CHNOSZ FAQ

How is ‘CHNOSZ’ pronounced?

As one syllable that starts with an sh sound and rhymes with Oz. CHNOSZ and schnoz are homophones.

Added on 2023-05-22.

How should CHNOSZ be cited?

• This paper is the general reference for CHNOSZ: Dick (2019).
• This paper describes diagrams with multiple metals: Dick (2021).
• This paper describes metastable equilibrium calculations for proteins: Dick (2008).
• The OBIGT thermodynamic database represents the work of many researchers. If you publish results that depend on any of these data, please cite the primary sources. Use info() to show the reference keys for particular species and thermo.refs() to list the bibliographic details. The following example shows the sources of data for aqueous alanine:

info(info("alanine"))[c("ref1", "ref2")]

##       ref1    ref2
## 1739 AH97b DLH06.1

thermo.refs(info("alanine"))

##         key                                      author year
## 72    AH97b              J. P. Amend and H. C. Helgeson 1997
## 154 DLH06.1 J. M. Dick, D. E. LaRowe and H. C. Helgeson 2006
##                                        citation                       note
## 72  J. Chem. Soc., Faraday Trans. 93, 1927-1941            amino acids GHS
## 154                   Biogeosciences 3, 311-336 amino acids HKF parameters
##                                       URL
## 72       https://doi.org/10.1039/A608126F
## 154 https://doi.org/10.5194/bg-3-311-2006

• Mineral data in OBIGT are based on Berman (1988) together with sulfides and other non-conflicting minerals from Helgeson et al. (1978). For a reaction such as the pyrite-pyrrhotite-magnetite (PPM) oxygen fugacity buffer, all the sources of data can be listed as follows:

basis(c("pyrite", "pyrrhotite", "oxygen"))

##      Fe O S ispecies logact state
## FeS2  1 0 2     2160      0    cr
## FeS   1 0 1     2161      0    cr
## O2    0 2 0     2762      0   gas

sres <- subcrt("magnetite", 1)
info(sres$reaction$ispecies)[, 1:6]

##            name abbrv formula state   ref1   ref2
## 2058  magnetite   Mag   Fe3O4    cr  Ber88   <NA>
## 2160     pyrite    Py    FeS2    cr HDNB78 RH95.7
## 2161 pyrrhotite    Po     FeS    cr HDNB78   <NA>
## 2762     oxygen    O2      O2   gas WEP+82  Kel60

thermo.refs(sres)

##       key                              author year
## 24  Ber88                        R. G. Berman 1988
## 8  HDNB78 H. C. Helgeson, J. M. Delany et al. 1978
## 15 WEP+82    D. D. Wagman, W. H. Evans et al. 1982
## 68 RH95.7     R. A. Robie and B. S. Hemingway 1995
## 1   Kel60                        K. K. Kelley 1960
##                                        citation                  note
## 24                       J. Petrol. 29, 445-522              minerals
## 8                       Am. J. Sci. 278A, 1-229              minerals
## 15 J. Phys. Chem. Ref. Data 11, Suppl. 2, 1-392             gases GHS
## 68           U. S. Geological Survey Bull. 2131 phase stability limit
## 1               U. S. Bureau of Mines Bull. 584              gases Cp
##                                            URL
## 24  https://doi.org/10.1093/petrology/29.2.445
## 8       https://www.worldcat.org/oclc/13594862
## 15 https://srd.nist.gov/JPCRD/jpcrdS2Vol11.pdf
## 68               https://doi.org/10.3133/b2131
## 1      https://www.worldcat.org/oclc/693388901

reset()

• Additional minerals from Helgeson et al. (1978), that were available in SUPCRT92 but may conflict with the Berman (1988) compilation, can be loaded from an optional database with add.OBIGT("SUPCRT92"). When using these data, it is appropriate to cite Helgeson et al. (1978) rather than SUPCRT92.

Added on 2023-05-27; PPM example added on 2023-11-15.

What thermodynamic models are used in CHNOSZ?

• The thermodynamic properties of liquid water are calculated using Fortran code from SUPCRT92 (Johnson et al., 1992) or optionally an implementation in R of the IAPWS-95 formulation (Wagner and Pruß, 2002).
• Thermodynamic properties of other species are taken from a database for minerals and inorganic and organic aqueous species including biomolecules, or from amino acid group additivity for proteins (Dick et al., 2006).
• The corresponding high-temperature properties are calculated using the Berman and Brown (1985) equations for minerals and the revised (Tanger and Helgeson, 1988; Shock and Helgeson, 1988) Helgeson-Kirkham-Flowers (Helgeson et al., 1981) equations for aqueous species.
• The revised HKF equations are augmented with the Deep Earth Water (DEW) model (Sverjensky et al., 2014) and estimates of parameters in the extended Debye-Hückel equation (Manning et al., 2013) to calculate standard-state properties and activity coefficients for given ionic strength at high pressure (to 6 GPa).
• Activity coefficients are implemented via adjusted standard Gibbs energies at specified ionic strength (Alberty, 1996), which converts all activity variables in the workflow to molalities.
• A related adjustment is available to convert standard Gibbs energies for gases from the 1 bar standard state used in SUPCRT92 to a variable-pressure standard state (Anderson and Crerar, 1993: Ch.12).

Added to https://chnosz.net/ website on 2018-11-13; moved to FAQ on 2023-05-27; added references for revised HKF on 2023-11-17.

When and why do equal-activity boundaries depend on total activity?

Short answer: When the species have the same number of the conserved element (let’s take C for example), their activities are raised to the same exponent in reaction quotient, so the activity ratio in the law of mass action becomes unity. But when the species have different numbers of the conserved element (for example, propanoate with 3 C and bicarbonate with 1 C), their activities are raised to different exponents, and the activity ratio does not become unity even when the activities are equal (except for the specific case where the activities themselves are equal to 1). Therefore, in general, the condition of “equal activity” is not sufficient to define boundaries on a relative stability diagram; instead, we need to say “activity of each species equal to x” or alternatively “total activity equal to y”.

Long answer: First, consider a reaction between formate and bicarbonate: HCO₂⁻ + 0.5 O₂ ⇌ HCO₃⁻. The law of mass action (LMA) is log K = log (a_HCO3⁻ / a_HCO2⁻) − 0.5 log f_O2. The condition of equal activity is a_HCO2⁻ = a_HCO3⁻. Then, the LMA simplifies to log K = − 0.5 log f_O2. The total activity of C is given by C_tot = a_HCO2⁻ + a_HCO3⁻. According to the LMA, log f_O2 is a function only of log K, so dlog f_O2/dlog C_tot = 0. In other words, the position of the equal-activity boundary is independent of the value of C_tot.

Next, consider a reaction between propanoate and bicarbonate: C₃H₅O₂⁻ + ⁷⁄₂ O₂ ⇌ 3 HCO₃⁻ + 2 H⁺. The LMA is log K = log (a³_HCO3⁻ / a_C3H5O2⁻) − pH − ⁷⁄₂ log f_O2. The condition of equal activity is a_C3H5O2⁻ = a_HCO3⁻. Then, the LMA simplifies to log K = log a²_HCO3⁻ − pH − ⁷⁄₂ log f_O2. The total activity of C is given by C_tot = 3 a_C3H5O2⁻ + a_HCO3⁻; combined with the condition of equal activity, this gives C_tot = 4 a_HCO3⁻. Substituting this into the LMA gives log K = log (C_tot / 4)² − pH − ⁷⁄₂ log f_O2, which can be rearranged to write log f_O2 = ²⁄₇ (2 log C_tot − log K − log 16 − pH). It follows that dlog f_O2/dlog C_tot = ⁴⁄₇, and the position of the equal-activity boundary depends on C_tot.

According to this analysis, increasing C_tot from 0.03 to 3 molal (a 2 log-unit increase) would have no effect on the location of the formate-bicarbonate equal-activity boundary, but would raise the propanoate-bicarbonate equal-activity boundary by ⁸⁄₇ units on the log f_O2 scale. Because the reaction between bicarbonate and CO₂ does not involve O₂ (but rather H₂O and H⁺), the same effect should occur on the propanoate-CO₂ equal-activity boundary. The plots below, which are made using equilibrate() for species in the Deep Earth Water (DEW) model, illustrate this effect.

### Based on demo/DEW.R in CHNOSZ

# Set up subplots
par(mfrow = c(1, 2), mar = c(3.0, 3.5, 2.5, 1.0), mgp = c(1.7, 0.3, 0), las = 1, tcl = 0.3, xaxs = "i", yaxs = "i")

# Activate DEW model
water("DEW")

###########
## logfO2-pH diagram for aqueous inorganic and organic carbon species at high pressure
## After Figure 1b of Sverjensky et al., 2014b [SSH14]
## (Nature Geoscience, https://doi.org/10.1038/NGEO2291)
###########

# Define system
basis("CHNOS+")
inorganic <- c("CO2", "HCO3-", "CO3-2", "CH4")
organic <- c("formic acid", "formate", "acetic acid", "acetate", "propanoic acid", "propanoate")
species(c(inorganic, organic), 0)
fill <- c(rep("aliceblue", length(inorganic)), rep("aquamarine", length(organic)))

# A function to make the diagrams
dfun <- function(T = 600, P = 50000, res = 200, Ctot = 0.03) {
  a <- affinity(pH = c(0, 10, res), O2 = c(-24, -12, res), T = T, P = P)
  # Set total C concentration to 0.03 molal
  # (from EQ3NR model for eclogite [Supporting Information of SSH14])
  e <- equilibrate(a, loga.balance = log10(Ctot))
  diagram(e, fill = fill)
  dp <- describe.property(c("     T", "     P"), c(T, P), digits = 0)
  legend("bottomleft", legend = dp, bty = "n")
}

water("DEW")
add.OBIGT("DEW")
dfun(Ctot = 0.03)
mtitle(c("Inorganic and organic species", "C[total] = 0.03 molal"))
dfun(Ctot = 3)
mtitle(c("Inorganic and organic species", "C[total] = 3 molal"))

# Restore default settings for the questions below
reset()

Added on 2023-05-17.

How can minerals with polymorphic transitions be added to the database?

The different crystal forms of a mineral are called polymorphs. Many minerals undergo polymorphic transitions upon heating. Each polymorph for a given mineral should have its own entry in OBIGT, including values of the standard thermodynamic properties (ΔG°_f, ΔH°_f, and S°) at 25 °C. The 25 °C (or 298.15 K) values for high-temperature polymorphs are often not listed in thermodynamic tables, but they can be calculated. This thermodynamic cycle shows how: we calculate the changes of a thermodyamic property (pictured here as DS1 and DS2) between 298.15 K and the transition temperature (Ttr) for two polymorphs, then combine those with the property of the polymorphic transition (DStr) to obtain the difference of the property between the polymorphs at 298.15 K (DS298).

               DStr              DStr: entropy of transition between polymorphs 1 and 2
      Ttr  o---------->o          Ttr: temperature of transition
           ^           |         
           |           |         
       DS1 |           | DS2      DS1: entropy change of polymorph 1 from 298.15 K to Ttr
           |           |          DS2: entropy change of polymorph 2 from 298.15 K to Ttr
           |           v
 298.15 K  o==========>o    DS298: entropy difference between polymorphs 1 and 2 at 298.15 K
               DS298        DS298 = DS1 + DStr - DS2
Polymorph  1           2

As an example, let’s add pyrrhotite (Fe0.877S) from Pankratz et al. (1987). The formula and thermodynamic properties of this pyrrhotite differ from those of FeS from Helgeson et al. (1978), which is already in OBIGT. We begin by defining all the input values in the next code block. In addition to G, H, S, and the heat capacity coefficients, non-NA values of volume (V) must be provided for the polymorph transitions to be calculated correctly by subcrt().

# The formula of the new mineral and literature reference
formula <- "Fe0.877S"
ref1 <- "PMW87"
# Because the properties from Pankratz et al. (1987) are listed in calories,
# we need to change the output of subcrt() to calories (the default is Joules)
E.units("cal")
# Use temperature in Kelvin for the calculations below
T.units("K")
# Thermodynamic properties of polymorph 1 at 25 °C (298.15 K)
G1 <- -25543
H1 <- -25200
S1 <- 14.531
Cp1 <- 11.922
# Heat capacity coefficients for polymorph 1
a1 <- 7.510
b1 <- 0.014798
# For volume, use the value from Helgeson et al. (1978)
V1 <- V2 <- 18.2
# Transition temperature
Ttr <- 598
# Transition enthalpy (cal/mol)
DHtr <- 95
# Heat capacity coefficients for polymorph 2
a2 <- -1.709
b2 <- 0.011746
c2 <- 3073400
# Maximum temperature of polymorph 2
T2 <- 1800

Use the temperature (Ttr) and enthalpy of transition (DHtr) to calculate the entropy of transition (DStr). Note that the Gibbs energy of transition (DGtr) is zero at Ttr.

DGtr <- 0  # DON'T CHANGE THIS
TDStr <- DHtr - DGtr  # TΔS° = ΔH° - ΔG°
DStr <- TDStr / Ttr

Start new database entries that include basic information, volume, and heat capacity coefficients for each polymorph. Pankratz et al. (1987) don’t list C_p° of the high-temperature polymorph extrapolated to 298.15 K, so leave it out. If the properties were in Joules, we would omit E_units = "cal" or change it to E_units = "J".

mod.OBIGT("pyrrhotite_new", formula = formula, state = "cr", ref1 = ref1,
  E_units = "cal", G = 0, H = 0, S = 0, V = V1, Cp = Cp1,
  a = a1, b = b1, c = 0, d = 0, e = 0, f = 0, lambda = 0, T = Ttr)
mod.OBIGT("pyrrhotite_new", formula = formula, state = "cr2", ref1 = ref1,
  E_units = "cal", G = 0, H = 0, S = 0, V = V2,
  a = a2, b = b2, c = c2, d = 0, e = 0, f = 0, lambda = 0, T = T2)

For the time being, we set G, H, and S (i.e., the properties at 25 °C) to zero in order to easily calculate the temperature integrals of the properties from 298.15 K to Ttr. Values of zero are placeholders that don’t satisfy ΔG°_f = ΔH°_f − TΔS°_f for either polymorph (the subscript f represents formation from the elements), as indicated by the following messages. We will check again for consistency of the thermodynamic parameters at the end of the example.

info(info("pyrrhotite_new", "cr"))

info(info("pyrrhotite_new", "cr2"))

In order to calculate the temperature integral of ΔG°_f, we need not only the heat capacity coefficients but also actual values of S°. Therefore, we start by calculating the entropy changes of each polymorph from 298.15 to 598 K (DS1 and DS2) and combining those with the entropy of transition to obtain the difference of entropy between the polymorphs at 298.15 K. For polymorph 1 (with state = "cr") it’s advisable to include use.polymorphs = FALSE to prevent subcrt() from trying to identify the most stable polymorph at the indicated temperature.

DS1 <- subcrt("pyrrhotite_new", "cr", P = 1, T = Ttr, use.polymorphs = FALSE)$out[[1]]$S
DS2 <- subcrt("pyrrhotite_new", "cr2", P = 1, T = Ttr)$out[[1]]$S
DS298 <- DS1 + DStr - DS2

Put the values of S° at 298.15 into OBIGT, then calculate the changes of all thermodynamic properties of each polymorph between 298.15 K and Ttr.

mod.OBIGT("pyrrhotite_new", state = "cr", S = S1)
mod.OBIGT("pyrrhotite_new", state = "cr2", S = S1 + DS298)
D1 <- subcrt("pyrrhotite_new", "cr", P = 1, T = Ttr, use.polymorphs = FALSE)$out[[1]]
D2 <- subcrt("pyrrhotite_new", "cr2", P = 1, T = Ttr)$out[[1]]

It’s a good idea to check that the entropy of transition is calculated correctly.

stopifnot(all.equal(D2$S - D1$S, DStr))

Now we’re ready to add up the contributions to ΔG°_f and ΔH°_f from the left, top, and right sides of the cycle. This gives us the differences between the polymorphs at 298.15 K, which we use to make the final changes to the database.

DG298 <- D1$G + DGtr - D2$G
DH298 <- D1$H + DHtr - D2$H
mod.OBIGT("pyrrhotite_new", state = "cr", G = G1, H = H1)
mod.OBIGT("pyrrhotite_new", state = "cr2", G = G1 + DG298, H = H1 + DH298)

It’s a good idea to check that the values of G, H, and S at 25 °C for a given polymorph are consistent with each other. Here we use check.GHS() to calculate the difference between the value given for G and the value calculated from H and S. The difference of less than 1 cal/mol can probably be attributed to small differences in the entropies of the elements used by Pankratz et al. (1987) and in CHNOSZ. We still get a message that the database value of C_p° at 25 °C for the high-temperature polymorph is NA; this is OK because the (extrapolated) value can be calculated from the heat capacity coefficients.

cr_parameters <- info(info("pyrrhotite_new", "cr"))
stopifnot(abs(check.GHS(cr_parameters)) < 1)
cr2_parameters <- info(info("pyrrhotite_new", "cr2"))

stopifnot(abs(check.GHS(cr2_parameters)) < 1)

For the curious, here are the parameter values:

cr_parameters

##                name abbrv  formula state  ref1 ref2 date model E_units      G
## 3571 pyrrhotite_new  <NA> Fe0.877S    cr PMW87 <NA> <NA>   CGL     cal -25543
##           H      S     Cp    V    a        b c d e f lambda   T
## 3571 -25200 14.531 11.922 18.2 7.51 0.014798 0 0 0 0      0 598

cr2_parameters

##                name abbrv  formula state  ref1 ref2 date model E_units
## 3572 pyrrhotite_new  <NA> Fe0.877S   cr2 PMW87 <NA> <NA>   CGL     cal
##              G        H        S       Cp    V      a        b       c d e f
## 3572 -25802.75 -27099.4 9.031592 36.36706 18.2 -1.709 0.011746 3073400 0 0 0
##      lambda    T
## 3572      0 1800

Finally, let’s look at the thermodynamic properties of the newly added pyrrhotite as a function of temperature around Ttr. Here, we use the feature of subcrt() that identifies the stable polymorph at each temperature. Note that ΔG°_f is a continuous function – visual confirmation that the parameters yield zero for DGtr – but ΔH°_f, S°, and C_p° are discontinuous at the transition temperature.

T <- seq(550, 650, 1)
sout <- subcrt("pyrrhotite_new", T = T, P = 1)$out[[1]]
par(mfrow = c(1, 4), mar = c(4, 4.2, 1, 1))
labels <- c(G = "DG0f", H = "DH0f", S = "S0", Cp = "Cp0")
for(property in c("G", "H", "S", "Cp")) {
  plot(sout$T, sout[, property], col = sout$polymorph,
    xlab = axis.label("T"), ylab = axis.label(labels[property])
  )
  abline(v = Ttr, lty = 3, col = 8)
  if(property == "G")
    legend("bottomleft", c("1", "2"), pch = 1, col = c(1, 2), title = "Polymorph")
}

# Restore default settings for the questions below
reset()

For additional polymorphs, we could repeat the above procedure using polymorph 2 as the starting point to calculate G, H, and S of polymorph 3, and so on.

Added on 2023-06-23.

How can I make a diagram with the trisulfur radical ion (S₃^-)?

A log f_O2–pH plot for aqueous sulfur species including S₃^- was first presented by Pokrovski and Dubrovinsky (2011). Later, Pokrovski and Dubessy (2015) reported parameters in the revised HKF equations of state for S₃^-, which are available in OBIGT.

The blocks of code are commented here:

1. Set temperature, pressure, and resolution.
2. Calculate molality of S from given weight percent [this is rather tedious and could be condensed to fewer lines of code].
   • Define the given weight percent (10 wt% S).
   • Calculate weight permil S.
   • Divide by molar mass to calculate moles of S in 1 kg of solution.
   • Calculate grams of H₂O in 1 kg of solution.
   • Calculate molality (moles of S per kg of H₂O, not kg of solution).
   • Calculate decimal logarithm of molality.
3. Define the basis species and formed species, calculate affinity, equilibrate activities, and make the diagram.
   • If we didn’t want to plot the buffer lines, we could just use basis(c("H2S", "H2O", "oxygen", "H+")).
   • Basis species with Fe, Si, and Ni are needed for the HM, QFM, and NNO buffers.
   • Note that “oxygen” matches O₂(gas), not O₂(aq), so the variable on the diagram is log f_O2.
4. Define Ni-NiO (NNO) buffer and plot buffer lines for HM, QFM, and NNO.
   • QFM (quartz-fayalite-magnetite) is also known as FMQ.
5. Calculate and plot pH of neutrality for water.
6. Add a legend and title.

## BLOCK 1
T <- 350
P <- 5000
res <- 200

## BLOCK 2
wt_percent_S <- 10
wt_permil_S <- wt_percent_S * 10
molar_mass_S <- mass("S") # 32.06
moles_S <- wt_permil_S / molar_mass_S
grams_H2O <- 1000 - wt_permil_S
molality_S <- 1000 * moles_S / grams_H2O
logm_S <- log10(molality_S)

## BLOCK 3
basis(c("Ni", "SiO2", "Fe2O3", "H2S", "H2O", "oxygen", "H+"))
species(c("H2S", "HS-", "SO2", "HSO4-", "SO4-2", "S3-"))
a <- affinity(pH = c(2, 10, res), O2 = c(-34, -22, res), T = T, P = P)
e <- equilibrate(a, loga.balance = logm_S)
diagram(e)

## BLOCK 4
mod.buffer("NNO", c("nickel", "bunsenite"), state = "cr", logact = 0)
for(buffer in c("HM", "QFM", "NNO")) {
  basis("O2", buffer)
  logfO2_ <- affinity(return.buffer = TRUE, T = T, P = P)$O2
  abline(h = logfO2_, lty = 3, col = 2)
  text(8.5, logfO2_, buffer, adj = c(0, 0), col = 2, cex = 0.9)
}

## BLOCK 5
pH <- subcrt(c("H2O", "H+", "OH-"), c(-1, 1, 1), T = T, P = P)$out$logK / -2
abline(v = pH, lty = 2, col = 4)

## BLOCK 6
lTP <- describe.property(c("T", "P"), c(T, P))
lS <- paste(wt_percent_S, "wt% S(aq)")
ltext <- c(lTP, lS)
legend("topright", ltext, bty = "n", bg = "transparent")
title(quote("Parameters for"~S[3]^"-"~"from Pokrovski and Dubessy (2015)"), xpd = NA)

species <- c("H2S", "SO4-2", "H+", "S3-", "oxygen", "H2O")
coeffs <- c(-2, -1, -1, 1, 0.75, 2.5)
(calclogK <- subcrt(species, coeffs, T = seq(300, 450, 50), P = 5000)$out$logK)

## [1] -16.669685 -14.013206 -11.686722  -9.622529

oldG <- info(info("S3-"))$G
newG <- oldG - 12548
mod.OBIGT("S3-", G = newG)
a <- affinity(pH = c(2, 10, res), O2 = c(-34, -22, res), T = T, P = P)
e <- equilibrate(a, loga.balance = logm_S)
diagram(e)
legend("topright", ltext, bty = "n", bg = "transparent")
title(quote("Modified"~log*italic(K)~"after Pokrovski and Dubrovinsky (2011)"), xpd = NA)
OBIGT()

T <- 700
P <- 10000 # 10000 bar = 1 GPa
oldwat <- water("DEW")
add.OBIGT("DEW")
info(species()$ispecies)[, 1:8]
##      name   abbrv formula state   ref1     ref2       date model
## 65    H2S  H2S(0)     H2S    aq  SHS89  DEW17.3 2017-09-26   DEW
## 22    HS-   HS(-)     HS-    aq SSWS97  DEW17.3 2017-09-26   DEW
## 73    SO2  SO2(0)     SO2    aq  SHS89 DEW17.38 2017-09-26   DEW
## 25  HSO4- HSO4(-)   HSO4-    aq SSWS97  DEW17.3 2017-09-26   DEW
## 24  SO4-2   SO4-2   SO4-2    aq   SH88     <NA> 1997-11-07   HKF
## 861   S3-   S3(-)     S3-    aq   PD15 DEW17.36 2017-09-26   DEW
a <- affinity(pH = c(2, 10, res), O2 = c(-18, -10, res), T = T, P = P)
e <- equilibrate(a, loga.balance = logm_S)
diagram(e)
lTP <- describe.property(c("T", "P"), c(T, P))
lS <- paste(wt_percent_S, "wt% S(aq)")
ltext <- c(lTP, lS)
legend("topright", ltext, bty = "n", bg = "transparent")
title(quote("Deep Earth Water (DEW)"~"model"))
water(oldwat)
OBIGT()

In OBIGT, what is the meaning of T for solids, liquids, and gases?

The value in this column can be one of the following:

1. The temperature of transition to the next polymorph of a mineral;
2. For the highest-temperature (or only) polymorph, if T is positive, it is the phase stability limit (i.e., the temperature of melting or decomposition of a solid or vaporization of a liquid);
3. For the highest-temperature polymorph, if T is negative, the opposite (positive) value is the T limit for validity of the C_p equation. (New feature in development version of CHNOSZ)

These cases are handled by subcrt() as follows. The units of T in OBIGT are Kelvin, but subcrt() by default uses °C:

1. For polymorphic transitions, the properties of specific polymorphs are returned:

subcrt("pyrrhotite", T = c(25, 150, 350), property = "G")$out

## $pyrrhotite
##     T          P         G polymorph
## 1  25   1.000000 -100767.5         1
## 2 150   4.757169 -109734.3         2
## 3 350 165.211289 -129984.5         3

Note: In both SUPCRT92 and OBIGT, tin, sulfur, and selenium are listed as minerals with one or more polymorphic transitions, but the highest-temperature polymorph actually represents the liquid state. Furthermore, quicksilver is listed as a mineral whose polymorphs actually correspond to the liquid and gaseous states.

2. For a phase stability limit, ΔG° is set to NA above the temperature limit:

subcrt("pyrite", T = seq(200, 1000, 200), P = 1)

## $species
##        name formula state ispecies model
## 2160 pyrite    FeS2    cr     2160   CGL
## 
## $out
## $out$pyrite
##      T P     logK         G          H         S     V       Cp
## 1  200 1 19.02722 -172355.1 -159662.59  84.11482 23.94 71.72282
## 2  400 1 14.89151 -191911.2 -144868.84 110.15205 23.94 75.71142
## 3  600 1 12.92264 -216018.0 -129487.09 130.14642 23.94 77.95838
## 4  800 1       NA        NA -113722.56 146.39738 23.94 79.62872
## 5 1000 1       NA        NA  -97651.55 160.12626 23.94 81.05409

This feature is intended to make it harder to obtain potentially unreliable results at temperatures where a mineral (or an organic solid or liquid) is not stable. If you want the extrapolated ΔG° above the listed phase stability limit, then add exceed.Ttr = TRUE to the function call to subcrt().

OBIGT has a non-exhaustive list of temperatures of melting, decomposition, or other phase change, some of which were taken from SUPCRT92 while others were taken from Robie and Hemingway (1995). These minerals are listed below:

file <- system.file("extdata/OBIGT/inorganic_cr.csv", package = "CHNOSZ")
dat <- read.csv(file)
# Reverse rows so highest-T polymorph for each mineral is listed first
dat <- dat[nrow(dat):1, ]
# Remove low-T polymorphs
dat <- dat[!duplicated(dat$name), ]
# Remove minerals with no T limit for phase stability (+ve) or Cp equation (-ve)
dat <- dat[!is.na(dat$z.T), ]
# Keep minerals with phase stability limit
dat <- dat[dat$z.T > 0, ]
# Get names of minerals and put into original order
rev(dat$name)
##  [1] "anhydrite"       "bunsenite"       "bromellite"      "chalcocite"     
##  [5] "chlorargyrite"   "cinnabar"        "copper"          "covellite"      
##  [9] "cuprite"         "galena"          "gold"            "halite"         
## [13] "iron"            "nickel"          "pyrite"          "pyrrhotite"     
## [17] "silver"          "sodium oxide"    "sphalerite"      "strontianite"   
## [21] "sylvite"         "cassiterite"     "uraninite"       "zincite"        
## [25] "sulfur"          "selenium"        "manganosite"     "wustite"        
## [29] "cobalt monoxide" "zinc"            "carrollite"      "rutherfordine"  
## [33] "beta-UO2(OH)2"   "Na2U2O7"

OBIGT now uses the decomposition temperature of covellite (780.5 K from Robie and Hemingway, 1995) in contrast to the previous Tmax from SUPCRT92 (1273 K, which is referenced to a equation described as “estimated” on p. 62 of Kelley, 1960). Selected organic solids and liquids have melting or vaporization temperatures listed as well. However, no melting temperatures are listed for minerals that use the Berman model.

3. For a C_p equation limit, extrapolated values of ΔG° are shown and a warning is produced:

add.OBIGT("SUPCRT92")
subcrt("muscovite", T = 850, P = 4500)

## $species
##           name             formula state ispecies model
## 2063 muscovite KAl2(AlSi3)O10(OH)2    cr     2063   CGL
## 
## $out
## $out$muscovite
##     T    P     logK        G        H        S      V       Cp
## 1 850 4500 280.7978 -6037836 -5533722 864.6487 140.71 523.7196

reset()

The warning is similar to that produced by SUPCRT92 (“CAUTION: BEYOND T LIMIT OF CP COEFFS FOR A MINERAL OR GAS”) at temperatures above maximum temperature of validity of the Maier-Kelley equation (Tmax). Notably, SUPCRT92 outputs ΔG° and other standard thermodynamic properties at temperatures higher than Tmax despite the warning.

This is a new feature in CHNOSZ version 2.1.0. In previous versions of CHNOSZ, values of ΔG° above the C_p equation limit were set to NA without a warning, as with the phase stability limit described above.

4. Finally, if T is NA or 0, then no upper temerature limit is imposed by subcrt().

Added on 2023-11-15.

How can mineral pH buffers be plotted?

Unlike mineral redox buffers, the K-feldspar–muscovite–quartz (KMQ) and muscovite–kaolinite (MC) pH buffers are known as “sliding scale” buffers because they do not determine pH but rather the activity ratio of K⁺ to H⁺ (Holm and Andersson, 2005). To add these buffers to a log f_O2–pH diagram in CHNOSZ, choose basis species that include Al⁺³ (the least mobile element, which the reactions are balanced on), quartz (this is needed for the KMQ buffer), the mobile ions K⁺ and H⁺, and the remaining elements in H₂O and O₂; oxygen denotes the gas in OBIGT. The formation reactions for these minerals don’t involve O₂, but it must be present so that the number of basis species equals the number of elements +1 (i.e. elements plus charge).

basis(c("Al+3", "quartz", "K+", "H+", "H2O", "oxygen"))

##      Al H K O Si Z ispecies logact state
## Al+3  1 0 0 0  0 3      741      0    aq
## SiO2  0 0 0 2  1 0     2073      0    cr
## K+    0 0 1 0  0 1        6      0    aq
## H+    0 1 0 0  0 1        3      0    aq
## H2O   0 2 0 1  0 0        1      0   liq
## O2    0 0 0 2  0 0     2762      0   gas

species(c("kaolinite", "muscovite", "K-feldspar"))

##   Al+3 SiO2 K+  H+ H2O O2 ispecies logact state       name
## 1    2    2  0  -6   5  0     2053      0    cr  kaolinite
## 2    3    3  1 -10   6  0     2063      0    cr  muscovite
## 3    1    3  1  -4   2  0     2067      0    cr K-feldspar

We could go right ahead and make a log f_O2–pH diagram, but the implied assumption would be that the K⁺ activity is unity, which may not be valid. Instead, we can obtain an independent estimate for K⁺ activity based on 1) the activity ratio of Na⁺ to K⁺ for the reaction between albite and K-feldspar and 2) charge balance among Na⁺, K⁺, and Cl^- for a given activity of the latter (Heinrich and Candela, 2014). Using the variables defined below, those conditions are expressed as K_AK = m_Na / m_K and m_Na + m_K = m_Cl, which combine to give m_K = m_Cl / (K_AK + 1). The reason for writing the equations with molality instead of activity is that ionic strength (IS) is provided in the arguments to subcrt(), so the function returns a value of log K adjusted for ionic strength. Furthermore, it is assumed that this is a chloride-dominated solution, so ionic strength is taken to be equal to the molality of Cl^-.

# Define temperature, pressure, and molality of Cl- (==IS)
T <- 150
P <- 500
IS <- m_Cl <- 1
# Calculate equilibrium constant for Ab-Kfs reaction, corrected for ionic strength
logK_AK <- subcrt(c("albite", "K+", "K-feldspar", "Na+"), c(-1, -1, 1, 1),
  T = T, P = P, IS = IS)$out$logK
K_AK <- 10 ^ logK_AK
# Calculate molality of K+
(m_K <- m_Cl / (K_AK + 1))

## [1] 0.07194125

This calculation gives a molality of K⁺ that is lower than unity and accordingly makes the buffers less acidic (Heinrich and Candela, 2014). Now we can apply the calculated molality of K⁺ to the basis species and add the buffer lines to the diagram. The IS argument is also used for affinity() so that activities are replaced by molalities (that is, affinity is calculated with standard Gibbs energies adjusted for ionic strength; this has the same effect as calculating activity coefficients).

basis("K+", log10(m_K))
a <- affinity(pH = c(2, 10), O2 = c(-55, -38), T = T, P = P, IS = IS)
diagram(a, srt = 90)
lTP <- as.expression(c(lT(T), lP(P)))
legend("topleft", legend = lTP, bty = "n", inset = c(-0.05, 0), cex = 0.9)
ltxt <- c(quote("Unit molality of Cl"^"-"), "Quartz saturation")
legend("topright", legend = ltxt, bty = "n", cex = 0.9)
title("Mineral data from Berman (1988)\nand Sverjensky et al. (1991) (OBIGT default)",
  font.main = 1, cex.main = 0.9)

The gray area, which is automatically drawn by diagram(), is below the reducing stability limit of water; that is, this area is where the equilibrium fugacity of H₂ exceeds unity. NOTE: Although the muscovite–kaolinite (MC) buffer was mentioned by Heinrich and Candela (2014) in the context of “clay-rich but feldspar-free sediments”, this example uses the feldspathic Ab–Kfs reaction for calculating K⁺ molality for both the KMQ and MC buffers. A more appropriate reaction to constrain the Na/K ratio with the MC buffer may be that between paragonite and muscovite (e.g., Yardley, 2005).

The diagram in Fig. 4 of Heinrich and Candela (2014) shows the buffer lines at somewhat higher pH values of ca. 5 and 6. Removing IS from the code moves the lines to lower rather than higher pH (not shown – try it yourself!), so the calculation of activity coefficients does not explain the differences. One possible reason for these differences is the use of different thermodynamic data for the minerals. The parameters for these minerals in the default OBIGT database come from Berman (1988) and Sverjensky et al. (1991).

thermo.refs(species()$ispecies)

##      key                                            author year
## 24 Ber88                                      R. G. Berman 1988
## 40 SHD91 D. A. Sverjensky, J. J. Hemley and W. M. D'Angelo 1991
##                                 citation
## 24                J. Petrol. 29, 445-522
## 40 Geochim. Cosmochim. Acta 55, 989-1004
##                                                 note
## 24                                          minerals
## 40 G and H revisions for K- and Al-bearing silicates
##                                             URL
## 24   https://doi.org/10.1093/petrology/29.2.445
## 40 https://doi.org/10.1016/0016-7037(89)90341-4

CHNOSZ doesn’t implement the thermodynamic model for minerals from Holland and Powell (1998), which is one of the sources cited by Heinrich and Candela (2014). If we use the thermodynamic parameters for minerals from Helgeson et al. (1978; these do not include the revisions for aluminosilicates described by Sverjensky et al., 1991), we get the lines shown in the second plot above, representing a larger stability field for muscovite. This moves the KMQ buffer closer to the value shown by Heinrich and Candela (2014), but the MC buffer further away, so this still doesn’t explain why we get a different result.

add.OBIGT("SUPCRT92")
a <- affinity(pH = c(2, 10), O2 = c(-55, -38), T = T, P = P, IS = IS)
diagram(a, srt = 90)
title("Mineral data from Helgeson et al. (1978)\n(as used in SUPCRT92)",
  font.main = 1, cex.main = 0.9)

Added on 2023-11-28.

Why are mineral stability boundaries curved on mosaic diagrams?

The reason they are curved has to do with mass balance of elements in aqueous solution. For example, take two reactions between pyrite (FeS₂) and pyrrhotite (FeS), one with H₂S and the other with HS^-:

1. FeS₂ + H₂O = FeS + 0.5 O₂ + H₂S
2. FeS₂ + H₂O = FeS + 0.5 O₂ + HS^- + H⁺

If a pH 4 solution at 150 °C has 0.001 mol/kg H₂S, then raising the pH to 8 would give 0.001 mol/kg of HS^- and essentially no H₂S. For the remainder of this discussion we will assume that mol/kg is equivalent to activity (i.e., that activity cofficients are unity). If we use the same value (0.001) for H₂S and HS^- in reactions 1 and 2 (the constant activity constraint), then we will get straight lines on a log f_O2–pH diagram. However, this is inconsistent with a constant sum constraint of activities that is sometimes attributed to these diagrams.

The constant activity constraint is compatible with the constant sum constraint only well inside the predominance field of a given aqueous species. The equivalence breaks down near the transitions between aqueous species. For instance, if the total activity of S is 0.001, then at the pK_a of H₂S (about 6.5 at 150 °C), the activities of H₂S and HS^- are equal to each other and by mass balance are both 0.0005. The position of the stability boundary should be calculated with these activities to satisfy the constant sum constraint.

The following code defines functions to calculate log f_O2 for these two reactions.

# Constants
a_S <- 0.001
T <- 150

# Get the pKa of H2S (note the minus sign!)
pKa_H2S <- - subcrt(c("H2S", "HS-", "H+"), c(-1, 1, 1), T = T)$out$logK

# Reaction 1 between pyrite and pyrrhotite with H2S
basis(c("pyrite", "H2S", "oxygen", "H2O", "H+"))
PyPo_H2S <- subcrt("pyrrhotite", 1, T = T)

# Reaction 1 law of mass action (LMA)
# logf_O2 = 2 logK_1 - 2 loga_H2S
logf_O2_1 <- function(loga_H2S) 2 * PyPo_H2S$out$logK - 2 * loga_H2S

# Reaction 2 between pyrite and pyrrhotite with HS-
basis(c("pyrite", "HS-", "oxygen", "H2O", "H+"))
PyPo_HS <- subcrt("pyrrhotite", 1, T = T)

# Reaction 2 LMA
# logf_O2 = 2 pH + 2 logK_2 - 2 loga_HS-
logf_O2_2 <- function(pH, loga_HS) 2 * pH + 2 * PyPo_HS$out$logK - 2 * loga_HS

# The logf_O2 for each reaction is the same at the pKa of H2S
stopifnot(all.equal(logf_O2_1(log10(a_S)), logf_O2_2(pKa_H2S, log10(a_S))))
stopifnot(all.equal(logf_O2_1(log10(a_S / 2)), logf_O2_2(pKa_H2S, log10(a_S / 2))))

At 150 °C and the pK_a of H₂S, we get log f_O2 = -54.68 for a_H2S = a_HS^- = 0.001 but log f_O2 = -54.08 for a_H2S + a_HS^- = 0.001. In other words, the constant activity and constant sum constraints produce different results; the former yields two straight lines while the latter yields a curve. This is shown graphically in the plots below.

par(mfrow = c(1, 2))

# Let's draw this out
thermo.plot.new(c(2, 10), c(-56, -46), xlab = "pH", ylab = axis.label("O2"))
lines(c(2, pKa_H2S), c(logf_O2_1(log10(a_S)), logf_O2_1(log10(a_S))), col = 2)
lines(c(pKa_H2S, 10), c(logf_O2_2(pKa_H2S, log10(a_S)), logf_O2_2(10, log10(a_S))), col = 4)
abline(v = pKa_H2S, lty = 2, col = 8)
text(6, -46.5, expr.species("H2S"), adj = c(0.5, 1))
text(7, -46.5, expr.species("HS-"), adj = c(0.5, 1))
text(4, -54, "pyrite")
text(4, -55.5, "pyrrhotite")
points(pKa_H2S, logf_O2_1(log10(a_S)), pch = 0)
points(pKa_H2S, logf_O2_1(log10(a_S / 2)), pch = 19)
legend("bottomright", c("Yes", "No"), pch = c(19, 0), title = as.expression(quote(sum(S) == "constant")), bty = "n")
legend("topleft", legend = lT(T), bty = "n")
title(quote("Straight lines for" ~ italic(a)[H[2]*S] ~ "=" ~ italic(a)[HS^"-"] == "0.001"), font.main = 1)

# Do it with mosaic()
basis(c("pyrite", "H2S", "oxygen", "H2O", "H+"))
# This sets the activity of H2S, which is used for total S when mosaic is called with blend = TRUE
basis("H2S", -3)
# This defines the basis species to swap through
bases <- c("H2S", "HS-")
species(c("pyrite", "pyrrhotite"))
m <- mosaic(bases, pH = c(2, 10, 500), O2 = c(-56, -46, 500), T = T)
diagram(m$A.species, dx = c(-1, -3), dy = c(-3, -1.5), col = 6)
abline(v = pKa_H2S, lty = 2, col = 8)
text(6, -46.5, expr.species("H2S"), adj = c(0.5, 1))
text(7, -46.5, expr.species("HS-"), adj = c(0.5, 1))
points(pKa_H2S, logf_O2_1(log10(a_S)), pch = 0)
points(pKa_H2S, logf_O2_1(log10(a_S / 2)), pch = 19)
legend("bottomright", c("Yes", "No"), pch = c(19, 0), title = as.expression(quote(sum(S) == "constant")), bty = "n")
legend("topleft", legend = lT(T), bty = "n")
title(quote("Curved line for" ~ italic(a)[H[2]*S] + italic(a)[HS^"-"] == "0.001"), font.main = 1)

The plot on the left is made “by hand” (using equilibrium constants calculated with subcrt()) while the plot on the right is made with the mosaic() and diagram() functions. The gray area is where water is unstable and is automatically added by diagram(). If you’d like to make a plot without curved lines (i.e., for constant activity instead of constant sum), then set blend = FALSE in mosaic().

There are relatively few published log f_O2–pH diagrams with curved mineral stability lines. An example of one is in Figure 5 of Cooke et al. (2000). The code below makes a diagram for the minerals shown in that figure:

basis(c("FeO", "SO4-2", "CO3-2", "H2O", "H+", "oxygen"))
basis("SO4-2", -3)
basis("CO3-2", -0.6)
species(c("hematite", "pyrite", "pyrrhotite", "magnetite", "siderite"))
bases <- list( c("SO4-2", "HSO4-", "HS-", "H2S"), c("CO3-2", "HCO3-", "CO2") )
m <- mosaic(bases, pH = c(0, 14, 500), O2 = c(-57, -35, 500), T = 150, IS = 0.77)
d <- diagram(m$A.species, fill = "terrain", dx = c(0, 0, 0, 0, 0.3))
water.lines(d)

This result suggests two improvements to Fig. 5A in Cooke et al. (2000). First, the triangular area above the water stability limit should be labeled as part of the siderite field (which is interrupted by the pyrite wedge), not as pyrrhotite. Second, the boundary between pyrite and magnetite has one kink, not two.

Added on 2024-04-01.