An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids

Introduction

The need for thermodynamic data of sufficient quality to make reliable calculations on rocks continues to grow, particularly to capitalize on new methods of application of phase equilibria that involve increasingly complex solid and fluid solutions, as well as on new advances in software.

The basic philosophy from our earlier summary (Holland & Powell, 1998; hereafter referred to as HP98) is maintained. 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. Where they are not known experimentally, they are estimated as outlined in our earlier papers. The new regression involves determination of the enthalpies of 254 end-members, of which 69 are new to the data set, with an overall fit in which is 1.09 ( being a goodness-of-fit parameter, identical to in geochronology that relates directly to the chi-squared test).

Major methodological changes from HP98 are embodied in this new data set, within the basic philosophy outlined above. They are documented below, along with minor ones that have arisen since HP98, some of which are incorporated in the currently used data set, tc-ds55.txt, from November 2003, but have not been documented properly before.

A list of the chemical compositions of the end-members considered in this study may be found in Table 1. The end-members are listed under the headings orthosilicates and ring silicates (garnet, olivine, etc.), chain silicates (pyroxene and pyroxenoid, amphibole, etc.), sheet silicates (mica, chlorite, etc.), framework silicates, oxides and hydroxides, carbonates, elements, high-pressure phases, gas species, melt species and aqueous species. The new data set itself is given in Table 2. Table 3 lists the calorimetric data used in the dataset generation. Appendix 1 gives the data sources for the thermodynamic properties, and Appendix 2 is a summary table of the experimental studies used in the data set regression. Appendix 3 provides information on minor changes since the publication of HP98. The table of all the experimentally determined mineral equilibrium brackets used in the least squares analysis and the calculated fit to them is presented in Table S1 as well as at http://www.esc.cam.ac.uk/people/academic-staff/tim-holland and http://www.metamorph.geo.uni-mainz.de/thermocalc/. This is in the form of full computer output from the data extraction program LSQDS. Table S2 contains the activity–composition relations that were used in the generation of the data set.

Table 1. The formulae and abbreviations of the end-members of the phases in the internally consistent data set. A bullet beside an abbreviated name indicates that it is a new end-member in the dataset.

Group	Abbreviation	End-member	Formula
Garnets & olivines	alm	almandine	Fe3Al2Si3O12
	andr	andradite	Ca3Fe2Si3O12
	gr	grossular	Ca3Al2Si3O12
	knor •	knorringite	Mg3Cr2Si3O12
	maj •	majorite	Mg4Si4O12
	py	pyrope	Mg3Al2Si3Ol2
	spss	spessartine	Mn3Al2Si3O12
	chum	clinohumite	Mg9Si4O16(OH)2
	fa	fayalite	Fe2SiO4
	fo	forsterite	Mg2SiO4
	lrn	larnite	Ca2SiO4
	mont	monticellite	CaMgSiO4
	teph	tephroite	Mn2SiO4
Aluminosilicates	and	andalusite	Al2SiO5
	ky	kyanite	Al2SiO5
	sill	sillimanite	Al2SiO5
	amul •	Al-mullite	Al2.5Si0.5O4.75
	smul •	Si-mullite	Al2SiO5
	fctd	Fe-chloritoid	FeAl2SiO5(OH)2
	mctd	Mg-chloritoid	MgAl2SiO5(OH)2
	mnctd	Mn-chloritoid	MnAl2SiO5(OH)2
	fst	Fe-staurolite	Fe 4Al18Si7.5O44(OH)4
	mst	Mg-staurolite	Mg4Al18Si7.5O44(OH)4
	mnst	Mn-staurolite	Mn4Al18Si7.5O44(OH)4
	tpz	hydroxy-topaz	Al2SiO4(OH)2
Other orthosilicates	ak	akermanite	Ca2MgSi2O7
	geh	gehlenite	Ca2Al2SiO7
	jgd •	julgoldite (FeFe)	Ca4Fe6Si6O21(OH)7
	merw	merwinite	Ca3MgSi2O8
	mpm	pumpellyite (MgAl)	Ca4MgAl5Si6O21(OH)7
	fpm	pumpellyite (FeAl)	Ca4FeAl5Si6O21(OH)7
	rnk	rankinite	Ca3Si2O7
	sph	sphene	CaTiSiO5
	spu	spurrite	Ca5Si2CO11
	ty	tilleyite	Ca5Si2C2O13
	zrc	zircon	ZrSiO4
Sorosilicates	cz	clinozoisite	Ca2Al3Si3O12(OH)
	ep	epidote(ordered)	Ca2FeAl2Si3O12(OH)
	fep	Fe-epidote	Ca2Fe2AlSi3O12(OH)
	law	lawsonite	CaAl2Si2O6(OH)4
	pmt •	piemontite (ordered)	Ca2MnAl2Si3Oi2(OH)
	zo	zoisite	Ca2Al3Si3O12(OH)
	vsv	vesuvianite	Ca19Mg2Al11Si18O69(OH)9
Cyclosilicates	crd	cordierite	Mg2Al4Si5O18
	hcrd	hydrous-cordierite	Mg2Al4Si5O17(OH)2
	fcrd	Fe-cordierite	Fe2Al4Si5O18
	mncrd	Mn-cordierite	Mn2Al4Si5O18
	osm1	osumilite (1)	KMg2Al5Si10O30
	osm2	osumilite (2)	KMg3Al3Si11O30
	fosm	Fe-osumilite	KFe2Al5Si10O30
High-P phases	apv •	Al-perovskite	AlAlO3
	cpv •	Ca-perovskite	CaSiO3
	cstn •	CaSi-titanite	CaSi2O5
	fak •	Fe-akimotoite	FeSiO3
	fpv •	Fe-perovskite	FeSiO3
	frw •	Fe-ringwoodite	Fe2SiO4
	fwd •	Fe-wadsleyite	Fe2SiO4
	mak •	akimotoite	MgSiO3
	mpv •	Mg-perovskite	MgSiO3
	mrw •	Mg-ringwoodite	Mg2SiO4
	mwd •	Mg-wadsleyite	Mg2SiO4
	phA	phaseA	Mg7Si2O8(OH)6
Pyroxenes & pyroxenoids	acm	acmite	NaFeSi2O6
	caes •	Ca-eskola pyroxene	Ca0.5AlSi2O6
	cats	Ca-tschermaks pyroxe	CaAl2SiO6
	cen •	clino enstatite	Mg2Si2O6
	di	diopside	CaMgSi2O6
	en	enstatite	Mg2Si2O6
	fs	ferrosilite	Fe2Si2O6
	hed	hedenbergite	CaFeSi2O6
	hen •	Hi-P clinoenstatite	Mg2Si2O6
	jd	jadeite	NaAlSi2O6
	kos •	kosmochlor	NaCrSi2O6
	mgts	Mg-tschermaks pyroxe	MgAl2SiO6
	pren •	protoenstatite	Mg2Si2O6
	pswo	pseudowollastonite	CaSiO3
	pxmn	pyroxmangite	MnSiO3
	rhod	rhodonite	MnSiO3
	wal •	walstromite	CaSiO3
	wo	wollastonite	CaSiO3
Amphibole	anth	anthophyllite	Mg7Si8O22(OH)2
	cumm	cummingtonite	Mg7Si8O22(OH)2
	fact	ferroactinolite	Ca2Fe5Si8O22(OH)2
	fanth	Fe-anthophyllite	Fe7Si8O22(OH)2
	fgl	ferroglaucophane	Na2Fe3Al2Si8O22(OH)2
	gl	glaucophane	Na2Mg3Al2Si8O22(OH)2
	grun	grunerite	Fe7Si8O22(OH)2
	parg	pargasite	NaCa2Mg4Al3Si6O22(OH)2
	rieb	riebeckite	Na2Fe5Si8O22(OH)2
	tr	tremolite	Ca2Mg5Si8O22 (OH)2
	ts	tschermakite	Ca2Mg3Al4Si6O22(OH)2
Other chain silicates	deer	deerite	Fe 18Si12O40(OH)10
	fcar	ferrocarpholite	FeAl2Si2O6(OH)4
	fspr	Fe-sapphirine (221)	Fe4Al8Si2O20
	mcar	magnesiocarpholite	MgAl2Si2O6(OH)4
	spr4	sapphirine (221)	Mg4Al8Si2O20
	spr5	sapphirine (351)	Mg3Al10SiO20
Micas	ann	annite	KFe3AlSi3O10(OH)2
	cel	celadonite	KMgAlSi4O10(OH)2
	east	eastonite	KMg2Al3Si2O10(OH)2
	fcel	ferroceladonite	KFeAlSi4O10(OH)2
	ma	margarite	CaAl4Si2O10(OH)2
	mnbi	Mn-biotite	KMn3AlSi3O10(OH)2
	mu	muscovite	KAl3Si3O10(OH)2
	naph	sodaphlogopite	NaMg3AlSi3O10(OH)2
	pa	paragonite	NaAl3Si3O10(OH)2
	phl	phlogopite	KMg3AlSi3O10(OH)2
Chlorites	afchl	Al-free chlorite	Mg6Si4O10(OH)8
	ames	amesite (14A)	Mg4Al4Si2O10(OH)8
	clin	clinochlore (ordered)	Mg5Al2Si3O10(OH)8
	daph	daphnite	Fe5Al2Si3O10(OH)8
	fsud	ferrosudoite	Fe2Al4Si3O10(OH)8
	mnchl	Mn-chlorite	Mn5Al2Si3O10(OH)8
	sud	sudoite	Mg2Al4Si3O10(OH)8
Other sheet silicates	atg	antigorite	Mg48Si34O85(OH)62
	chr	chrysotile	Mg3Si2O5(OH)4
	fpre •	ferri-prehnite	Ca2FeAlSi3O10(OH)2
	fstp •	ferrostilpnomelane	K0.5Fe5Al2Si8O18(OH)12.5
	fta	ferrotalc	Fe3Si4O10(OH)2
	glt •	greenalite	Fe3Si2O5(OH)4
	kao	kaolinite	Al2Si2O5(OH)4
	liz •	lizardite	Mg3Si2O5(OH)4
	minm •	Mg-minnesotaite	Mg3Si4O10(OH)2
	minn •	minnesotaite	Fe3Si4O10(OH)2
	mstp •	Mg-stilpnomelane	K0.5Mg5Al2Si8O18(OH)12.5
	pre	prehnite	Ca2Al2Si3O10(OH)2
	prl	pyrophyllite	Al2Si4O10(OH)2
	ta	talc	Mg3Si4O10(OH)2
	tap •	prl-talc	Al2Si4O10(OH)2
	tats	tschermak-talc	Mg2Al2Si3O10(OH)2
Feldspars & feldspathoid	abh	albite (high)	NaAlSi3O8
	albite	ab	NaAlSi3O8
	an	anorthite	CaAl2Si2O8
	anl	analcite	NaAlSi2O5(OH)2
	cg •	carnegieite (low)	NaAlSiO4
	cgh •	carnegieite (high)	NaAlSiO4
	kcm •	K-cymrite	KAlSi3O7(OH)2
	kls	kalsilite	KAlSiO4
	lc	leucite	KAlSi2O6
	mic	microcline	KAlSi3O8
	ne	nepheline	NaAlSiO4
	san	sanidine	KAlSi3O8
Silica minerals	coe	coesite	SiO2
	crst	cristobalite (high)	SiO2
	q	quartz	SiO2
	stv	stishovite	SiO2
	trd	tridymite (high)	SiO2
Other framework silicates	heu	heulandite	CaAl2Si7O12(OH)12
	hol •	hollandite	KAlSi3O8
	lmt	laumontite	CaAl2Si4O8(OH)8
	me	meionite	Ca4Al6Si6CO27
	sdl •	sodalite	Na8Al6Si6O24Cl2
	stlb	stilbite	CaAl2Si7O11(OH)14
	wa •	Si-wadeite	K2Si4O9
	wrk	wairakite	CaAl2Si4Oio(OH)4
Oxides	bdy	baddeleyite	ZrO2
	bix •	bixbyite	Mn2O3
	cor	corundum	Al2O3
	cup •	cuprite	Cu2O
	esk •	eskolaite	Cr2O3
	fper •	ferropericlase	FeO
	geik	geikielite	MgTiO3
	hem	hematite	Fe2O3
	herc	hercynite	FeAl2O4
	ilm	ilmenite	FeTiO3
	lime	lime	CaO
	mang	manganosite	MnO
	mcor •	MgSi-corundum	MgSiO3
	mft	magnesioferrite	MgFe2O4
	mt	magnetite	Fe3O4
	NiO	nickel oxide	NiO
	per	periclase	MgO
	picr •	picrochromite	MgCr2O4
	pnt	pyrophanite	MnTiO3
	ru	rutile	TiO2
	sp	spinel	MgAl2O4
	ten •	tenorite	CuO
	usp	ulvospinel	Fe2TiO4
Hydroxides	br	brucite	Mg(OH)2
	dsp	diaspore	AlO(OH)
	gth	goethite	FeO (OH)
Carbonates	ank	ankerite	CaFe(CO3)2
	arag	aragonite	CaCO3
	cc	calcite	CaCO3
	dol	dolomite	CaMg(CO3)2
	mag	magnesite	MgCO3
	rhc	rhodochrosite	MnCO3
	sid	siderite	FeCO3
Halides & sulphides	any •	anhydrite	CaSO4
	hlt •	halite	NaCl
	lot •	low troilite	FeS
	pyr •	pyrite	FeS2
	syv •	sylvite	KCl
	tro •	troilite	FeS
	trot •	pyrrhotite	FeS
	trov •	pyrrhotite	Fe0.875S
Elements	Cu •	copper	Cu
	diam	diamond	C
	gph	graphite	C
	iron	iron	Fe
	Ni	nickel	Ni
	S •	sulphur	S
Gas species	H2O	water	H2O
	CO2	carbon dioxide	CO2
	CO	carbon monoxide	CO
	CH4	methane	CH4
	O2	oxygen	O2
	H2	hydrogen	H2
	S2 •	sulphur gas	S2
	H2S •	Hydrogen sulphide	H2S
Melt species	abL	albite liquid	NaAlSi3O8
	anL	anorthite liquid	CaAl2Si2O8
	corL •	corundum liquid	Al2O3
	diL	diopside liquid	CaMgSi2O6
	enL	enstatite liquid	Mg2Si2O6
	faL	fayalite liquid	Fe2SiO4
	foL	forsterite liquid	Mg2SiO4
	h2oL	H2O liquid	H2O
	hltL •	halite liquid)	NaCl
	kspL	K-feldspar liquid	KAlSi3O8
	lcL •	leucite liquid	KAlSi2O6
	limL •	CaO liquid	CaO
	neL •	nepheline liquid	NaAlSiO4
	perL •	MgO liquid	MgO
	qL	quartz liquid	SiO2
	silL	sillimanite liquid	Al2SiO5
	syvL •	sylvite (liquid)	KCl
	woL •	wollastonite liquid	CaSiO3
Aqueous species	H+	hydrogen ion	H+
	Cl−	chloride ion	Cl−
	OH−	hydroxyl ion	HO−
	Na+	sodium ion	Na+
	K+	potassium ion	K+
	Ca++	calcium ion	Ca2+
	Mg++	magnesium ion	Mg2+
	Fe++	ferrous ion	Fe 2+
	Al+++	aluminium ion	Al3+
	CO3−	carbonate ion
	AlOH3	aluminium hydroxide	Al(OH)3
	AlOH4−	aluminium hydroxide
	KOH	potassium hydroxide	K(OH)
	HCl	hydrogen chloride	HCl
	KCl	potassium chloride	KCl
	NaCl	sodium chloride	NaCl
	CaCl2	calcium chloride	CaCl2
	CaCl+	calcium chloride	CaCl+
	MgCl2	magnesium chloride	MgCl2
	MgCl+	magnesium chloride	MgCl+
	FeCl2	ferrous chloride	FeCl2
	aqSi	silica (aq)	SiO2
	HS−•	sulphide (aq)	HS−
	HSO3−•	sulphite (aq)
	SO42−•	sulphate (aq)
	HSO4−•	sulphate2 (aq)

Table 2a. Molar thermodynamic properties (units: kJ, K, kbar) of the end-members whose formulae can be found in Table 1.

Group	End-member			S	V
						a	b	c	d
Garnet and olivine	Almandine (alm)	−5260.65	1.31	342.00	11.525	0.6773	0	−3772.7	−5.0440	2.12	1900.0	2.98	−0.0016
	Andradite (andr)	−5769.08	1.56	316.40	13.204	0.6386	0	−4955.1	−3.9892	2.86	1588.0	5.68	−0.0036
	grossular (gr)	−6642.95	1.46	255.00	12.535	0.6260	0	−5779.2	−4.0029	2.20	1720.0	5.53	−0.0032
	Knorringite (knor)	−5687.75	3.88	317.00	11.738	0.6130	0.3606	−4178.0	−3.7294	2.37	1743.0	4.05	−0.0023
	Majorite (maj)	−6050.33	9.62	255.20	11.457	0.7136	−0.0997	−1158.2	−6.6223	1.83	1600.0	4.56	−0.0028
	Pyrope (py)	−6282.13	1.06	269.50	11.313	0.6335	0	−5196.1	−4.3152	2.37	1743.0	4.05	−0.0023
	Spessartine (spss)	−5693.65	3.14	335.30	11.792	0.6469	0	−4525.8	−4.4528	2.27	1740.0	6.68	−0.0038
	Clinohumite (chum)	−9609.82	2.49	443.00	19.785	1.0700	−1.6533	−7899.6	−7.3739	2.91	1194.0	4.79	−0.0040
	Fayalite (fa)	−1477.74	0.68	151.00	4.631	0.2011	1.7330	−1960.6	−0.9009	2.82	1256.0	4.68	−0.0037
	Forsterite (fo)	−2172.57	0.57	95.10	4.366	0.2333	0.1494	−603.8	−1.8697	2.85	1285.0	3.84	−0.0030
	Larnite (lrn)	−2307.04	0.90	127.60	5.160	0.2475	−0.3206	0	−2.0519	2.90	985.0	4.07	−0.0041	1
	Monticellite (mont)	−2251.31	0.52	109.50	5.148	0.2507	−1.0433	−797.2	−1.9961	2.87	1134.0	3.87	−0.0034
	Tephroite (teph)	−1733.95	1.05	155.90	4.899	0.2196	0	−1292.7	−1.3083	2.86	1256.0	4.68	−0.0037
Aluminosilicates	Andalusite (and)	−2588.72	0.68	92.70	5.153	0.2773	−0.6588	−1914.1	−2.2656	1.81	1442.0	6.89	−0.0048
	Kyanite (ky)	−2593.02	0.67	83.50	4.414	0.2794	−0.7124	−2055.6	−2.2894	1.92	1601.0	4.05	−0.0025
	Sillimanite (sill)	−2585.85	0.68	95.40	4.986	0.2802	−0.6900	−1375.7	−2.3994	1.12	1640.0	5.06	−0.0031	2
	Mullite (amul)	−2485.51	0.91	113.00	5.083	0.2448	0.0968	−2533.3	−1.6416	1.36	1740.0	4.00	−0.0023
	Mullite (smul)	−2569.28	0.69	101.50	4.987	0.2802	−0.6900	−1375.7	−2.3994	1.36	1740.0	4.00	−0.0023
	Chloritoid (fctd)	−3208.31	0.80	167.00	6.980	0.4161	−0.3477	−2835.9	−3.3603	2.80	1456.0	4.06	−0.0028
	Chloritoid (mctd)	−3549.31	0.75	146.00	6.875	0.4174	−0.3771	−2920.6	−3.4178	2.63	1456.0	4.06	−0.0028
	Chloritoid (mnctd)	−3336.20	1.68	166.00	7.175	0.4644	−1.2654	−1147.2	−4.3410	2.60	1456.0	4.06	−0.0028
	Staurolite (fst)	−23 755.04	6.34	1010.00	44.880	2.8800	−5.6595	−10642.0	−25.3730	1.83	1800.0	4.76	−0.0026
	Staurolite (mnst)	−24 246.42	8.60	1034.00	45.460	2.8733	−8.9064	−12688.0	−24.7490	2.09	1800.0	4.76	−0.0026
	Staurolite (mst)	−25 124.32	6.28	910.00	44.260	2.8205	−5.9366	−13774.0	−24.1260	1.81	1684.0	4.05	−0.0024
	Topaz (tpz)	−2900.76	0.96	100.50	5.339	0.3877	−0.7120	−857.2	−3.7442	1.57	1315.0	4.06	−0.0031
Other orthosilicates	Akermanite (ak)	−3865.63	0.94	212.50	9.254	0.3854	0.3209	−247.5	−2.8899	2.57	1420.0	4.06	−0.0029
	Gehlenite (geh)	−3992.26	1.33	198.50	9.024	0.4057	−0.7099	−1188.3	−3.1744	2.23	1080.0	4.08	−0.0038	2
	Julgoldite (jgd)	−11 809.63	8.50	830.00	31.080	1.7954	−3.7986	−4455.7	−14.8880	2.49	1615.0	4.05	−0.0025
	Merwinite (merw)	−4545.87	1.36	253.10	9.847	0.4175	0.8117	−2923.0	−2.3203	3.19	1200.0	4.07	−0.0034
	Pumpellyite (fpm)	−14 033.82	2.63	657.00	29.680	1.7372	−2.4582	−5161.1	−14.9630	2.49	1615.0	4.05	−0.0025
	Pumpellyite (mpm)	−14 386.75	2.41	629.00	29.550	1.7208	−2.4928	−5998.7	−14.6203	2.47	1615.0	4.05	−0.0025
	Rankinite (rnk)	−3943.92	1.36	210.00	9.651	0.3723	−0.2893	−2462.4	−2.1813	3.28	950.0	4.09	−0.0043
	Sphene (sph)	−2601.65	0.96	124.00	5.565	0.2279	0.2924	−3539.5	−0.8943	1.58	1017.0	9.85	−0.0097	1
	Spurrite (spu)	−5847.08	2.23	332.00	14.697	0.6141	−0.3508	−2493.1	−4.1680	3.40	950.0	4.09	−0.0043
	Tilleyite (ty)	−6368.39	2.21	390.00	17.039	0.7417	−0.5345	−1434.6	−5.8785	3.41	950.0	4.09	−0.0043
	Zircon (zrc)	−2035.05	1.66	83.03	3.926	0.2320	−1.4405	0	−2.2382	1.25	2301.0	4.04	−0.0018
Sorosilicates	Clinozoisite (cz)	−6895.42	1.31	301.00	13.630	0.6309	1.3693	−6645.8	−3.7311	2.33	1197.0	4.07	−0.0034
	Epidote (ep)	−6473.90	1.17	315.00	13.920	0.6133	2.2070	−7160.0	−2.9877	2.34	1340.0	4.00	−0.0030
	Epidote (fep)	−6027.57	1.23	329.00	14.210	0.5847	3.0447	−7674.2	−2.2443	2.31	1513.0	4.00	−0.0026
	Lawsonite (law)	−4868.61	0.81	229.00	10.132	0.6878	0.1566	375.9	−7.1792	2.65	1229.0	5.45	−0.0044
	Piemontite (pmt)	−6543.04	2.70	340.00	13.820	0.5698	2.7790	−5442.9	−2.8126	2.38	1197.0	4.07	−0.0034
	Zoisite (zo)	−6896.21	1.31	298.00	13.575	0.6620	1.0416	−6006.4	−4.2607	3.12	1044.0	4.00	−0.0038
	Vesuvianite (vsv)	−42 345.19	8.95	1890.00	85.200	4.4880	−5.7952	−22269.3	−33.4780	2.75	1255.0	4.80	−0.0038
Cyclosilicates	Cordierite (crd)	−9163.48	1.51	404.10	23.322	0.9061	0	−7902.0	−6.2934	0.68	1290.0	4.10	−0.0031	2
	Cordierite (fcrd)	−8444.02	1.66	461.00	23.710	0.9240	0	−7039.4	−6.4396	0.67	1290.0	4.10	−0.0031	2
	Cordierite (hcrd)	−9449.32	1.52	475.60	23.322	0.9802	0	−7035.9	−6.6808	0.67	1290.0	4.10	−0.0031	2
	Cordierite (mncrd)	−8693.64	3.60	473.00	24.027	0.8865	0	−8840.0	−5.5904	0.69	1290.0	4.10	−0.0031	2
	Osumilite (fosm)	−14 238.91	3.99	762.00	38.320	1.6560	−3.4163	−6497.7	−14.1143	0.49	800.0	4.10	−0.0051
	Osumilite (osm1)	−14 959.21	3.83	701.00	37.893	1.6258	−3.5548	−8063.5	−13.4909	0.47	810.0	4.10	−0.0051
	Osumilite (osm2)	−14 799.99	4.05	724.00	38.440	1.6106	−3.4457	−8262.1	−13.1288	0.47	810.0	4.10	−0.0051
High-pressure phases	akimotoite (fak)	−1142.14	10.12	91.50	2.760	0.1003	1.3328	−4364.9	0.4198	2.12	2180.0	4.55	−0.0022
	Akimotoite (mak)	−1490.85	0.62	59.30	2.635	0.1478	0.2015	−2395.0	−0.8018	2.12	2110.0	4.55	−0.0022
	CaSi-titanite (cstn)	−2496.17	2.81	99.50	4.818	0.2056	0.6034	−5517.7	−0.3526	1.58	1782.0	4.00	−0.0022
	Perovskite (apv)	−1646.76	1.12	51.80	2.540	0.1395	0.5890	−2460.6	−0.5892	1.80	2030.0	4.00	−0.0020
	Perovskite (cpv)	−1541.73	1.80	73.50	2.745	0.1593	0	−967.3	−1.0754	1.87	2360.0	3.90	−0.0016
	Perovskite (fpv)	−1084.64	8.14	91.00	2.548	0.1332	1.0830	−3661.4	−0.3147	1.87	2810.0	4.14	−0.0016
	Perovskite (mpv)	−1443.02	0.69	62.60	2.445	0.1493	0.2918	−2983.0	−0.7991	1.87	2510.0	4.14	−0.0016
	PhaseA (phA)	−7132.27	1.90	348.00	15.442	0.9640	−1.1521	−4517.8	−7.7247	3.79	1450.0	4.06	−0.0028
	Ringwoodite (frw)	−1471.79	0.76	140.00	4.203	0.1668	4.2610	−1705.4	−0.5414	2.22	1977.0	4.92	−0.0025
	Ringwoodite (mrw)	−2127.66	0.78	90.00	3.949	0.2133	0.2690	−1410.4	−1.4959	2.01	1781.0	4.35	−0.0024
	Wadsleyite (fwd)	−1467.92	0.97	146.00	4.321	0.2011	1.7330	−1960.6	−0.9009	2.73	1690.0	4.35	−0.0026
	Wadsleyite (mwd)	−2138.50	0.76	93.90	4.051	0.2087	0.3942	−1709.5	−1.3028	2.37	1726.0	3.84	−0.0022
Pyroxene and pyroxenoid	Acmite (acm)	−2583.50	2.43	170.60	6.459	0.3071	1.6758	−1685.5	−2.1258	2.11	1060.0	4.08	−0.0038
	Ca-eskola pyroxene (caes)	−3002.01	1.74	127.00	6.050	0.3620	−1.6944	−175.9	−3.5657	2.31	1192.0	5.19	−0.0044
	Ca-Tschermak pyroxene (cats)	−3310.14	0.80	135.00	6.356	0.3476	−0.6974	−1781.6	−2.7575	2.08	1192.0	5.19	−0.0044	2
	Clinoenstatite (cen)	−3091.12	0.66	132.00	6.264	0.3060	−0.3793	−3041.7	−1.8521	2.11	1059.0	8.65	−0.0082
	Clinoenstatite high-P (hen)	−3082.74	0.67	131.70	6.099	0.3562	−0.2990	−596.9	−3.1853	2.26	1500.0	5.50	−0.0036
	Diopside (di)	−3201.69	0.62	142.90	6.619	0.3145	0.0041	−2745.9	−2.0201	2.73	1192.0	5.19	−0.0044
	Enstatite (en)	−3090.23	0.66	132.50	6.262	0.3562	−0.2990	−596.9	−3.1853	2.27	1059.0	8.65	−0.0082
	Ferrosilite (fs)	−2388.72	0.81	189.90	6.592	0.3987	−0.6579	1290.1	−4.0580	3.26	1010.0	4.08	−0.0040
	Hedenbergite (hed)	−2841.92	0.94	175.00	6.795	0.3402	0.0812	−1047.8	−2.6467	2.38	1192.0	3.97	−0.0033
	Jadeite (jd)	−3025.26	1.67	133.50	6.040	0.3194	0.3616	−1173.9	−2.4695	2.10	1281.0	3.81	−0.0030
	Kosmochlore (kos)	−2746.80	2.46	149.65	6.309	0.3092	0.5419	−664.6	−2.1766	1.94	1308.0	3.00	−0.0023
	Mg-Tschermak pyroxene (mgts)	−3196.61	0.73	131.00	6.050	0.3714	−0.4082	−398.4	−3.5471	2.17	1028.0	8.55	−0.0083
	Protoenstatite (pren)	−3084.57	0.67	137.00	6.476	0.3562	−0.2990	−596.9	−3.1853	2.30	1059.0	8.65	−0.0082
	Pseudowollastonite (pswo)	−1627.94	0.47	87.80	4.008	0.1578	0	−967.3	−1.0754	2.85	1100.0	4.08	−0.0037
	Pyroxmangite (pxmn)	−1323.14	0.73	99.30	3.472	0.1384	0.4088	−1936.0	−0.5389	2.80	840.0	4.00	−0.0048
	Rhodonite (rhod)	−1322.35	0.73	100.50	3.494	0.1384	0.4088	−1936.0	−0.5389	2.81	840.0	4.00	−0.0048
	Walstromite (wal)	−1625.88	0.48	83.50	3.763	0.1593	0	−967.3	−1.0754	2.54	795.0	4.10	−0.0052
	Wollastonite (wo)	−1633.75	0.47	82.50	3.993	0.1593	0	−967.3	−1.0754	2.54	795.0	4.10	−0.0052
Amphibole	Anthophyllite (anth)	−12066.85	2.48	537.00	26.540	1.2773	2.5825	−9704.6	−9.0747	2.52	700.0	4.11	−0.0059
	Anthophyllite (fanth)	−9624.53	8.80	725.00	27.870	1.3831	3.0669	−4224.7	−11.2576	2.74	700.0	4.11	−0.0059
	Cummingtonite (cumm)	−12064.71	2.48	538.00	26.330	1.2773	2.5825	−9704.6	−9.0747	2.52	700.0	4.11	−0.0059
	Ferroactinolite (fact)	−10503.82	2.88	710.00	28.420	1.2900	2.9992	−8447.5	−8.9470	2.88	760.0	4.10	−0.0054
	Glaucophane (fgl)	−10880.25	5.15	624.00	26.590	1.7629	−11.8992	9423.7	−20.2071	1.83	890.0	4.09	−0.0046
	Glaucophane (gl)	−11960.24	3.55	530.00	25.980	1.7175	−12.1070	7075.0	−19.2720	1.49	883.0	4.09	−0.0046
	Grunerite (grun)	−9607.15	3.02	735.00	27.840	1.3831	3.0669	−4224.7	−11.2576	2.74	648.0	4.12	−0.0064
	Pargasite (parg)	−12664.49	2.27	635.00	27.190	1.2802	2.2997	−12359.5	−8.0658	2.80	912.0	4.09	−0.0045
	Riebeckite (rieb)	−10024.77	5.30	695.00	27.490	1.7873	−12.4882	9627.1	−20.2755	1.80	890.0	4.09	−0.0046
	Tremolite (tr)	−12304.56	2.17	553.00	27.270	1.2602	0.3830	−11455.0	−8.2376	2.61	762.0	4.10	−0.0054
	Tschermakite (ts)	−12555.30	1.77	533.00	26.800	1.2448	2.4348	−11965.0	−8.1121	2.66	760.0	4.10	−0.0054
Other chain silicates	Deerite (deer )	−18341.50	6.45	1650.00	55.740	3.1644	−2.7883	−5039.1	−26.7210	2.75	630.0	4.12	−0.0065
	Carpholite (fcar)	−4411.57	1.01	251.10	10.695	0.6866	−1.2415	186.0	−6.8840	2.21	525.0	4.14	−0.0079
	Carpholite (mcar)	−4771.22	0.79	221.50	10.590	0.6830	−1.4054	291.0	−6.9764	2.43	525.0	4.14	−0.0079
	Sapphirine (fspr)	−9659.86	5.87	485.00	19.923	1.1329	−0.7348	−10420.2	−7.0366	1.96	2500.0	4.04	−0.0017
	Sapphirine (spr4)	−11022.40	3.10	425.50	19.900	1.1331	−0.7596	−8816.6	−8.1806	2.05	2500.0	4.04	−0.0016
	Sapphirine (spr5)	−11135.69	3.83	419.50	19.750	1.1034	0.1015	−10957.0	−7.4092	2.06	2500.0	4.04	−0.0016
Mica	annite (ann)	−5144.23	3.19	418.00	15.432	0.8157	−3.4861	19.8	−7.4667	3.80	513.0	7.33	−0.0143
	Celadonite (cel)	−5834.87	2.83	290.00	13.957	0.7412	−1.8748	−2368.8	−6.6169	3.07	700.0	4.11	−0.0059
	Celadonite (fcel)	−5468.47	2.86	330.00	14.070	0.7563	−1.9147	−1586.1	−6.9287	3.18	700.0	4.11	−0.0059
	Eastonite (east)	−6330.48	3.04	318.00	14.738	0.7855	−3.8031	−2130.3	−6.8937	3.80	530.0	7.33	−0.0143
	Margarite (ma)	−6242.11	1.40	265.00	12.964	0.7444	−1.6800	−2074.4	−6.7832	2.33	1000.0	4.08	−0.0041
	Mn-biotite (mnbi)	−5477.59	4.85	433.00	15.264	0.8099	−5.9213	−1514.4	−6.9987	3.80	530.0	7.33	−0.0143
	Muscovite (mu)	−5976.56	2.90	292.00	14.083	0.7564	−1.9840	−2170.0	−6.9792	3.07	490.0	4.15	−0.0085
	Na-phlogopite (naph)	−6171.92	1.99	318.00	14.450	0.7735	−4.0229	−2597.9	−6.5126	3.28	513.0	7.33	−0.0143
	Paragonite (pa)	−5942.91	1.81	277.00	13.211	0.8030	−3.1580	217.0	−8.1510	3.70	515.0	6.51	−0.0126
	Phlogopite (phl)	−6214.95	2.90	326.00	14.964	0.7703	−3.6939	−2328.9	−6.5316	3.80	513.0	7.33	−0.0143
Chlorites	Al-free chlorite (afchl)	−8728.65	2.27	439.00	21.570	1.1550	−0.0417	−4024.4	−9.9529	2.04	870.0	4.09	−0.0047
	Amesite (ames)	−9039.80	1.96	413.00	20.710	1.1860	−0.2599	−3627.2	−10.6770	2.00	870.0	4.09	−0.0047
	Clinochlore (clin)	−8909.23	1.55	437.00	21.140	1.1708	−0.1508	−3825.8	−10.3150	2.04	870.0	4.09	−0.0047
	Daphnite (daph)	−7116.71	3.20	584.00	21.620	1.1920	−0.5940	−4826.4	−9.7683	2.27	870.0	4.09	−0.0047
	Mn-chlorite (mnchl)	−7702.37	8.36	595.00	22.590	1.1365	−0.5243	−5548.1	−8.9115	2.23	870.0	4.09	−0.0047
	Sudoite (fsud)	−7900.11	2.08	456.00	20.400	1.4663	−4.7365	−1182.8	−14.3880	2.08	870.0	4.09	−0.0047
	Sudoite (sud)	−8626.91	1.65	395.00	20.300	1.4361	−4.8749	−2748.5	−13.7640	1.99	870.0	4.09	−0.0047
Other sheet silicates	Antigorite (atg)	−71416.61	15.14	3600.00	175.480	9.6210	−9.1183	−35941.6	−83.0342	2.60	496.0	6.31	−0.0127
	Chrysotile (chr)	−4360.96	0.98	221.30	10.746	0.6247	−2.0770	−1721.8	−5.6194	2.20	628.0	4.00	−0.0064
	Fe-talc (fta)	−4798.43	4.24	352.00	14.225	0.5797	3.9494	−6459.3	−3.0881	1.80	430.0	6.17	−0.0144
	Greenalite (glt)	−3297.65	1.69	310.00	11.980	0.5764	0.2984	−3757.0	−4.1662	2.28	630.0	4.00	−0.0063
	Kaolinite (kao)	−4122.10	0.78	203.70	9.934	0.4367	−3.4295	−4055.9	−2.6991	2.51	645.0	4.12	−0.0064
	Lizardite (liz)	−4369.14	1.08	212.00	10.645	0.6147	−2.0770	−1721.8	−5.6194	2.20	710.0	3.20	−0.0045
	Minnesotaite (minn)	−4819.29	1.49	355.00	14.851	0.5797	3.9494	−6459.3	−3.0881	1.80	430.0	6.17	−0.0144
	Minnesotaite (minm)	−5866.01	10.26	263.90	14.291	0.6222	0	−6385.5	−3.9163	1.80	430.0	6.17	−0.0144
	Prehnite (fpre)	−5766.75	1.35	320.00	14.800	0.7371	−1.6810	−1957.3	−6.3581	1.58	1093.0	4.01	−0.0037
	Prehnite (pre)	−6202.10	1.11	292.80	14.026	0.7249	−1.3865	−2059.0	−6.3239	1.58	1093.0	4.01	−0.0037
	Prl-talc (tap)	−5589.24	1.03	245.00	13.450	0.7845	−4.2948	1251.0	−8.4959	4.50	370.0	10.00	−0.0271
	Pyrophyllite (prl)	−5640.68	1.01	239.00	12.804	0.7845	−4.2948	1251.0	−8.4959	4.50	370.0	10.00	−0.0271
	Stilpnomelane (fstp)	−12550.45	9.09	930.20	37.239	1.9443	−1.2289	−4840.2	−16.6350	3.68	513.0	7.33	−0.0143
	Stilpnomelane (mstp)	−14288.03	25.51	847.40	36.577	1.8622	−1.4018	−8983.1	−14.9230	3.71	513.0	7.33	−0.0143
	Talc (ta)	−5897.17	1.16	259.00	13.665	0.6222	0	−6385.5	−3.9163	1.80	430.0	6.17	−0.0144
	Tschermak-talc (tats)	−5992.20	0.98	259.00	13.510	0.5495	3.6324	−8606.6	−2.5153	1.80	430.0	6.17	−0.0144
Feldspar and feldspathoid	Albite (ab)	−3935.49	1.69	207.40	10.067	0.4520	−1.3364	−1275.9	−3.9536	2.36	541.0	5.91	−0.0109	2
	Albite-high (abh)	−3921.49	1.68	224.30	10.105	0.4520	−1.3364	−1275.9	−3.9536	2.40	541.0	5.91	−0.0109
	Analcite (anl)	−3307.25	1.68	232.00	9.740	0.6435	−1.6067	9302.3	−9.1796	2.76	400.0	4.18	−0.0104
	Anorthite (an)	−4232.70	0.79	200.50	10.079	0.3705	1.0010	−4339.1	−1.9606	1.41	860.0	4.09	−0.0048	2
	Carnegieite-high (cgh)	−2077.99	1.76	135.00	5.670	0.2292	1.1876	0	−1.9707	4.67	465.0	4.16	−0.0089
	Carnegieite-low (cg)	−2091.70	1.76	118.70	5.603	0.1161	8.6021	−1992.7	0	4.50	465.0	4.16	−0.0089
	Kalsilite (kls)	−2122.89	2.91	136.00	6.052	0.2420	−0.4482	−895.8	−1.9358	3.16	514.0	2.00	−0.0039
	Leucite (lc)	−3029.23	2.82	198.50	8.826	0.3698	−1.6332	684.7	−3.6831	1.85	450.0	5.70	−0.0127	2
	Microcline (mic)	−3975.33	2.80	214.30	10.871	0.4488	−1.0075	−1007.3	−3.9731	1.65	583.0	4.02	−0.0069
	Nepheline (ne)	−2094.54	1.75	124.40	5.419	0.2727	−1.2398	0	−2.7631	4.63	465.0	4.16	−0.0089	1
	Sanidine (san)	−3966.68	2.80	214.30	10.871	0.4488	−1.0075	−1007.3	−3.9731	1.65	583.0	4.02	−0.0069	2
Silica minerals	Coesite (coe)	−907.02	0.27	39.60	2.064	0.1078	−0.3279	−190.3	−1.0416	1.23	979.0	4.19	−0.0043
	Cristobalite (crst)	−904.24	0.27	50.86	2.745	0.0727	0.1304	−4129.0	0	0	160.0	4.35	−0.0272
	Quartz (q)	−910.70	0.27	41.43	2.269	0.0929	−0.0642	−714.9	−0.7161	0	730.0	6.00	−0.0082	1
	Stishovite (stv)	−876.39	0.49	24.00	1.401	0.0681	0.6010	−1978.2	−0.0821	1.58	3090.0	4.60	−0.0015
	Tridymite (trd)	−907.08	0.27	44.10	2.800	0.0749	0.3100	−1174.0	−0.2367	0	150.0	4.36	−0.0291
Other framework silicates	Heulandite (heu)	−10 545.09	1.80	783.00	31.700	1.5048	−3.3224	−2959.3	−13.2972	1.57	274.0	4.00	−0.0146
	Hollandite (hol)	−37 91.94	5.27	166.20	7.128	0.4176	−0.3617	−4748.1	−2.8199	2.80	1800.0	4.00	−0.0022
	Laumontite (lmt)	−7262.64	1.12	465.00	20.370	1.0134	−2.1413	−2235.8	−8.8067	1.37	860.0	4.09	−0.0048
	Meionite (me)	−13 841.95	2.61	752.00	33.985	1.3590	3.6442	−8594.7	−9.5982	1.82	870.0	4.09	−0.0047
	K-cymrite (kcm)	−4232.63	2.81	281.50	11.438	0.5365	−1.0090	−980.4	−4.7350	3.21	425.0	2.00	−0.0047
	Sodalite (sdl)	−13405.41	10.54	910.00	42.130	1.5327	4.7747	−2972.8	−12.4270	4.63	465.0	4.16	−0.0089
	Stilbite (stlb)	−10 896.63	2.23	710.00	32.870	1.5884	−3.2043	−3071.6	−13.9669	1.51	860.0	4.09	−0.0048
	Wadeite (wa)	−4271.79	6.46	254.00	10.844	0.4991	0	0	−4.3501	2.66	900.0	4.00	−0.0044
	Wairakite (wrk)	−6662.40	1.11	380.00	19.040	0.8383	−2.1460	−2272.0	−7.2923	1.49	860.0	4.09	−0.0048
Oxides	Baddelyite (bdy)	−1100.34	1.63	50.40	2.115	0.1035	−0.4547	−416.2	−0.7136	2.00	953.0	3.88	−0.0041
	Bixbyite (bix)	−959.00	1.09	113.70	3.137	0.1451	2.3534	721.6	−1.0084	2.91	2230.0	4.04	−0.0018
	Corundum (cor)	−1675.33	0.75	50.90	2.558	0.1395	0.5890	−2460.6	−0.5892	1.80	2540.0	4.34	−0.0017
	Cuprite (cup)	−170.60	0.11	92.40	2.344	0.1103	0	0	−0.6748	3.33	1310.0	5.70	−0.0043
	Eskolaite (esk)	−1137.35	4.31	83.00	2.909	0.1190	0.9496	−1442.0	−0.0034	1.59	2380.0	4.00	−0.0017
	Geikielite (geik)	−1568.97	0.89	73.60	3.086	0.1510	0	−1890.4	−0.6522	2.15	1700.0	8.30	−0.0049
	Hematite (hem)	−825.65	0.68	87.40	3.027	0.1639	0	−2257.2	−0.6576	2.79	2230.0	4.04	−0.0018	1
	Hercynite (herc)	−1953.09	0.85	113.90	4.075	0.2167	0.5868	−2430.2	−1.1783	2.06	1922.0	4.04	−0.0021	2
	Ilmenite (ilm)	−1230.43	0.84	109.50	3.169	0.1389	0.5081	−1288.8	−0.4637	2.40	1700.0	8.30	−0.0049	1
	Lime (lime)	−634.61	0.50	38.10	1.676	0.0524	0.3673	−750.7	−0.0510	3.41	1130.0	3.87	−0.0034
	Manganosite (mang)	−385.55	0.41	59.70	1.322	0.0598	0.3600	−31.4	−0.2826	3.69	1645.0	4.46	−0.0027
	Mg-corundum (mcor)	−1474.43	2.87	59.30	2.635	0.1478	0.2015	−2395.0	−0.8018	2.12	2110.0	4.55	−0.0022
	Magnesioferrite (mft)	−1442.29	2.71	121.00	4.457	0.2705	−0.7505	−999.2	−2.0224	3.63	1857.0	4.05	−0.0022	1
	Magnetite (mt)	−1114.51	0.95	146.90	4.452	0.2625	−0.7205	−1926.2	−1.6557	3.71	1857.0	4.05	−0.0022	1
	Ni-oxide (NiO )	−239.47	0.36	38.00	1.097	0.0477	0.7824	−392.5	0	3.30	2000.0	3.94	−0.0020	1
	Periclase (per)	−601.55	0.27	26.50	1.125	0.0605	0.0362	−535.8	−0.2992	3.11	1616.0	3.95	−0.0024
	Periclase (fper)	−271.97	2.05	60.60	1.206	0.0444	0.8280	−1214.2	0.1852	7.43	1520.0	4.90	−0.0032
	Picrochromite (picr)	−1762.60	3.28	118.30	4.356	0.1961	0.5398	−3126.0	−0.6169	1.80	1922.0	4.04	−0.0021	2
	Pyrophanite (pnt)	−1361.99	2.16	105.50	3.288	0.1435	0.3373	−1940.7	−0.4076	2.40	1700.0	8.30	−0.0049
	Rutile (ru)	−944.37	0.78	50.50	1.882	0.0904	0.2900	0	−0.6238	2.24	2220.0	4.24	−0.0019
	Spinel (sp)	−2301.26	0.84	82.00	3.978	0.2229	0.6127	−1686.0	−1.5510	1.93	1922.0	4.04	−0.0021	2
	Tenorite (ten)	−156.10	2.18	42.60	1.222	0.0310	1.3740	−1258.0	0.3693	3.57	2000.0	3.94	−0.0020
	Ulvospinel (usp)	−1491.10	1.01	180.00	4.682	−0.1026	14.2520	−9144.5	5.2707	3.86	1857.0	4.05	−0.0022
Hydroxides	Brucite (br)	−923.65	0.30	63.20	2.463	0.1584	−0.4076	−1052.3	−1.1713	6.20	415.0	6.45	−0.0155
	Diaspore (dsp)	−999.86	0.38	34.50	1.786	0.1451	0.8709	584.4	−1.7411	3.57	2280.0	4.04	−0.0018
	Goethite (gth)	−561.79	0.35	60.30	2.082	0.1393	0.0147	−212.7	−1.0778	4.35	2500.0	4.03	−0.0016
Carbonates	Ankerite (ank)	−1970.62	0.77	188.46	6.606	0.3410	−0.1161	0	−3.0548	3.46	914.0	3.88	−0.0043	2
	Aragonite (arag)	−1207.82	0.46	89.80	3.415	0.1923	−0.3052	1149.7	−2.1183	6.14	614.0	5.87	−0.0096	1
	Calcite (cc)	−1207.88	0.46	92.50	3.689	0.1409	0.5029	−950.7	−0.8584	2.52	733.0	4.06	−0.0055	1
	Dolomite (dol)	−2325.76	0.58	156.10	6.429	0.3589	−0.4905	0	−3.4562	3.28	943.0	3.74	−0.0040	2
	Magnesite (mag)	−1110.93	0.32	65.50	2.803	0.1864	−0.3772	0	−1.8862	3.38	1028.0	5.41	−0.0053
	Rhodochrosite (rhc)	−892.28	0.41	98.00	3.107	0.1695	0	0	−1.5343	2.44	953.0	3.88	−0.0041
	Siderite (sid)	−762.22	0.57	93.30	2.943	0.1684	0	0	−1.4836	4.39	1200.0	4.07	−0.0034
Sulphides and halides	Anhydrite (any)	−1434.40	3.50	106.90	4.594	0.1287	4.8545	−1223.0	−0.5605	4.18	543.8	4.19	−0.0077
	Halite (hlt)	−411.30	0.22	72.10	2.702	0.0452	1.7970	0	0	11.47	238.0	5.00	−0.0210
	Pyrite (pyr)	−171.64	1.28	52.90	2.394	0.0373	2.6715	−1817.0	0.6493	3.10	1395.0	4.09	−0.0029
	Pyrrhotite (trot)	−99.03	1.34	65.50	1.819	0.0502	1.1052	−940.0	0	5.68	658.0	4.17	−0.0063	1
	Pyrrhotite (trov)	−96.02	1.17	57.50	1.738	0.0511	0.8307	−669.7	0	5.94	658.0	4.17	−0.0063	1
	Troilite (lot)	−102.16	0.48	60.00	1.818	0.0502	1.1052	−940.0	0	4.93	658.0	4.17	−0.0063	1
	Troilite (tro)	−97.76	0.48	70.80	1.819	0.0502	1.1052	−940.0	0	5.73	658.0	4.17	−0.0063	1
	Sylvite (syv)	−436.50	0.22	82.60	3.752	0.0462	1.7970	0	0	11.09	170.0	5.00	−0.0294
Elements	Copper (Cu)	0	0.00	33.14	0.711	0.0124	0.9220	−379.9	0.2335	3.58	1625.0	4.24	−0.0026
	Diamond (diam)	2.00	0.06	2.38	0.342	0.0243	0.6272	−377.4	−0.2734	0.49	4465.0	1.61	−0.0004
	Graphite (gph)	0.00	0.00	5.74	0.530	0.0510	−0.4429	488.6	−0.8055	1.67	312.0	3.90	−0.0125
	Iron (iron)	0.00	0.00	27.09	0.709	0.0462	0.5159	723.1	−0.5562	3.56	1640.0	5.16	−0.0031	1
	Nickel (Ni)	0.00	0.00	29.87	0.659	0.0498	0	585.9	−0.5339	4.28	1905.0	4.25	−0.0022	1
	Sulphur (S)	0.00	0.00	32.05	1.551	0.0566	−0.4557	638.0	−0.6818	6.40	145.0	7.00	−0.0063
Gas species	Methane (CH4)	−74.81	0.37	186.26	0	0.1501	0.2063	3427.7	−2.6504	0	0	0	0
	Carbon monoxide (CO)	−110.53	0.19	197.67	0	0.0457	−0.0097	662.7	−0.4147	0	0	0	0
	Carbon dioxide (CO2)	−393.51	0.08	213.70	0	0.0878	−0.2644	706.4	−0.9989	0	0	0	0
	Hydrogen (H2)	0.00	0.00	130.70	0	0.0233	0.4627	0	0.0763	0	0	0	0
	Hydrogen sulphide (H2S)	−20.30	0.44	205.77	0	0.0474	1.0240	615.9	−0.3978	0	0	0	0
	Oxygen (O2)	−0.00	0.00	205.20	0	0.0483	−0.0691	499.2	−0.4207	0	0	0	0
	Sulphur gas (S2)	128.54	0.32	231.00	0	0.0371	0.2398	−161.0	−0.0650	0	0	0	0
	Water (H2O)	−241.81	0.02	188.80	0	0.0401	0.8656	487.5	−0.2512	0	0	0	0
Melt species	Albite liq (abL)	−3926.05	1.69	149.90	10.858	0.3580	0	0	0	3.37	176.0	14.35	−0.0815	4
	Anorthite liq (anL)	−4277.91	0.84	29.00	10.014	0.4300	0	0	0	5.14	210.0	6.38	−0.0304	4
	Corundum liq (corL)	−1632.02	1.02	14.90	3.369	0.1576	0	0	0	7.03	150.0	6.00	0	4
	Diopside liq (diL)	−3193.70	0.70	42.10	7.288	0.3340	0	0	0	8.51	249.0	8.04	−0.0323	4
	Enstatite liq (enL)	−3096.58	0.80	−4.00	6.984	0.3536	0	0	0	6.81	218.0	7.20	−0.0330	4
	Fayalite liq (faL)	−1463.04	0.71	96.00	4.677	0.2437	0	0	0	10.71	290.0	10.42	−0.0359	4
	Forsterite liq (foL)	−2237.32	0.60	−62.00	4.312	0.2694	0	0	0	9.20	362.0	10.06	−0.0278	4
	Water liq (h2oL)	−295.01	0.03	45.50	1.460	0.0800	0	0	0	46.33	46.2	1.50	−0.0325	4
	Halite liq (hltL)	−392.99	0.23	80.10	2.938	0.0720	−0.3223	0	0	29.50	64.0	4.61	−0.0720	4
	K-feldspar liq (kspL)	−3980.06	2.80	132.20	11.431	0.3680	0	0	0	4.93	174.0	6.84	−0.0393	4
	Leucite liq (lcL)	−3068.37	2.82	102.00	8.590	0.2870	0	0	0	6.70	175.0	7.00	−0.0394	4
	Lime liq ( limL)	−692.37	0.52	−47.50	1.303	0.0990	0	0	0	17.50	362.0	10.06	−0.0278	4
	Nepheline liq (neL)	−2116.71	1.76	52.90	5.200	0.2165	0	0	0	13.70	250.0	7.37	−0.0295	4
	Periclase liq (perL)	−654.14	0.36	−64.30	0.839	0.0990	0	0	0	22.60	362.0	10.06	−0.0278	4
	Quartz liq (qL)	−921.03	0.27	16.30	2.730	0.0825	0	0	0	0	220.0	9.46	−0.0430	4
	Sillimanite liq (silL)	−2594.05	1.79	10.00	6.051	0.2530	0	0	0	4.08	220.0	6.36	−0.0289	4
	Sylvite liq (syvL)	−417.41	0.23	94.50	3.822	0.0669	0	0	0	30.10	56.0	4.65	−0.0830	4
	Wollastonite liq (woL)	−1642.20	0.51	22.50	3.965	0.1674	0	0	0	6.69	305.0	9.38	−0.0308	4
Aqueous species	H+	0	0.00	0	0	0	0	0	0	0	0	0	0	3
		−167.08	0.11	56.73	1.779	0	0	0	0	0	0	0	0	3
		−230.02	0.11	−10.71	−0.418	0	0	0	0	0	0	0	0	3
	Na+	−240.30	0.11	58.40	−0.111	0	19.1300	0	0	0	0	0	0	3
	K+	−252.17	0.11	101.04	0.906	0	7.2700	0	0	0	0	0	0	3
	Ca++	−543.30	1.09	−56.50	−1.806	0	−6.9000	0	0	0	0	0	0	3
	Mg++	−465.96	1.09	−138.10	−2.155	0	−4.6200	0	0	0	0	0	0	3
	Fe++	−90.42	3.28	−107.11	−2.220	0	0	0	0	0	0	0	0	3
	Al+++	−527.23	1.64	−316.30	−4.440	0	0	0	0	0	0	0	0	3
		−675.23	0.11	−50.00	−0.502	0	0	0	0	0	0	0	0	3
	AlOH3	−1251.85	1.09	53.60	0	0	0	0	0	0	0	0	0	3
	AlOH4−	−1495.78	1.09	126.90	0	0	0	0	0	0	0	0	0	3
	KOH	−473.62	1.31	109.62	−0.800	0	9.4500	0	0	0	0	0	0	3
	HCl	−162.13	0.87	56.73	1.779	0	9.0300	0	0	0	0	0	0	3
	KCl	−400.03	1.42	184.81	4.409	0	5.4300	0	0	0	0	0	0	3
	NaCl	−399.88	1.20	126.09	2.226	0	19.1300	0	0	0	0	0	0	3
	CaCl2	−877.06	1.31	46.00	3.260	0	13.6900	0	0	0	0	0	0	3
	CaCl+	−701.28	1.75	27.36	0.574	0	−6.9000	0	0	0	0	0	0	3
	MgCl2	−796.08	2.29	−22.43	2.920	0	23.9900	0	0	0	0	0	0	3
	MgCl+	−632.48	0.87	−81.37	0.126	0	−4.6200	0	0	0	0	0	0	3
	FeCl2	−375.34	3.28	109.88	2.700	0	45.0300	0	0	0	0	0	0	3
	aqSi	−887.81	0.68	46.35	1.832	0	17.7500	0	0	0	0	0	0	3
		−16.04	5.46	68.00	2.065	0	0	0	0	0	0	0	0	3
	HSO3−	−623.82	5.46	139.00	3.330	0	0	0	0	0	0	0	0	3
	SO42−	−906.12	5.46	18.80	1.388	0	0	0	0	0	0	0	0	3
	HSO4−	−885.70	5.46	125.04	3.520	0	0	0	0	0	0	0	0	3

• is the regressed enthalpy of formation from the elements; is 1SD on the enthalpy of formation; is the entropy; the volume (all properties at 1 bar and 298 K); , , and are the coefficients in the heat capacity polynomial ; and are thermal expansion and bulk modulus; is the thermal expansion parameter; , and are the bulk modulus (at 298 K, 1 bar) and its first and second pressure derivatives; is a flag, 1 signifying a phase transition described via Landau theory and 2 signifying a phase transition described via Bragg-Williams theory, 3 signifies an aqueous species and 4 signifies a melt end-member.

Table 2b. Landau theory parameters used for end-members in the data set.

lrn	1710	10.03	0.0500
sph	485	0.40	0.0050
q	847	4.95	0.1188
ne	467	10.00	0.0800
hem	955	15.60	0
NiO	520	5.70	0
ilm	1900	12.00	0.0200
mt	848	35.00	0
mft	665	17.00	0
cc	1240	10.00	0.0400
arag	1240	9.00	0.0450
trot	598	12.00	0.0410
tro	598	12.00	0.0410
lot	420	10.00	0
trov	595	10.00	0.0160
iron	1042	8.30	0
Ni	631	3.00	0

• is the critical temperature at 1 bar, and are the entropy and volume of disordering at . See Holland & Powell (1998) for further details.

Table 2c. Symmetric formalism (SF; a generalized Bragg–Williams theory) parameters used for end-members in the data set.

						Fac
sill	4.75	0.0100	4.75	0.0100	1	0.25
geh	7.51	0.0900	7.50	0.0900	1	0.80
crd	36.71	0.1000	36.70	0.1000	2	1.50
hcrd	36.71	0.1000	36.70	0.1000	2	1.50
fcrd	36.71	0.1000	36.70	0.1000	2	1.50
mncrd	36.71	0.1000	36.70	0.1000	2	1.50
cats	3.80	0.0100	3.80	0.0100	1	0.25
ab	14.00	0.0420	13.00	0.0420	3	0.90
san	8.65	0.0240	8.50	0.0240	3	0.80
an	42.01	0.1000	42.00	0.1000	1	2.00
lc	11.61	0.4000	11.60	0.4000	2	0.70
sp	8.00	0	1.20	0	2	0.50
herc	18.30	0	13.60	0	2	1.00
picr	8.00	0	1.20	0	2	0.50
dol	11.91	0.0160	11.90	0.0160	1	1.00
ank	11.91	0.0160	11.90	0.0160	1	1.00

• and are the total enthalpy and volume of disordering, and are the interaction energy terms used in , is the number of Si disordering with each Al, and fac is a scaling factor on the energy of disordering. See Holland & Powell (1996a,b) for further details.

Table 2d. Values for , the temperature dependence of the bulk modulus for melt end-members in the data set.

SyvL	−0.02000
hltL	−0.01500
perL	−0.04100
limL	−0.04100
corL	−0.03500
qL	−0.03500
h2oL	−0.00001
foL	−0.04400
faL	−0.05500
woL	−0.02000
enL	−0.02400
diL	−0.03730
silL	−0.02900
anL	−0.05500
kspL	−0.00900
abL	−0.02600
neL	−0.00800
lcL	0

• See Holland & Powell (1998) for further details.

Table 2e. , the augmented term in the heat capacity for aqueous species in the modified density model of Anderson et al., (1991), .

Na+	0.0306
K+	0.0072
AlOH3	0.1015
	0.0965
HCl	0.0540
CaCl2	0.0343
CaCl+	0.0400
MgCl2	0.0186
MgCl+	0.1126
FeCl2	0.0124
aqSi	0.0283
	0.2680
HSO4−	0.0220

• See Holland & Powell (1998) for further details.

Changes to Methodology

The principal differences in methodology from HP98 are outlined before the details of the new data set are presented and discussed.

Equation of state (EOS) for solids

The EOS for solid phases in HP98 involved a thermal expansion expression at 1 bar pressure, with an independent Murnaghan EOS to take the ambient pressure molar volumes to high pressures. To link the expansion and compression terms, a simple linear temperature dependence for the bulk modulus was used. This is now replaced with a more general EOS, and the expansion and compression terms are now linked.

Freund & Ingalls (1989) investigated nine separate EOS to determine which might be most suitable for high pressure work in solids. Their aim was to find a suitable EOS with only two or three adjustable parameters which best fit compression data to very high pressures. The modified Tait equation of Huang & Chow (1974) was one of the best of the equations investigated, in terms of fits to the compression data, and it is adopted here. We then augment this EOS for high temperature use by adding a thermal pressure term, as outlined below, thus integrating the expansion and compression contributions to Gibbs energy. Below, this modified Tait EOS, augmented with a thermal pressure term, is referred to as TEOS.

The 298K (ambient) temperature TEOS, expressed as a three-parameter equation in volume at (where  = 298.15K) is:

(1)

and, in terms of pressure may be rearranged as:

(2)

The relationship of the parameters to the bulk modulus and its derivatives at zero pressure is (Freund & Ingalls, 1989):

(3)

where is the bulk modulus at ambient conditions,

and and are the first and second derivatives of with pressure also at ambient conditions. Conversely,

(4)

By substituting equation (3) into equation (1) or (2) and setting , TEOS reduces to the simpler two-parameter Murnaghan equation, with

and

as used in HP98, with, as a default there, (or ).

A major advantage of the three-parameter TEOS over Murnaghan is that the inclusion of the second derivative of bulk modulus gives more flexibility, and allows extrapolation to very high pressures in a sensible fashion when the size and sign of is known. Although Freund & Ingalls (1989) state that experiments do not allow this term to be determined to better than 100% error, their applications suggest that all the successful EOS do seem to point to a fairly uniform but small negative value of for the range of elements and compressible compounds investigated. Jackson & Niesler (1982) suggested that , where is a small number between 0 and 10, and this was confirmed for periclase by Jacobs & Oonk (2000). More importantly, a negative value for is shown to be a requirement in the analysis of Stacey (2005), and should therefore be implemented in such an EOS. Here, to maintain this requirement for a small negative , we adopt the heuristic , with chosen to scale with (see below). With this, the isothermal TEOS can be written in two-parameter form as:

or as

(5)

The relationship between TEOS and the commonly used third-order Birch-Murnaghan, can be seen in series expansion. The latter can be written as:

with the Eulerian strain , and . Now, Murnaghan in terms of y is:

(6)

Accepting that this EOS works well at small compression, TEOS, equation (2), and third-order Birch-Murnaghan, equation (6), can be expanded in terms of around 1 (i.e. no compression). For TEOS to the third power in this gives

(7)

and for third-order Birch–Murnaghan

(8)

with this written such that the term in curly brackets corresponds to

(9)

This brings out that in third-order Birch–Murnaghan, is specified by and , in contrast to TEOS where is a free parameter to be determined from data (or, e.g. via the heuristic above). Note that the term in brackets in equation (9) is close to for , in relation to the heuristic adopted above to approximate . Note also that fourth-order Birch–Murnaghan reduces to third order if the adjustable parameter is substituted with the above expression for . Analogously fourth-order Birch–Murnaghan reduces to third-order Birch–Murnaghan, approximately, if the above heuristic, is adopted. Similar to third-order Birch–Murnaghan, in the so-called universal EOS of Vinet (e.g. Stacey, 2005), is specified by and

(10)

and an exactly equivalent expression to equation (8) can be written for it.

The EOS adopted here, equation (1), or with the heuristic, equation (5), is derived only for ambient temperature. We may extend it to high temperature by adding a thermal pressure term to equation (2), and using the relationship (Anderson, 1997):

(11)

For the very few phases that there are sufficient data, Anderson (1997) showed that there is no simple relationship to use for as a function of T, with for some phases becoming constant to high-T, while others increase or decrease slightly. Rearranging the Grüneisen relation gives , and noting that is nearly independent of temperature, the form of should have the shape of a heat capacity function, rising to an approximately constant value. That this is approximately so may be seen for the phases tabulated in Anderson & Isaak (1995) and illustrated here for their forsterite data in Fig. 1a. Here we adopt the simplest regularization that becomes constant to high-T, taking an Einstein function to represent how decreases to zero as temperature decreases to OK:

with , and the Einstein temperature. For equation (11), is written as , where n is a normalization constant, equal to at infinite temperature, so , and , with , and being the values of , and at ambient temperature. Then, using equation (11)

Writing , this may be rearranged in volume explicit form as:

(12)

Integrating V with respect to P gives the G contribution

(13)

This EOS contains an implicit thermal expansion at ambient pressure conditions. At , the thermal expansion is:

The compressibility is also a function of temperature and pressure, given by

The form of TEOS for thermal expansion is shown in Fig. 1b, with the characteristic shape provided by the Einstein function, and in Fig. 1c the implicit negative temperature dependence of the bulk modulus. These curves are fits of TEOS to the experimental data for forsterite tabulated in Anderson & Isaak (1995). Use of the expressions above necessitates a value for the Einstein temperature for each end-member. Only very rarely are accurate thermal expansion data made at temperatures below ambient, thus making direct determination of by data fitting effectively impossible. We have found that the value of needs only to be known approximately, and affects mainly the low temperature thermal expansion and volume behaviour. An approximate value for is derived for each end-member from the measured entropy (or via Holland, 1989). Thus for end-member i the value of is given by the empirical relationship, , where is the molar entropy (in J ) of i and is the number of atoms in i.

TEOS relates the volume at any P–T to the standard state volume with only three adjustable parameters ( and ). The data set includes a term for to anticipate for the rare occasion where a value other than might be warranted. Fitting TEOS to volume data for phases where volumes have been measured to very high pressures and temperatures (grossular garnet, stishovite and periclase) and for phases where simultaneous high temperature and high pressure measurements have been made (magnesite, dolomite, aragonite, brucite, grossular, andradite, jadeite and muscovite) shows that it behaves very well (see Fig. 3), in fitting all the data, whether at ambient pressures and high temperatures, ambient temperature and high pressures or at combined high pressures and temperatures.

As an example, the data for stishovite to 2300 kbar are shown in Fig. 2a where the lower pressure data (up to 500 kbar) of Andrault et al. (2003) have been fitted with TEOS and, on extrapolation, appear to fit nicely the very high pressure data of Luo et al. (2002). The extrapolatory power of TEOS is seen to be excellent. Also shown in Fig. 2b is the volume thermal expansion data and the good form of the fit to the data. The way volume levels off at low temperature is a reflection of the way thermal expansion drops off to zero (Fig. 1) at low temperatures. Figure 3 illustrates the fit of the high pressure volume data for grossular from Pavese et al. (2001a,b), first as a function of pressure to over 350 kbar, and second as a function of both pressure and temperature to 1000 K and 40 kbar. TEOS appears to have a form that is well suited to represent such data.

Although using TEOS in place of Murnaghan makes little difference to the derived thermodynamic data, two related factors have led to significant improvement in the overall data fitting. First, not restricting the value of to 4.0 has allowed better extrapolations to very high pressure, and second (and more significantly) the incorporation of the implicit thermal expansion and the consequent temperature dependence of bulk modulus through the thermal pressure has made the volume behaviour at high pressures and temperatures more reliable.

New End-Members in The Data set

The following is a brief outline of additions to the data set in a mineral group or system context; all the new end-members are indicated in Table 1. Changes in activity–composition relations that are implicit in data set generation for these and other end-members are included below in the next subsection.

For the first time, sulphides and sulphur-bearing minerals and fluid species have been incorporated into the data set. The details are published in Evans et al. (2010) and encompass the solid phases pyrite (FeS₂), troilite (FeS), pyrrhotites (solid solution between hypothetical end-member trot, FeS and vacancy-bearing trov, S), anhydrite (CaSO₄), elemental sulphur S, gaseous S₂ and H₂S as well as aqueous species , , and HS. Troilite is described as a low temperature form (lot) from 298 K up to 420 K and a high temperature form (tro) above 420 K. These solids are complicated, involving two lambda transitions in troilites (one at 420 K, one at 598K) and a lambda transition in trov at 595 K. Examples of phase diagram calculations, including pseudosections involving mixed silicates, carbonates and sulphides may be found in Evans et al. (2010).

Several new pyroxene end-members are now included. Clinoenstatite (cen, Mg₂Si₂O₆) and protoenstatite (pren) are new end-members whose enthalpy of formation and entropy are derived from experiments of Atlas (1952), Chen & Presnall (1975) and Boyd & England (1965). A calcium-eskola pyroxene end-member (caes, AlSi₂O₆) is introduced to account for vacancy substitutions seen in calcic pyroxene at high pressures, and is calibrated on the experimental results of Gasparik (1984). The activity model used assumes that some short-range ordering between Si–Al on tetrahedral and Mg–Al on octahedral sites can be accommodated by reducing the tetrahedral entropy of mixing to a quarter of the configurational contribution. This then gives the activities of caes and cats in a binary pyroxene as and with activity coefficients from a regular solution with  kJ.

Chromium-bearing end-members are now included: the oxide eskolaite (esk, Cr₂O₃), the pyroxene kosmochlor (kos, NaCrSi₂O₆), the garnet knorringite (knor, Mg₃Cr₂Si₃) and the spinel picrochromite (picr, MgCr₂O₄). We have fitted the experiments on the exchange reaction 2jd + picr = 2kos + sp, assuming that jd–kos is ideal and that the sp–picr solid solution is non-ideal with a symmetrical interaction energy  kJ (Carroll Webb & Wood, 1986). We have not added a large entropy increment to knorringite (as done by Klemme, 2004, and Klemme et al., 2000, who assumed that the low-T anomaly seen in the heat capacity of uvarovite applies to knorringite), and thus we have been able to fit the slope and positions of both the reactions 2knor = 3en + 2esk (Turkin et al., 1983) and knor + fo = picr + 2en (Klemme, 2004). The P–T slope of the experimental brackets of Irifune et al. (1982) for 2knor = 3en + 2esk are incompatible with the other studies and with the thermodynamic data.

Carnegieite and high-carnegieite (cg, cgh, NaAlSiO₄) are fitted to the experiments of Bowen & Greig (1923), Greig & Barth (1938) and Cohen & Klement (1967). These data depend on those for nepheline, and are in turn used to determine those for nepheline liquid and sodalite.

Stilpnomelane with end-members ferrostilpnomelane (fstp, (Fe₅Al)[Si₈Al]4H₂O) and magnesiostilpnomelane (mstp, (Mg₅Al)[Si₈Al]4H₂O) is now included. The formula for stilpnomelane is not fully known, but the chosen formula units are based on Eggleton (1972) simplified and normalized to 8 Si pfu. The activities are given by assuming that octahedral Al resides on one site, with Fe and Mg mixing on five sites, so that and with activity coefficients from a regular solution with  kJ. The data for the end-members are derived from the reaction 28fstp = 14ann + 5grun + 21alm + 79q + 156H₂O and the partitioning of Fe and Mg between stilpnomelane and chlorite (Miyano & Klein, 1989).

Minnesotaite [minn, Fe₃Si₄O₁₀(OH)₂] and its Mg equivalent [minm, Mg₃Si₄O₁₀(OH)₂] are derived from the experiments of Engi (1983) for the reaction 2minn = 3fa + 5q + 2H₂O along with data for partitioning of Fe and Mg between carbonate and minnesotaite of Klein (1974). The activities are given by assuming that Fe and Mg mix on three sites, so that and with activity coefficients from a regular solution with  kJ.

Greenalite [glt, Fe₃Si₂O₅(OH)₄] was derived using reactions glt + 2q = minn + H₂O and 2glt + 5min = 3grun + 6H₂O using the constraints discussed by Rasmussen et al. (1998).

Considering pumpellyite, in addition to the original MgAl pumpellyite in HP98 data are presented for a solid solution between three end-members, the MgAl end-member [mpm, Ca₄MgAlAl₄Si₆(OH)₇], the FeAl end-member [fpm, Ca₄FeAlAl₄Si₆(OH)₇] and the Fe end-member julgoldite [jgd, Ca₄FeSi₆(OH)₇] are included. As in HP98, the mpm end-member is derived from the experiments of Schiffman & Liou (1980), while data for the iron analogue are taken from the Fe–Mg partition between pumpellyite and chlorite of Evans (1990). The jgd end-member is derived from the –Al partitioning data between epidote and pumpellyite given by Cho et al. (1986). Ordering of Mg and Fe onto a single M2a site is assumed for these pumpellyites and activities are given by

and

Talc now includes a pyrophyllitic end-member [tap, ] fitted to the experimental compositions reported by Newton (1972). All experiments involving aluminous talc (e.g. Chernosky, 1978; Massonne et al., 1981; Massonne, 1989; Massonne & Schreyer, 1989; Hoschek, 1995) have been fitted with a model involving both the tschermak substitution and the pyrophyllite-like substitution.

Prehnite now includes a ferric end-member [fpre, Ca₂AlFeSi₃O₁₀(OH)₂]. Ferric iron is assumed to substitute for Al on one octahedral site only, and the activity relations simplify to and with activity coefficients from a regular solution with  kJ. The data for fpre are derived from the –Al partitioning data between epidote and prehnite given by Cho et al. (1986).

The halide minerals halite (hlt, NaCl) and sylvite (syv, KCl) and their molten equivalents (hltL and syvL) are included in the data set. The enthalpies of formation of halite and sylvite are taken from Robie & Hemingway (1995), and the molten end-members from fitting to the melting curves to 20 kbar pressure from Clark (1966). The experimental data of Aranovich & Newton (1997, 1998) involving concentrated brines (KCl and NaCl) in equilibrium with brucite and periclase may now be reproduced by direct calculation with the new data set.

Sapphirine has been a difficult phase to quantify thermodynamically, largely because available experiments have not been able to involve characterization of the composition of the sapphirine. A new model for sapphirine is adopted here, based on the revision of Kelsey et al. (2004), which involves the 2:2:1 end-members spr4 (Mg₄Al₈Si₂) and fspr (Fe₄Al₈Si₂) and the 3:5:1 end-member spr5 (Mg₃Al₁₀Si). The activity relations, as discussed below, are found by optimization of the fit to the experimental data on sapphirine equilibria (Boyd & England, 1959; Hensen, 1972; Newton, 1972; Seifert, 1974; Doroshev & Malinovskiy, 1974; Malinovsky & Doroshev, 1975; Ackermand et al., 1975; Arima & Onuma, 1977; Perkins et al., 1981; Podlesskii, 1996; Fockenberg, 2008). In the fitting process, the compositions of sapphirine are predicted; they fall in the range  = 0.36–0.45 for most of the high pressure experiments, but do rise to when coexisting with mullite. The fit to all these experiments is now quite good. Although a similar quality fit to the H₂O-absent subset of the data in MAS was made by Podlesskii et al. (2008), their data set was only constrained within this subset of MAS rather than by all the other phases and equilibria used in this study.

Mullite is a complex solid solution involving an end-member of sillimanite composition (Al₂SiO₅) into which the substitution Si + O = Al +  occurs. This could in principle extend from Al₂SiO₅ (x = 0) to a Si-free end-member Al₂Al (x = 1), where x is the amount of the substitution above, but in practice rarely extends beyond x = 0.5 (Cameron, 1977). We have elected to use this intermediate composition (amul, Al₂) as the aluminous end-member in mullite in part because natural compositions rarely become more aluminous than this and in part because of the strong ordering of Al + Si and O + . These two different ordering patterns (Al + Si and O + ) lead to two different symmetries, and and an overall structure with an incommensurate modulation (Angel et al., 1991). Rather than attempt a detailed, and probably incorrect, activity model for this solid solution we take a pragmatic approach that assumes that the high degrees of Al,Si and ,O ordering can be approximated by a simple two-site mixture of the end-members, such that and . Mullite enthalpies (for smul and amul) and the interaction energy () are derived from the experiments on the reactions muscovite + quartz = mullite + sanidine + H₂O (Segnit & Kennedy, 1961), pyrophyllite = mullite + quartz + H₂O (Carr & Fyfe, 1960), cordierite + corundum = sapphirine + mullite (Seifert, 1974) and the melting equilibria cristobalite + mullite + liquid and mullite + corundum + liquid (Klug et al., 1987). The calculated compositions of mullite are close to that of sillimanite at low temperatures and reproduce the aluminous compositions observed by Klug et al. (1987) at the melting temperatures. Calculations involving this mullite are included below.

Lizardite, one of the serpentine group minerals (with antigorite and chrysotile) is now included in the data set. Its properties are assumed to be like those of chrysotile, but with slightly smaller values for volume and entropy (Evans, 2004; Hilairet et al., 2006). We have accordingly also lowered the heat capacity and compressibility of lizardite. The enthalpy for lizardite, following the arguments of Evans (2004), is derived from accepting that lizardite transforms (metastably) to chrysotile between 413 and 431 °C at 2 kbar (Chernosky, 1975). The calculated stability of lizardite extends only up to 170 °C at 2 kbar where it breaks down to antigorite + brucite. More work needs to be done to determine unambiguously the stability of lizardite relative to chrysotile. The new measured compressibilities for lizardite and chrysotile (Hilairet et al., 2006) and for antigorite (Bose & Navrotsky, 1998) are used, allowing good fits to antigorite in very high pressure experiments (Wunder & Schreyer, 1997; Bose & Navrotsky, 1998; Pawley, 1998).

The new modified TEOS for solids allows reliable extrapolation of mineral volumes to very high pressures, and so we are starting to accumulate a set of thermodynamic data for phases at deep mantle pressures and temperatures. We present preliminary data on the end-members ferropericlase (fper, FeO), Mg-wadsleyite (mwd, Mg₂SiO₄), Fe-wadsleyite (fwd, Fe₂SiO₄), Mg-ringwoodite (mrw, Mg₂SiO₄), Fe-ringwoodite (frw, Fe₂SiO₄), Mg-perovskite (mpv, MgSiO₃), Fe-perovskite (fpv, FeSiO₃), Al-perovskite (apv, AlAlO₃), Ca-perovskite (cpv, CaSiO₃), Mg-akimotoite (mak, MgSiO₃), Fe-akimotoite (fak, FeSiO₃), majorite garnet (maj, Mg₄Si₄), high-pressure clinoenstatite (hen, Mg₂Si₂O₆), Ca-Si-titanite (cstn, CaSi₂O₅), walstromite (wal, CaSiO₃), MgSi-corundum (mcor, MgSiO₃), K-cymrite (kcm, KAlSi₃O₈.H₂O), wadeite (wa, K₂Si₂₄O₉) and hollandite (hol, KAlSi₃O₈). Experimental details for the equilibria used to extract the data may be found in Appendix 2. These data are tied into, and are consistent with the thermodynamic data for end-members at lower P–T (crustal) conditions.

Mixing model changes

Since HP98 we have changed slightly some solid solution models used in the data set generation. Only the ones which directly affect the fitted enthalpies are discussed here.

For MgAl orthopyroxene, the entropy of mixing is taken over octahedral and tetrahedral sites rather than the earlier octahedral site only model as in Wood & Banno (1973). This is done to facilitate multicomponent extensions to the model involving other substitutions. We take only a one-fourth of the full tetrahedral site entropy as an approximation for Al–Si and Mg–Al ordering, writing the activities of en and mgts as and , with the activity coefficients taken from a macroscopic regular model (symmetric formalism; Powell & Holland, 1993a,b) with  kJ derived from the measurements of Al solubility in aluminous pyroxenes coexisting with other phases in the data set, principally garnet and spinel.

For tremolite–tschermakite amphibole, we now take the tetrahedral contribution to be only one-fourth that of the full configurational entropy, as in the pyroxenes above, as was done in Diener et al. (2007) to make a comprehensive amphibole mixing model from natural and experimental data. Allowing a small cummingtonite component, the activities are written as

with the activity coefficients taken from a regular model with  kJ,  kJ and  kJ derived from the experiments of Jenkins (1994), Hoschek (1995) and the results of Diener et al. (2007).

Chlorite has been slightly simplified since HP98, keeping the basic model the same, but relaxing the degree of ordering required slightly. This has come about in part due to using the X-ray calibration of chlorite compositions from Jenkins & Chernosky (1986), Roots (1994) and Shirozu & Momoi (1972) rather than the data of Baker & Holland (1996) which yielded slightly lower volumes than the other studies. This has affected the adopted molar volumes of the clin, ames and afchl end-members. The molar volume of daph has been changed from the old value (213.4 J ) taken from Helgeson et al. (1978) and Holdaway & Lee (1977) to 216.2 J  from Parra et al. (2005) as, even though their measurements are quite scattered, they are in better agreement with the measured data of James et al. (1976), Vidal et al. (2001) and with simple exchange models involving chlorite and biotite, olivine, orthopyroxene and chloritoid. In addition the entropy of clinochlore and daphnite have been taken from Bertoldi et al. (2007) with an extra 11.5 J  added for tetrahedral site configurational entropy. The entropies of afchl and ames were adjusted slightly in fitting to the phase equilibrium experimental results. The heat capacities were taken from Bertoldi et al. (2007), the thermal expansion from Nelson & Guggenheim (1993) and compressibility from Pawley et al. (2002). The mixing energies are very similar to those of the earlier data set  kJ,  kJ and  kJ with an enthalpy of  kJ for the internal equilibrium afchl + ames = 2 clin.

Epidote has also been slightly modified since HP98. The heat capacities of zoisite and clinozoisite have been refitted to high temperatures using a simple vibrational model. The values for both polymorphs are now very similar, with clinozoisite being very slightly lower than zoisite. The heat capacity of epidote is similarly extrapolated to high temperatures, fitting the experimental data of Kiseleva et al. (1974) and the entropy of epidote is taken from Kiseleva & Ogorodova (1987). The entropy of cz and fep end-members are adjusted slightly to fit phase equilibrium data for the reaction epidote = anorthite + garnet + hematite + quartz + H₂O from Holdaway (1972) and Liou (1973). The activity model is the same as in HP98, but the mixing energies are changed (simplified) to  kJ,  kJ and  kJ. These small values are based on a value for  kJ for Al– mixing in grossular-andradite garnet derived from fitting the experiments of Holdaway (1972) for coexisting garnet + anorthite + wollastonite + quartz. The enthalpy of the internal equilibrium fep + cz = 2ep is  kJ to account for the degree of order in natural epidote (Dollase, 1973; Bird & Helgeson, 1980).

Talc now incorporates a pyrophyllite as well as a tschermak substitution. The mixing properties are assumed to be given by an ideal solution of the three end-members, ta, tats and tap (see above). The activities are given by

Sapphirine, following the treatment in Kelsey et al. (2004) involves two end-members spr4 and spr5 (see above) related by a tschermak substitution. The activities for the binary are given by and , with gammas found from a regular model with  kJ.

Pyrrhotite is treated as a non-ideal solid solution of trov and trot (see above), with activities given by and . The activity coefficients may be found from a regular model with  kJ. More details may be found in Evans et al. (2010).

There are many additional changes to the data set, mainly relating to changes to thermodynamic parameters taken as assumed in data set generation (entropy, volume, heat capacity, etc.), and in the use of newer experimental data on phase stability that can be included in data set generation. Some changes are very minor and may be found by comparison with the tables in HP98, whereas others are more significant and are listed briefly in Appendix 3. One change that may be of greatest import to metamorphic petrologists is highlighted here, and concerns the aluminium silicate phases kyanite, andalusite and sillimanite. The choice of the Holdaway (1971) experiments, as opposed to those of Richardson et al. (1969) for the and = sill reaction is no longer arbitrarily imposed as a constraint. Instead, we prefer to return to the situation in our earlier data sets (Holland & Powell, 1985; 1998) in which no and = sill experimental brackets were used, and a triple point is allowed to emerge from the multitude of other equilibria involved in the data set. The calculated triple point from data in this study lies at 4.3 kbar, 534 °C, in between that of Holdaway (1971) and Richardson et al. (1969). The fact that the relaxation of the and = sill constraint yields a triple point almost identical to that advocated by Pattison et al. (2002) on the basis of field, petrographic and phase equilibria arguments, suggested to us that the combined reaction data used in the regression provide a reasonable justification of this decision.