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page last updated: 28.11.2011

Internally Consistent Dataset Documentation

The following text is taken from the thermocalc shortcourse notes and was written by Roger Powell in 2001.

In the application of equilibrium thermodynamics, we take the starting point to be what I call the “equilibrium relationship”: the relationship for a balanced chemical reaction between the end-members of phases that are in equilibrium with each other:

0=∆G0 +RT ln K                           (1)

in which ∆G0 is the Gibbs energy of the reaction between the pure end-members in the same structure as the phases in which they occur, K is the equilibrium constant, in terms of the activities of the end-members in their phases, T is temperature, and R is the gas constant.

Looking at (1), the first practical concern is where we get the numbers from to insert into ∆G0 for any particular reaction. There are actually two sides to this: the form that the Gibbs energies of pure end-members should have as a function of P and T, and what the numbers are. These two go hand-in-hand, and in the context of the internally-consistent dataset that thermocalc uses, the papers to read are:

Powell, R, and Holland, TJB, 1985. An internally consistent thermodynamic dataset with un­certainties and correlations : 1 : Methods and a worked example. Journal of Metamorphic Geology 3, 327–342.

Holland, TJB, and Powell, R, 1985. An internally consistent thermodynamic dataset with uncertainties and correlations : 2 : Data and results. Journal of Metamorphic Geology 3, 343–370.

Holland, TJB, and Powell, R, 1990. An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O-Na2O-CaO-MgO-MnO-FeO-Fe2O3-Al2O3-TiO2 -SiO2-C-H2-O2. Journal of Metamorphic Geology 8, 89–124.

Powell, R, and Holland, TJB, 1993. Is Least Squares an appropriate methodology to be used in the extraction of thermodynamic data from experimentally-bracketed mineral equilibria? American Mineralogist, 78, 107-112.

Holland, TJB, and Powell, R, 1998. An internally-consistent thermodynamic dataset for phases of petrological interest. Journal of Metamorphic Geology 16, 309–344.

How much of this you should read depends very much on how much you really think you need to know. If you are going to use thermocalc datafiles that we provide, there may be little point getting too involved. If, however, you want to fiddle with the data (via DQF) it is as well to have a clear understanding of the correlations within the data, and also what is assumed about activity-composition relationships in the data (as spelt out most clearly in the 1998 paper). If you are interested just in our philosophy of data extraction from experimental work, start with the 1993 paper. If you want to know more, having read the 1993 paper, continue with the 1998 paper, going to the earlier papers if there is something that you don’t understand otherwise.

A brief outline

Whereas there is no substitute for reading the papers, two paragraphs extracted from the papers bring out some of what we have developed and what we follow. From the introduction of the Holland and Powell (1998) paper:

"The thermodynamic data extraction involves using weighted least squares on the different types of data (calorimetric, phase equilibria, natural mineral partitioning) to determine enthalpies of formation of the end-members of the phases. Entropies, volumes, heat capacities, thermal expansions and compressibilities are not derived by regression, but are taken as known in this process. Other parameters intimately involved, for example regular solution parameters in exchange equilibria, are also taken as known, having been determined separately by pre-processing the data. The entropies of the end-members in the data set are not determined along with the enthalpies by regression because, in most circumstances, they are determined more reliably by estimation techniques (e.g. Holland, 1989) than by fitting to experimental brackets. Where appropriate, such estimated entropies have been adjusted, within their likely uncertainties, to improve agreement with the experiments. The regression involves determination of the enthalpies of 189 end-members using 319 reaction equilibria, 82 direct calorimetric constraints on the end-member enthalpies of formation at 298 K, and 30 constraints from enthalpies of reaction and high-temperature calorimetry. Thus the total number of degrees of freedom in the regression is 242 (319 + 82 + 30 − 189), and the value for σfit is 1.14."

The abstract of the Powell & Holland (1993) encapsulates the least squares philosophy that has been followed in dataset generation, written in the context of some criticisms in the literature of our approach to constraining thermodynamic data using experimental data:

"The applicability of least squares in the extraction of thermodynamic data from experimentally-bracketed mineral equilibria is considered primarily as a statistical (and logical) problem concerning the nature of the experimental data, and the nature of the information which is to be extracted. The former relates particularly to the bracketed nature of the data, the latter to the requirement that not only thermodynamic data, but also the uncertainties on, and the correlations between the data, are to be extracted. By examining the probability distributions, it is shown that the majority of experimental brackets are approximately Gaussian distributed, primarily because experimental brackets are not generally very wide compared with experimental uncertainties on the bracket ends. Thus, using least squares on all the experimental brackets would be apposite for the thermodynamic data extraction problem. However, rather than fitting all the experimental brackets, we fit composite data formed from the individual experimental brackets for each experimentally-determined reaction. It is shown that the use of composite data is equivalent to using all the brackets as long as the composite data are determined appropriately. The main reason for wishing to use composite data is that it allows the deleterious effect on the least squares caused by inconsistent brackets to be minimised. The uncertainties on very few of the composite data are large compared with the uncertainties on the ends of individual brackets. Therefore, least squares on composite data is appropriate for data extraction. Moreover much of the uncertainty on the extracted thermodynamic data comes from uncertainty on the position of the bracket ends rather than the width of the brackets themselves."

Tim Holland regularly (continuously) upgrades the dataset, and the version currently available (ds55) is one from Nov 22, 2003 with a σfit of 1.067, which is an updated version of the Holland & Powell (1998) dataset. RP wrote and maintains the lsqds software.

Endmember Abbreviations

endmember abbreviations: Ortho and Ring Silicates
Ortho- & Ring-silicates
fayalite fa
tephroite teph
larnite-bredigite lrn
monticellite mont
clinohumite chum
pyrope py
almandine alm
spessartine spss
grossular gr
andradite andr
osumilite(1) osm1
osumilite(2) osm2
Fe-osumilite fosm
vesuvianite vsv
andalusite and
kyanite ky
sillimanite sill
hydroxy-topaz tpz
Mg-staurolite mst
Fe-staurolite fst
Mn-staurolite mnst
Mg-chloritoid mctd
Fe-chloritoid fctd
Mn-chloritoid mnctd
merwinite merw
spurrite spu
zoisite zo
clinozoisite cz
Fe-epidote fep
epidote ep
lawsonite law
pumpellyite pump
akermanite ak
rankinite rnk
tilleyite ty
hydrous cordierite hcrd
Fe-cordierite fcrd
Mn-cordierite mncrd
phase A phA
sphene sph
zircon zrc

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endmember abbreviations: chain silicates
Chain Silicates
enstatite en
ferrosilite fs
Mg-Tschermak pyroxene mgts
diopside di
hedenbergite hed
jadeite jd
acmite acm
Ca-Tschermak pyroxene cats
rhodonite rhod
pyroxmangite pxmn
wollastonite wo
pseudowollastonite pswo
tremolite tr
ferroactinolite fact
tschermakite ts
pargasite parg
glaucophane gl
Fe-glaucophane fgl
riebeckite rieb
anthophyllite anth
Fe-anthophyllite fanth
cummingtonite cumm
grunerite grun
gedrite ged
sapphirine (442) spr4
sapphirine (793) spr7
Fe-sapphirine fspr
Mg-carpholite mcar
Fe-carpholite fcar
deerite deer

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endmember abbreviations: sheet silicates
Sheet Silicates
muscovite mu
celadonite cel
Fe-celadonite fcel
paragonite pa
margarite ma
phlogopite phl
annite ann
Mn-biotite mnbi
eastonite east
Na-phlogopite naph
clinochlore clin
amesite ames
Al-free chlorite afchl
daphnite daph
Mn-chlorite mnchl
sudoite sud
Fe-sudoite fsud
pyrophyllite prl
talc ta
Fe-talc fta
tschermak-talc tats
kaolinite kao
prehnite pre
chrysotile chr
antigorite atg

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endmember abbreviations: framework silicates
Framework Silicates
albite ab
high albite abh
microcline mic
sanidine san
anorthite an
quartz q
tridymite trd
cristobalite crst
coesite coe
stishovite stv
nepheline ne
kalsilite kals
leucite lc
meionite me
wairakite wrk
laumontite lmt
heulandite heu
stilbite stlb
analcite anl

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endmember abbreviations: oxides and hydroxides
Oxides nnd Hydroxides
lime lime
rutile ru
periclase per
manganosite mang
corundum cor
hematite hem
nickel oxide NiO
pyrophanite pnt
geikielite geik
ilmenite ilm
baddeleyite bdy
spinel sp
hercynite herc
magnetite mt
magnesioferrite mft
ulvospinel usp
brucite br
diaspore dsp
goethite gth

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endmember abbreviations: carbonates
calcite cc
aragonite arag
magnesite mag
siderite sid
rhodochrosite rhc
dolomite dol
ankerite ank

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endmember abbreviations: elements and gases
Elements and Gases
iron iron
nickel Ni
graphite gph
diamond diam
water fluid H2O
carbon dioxide CO2
carbon monoxide CO
methane CH4
oxygen O2
hydrogen H2

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endmember abbreviations: melt species
Melt Species
forsterite liquid foL
fayalite liquid faL
sillimanite liquid silL
anorthite liquid anL
H2O liquid h2oL
enstatite liquid enL
K-feldspar liquid kspL
Silica liquid qL
diopside liquid diL
albite liquid abL
Mg-pelitic liquid mliq
Fe-pelitic liquid fliq
H2O pelitic liquid hliq

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endmember abbreviations: aqueous species
Aqueous Species
hydrogen ion (aq) H+
chloride ion (aq) Cl-
hydroxyl ion (aq) OH-
sodium ion (aq) Na+
potassium ion (aq) K+
calcium ion (aq) Ca++
magnesium ion (aq) Mg++
ferrous ion (aq) Fe++
aluminium ion (aq) Al+++
carbonate ion (aq) CO3--
Al(OH)3° (aq) AlOH3
Al(OH)4- ion (aq) AlOH4-
KOH° (aq) KOH
HCl° (aq) HCl
KCl° (aq) KCl
NaCl° (aq) NaCl
CaCl2° (aq) CaCl2
CaCl+ ion (aq) CaCl+
MgCl2° (aq) MgCl2
MgCl+ ion (aq) MgCl+
FeCl2° (aq) FeCl2
aqueous silica aqSi

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