diagram: Chemical Activity Diagrams
In CHNOSZ: Thermodynamic Calculations and Diagrams for Geochemistry
diagram R Documentation
Chemical Activity Diagrams
Description
Plot equilibrium chemical activity (1-D speciation) or equal-activity (2-D predominance) diagrams as a function of chemical activities of basis species, temperature and/or pressure.
Usage
diagram(
# species affinities or activities
eout,
# type of plot
type = "auto", alpha = FALSE, normalize = FALSE,
as.residue = FALSE, balance = NULL, groups = as.list(1:length(eout$values)),
# figure size and sides for axis tick marks
xrange = NULL, mar = NULL, yline = par("mgp")[1]+0.3, side = 1:4,
# axis limits and labels
ylog = TRUE, xlim = NULL, ylim = NULL, xlab = NULL, ylab = NULL,
# character sizes
cex = par("cex"), cex.names = 1, cex.axis = par("cex"),
# line styles
lty = NULL, lty.cr = NULL, lty.aq = NULL, lwd = par("lwd"), dotted = NULL,
spline.method = NULL, contour.method = "edge", levels = NULL,
# colors
col = par("col"), col.names = par("col"), fill = NULL,
fill.NA = "gray80", limit.water = NULL,
# field and line labels
names = NULL, format.names = TRUE, bold = FALSE, italic = FALSE,
font = par("font"), family = par("family"), adj = 0.5,
dx = 0, dy = 0, srt = 0, min.area = 0,
# title and legend
main = NULL, legend.x = NA,
# plotting controls
add = FALSE, plot.it = TRUE, tplot = TRUE, ...)
find.tp(x)
Arguments
eout
list, object returned by affinity, equilibrate or related functions
type
character, type of plot, or name of basis species whose activity to plot
alpha
logical or character (‘balance’), for speciation diagrams, plot degree of formation instead of activities?
normalize
logical, divide chemical affinities by balance coefficients and rescale activities to whole formulas?
as.residue
logical, divide chemical affinities by balance coefficients (no rescaling)?
balance
character, balancing constraint; see equilibrate
groups
list of numeric, groups of species to consider as a single effective species
xrange
numeric, range of x-values between which predominance field boundaries are plotted
mar
numeric, margins of plot frame
yline
numeric, margin line on which to plot the y-axis name
side
numeric, which sides of plot to draw axes
xlim
numeric, limits of x-axis
ylim
numeric, limits of y-axis
xlab
character, label to use for x-axis
ylab
character, label to use for y-axis
ylog
logical, use a logarithmic y-axis (on 1D degree diagrams)?
cex
numeric, character expansion (scaling relative to current)
cex.names
numeric, character expansion factor to be used for names of species on plots
cex.axis
numeric, character expansion factor for names of axes
lty
numeric, line types to be used in plots
lty.cr
numeric, line types for cr-cr boundaries (between two minerals)
lty.aq
numeric, line types for aq-aq boundaries (between two aqueous species)
lwd
numeric, line width
dotted
numeric, how often to skip plotting points on predominance field boundaries (to gain the effect of dotted or dashed boundary lines)
spline.method
character, method used in splinefun
contour.method
character, labelling method used in contour (use NULL for no labels).
levels
numeric, levels at which to draw contour lines
col
character, color of activity lines (1D diagram) or predominance field boundaries (2D diagram)
col.names
character, colors for labels of species
fill
character, colors used to fill predominance fields
fill.NA
character, color for grid points with NA values
limit.water
NULL or logical, set NA values beyond water stability limits?
names
character, names of species for activity lines or predominance fields
format.names
logical, apply formatting to chemical formulas?
bold
logical, use bold formatting for names?
italic
logical, use italic formatting for names?
font
character, font type for names (has no effect if format.names is TRUE)
family
character, font family for names
adj
numeric, adjustment for line labels
dx
numeric, x offset for line or field labels
dy
numeric, y offset for line or field labels
srt
numeric, rotation for line labels
min.area
numeric, minimum area of fields that should be labeled, expressed as a fraction of the total plot area
main
character, a main title for the plot; NULL means to plot no title
legend.x
character, description of legend placement passed to legend
add
logical, add to current plot?
plot.it
logical, make a plot?
tplot
logical, set up plot with thermo.plot.new?
x
matrix, value of the predominant list element from diagram
...
additional arguments passed to plot or barplot
Details
This function displays diagrams representing either chemical affinities or equilibrium chemical activities of species.
The first argument is the output from affinity, rank.affinity, equilibrate, or solubility.
0-D diagrams, at a single point, are shown as barplots.
1-D diagrams, for a single variable on the x-axis, are plotted as lines.
2-D diagrams, for two variables, are plotted as predominance fields.
The allowed variables are any that affinity or the other functions accepts: temperature, pressure, or the chemical activities of the basis species.
A new plot is started unless add is TRUE.
If plot.it is FALSE, no plot will be generated but all the intermediate computations will be performed and the results returned.
Line or field labels use the names of the species as provided in eout; formatting is applied to chemical formulas (see expr.species) unless format.names is FALSE.
Set names to TRUE or NULL to plot the names, or FALSE, NA, or "" to prevent plotting the names, or a character argument to replace the default species names.
Alternatively, supply a numeric value to names to indicate a subset of default names that should or shouldn't be plotted (positive and negative indices, respectively).
Use col.names and cex.names to change the colors and size of the labels.
Use cex and cex.axis to adjust the overall character expansion factors (see par) and those of the axis labels.
The x- and y-axis labels are automatically generated unless they are supplied in xlab and ylab.
If groups is supplied, the activities of the species identified in each numeric element of this list are multiplied by the balance coefficients of the species, then summed together.
The names of the list are used to label the lines or fields for the summed activities of the resulting groups.
Normalizing protein formulas by length gives “residue equivalents” (Dick and Shock, 2011) that are useful for equilibrium calculations with proteins.
normalize and as.residue are only usable when eout is the output from affinity, and only one can be TRUE.
If normalize is TRUE, formation reactions and their affinities are first divided by protein length, so equal activities of residue equivalents are considered; then, the residue activities are rescaled to whole proteins for making the plot.
If as.residue is TRUE, no rescaling is performed, so the diagram represents activities of the residues, not the whole proteins.
type argument
This paragraph describes the effect of the type argument when the output from affinity is being used.
For type set to ‘auto’, and with 0 or 1 variables defined in affinity, the property computed by affinity for each species is plotted.
This is usually the affinity of the formation reactions, but can be set to some other property (using the property argument of affinity), such as the equilibrium constant (‘logK’).
For two variables, equilibrium predominance (maximum affinity) fields are plotted.
This “maximum affinity method” (Dick, 2019) uses balancing coefficients that are specified by the balance argument.
If type is ‘saturation’, the function plots the line for each species where the affinity of formation equals zero (see demo("saturation") for an example).
If for a given species no saturation line is possible or the range of the diagram does not include the saturation line, the function prints a message instead.
If type is the name of a basis species, then the equilibrium activity of the selected basis species in each of the formation reactions is plotted (see the \CO2-acetic acid example in buffer).
In the case of 2-D diagrams, both of these options use contour to draw the lines, with the method specified in contour.method.
This paragraph describes the effect of the type argument when the output from solubility is being used.
For one mineral or gas, if type set to ‘auto’, the equilibrium activities of each aqueous species are plotted.
If type is ‘loga.balance’, the activity of the balancing basis species (i.e. total solubility) is plotted; this is represented by contours on a 2-D diagram.
For two or more minerals or gases, if type set to ‘auto’, the values of ‘loga.balance’ (overall minimum solubility) are plotted.
If type is ‘loga.equil’, the solubilities of the individual minerals and gases are plotted.
For examples that use these features, see solubility and various demos: ‘DEW’, ‘contour’, ‘gold’, ‘solubility’, ‘sphalerite’.
1-D diagrams
For 1-D diagrams, the default setting for the y-axis is a logarithmic scale (unless alpha is TRUE) with limits corresponding to the range of logarithms of activities (or 0,1 if alpha is TRUE); these actions can be overridden by ylog and ylim.
If legend.x is NA (the default), the lines are labeled with the names of the species near the maximum value.
Otherwise, a legend is placed at the location identified by legend.x, or omitted if legend.x is NULL.
If alpha is TRUE, the fractional degrees of formation (ratios of activities to total activity) are plotted.
Or, setting alpha to ‘balance’ allows the activities to be multiplied by the number of the balancing component; this is useful for making “percent carbon” diagrams where the species differ in carbon number.
The line type and line width can be controlled with lty and lwd, respectively.
To connect the points with splines instead of lines, set spline.method to one of the methods in splinefun.
2-D diagrams
On 2-D diagrams, the fields represent the species with the highest equilibrium activity.
fill determines the color of the predominance fields, col that of the boundary lines.
The default of NULL for fill uses a light blue, light tan, and darker tan color for fields with aqueous species, one solid, or two solids.
These correspond to the web colors "aliceblue", "antiquewhite", and "burlywood" with some transparency added; see \viglinkmulti-metal for an example with two solids produced using mix.
If all the species in the diagram have the same state, or if the fill argument is NA or a 0-length value, the predominance fields are transparent, i.e. no fill color is used.
Otherwise, fill can be any colors, or the word ‘rainbow’, ‘heat’, ‘terrain’, ‘topo’, or ‘cm’, indicating a palette from grDevices.
Starting with R version 3.6.0, fill can be the name of any available HCL color palette, matched in the same way as the palette argument of hcl.colors.
fill.NA gives the color for empty fields, i.e. points at which NA values are present for any species.
This may occur when there are missing thermodynamic data or the temperature or pressure are not in the range of the equations of state.
To make overlay diagrams easier to construct, the default for fill.NA is automatically changed to ‘transparent’ when add is TRUE.
If limit.water is TRUE, the diagram is clipped to the the water stability region on Eh-pH (and some other) diagrams.
That is, predominance fields are shown only where water is stable, and fill.NA is used for areas where \H2O is not stable.
The default of NULL for limit.water does not clip the main diagram but instead overlays it on the water stability fields.
Change limit.water to FALSE to not show the water stability regions at all; this is automatically done if limit.water is missing and add is TRUE.
The default line-drawing algorithm uses contourLines to obtain smooth-looking diagonal and curved lines, at the expense of not coinciding exactly with the rectangular grid that is used for drawing colors.
lty, col, and lwd can be specified, but limiting the lines via xrange is not currently supported.
Set lty.cr or lty.aq to 0 to suppress boundary lines between minerals or aqueous species.
To go back to the old behavior for drawing lines, set dotted to ‘0’.
The old behavior does not respect lty; instead, the style of the boundary lines on 2-D diagrams can be altered by supplying one or more non-zero integers in dotted, which indicates the fraction of line segments to omit; a value of ‘1’ or NULL for dotted has the effect of not drawing the boundary lines.
Activity Coefficients
The wording in this page and names of variables in functions refer exclusively to ‘activities’ of aqueous species.
However, if activity coefficients are calculated (using the IS argument in affinity), then these variables are effectively transformed to molalities (see inst/tinytest/test-logmolality.R).
So that the labels on diagrams are adjusted accordingly, diagram sets the molality argument of axis.label to TRUE if IS was supplied as an argument to affinity.
The labeling as molality takes effect even if IS is set to 0; this way, by including (or not) the IS = 0 argument to affinity, the user decides whether to label aqueous species variables as molality (or activity) for calculations at zero ionic strength (where molality = activity).
Other Functions
find.tp finds the locations in a matrix of integers that are surrounded by the greatest number of different values.
The function counts the unique values in a 3x3 grid around each point and returns a matrix of indices (similar to which(..., arr.ind = TRUE)) for the maximum count (ties result in more than one pair of indices).
It can be used with the output from diagram for calculations in 2 dimensions to approximately locate the triple points on the diagram.
Value
diagram returns an invisible list containing, first, the contents of eout, i.e. the output of affinity or equilibrate supplied in the function call.
To this are added the names of the plotted variable in plotvar, the labels used for species (which may be plotmath expressions if format.names is TRUE) in names, and the values used for plotting in a list named plotvals.
For 1-D diagrams, plotvals usually corresponds to the chemical activities of the species (i.e. eout$loga.equil), or, if alpha is TRUE, their mole fractions (degrees of formation).
For 2-D diagrams, plotvals corresponds to the values of affinity (from eout$values) divided by the respective balancing coefficients for each species.
For 2-D diagrams, the output also contains the matrices predominant, which identifies the predominant species in eout$species at each grid point, and predominant.values, which has the affinities of the predominant species divided by the balancing coefficients (if eout is the output of affinity) or the activities of the predominant species (if eout is the output of equilibrate).
The rows and columns of these matrices correspond to the x and y variables, respectively.
References
Aksu, S. and Doyle, F. M. (2001) Electrochemistry of copper in aqueous glycine solutions. J. Electrochem. Soc. 148, B51–B57.
Dick, J. M. (2019) CHNOSZ: Thermodynamic calculations and diagrams for geochemistry. Front. Earth Sci. 7:180. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3389/feart.2019.00180")}
Dick, J. M. and Shock, E. L. (2011) Calculation of the relative chemical stabilities of proteins as a function of temperature and redox chemistry in a hot spring. PLOS One 6, e22782. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0022782")}
Helgeson, H. C. (1970) A chemical and thermodynamic model of ore deposition in hydrothermal systems. Mineral. Soc. Amer. Spec. Pap. 3, 155–186. https://www.worldcat.org/oclc/583263
Helgeson, H. C., Delany, J. M., Nesbitt, H. W. and Bird, D. K. (1978) Summary and critique of the thermodynamic properties of rock-forming minerals. Am. J. Sci. 278-A, 1–229. https://www.worldcat.org/oclc/13594862
LaRowe, D. E. and Helgeson, H. C. (2007) Quantifying the energetics of metabolic reactions in diverse biogeochemical systems: electron flow and ATP synthesis. Geobiology 5, 153–168. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1472-4669.2007.00099.x")}
Majzlan, J., Navrotsky, A., McClesky, R. B. and Alpers, C. N. (2006) Thermodynamic properties and crystal structure refinement of ferricopiapite, coquimbite, rhomboclase, and Fe\s2(SO\s4)\s3(H\s2O)\s5. Eur. J. Mineral. 18, 175–186. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1127/0935-1221/2006/0018-0175")}
Tagirov, B. and Schott, J. (2001) Aluminum speciation in crustal fluids revisited. Geochim. Cosmochim. Acta 65, 3965–3992. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0016-7037(01)00705-0")}
See Also
Berman, mix, mosaic, nonideal, solubility, and util.plot are other help topics that use diagram in their examples.
See the demos for even more examples.
Examples
## Calculate the equilibrium logarithm of activity of a
## basis species in different reactions
basis("CHNOS")
species(c("ethanol", "lactic acid", "deoxyribose", "ribose"))
a <- affinity(T = c(0, 150))
diagram(a, type = "O2", legend.x = "topleft", col = rev(rainbow(4)), lwd = 2)
title(main = "Equilibrium logfO2 for 1e-3 mol/kg of CO2 and ... ")
### 1-D diagrams: logarithms of activities
## Degrees of formation of ionized forms of glycine
## After Fig. 1 of Aksu and Doyle, 2001
basis("CHNOS+")
species(ispecies <- info(c("glycinium", "glycine", "glycinate")))
a <- affinity(pH = c(0, 14))
e <- equilibrate(a)
diagram(e, alpha = TRUE, lwd = 1)
title(main = paste("Degrees of formation of aqueous glycine species\n",
"after Aksu and Doyle, 2001"))
## Degrees of formation of ATP species as a function of
## temperature, after LaRowe and Helgeson, 2007, Fig. 10b
# to make a similar diagram, activity of Mg+2 here is set to
# 10^-4, which is different from LH07, who used 10^-3 total molality
basis(c("CO2", "NH3", "H2O", "H3PO4", "O2", "H+", "Mg+2"),
c(999, 999, 999, 999, 999, -5, -4))
species(c("HATP-3", "H2ATP-2", "MgATP-2", "MgHATP-"))
a <- affinity(T = c(0, 120, 25))
e <- equilibrate(a)
diagram(e, alpha = TRUE)
title(main = paste("Degrees of formation of ATP species,\n",
"pH=5, log(aMg+2)=-3. After LaRowe and Helgeson, 2007"),
cex.main = 0.9)
### 2-D diagrams: predominance diagrams
### These use the maximum affinity method
## Fe-S-O at 200 deg C, after Helgeson, 1970
basis(c("Fe", "oxygen", "S2"))
species(c("iron", "ferrous-oxide", "magnetite",
"hematite", "pyrite", "pyrrhotite"))
# The calculations include the polymorphic transitions of
# pyrrhotite; no additional step is needed
a <- affinity(S2 = c(-50, 0), O2 = c(-90, -10), T=200)
diagram(a, fill = "heat")
title(main = paste("Fe-S-O, 200 degrees C, 1 bar",
"After Helgeson, 1970", sep = "\n"))
## pe-pH diagram for hydrated iron sulfides,
## goethite and pyrite, after Majzlan et al., 2006
basis(c("Fe+2", "SO4-2", "H2O", "H+", "e-"),
c(0, log10(3), log10(0.75), 999, 999))
species(c("rhomboclase", "ferricopiapite", "hydronium jarosite",
"goethite", "melanterite", "pyrite"))
a <- affinity(pH = c(-1, 4, 256), pe = c(-5, 23, 256))
d <- diagram(a, main = "Fe-S-O-H, after Majzlan et al., 2006")
water.lines(d, lwd = 2)
text(3, 22, describe.basis(2:3, digits = 2, oneline = TRUE))
text(3, 21, describe.property(c("T", "P"), c(25, 1), oneline = TRUE))
## Aqueous Al species, after Tagirov and Schott, 2001
basis(c("Al+3", "F-", "H+", "O2", "H2O"))
AlOH <- c("Al(OH)4-", "Al(OH)3", "Al(OH)2+", "AlOH+2")
Al <- "Al+3"
AlF <- c("AlF+2", "AlF2+", "AlF3", "AlF4-")
AlOHF <- c("Al(OH)2F2-", "Al(OH)2F", "AlOHF2")
species(c(AlOH, Al, AlF, AlOHF), "aq")
res <- 300
a <- affinity(pH = c(0.5, 6.5, res), `F-` = c(-2, -9, res), T = 200)
diagram(a, fill = "terrain")
dprop <- describe.property(c("T", "P"), c(200, "Psat"))
legend("topright", legend = dprop, bty = "n")
mtitle(c("Aqueous aluminum species",
"After Tagirov and Schott, 2001 Fig. 4d"), cex = 0.95)
## Temperature-Pressure: kayanite-sillimanite-andalusite
# cf. Fig. 49 of Helgeson et al., 1978
# this is a system of one component (Al2SiO5), however:
# - number of basis species must be the same as of elements
# - avoid using H2O or other aqueous species because of
# T/P limits of the water() calculations;
basis(c("corundum", "quartz", "oxygen"))
species(c("kyanite", "sillimanite", "andalusite"))
# Database has transition temperatures of kyanite and andalusite
# at 1 bar only, so we permit calculation at higher temperatures
a <- affinity(T = c(200, 900, 99), P = c(0, 9000, 101), exceed.Ttr = TRUE)
d <- diagram(a, fill = NULL)
slab <- syslab(c("Al2O3", "SiO2", "H2O"))
mtitle(c(as.expression(slab), "after Helgeson et al., 1978"))
# Find the approximate position of the triple point
tp <- find.tp(d$predominant)
Ttp <- a$vals[[1]][tp[1, 2]]
Ptp <- rev(a$vals[[2]])[tp[1, 1]]
points(Ttp, Ptp, pch = 10, cex = 5)
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| diagram | R Documentation |
Chemical Activity Diagrams
Description
Plot equilibrium chemical activity (1-D speciation) or equal-activity (2-D predominance) diagrams as a function of chemical activities of basis species, temperature and/or pressure.
Usage
diagram(
# species affinities or activities
eout,
# type of plot
type = "auto", alpha = FALSE, normalize = FALSE,
as.residue = FALSE, balance = NULL, groups = as.list(1:length(eout$values)),
# figure size and sides for axis tick marks
xrange = NULL, mar = NULL, yline = par("mgp")[1]+0.3, side = 1:4,
# axis limits and labels
ylog = TRUE, xlim = NULL, ylim = NULL, xlab = NULL, ylab = NULL,
# character sizes
cex = par("cex"), cex.names = 1, cex.axis = par("cex"),
# line styles
lty = NULL, lty.cr = NULL, lty.aq = NULL, lwd = par("lwd"), dotted = NULL,
spline.method = NULL, contour.method = "edge", levels = NULL,
# colors
col = par("col"), col.names = par("col"), fill = NULL,
fill.NA = "gray80", limit.water = NULL,
# field and line labels
names = NULL, format.names = TRUE, bold = FALSE, italic = FALSE,
font = par("font"), family = par("family"), adj = 0.5,
dx = 0, dy = 0, srt = 0, min.area = 0,
# title and legend
main = NULL, legend.x = NA,
# plotting controls
add = FALSE, plot.it = TRUE, tplot = TRUE, ...)
find.tp(x)
Arguments
eout |
list, object returned by |
type |
character, type of plot, or name of basis species whose activity to plot |
alpha |
logical or character (‘balance’), for speciation diagrams, plot degree of formation instead of activities? |
normalize |
logical, divide chemical affinities by balance coefficients and rescale activities to whole formulas? |
as.residue |
logical, divide chemical affinities by balance coefficients (no rescaling)? |
balance |
character, balancing constraint; see |
groups |
list of numeric, groups of species to consider as a single effective species |
xrange |
numeric, range of x-values between which predominance field boundaries are plotted |
mar |
numeric, margins of plot frame |
yline |
numeric, margin line on which to plot the y-axis name |
side |
numeric, which sides of plot to draw axes |
xlim |
numeric, limits of x-axis |
ylim |
numeric, limits of y-axis |
xlab |
character, label to use for x-axis |
ylab |
character, label to use for y-axis |
ylog |
logical, use a logarithmic y-axis (on 1D degree diagrams)? |
cex |
numeric, character expansion (scaling relative to current) |
cex.names |
numeric, character expansion factor to be used for names of species on plots |
cex.axis |
numeric, character expansion factor for names of axes |
lty |
numeric, line types to be used in plots |
lty.cr |
numeric, line types for cr-cr boundaries (between two minerals) |
lty.aq |
numeric, line types for aq-aq boundaries (between two aqueous species) |
lwd |
numeric, line width |
dotted |
numeric, how often to skip plotting points on predominance field boundaries (to gain the effect of dotted or dashed boundary lines) |
spline.method |
character, method used in |
contour.method |
character, labelling method used in |
levels |
numeric, levels at which to draw contour lines |
col |
character, color of activity lines (1D diagram) or predominance field boundaries (2D diagram) |
col.names |
character, colors for labels of species |
fill |
character, colors used to fill predominance fields |
fill.NA |
character, color for grid points with NA values |
limit.water |
NULL or logical, set NA values beyond water stability limits? |
names |
character, names of species for activity lines or predominance fields |
format.names |
logical, apply formatting to chemical formulas? |
bold |
logical, use bold formatting for names? |
italic |
logical, use italic formatting for names? |
font |
character, font type for names (has no effect if |
family |
character, font family for names |
adj |
numeric, adjustment for line labels |
dx |
numeric, x offset for line or field labels |
dy |
numeric, y offset for line or field labels |
srt |
numeric, rotation for line labels |
min.area |
numeric, minimum area of fields that should be labeled, expressed as a fraction of the total plot area |
main |
character, a main |
legend.x |
character, description of legend placement passed to |
add |
logical, add to current plot? |
plot.it |
logical, make a plot? |
tplot |
logical, set up plot with |
x |
matrix, value of the |
... |
additional arguments passed to |
Details
This function displays diagrams representing either chemical affinities or equilibrium chemical activities of species.
The first argument is the output from affinity, rank.affinity, equilibrate, or solubility.
0-D diagrams, at a single point, are shown as barplots.
1-D diagrams, for a single variable on the x-axis, are plotted as lines.
2-D diagrams, for two variables, are plotted as predominance fields.
The allowed variables are any that affinity or the other functions accepts: temperature, pressure, or the chemical activities of the basis species.
A new plot is started unless add is TRUE.
If plot.it is FALSE, no plot will be generated but all the intermediate computations will be performed and the results returned.
Line or field labels use the names of the species as provided in eout; formatting is applied to chemical formulas (see expr.species) unless format.names is FALSE.
Set names to TRUE or NULL to plot the names, or FALSE, NA, or "" to prevent plotting the names, or a character argument to replace the default species names.
Alternatively, supply a numeric value to names to indicate a subset of default names that should or shouldn't be plotted (positive and negative indices, respectively).
Use col.names and cex.names to change the colors and size of the labels.
Use cex and cex.axis to adjust the overall character expansion factors (see par) and those of the axis labels.
The x- and y-axis labels are automatically generated unless they are supplied in xlab and ylab.
If groups is supplied, the activities of the species identified in each numeric element of this list are multiplied by the balance coefficients of the species, then summed together.
The names of the list are used to label the lines or fields for the summed activities of the resulting groups.
Normalizing protein formulas by length gives “residue equivalents” (Dick and Shock, 2011) that are useful for equilibrium calculations with proteins.
normalize and as.residue are only usable when eout is the output from affinity, and only one can be TRUE.
If normalize is TRUE, formation reactions and their affinities are first divided by protein length, so equal activities of residue equivalents are considered; then, the residue activities are rescaled to whole proteins for making the plot.
If as.residue is TRUE, no rescaling is performed, so the diagram represents activities of the residues, not the whole proteins.
type argument
This paragraph describes the effect of the type argument when the output from affinity is being used.
For type set to ‘auto’, and with 0 or 1 variables defined in affinity, the property computed by affinity for each species is plotted.
This is usually the affinity of the formation reactions, but can be set to some other property (using the property argument of affinity), such as the equilibrium constant (‘logK’).
For two variables, equilibrium predominance (maximum affinity) fields are plotted.
This “maximum affinity method” (Dick, 2019) uses balancing coefficients that are specified by the balance argument.
If type is ‘saturation’, the function plots the line for each species where the affinity of formation equals zero (see demo("saturation") for an example).
If for a given species no saturation line is possible or the range of the diagram does not include the saturation line, the function prints a message instead.
If type is the name of a basis species, then the equilibrium activity of the selected basis species in each of the formation reactions is plotted (see the \CO2-acetic acid example in buffer).
In the case of 2-D diagrams, both of these options use contour to draw the lines, with the method specified in contour.method.
This paragraph describes the effect of the type argument when the output from solubility is being used.
For one mineral or gas, if type set to ‘auto’, the equilibrium activities of each aqueous species are plotted.
If type is ‘loga.balance’, the activity of the balancing basis species (i.e. total solubility) is plotted; this is represented by contours on a 2-D diagram.
For two or more minerals or gases, if type set to ‘auto’, the values of ‘loga.balance’ (overall minimum solubility) are plotted.
If type is ‘loga.equil’, the solubilities of the individual minerals and gases are plotted.
For examples that use these features, see solubility and various demos: ‘DEW’, ‘contour’, ‘gold’, ‘solubility’, ‘sphalerite’.
1-D diagrams
For 1-D diagrams, the default setting for the y-axis is a logarithmic scale (unless alpha is TRUE) with limits corresponding to the range of logarithms of activities (or 0,1 if alpha is TRUE); these actions can be overridden by ylog and ylim.
If legend.x is NA (the default), the lines are labeled with the names of the species near the maximum value.
Otherwise, a legend is placed at the location identified by legend.x, or omitted if legend.x is NULL.
If alpha is TRUE, the fractional degrees of formation (ratios of activities to total activity) are plotted.
Or, setting alpha to ‘balance’ allows the activities to be multiplied by the number of the balancing component; this is useful for making “percent carbon” diagrams where the species differ in carbon number.
The line type and line width can be controlled with lty and lwd, respectively.
To connect the points with splines instead of lines, set spline.method to one of the methods in splinefun.
2-D diagrams
On 2-D diagrams, the fields represent the species with the highest equilibrium activity.
fill determines the color of the predominance fields, col that of the boundary lines.
The default of NULL for fill uses a light blue, light tan, and darker tan color for fields with aqueous species, one solid, or two solids.
These correspond to the web colors "aliceblue", "antiquewhite", and "burlywood" with some transparency added; see \viglinkmulti-metal for an example with two solids produced using mix.
If all the species in the diagram have the same state, or if the fill argument is NA or a 0-length value, the predominance fields are transparent, i.e. no fill color is used.
Otherwise, fill can be any colors, or the word ‘rainbow’, ‘heat’, ‘terrain’, ‘topo’, or ‘cm’, indicating a palette from grDevices.
Starting with R version 3.6.0, fill can be the name of any available HCL color palette, matched in the same way as the palette argument of hcl.colors.
fill.NA gives the color for empty fields, i.e. points at which NA values are present for any species.
This may occur when there are missing thermodynamic data or the temperature or pressure are not in the range of the equations of state.
To make overlay diagrams easier to construct, the default for fill.NA is automatically changed to ‘transparent’ when add is TRUE.
If limit.water is TRUE, the diagram is clipped to the the water stability region on Eh-pH (and some other) diagrams.
That is, predominance fields are shown only where water is stable, and fill.NA is used for areas where \H2O is not stable.
The default of NULL for limit.water does not clip the main diagram but instead overlays it on the water stability fields.
Change limit.water to FALSE to not show the water stability regions at all; this is automatically done if limit.water is missing and add is TRUE.
The default line-drawing algorithm uses contourLines to obtain smooth-looking diagonal and curved lines, at the expense of not coinciding exactly with the rectangular grid that is used for drawing colors.
lty, col, and lwd can be specified, but limiting the lines via xrange is not currently supported.
Set lty.cr or lty.aq to 0 to suppress boundary lines between minerals or aqueous species.
To go back to the old behavior for drawing lines, set dotted to ‘0’.
The old behavior does not respect lty; instead, the style of the boundary lines on 2-D diagrams can be altered by supplying one or more non-zero integers in dotted, which indicates the fraction of line segments to omit; a value of ‘1’ or NULL for dotted has the effect of not drawing the boundary lines.
Activity Coefficients
The wording in this page and names of variables in functions refer exclusively to ‘activities’ of aqueous species.
However, if activity coefficients are calculated (using the IS argument in affinity), then these variables are effectively transformed to molalities (see inst/tinytest/test-logmolality.R).
So that the labels on diagrams are adjusted accordingly, diagram sets the molality argument of axis.label to TRUE if IS was supplied as an argument to affinity.
The labeling as molality takes effect even if IS is set to 0; this way, by including (or not) the IS = 0 argument to affinity, the user decides whether to label aqueous species variables as molality (or activity) for calculations at zero ionic strength (where molality = activity).
Other Functions
find.tp finds the locations in a matrix of integers that are surrounded by the greatest number of different values.
The function counts the unique values in a 3x3 grid around each point and returns a matrix of indices (similar to which(..., arr.ind = TRUE)) for the maximum count (ties result in more than one pair of indices).
It can be used with the output from diagram for calculations in 2 dimensions to approximately locate the triple points on the diagram.
Value
diagram returns an invisible list containing, first, the contents of eout, i.e. the output of affinity or equilibrate supplied in the function call.
To this are added the names of the plotted variable in plotvar, the labels used for species (which may be plotmath expressions if format.names is TRUE) in names, and the values used for plotting in a list named plotvals.
For 1-D diagrams, plotvals usually corresponds to the chemical activities of the species (i.e. eout$loga.equil), or, if alpha is TRUE, their mole fractions (degrees of formation).
For 2-D diagrams, plotvals corresponds to the values of affinity (from eout$values) divided by the respective balancing coefficients for each species.
For 2-D diagrams, the output also contains the matrices predominant, which identifies the predominant species in eout$species at each grid point, and predominant.values, which has the affinities of the predominant species divided by the balancing coefficients (if eout is the output of affinity) or the activities of the predominant species (if eout is the output of equilibrate).
The rows and columns of these matrices correspond to the x and y variables, respectively.
References
Aksu, S. and Doyle, F. M. (2001) Electrochemistry of copper in aqueous glycine solutions. J. Electrochem. Soc. 148, B51–B57.
Dick, J. M. (2019) CHNOSZ: Thermodynamic calculations and diagrams for geochemistry. Front. Earth Sci. 7:180. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3389/feart.2019.00180")}
Dick, J. M. and Shock, E. L. (2011) Calculation of the relative chemical stabilities of proteins as a function of temperature and redox chemistry in a hot spring. PLOS One 6, e22782. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0022782")}
Helgeson, H. C. (1970) A chemical and thermodynamic model of ore deposition in hydrothermal systems. Mineral. Soc. Amer. Spec. Pap. 3, 155–186. https://www.worldcat.org/oclc/583263
Helgeson, H. C., Delany, J. M., Nesbitt, H. W. and Bird, D. K. (1978) Summary and critique of the thermodynamic properties of rock-forming minerals. Am. J. Sci. 278-A, 1–229. https://www.worldcat.org/oclc/13594862
LaRowe, D. E. and Helgeson, H. C. (2007) Quantifying the energetics of metabolic reactions in diverse biogeochemical systems: electron flow and ATP synthesis. Geobiology 5, 153–168. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1472-4669.2007.00099.x")}
Majzlan, J., Navrotsky, A., McClesky, R. B. and Alpers, C. N. (2006) Thermodynamic properties and crystal structure refinement of ferricopiapite, coquimbite, rhomboclase, and Fe\s2(SO\s4)\s3(H\s2O)\s5. Eur. J. Mineral. 18, 175–186. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1127/0935-1221/2006/0018-0175")}
Tagirov, B. and Schott, J. (2001) Aluminum speciation in crustal fluids revisited. Geochim. Cosmochim. Acta 65, 3965–3992. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0016-7037(01)00705-0")}
See Also
Berman, mix, mosaic, nonideal, solubility, and util.plot are other help topics that use diagram in their examples.
See the demos for even more examples.
Examples
## Calculate the equilibrium logarithm of activity of a
## basis species in different reactions
basis("CHNOS")
species(c("ethanol", "lactic acid", "deoxyribose", "ribose"))
a <- affinity(T = c(0, 150))
diagram(a, type = "O2", legend.x = "topleft", col = rev(rainbow(4)), lwd = 2)
title(main = "Equilibrium logfO2 for 1e-3 mol/kg of CO2 and ... ")
### 1-D diagrams: logarithms of activities
## Degrees of formation of ionized forms of glycine
## After Fig. 1 of Aksu and Doyle, 2001
basis("CHNOS+")
species(ispecies <- info(c("glycinium", "glycine", "glycinate")))
a <- affinity(pH = c(0, 14))
e <- equilibrate(a)
diagram(e, alpha = TRUE, lwd = 1)
title(main = paste("Degrees of formation of aqueous glycine species\n",
"after Aksu and Doyle, 2001"))
## Degrees of formation of ATP species as a function of
## temperature, after LaRowe and Helgeson, 2007, Fig. 10b
# to make a similar diagram, activity of Mg+2 here is set to
# 10^-4, which is different from LH07, who used 10^-3 total molality
basis(c("CO2", "NH3", "H2O", "H3PO4", "O2", "H+", "Mg+2"),
c(999, 999, 999, 999, 999, -5, -4))
species(c("HATP-3", "H2ATP-2", "MgATP-2", "MgHATP-"))
a <- affinity(T = c(0, 120, 25))
e <- equilibrate(a)
diagram(e, alpha = TRUE)
title(main = paste("Degrees of formation of ATP species,\n",
"pH=5, log(aMg+2)=-3. After LaRowe and Helgeson, 2007"),
cex.main = 0.9)
### 2-D diagrams: predominance diagrams
### These use the maximum affinity method
## Fe-S-O at 200 deg C, after Helgeson, 1970
basis(c("Fe", "oxygen", "S2"))
species(c("iron", "ferrous-oxide", "magnetite",
"hematite", "pyrite", "pyrrhotite"))
# The calculations include the polymorphic transitions of
# pyrrhotite; no additional step is needed
a <- affinity(S2 = c(-50, 0), O2 = c(-90, -10), T=200)
diagram(a, fill = "heat")
title(main = paste("Fe-S-O, 200 degrees C, 1 bar",
"After Helgeson, 1970", sep = "\n"))
## pe-pH diagram for hydrated iron sulfides,
## goethite and pyrite, after Majzlan et al., 2006
basis(c("Fe+2", "SO4-2", "H2O", "H+", "e-"),
c(0, log10(3), log10(0.75), 999, 999))
species(c("rhomboclase", "ferricopiapite", "hydronium jarosite",
"goethite", "melanterite", "pyrite"))
a <- affinity(pH = c(-1, 4, 256), pe = c(-5, 23, 256))
d <- diagram(a, main = "Fe-S-O-H, after Majzlan et al., 2006")
water.lines(d, lwd = 2)
text(3, 22, describe.basis(2:3, digits = 2, oneline = TRUE))
text(3, 21, describe.property(c("T", "P"), c(25, 1), oneline = TRUE))
## Aqueous Al species, after Tagirov and Schott, 2001
basis(c("Al+3", "F-", "H+", "O2", "H2O"))
AlOH <- c("Al(OH)4-", "Al(OH)3", "Al(OH)2+", "AlOH+2")
Al <- "Al+3"
AlF <- c("AlF+2", "AlF2+", "AlF3", "AlF4-")
AlOHF <- c("Al(OH)2F2-", "Al(OH)2F", "AlOHF2")
species(c(AlOH, Al, AlF, AlOHF), "aq")
res <- 300
a <- affinity(pH = c(0.5, 6.5, res), `F-` = c(-2, -9, res), T = 200)
diagram(a, fill = "terrain")
dprop <- describe.property(c("T", "P"), c(200, "Psat"))
legend("topright", legend = dprop, bty = "n")
mtitle(c("Aqueous aluminum species",
"After Tagirov and Schott, 2001 Fig. 4d"), cex = 0.95)
## Temperature-Pressure: kayanite-sillimanite-andalusite
# cf. Fig. 49 of Helgeson et al., 1978
# this is a system of one component (Al2SiO5), however:
# - number of basis species must be the same as of elements
# - avoid using H2O or other aqueous species because of
# T/P limits of the water() calculations;
basis(c("corundum", "quartz", "oxygen"))
species(c("kyanite", "sillimanite", "andalusite"))
# Database has transition temperatures of kyanite and andalusite
# at 1 bar only, so we permit calculation at higher temperatures
a <- affinity(T = c(200, 900, 99), P = c(0, 9000, 101), exceed.Ttr = TRUE)
d <- diagram(a, fill = NULL)
slab <- syslab(c("Al2O3", "SiO2", "H2O"))
mtitle(c(as.expression(slab), "after Helgeson et al., 1978"))
# Find the approximate position of the triple point
tp <- find.tp(d$predominant)
Ttp <- a$vals[[1]][tp[1, 2]]
Ptp <- rev(a$vals[[2]])[tp[1, 1]]
points(Ttp, Ptp, pch = 10, cex = 5)
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