 
VQz <- Qz_1bar$V + Vlambda
# Above 848K, we have beta quartz
Qz_beta <- Berman("quartz,beta", T = T, P = 1)
VQz[T >=  848.15] <- Qz_beta$V[T >=  848.14]
lines(TC, VQz, lty = 2)
legend("topleft", legend = "1 bar", bty = "n")
labplot("a")

## Fig. 1b: heat capacity
plot(TC, Qz_1bar$Cp, type = "l", xlab = Tlab, ylab = Cplab)
lines(TC, Qz_1bar_notrans$Cp, lty = 3)
legend("topleft", legend = "1 bar", bty = "n")
labplot("b")

## Calculate properties at 10 kbar with and without transition
Qz_10bar <- Berman("quartz", T = T, P = 10000)
Qz_10bar_notrans <- Berman("quartz", T = T, P = 10000, calc.transition = FALSE)
## Fig. 1c: heat capacity
plot(TC, Qz_10bar$Cp, type = "l", xlab = Tlab, ylab = Cplab)
lines(TC, Qz_10bar_notrans$Cp, lty = 3)
legend("topleft", legend = "10 kb", bty = "n")
labplot("c")

# Like Ber88 Fig. 2
Tlambda <- 848 # Kelvin
dTdP <- 0.0237
Pkb <- seq(1, 50, 1)
P <- 1000 * Pkb
T <- Tlambda + dTdP * (P - 1)
Qz_withtrans <- Berman("quartz", T = T, P = P)
Qz_notrans <- Berman("quartz", T = T, P = P, calc.transition = FALSE)
Qz_lambda <- Qz_withtrans - Qz_notrans
Plab <- expression(list(italic(P), "kb"))
plot(Pkb, Qz_lambda$G, type = "l", ylim = c(-300, -50), ylab = axis.label("DlG"), xlab = Plab)
labplot("d")
plot(Pkb, Qz_lambda$H, type = "l", ylim = c(1200, 1800), ylab = axis.label("DlH"), xlab = Plab)
labplot("e")
plot(Pkb, Qz_lambda$S, type = "l", ylim = c(0, 3), ylab = axis.label("DlS"), xlab = Plab)
labplot("f")

reset()

layout(matrix(1))
par(opar)