util.misc {CHNOSZ} | R Documentation |

## Functions for Miscellaneous Tasks

### Description

Calculate `dP/dT`

and temperature of polymorphic transitions; scale logarithms of activity to a desired total activity.

### Usage

```
dPdTtr(ispecies, ispecies2 = NULL)
Ttr(ispecies, ispecies2 = NULL, P = 1, dPdT = NULL)
GHS_Tr(ispecies, Htr)
unitize(logact = NULL, length = NULL, logact.tot = 0)
```

### Arguments

`ispecies` |
numeric, species index of a mineral phase |

`ispecies2` |
numeric, species index of next mineral phase (the default is ispecies + 1) |

`P` |
numeric, pressure (bar) |

`dPdT` |
numeric, values of ( |

`Htr` |
numeric, enthalpy(ies) of transition (cal/mol) |

`logact` |
numeric, logarithms of activity |

`length` |
numeric, numbers of residues |

`logact.tot` |
numeric, logarithm of total activity |

### Details

`dPdTtr`

returns values of `(dP/dT)_{Ttr}`

, where `Ttr`

represents the transition temperature, of the polymorphic transition at the high-`T`

stability limit of the `ispecies`

in `thermo()$OBIGT`

(other than checking that the names match, the function does not check that the species in fact represent different phases of the same mineral).
`dPdTtr`

takes account of the Clapeyron equation, `(dP/dT)_{Ttr}`

=`{\Delta}S/{\Delta}V`

, where `{\Delta}S`

and `{\Delta}V`

represent the changes in entropy and volume of polymorphic transition, and are calculated using `subcrt`

at Ttr from the standard molal entropies and volumes of the two phases involved.
Using values of `dPdT`

calculated using `dPdTtr`

or supplied in the arguments, `Ttr`

returns as a function of `P`

values of the upper transition temperature of the mineral phase represented by `ispecies`

.

`GHS_Tr`

can be used to calculate values of G, H, and S at Tr for the cr2, cr3, and cr4 phases in the database.
It combines the given `Htr`

(enthalpies of transition) with the database values of GHS @ Tr only for the phase that is stable at 298.15 K (cr) and the transition temperatures and Cp coefficients for higher-temperature phases, to calculate the GHS @ Tr (i.e. low-temperature metastable conditions) of the phases that are stable at higher temperatures.

`unitize`

scales the logarithms of activities given in `logact`

so that the logarithm of total activity of residues is equal to zero (i.e. total activity of residues is one), or to some other value set in `logact.tot`

.
`length`

indicates the number of residues in each species.
If `logact`

is NULL, the function takes the logarithms of activities from the current species definition.
If any of those species are proteins, the function gets their lengths using `protein.length`

.

### Examples

```
# We need the Helgeson et al., 1978 minerals for this example
add.OBIGT("SUPCRT92")
# That replaces the existing enstatite with the first phase;
# the other phases are appended to the end of thermo()$OBIGT
i1 <- info("enstatite")
i2 <- info("enstatite", "cr2")
i3 <- info("enstatite", "cr3")
# (dP/dT) of transitions
dPdTtr(i1, i2) # first transition
dPdTtr(i2, i3) # second transition
# Temperature of transitions (Ttr) as a function of P
Ttr(i1, i2, P = c(1,10,100,1000))
Ttr(i2, i3, P = c(1,10,100,1000))
# Restore default database
OBIGT()
# Calculate the GHS at Tr for the high-temperature phases of iron
# using transition enthalpies from the SUPCRT92 database (sprons92.dat)
Htr <- c(326.0, 215.0, 165.0)
iiron <- info("iron")
GHS_Tr(iiron, Htr)
# The results calculated above are stored in the database ...
info(1:3 + iiron)[, c("G", "H", "S")]
# ... meaning that we can recalculate the transition enthalpies using subcrt()
sapply(info(0:2 + iiron)$T, function(T) {
# A very small T increment around the transition temperature
T <- convert(c(T-0.01, T), "C")
# Use suppressMessages to make the output less crowded
sres <- suppressMessages(subcrt("iron", T = T, P = 1))
diff(sres$out$iron$H)
})
## Scale logarithms of activity
# Suppose we have two proteins whose lengths are 100 and
# 200; what are the logarithms of activity of the proteins
# that are equal to each other and that give a total
# activity of residues equal to unity?
logact <- c(-3, -3) # could be any two equal numbers
length <- c(100, 200)
logact.tot <- 0
loga <- unitize(logact, length, logact.tot)
# The proteins have equal activity
loga[1] == loga[2]
# The sum of activity of the residues is unity
all.equal(sum(10^loga * length), 1)
## What if the activity of protein 2 is ten times that of protein 1?
logact <- c(-3, -2)
loga <- unitize(logact, length, logact.tot)
# The proteins have unequal activity,
# but the activities of residues still add up to one
all.equal(loga[2] - loga[1], 1)
all.equal(sum(10^loga * length), 1)
```

*CHNOSZ*version 2.1.0 Index]