Databases information

A comprehensive overview of all thermodynamic databases available in MAGEMin, including their acronyms, chemical systems, phases, and primary references.

Info

• Quick Reference Table

• Detailed Database Descriptions

• Important Notes

• Reference Citations

• Phase and End-member Listing

• Deep Earth Water (DEW) aqueous fluid model

• Trace-element partitioning models

  • OL fixed Kd database

  • Yak25 fixed Kd database

  • CO lattice strain model

Important

The acronyms are used to construct the bulk-rock input file for the app, and link the bulk to a targeted database. The acronyms are also used when using MAGEMin_C to initialize MAGEMin_C.jl with the desired database.

Quick Reference Table

Acronym	Name	Version	Primary Reference
mp	Metapelite	v1.3.0	White et al., 2014a, 2014b
um	Ultramafic	v1.3.2	Evans & Frost, 2021
mb	Metabasite	v1.3.5	Green et al., 2016
mtl	Mantle	v1.5.5	Holland et al., 2013
ig	Igneous	v1.6.2	Green et al., 2025 (updated from Holland et al., 2018)
igd	Igneous	v1.9.9	Su et al., 2026 (corrected from Tomlinson & Holland, 2021)
igad	Igneous alkaline	v1.6.2	Weller et al., 2024
sb11	Mantle (Stixrude & Lithgow-Bertelloni)	v1.7.7	Stixrude & Lithgow-Bertelloni, 2011
sb21	Mantle (Stixrude & Lithgow-Bertelloni)	v1.7.7	Stixrude & Lithgow-Bertelloni, 2021
sb24	Mantle (Stixrude & Lithgow-Bertelloni)	v1.8.0	Stixrude & Lithgow-Bertelloni, 2024
ume	Ultramafic extended	-	Evans & Frost, 2021 + Green et al., 2016
mpe	Extended metapelite	-	White et al., 2014 + Green et al., 2016 + Franzolin et al., 2011 + Diener et al., 2007
mbe	Extended metabasite	-	Green et al., 2016 + Diener et al., 2007 + Rebay et al., 2022
po	HP/LT Metapelite (Berman)	Added September 2026	Pourteau et al., 2014 (Berman, 1988 formalism)
all	Global (union of mp/mb/mbe/ig/igd/igad/um/ume/mpe)	Added August 2026	see individual databases above, plus DEW aqueous fluid model

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Detailed Database Descriptions

The metapelitic model (extended with MnO, White et al., 2014) allows to compute the mineral assemblage from low temperature to supra-solidus conditions.

• Added March 2023, `MAGEMin v1.3.0`
• White et al., 2014a, 2014b (see http://hpxeosandthermocalc.org)
• K2O-Na2O-CaO-FeO-MgO-Al2O3-SiO2-H2O-TiO2-O-MnO chemical system
• Pure stoichiometric phases quartz (q), cristobalite (crst), tridymite (trd), coesite (coe), stishovite (stv), kyanite (ky), sillimanite (sill), andalusite (and), rutile (ru), corundum (cor) and sphene (sph).
• Solution phases spinel (spl), biotite (bi), cordierite (cd), orthopyroxene (opx), epidote (ep), garnet (g), ilmenite (ilm), silicate melt (liq), muscovite (mu), ternary feldspar (pl4T), sapphirine (sa), staurolite (st), magnetite (mt), chlorite (chl), chloritoid (ctd) and margarite (ma).

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Important Notes

Important

The datasets are only calibrated for a limited range of P, T, and bulk rock conditions. If you go too far outside those ranges, MAGEMin (or most other thermodynamic software packages for that matter) may not converge or give bogus results.

Important

Developing new, more widely applicable, thermodynamic datasets is a huge research topic, which will require funding to develop the models themselves, as well as to perform targeted experiments to calibrate those models.

Warning

For most users, we recommend starting with the relevant single-system database (mp, um, mb, ig, igd, igad, or mtl) before exploring extended/composite databases, including all. When using an extended or composite database, mind that all phases are active by default and that the user needs to select the adequate subset (see select_phases/remove_phases in MAGEMin_C.jl: options).

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Reference Citations

• Su et al. (2026). Igneous thermodynamic model (igd database), corrected from Tomlinson & Holland (2021).

• Green, E.C.R., Holland, T.J.B., Powell, R., Weller, O.M., & Riel, N. (2025). Journal of Petrology, 66. doi: 10.1093/petrology/egae079

• Weller, O.M., Holland, T.J.B., Soderman, C.R., Green, E.C.R., Powell, R., Beard, C.D., & Riel, N. (2024). New Thermodynamic Models for Anhydrous Alkaline-Silicate Magmatic Systems. Journal of Petrology, 65. doi: 10.1093/petrology/egae098

• Holland, T.J.B., Green, E.C.R., & Powell, R. (2022). A thermodynamic model for feldspars in KAlSi₃O₈-NaAlSi₃O₈-CaAl₂Si₂O₈ for mineral equilibrium calculations. Journal of Metamorphic Geology, 40, 587-600. doi: 10.1111/jmg.12639

• Tomlinson, E.L., & Holland, T.J.B. (2021). A Thermodynamic Model for the Subsolidus Evolution and Melting of Peridotite. Journal of Petrology, 62. doi: 10.1093/petrology/egab012

• Holland, T.J.B., Green, E.C.R., & Powell, R. (2018). Melting of Peridotites through to Granites: A Simple Thermodynamic Model in the System KNCFMASHTOCr. Journal of Petrology, 59, 881-900. doi: 10.1093/petrology/egy048

• Green, E.C.R., White, R.W., Diener, J.F.A., Powell, R., Holland, T.J.B., & Palin, R.M. (2016). Activity-composition relations for the calculation of partial melting equilibria in metabasic rocks. Journal of Metamorphic Geology, 34, 845-869. doi: 10.1111/jmg12211

• White, R.W., Powell, R., Holland, T.J.B., Johnson, T.E., & Green, E.C.R. (2014). New mineral activity-composition relations for thermodynamic calculations in metapelitic systems. Journal of Metamorphic Geology, 32, 261-286. doi: 10.1111/jmg.12071

• Holland, T.J.B., & Powell, R.W. (2011). An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. Journal of Metamorphic Geology, 29, 333-383. doi: 10.1111/j.1525-1314.2010.00923.x

• Stixrude, L., & Lithgow-Bertelloni, C. (2011). Thermodynamics of mantle minerals - II. Phase equilibria. Geophysical Journal International, 184, 1456-1475. doi: 10.1111/j.1365-246X.2010.04890.x

• Stixrude, L., & Lithgow-Bertelloni, C. (2021). Thermal expansivity, heat capacity and isothermal compressibility of the mantle. Geophysical Journal International, 228, 1296-1314. doi: 10.1093/gji/ggab394

• Stixrude, L., & Lithgow-Bertelloni, C. (2024). Thermodynamics of mantle minerals – III: the role of iron. Geophysical Journal International, 237(3), 1699-1733. doi: 10.1093/gji/ggae126

• Evans, K.A., & Frost, B.R. (2021). Deserpentinization in Subduction Zones as a Source of Oxidation in Arcs: a Reality Check. Journal of Petrology, 62(3), egab016. doi: 10.1093/petrology/egab016

• Diener, J.F.A., Powell, R., White, R.W., & Holland, T.J.B. (2007). A new thermodynamic model for clino- and orthoamphiboles in the system Na₂O-CaO-FeO-MgO-Al₂O₃-SiO₂-H₂O-O. Journal of Metamorphic Geology, 25, 631-656.

• Rebay, G., Powell, R., & Diener, J.F.A. (2022). New activities for the system FeO-MgO-Al₂O₃-SiO₂ with applications to metamorphic rocks. Journal of Metamorphic Geology.

• Franzolin, E., Schmidt, M.W., & Poli, S. (2011). Ternary Ca–Fe–Mg carbonates: subsolidus phase relations at 3.5 GPa and a thermodynamic solid solution model including order/disorder. Contributions to Mineralogy and Petrology, 161(2), 213-227.

• Pourteau, A., Bousquet, R., Vidal, O., Plunder, A., Duesterhoeft, E., Candan, O., & Oberhänsli, R. (2014). Multistage growth of Fe–Mg–carpholite and Fe–Mg–chloritoid, from field evidence to thermodynamic modelling. Contributions to Mineralogy and Petrology, 168, 1090. doi: 10.1007/s00410-014-1090-7

• Berman, R.G. (1988). Internally-consistent thermodynamic data for minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2. Journal of Petrology, 29(2), 445-522. doi: 10.1093/petrology/29.2.445

• Connolly, J.A.D. Perple_X thermodynamic data file hp02ver.dat, solution model Scap (2013), after an unpublished THERMOCALC scapolite model by B. Kuhn (source of the scp/scp_K04 model).

• Warr, L.N. (2021). IMA-CNMNC approved mineral symbols. Mineralogical Magazine, 85, 291-320. doi: 10.1180/mgm.2021.43

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Phase and End-member Listing

Complete list of solution phases, end-members and pure phases for each supported database. Model name labels (W14, G16, H22, …) follow the source publication abbreviations used internally.

Note

The Warr (2021) column lists the corresponding IMA-CNMNC approved mineral abbreviation from Warr (2021). Lower-case entries (e.g. liq, fl, nal, cf) have no official Warr equivalent and are composite, theoretical, or model-specific phases.

Note

The Buffers row lists oxygen fugacity reference assemblages available as constraints (qfm, mw, qif, nno, hm, iw, cco). The Activities row lists oxide activities that can be fixed as independent variables (aH2O, aO2, aMgO, aFeO, aAl2O3, aTiO2).

Phase	Warr (2021)	Model	em	End-members
liq	liq	liq_W14	8	q4L · abL · kspL · anL · slL · fo2L · fa2L · h2oL
fsp	Fsp	fsp_H22	3	ab · an · san
bi	Bt	bi_W14	7	phl · annm · obi · east · tbi · fbi · mmbi
g	Grt	g_W14	5	py · alm · spss · gr · kho
ep	Ep	ep_H11	3	cz · ep · fep
ma	Mrg	ma_W14	6	mut · celt · fcelt · pat · ma · fmu
mu	Ms	mu_W14	6	mut · cel · fcel · pat · ma · fmu
opx	Opx	opx_W14	7	en · fs · fm · mgts · fopx · mnopx · odi
sa	Spr	sa_W14	5	spr4 · spr5 · fspm · spro · ospr
cd	Crd	cd_W14	4	crd · fcrd · hcrd · mncd
st	St	st_W14	5	mstm · fst · mnstm · msto · mstt
chl	Chl	chl_W14	8	clin · afchl · ames · daph · ochl1 · ochl4 · f3clin · mmchl
ctd	Cld	ctd_W14	4	mctd · fctd · mnct · ctdo
sp	Spl	sp_W02	4	herc · sp · mt · usp
mt	Mag	mt_W00	3	imt · dmt · usp
ilm	Ilm	ilm_W00	3	oilm · dilm · dhem
ilmm	Ilm	ilmmn_W14	5	oilm · dilm · dhem · geik · pnt

Pure phases: q · crst · trd · coe · stv · ky · sill · and · ru · sph · O2 · H2O · zo · cor

Buffers: qfm · mw · qif · nno · hm · iw · cco    Activities: aH2O · aO2 · aMgO · aFeO · aAl2O3 · aTiO2

Ilmenite (ilmm, ilmmn_W14). The W14 ilmenite-hematite with the Mn end-member pyrophanite (pnt) is labelled ilmmn_W14. Its short name in mp/mpe remains ilmm, so remove_phases(["ilmm"], "mpe") is unchanged; only the model name reported in the outputs differs.

== HP/LT Metapelite (po)

Berman (1988) formalism (br research group), not the Holland-Powell-family datasets used elsewhere in this table.

Phase	Warr (2021)	Model	em	End-members
ctd	Cld	ctd_BR	2	fctd · mctd
car	Cph	car_BR	2	fcar · mcar
chl	Chl	chl_BR	5	dph · clin · feam · sud · ames
mica	Ms	mica_BR	5	mu · pa · cel · fcel · prlph
talc	Tlc	talc_BR	2	ftlc · mtlc
ilm	Ilm	ilm_BR	2	ilm · gk
bt	Bt	bt_BR	2	phl · ann
ol	Ol	ol_BR	2	fa · fo
ep	Ep	ep_BR	2	czo · ep
opx	Opx	opx_BR	2	en · fs
spl	Spl	spl_BR	2	spin · herc
stau	St	stau_BR	2	fst · mst
crd	Crd	crd_BR	2	crd · fcrd
grt	Grt	grt_BR	2	py · alm
omph	Omp	omph_BR	3	di · jd · hed
amphx	Amp	amphx_BR	3	tr · tsch · parg
fsp	Fsp	fsp_BR	3	ab · kfs · an

Pure phases: cor · coe · q · ky · and · sill · mtlc · ftlc · law · glc · dsp · h2o · mt · hem

== Mantle SB11

Stixrude & Lithgow-Bertelloni (2011). End-member names follow the SLB internal convention.

Phase	Warr (2021)	Model	em	End-members
plg	Pl	plg_SB11	2	an · ab
sp	Spl	sp_SB11	2	sp · hc
ol	Ol	ol_SB11	2	fo · fa
wa	Wds	wa_SB11	2	mgwa · fewa
ri	Rwd	ri_SB11	2	mgri · feri
opx	Opx	opx_SB11	4	en · fs · mgts · odi
cpx	Cpx	cpx_SB11	5	di · he · cen · cats · jd
hpcpx	hpcpx	hpcpx_SB11	2	hpcen · hpcfs
ak	Aki	ak_SB11	3	mgak · feak · co
gtmj	Grt	gtmj_SB11	5	py · alm · gr · mgmj · jdmj
pv	pv	pv_SB11	3	mgpv · fepv · alpv
ppv	ppv	ppv_SB11	3	mppv · fppv · appv
mw	mw	mw_SB11	2	pe · wu
cf	cf	cf_SB11	3	mgcf · fecf · nacf

Pure phases: neph · ky · st · coe · qtz · capv · co

Activities: aMgO · aFeO · aAl2O3

== Mantle SB21

Stixrude & Lithgow-Bertelloni (2021). Extends SB11 with new-aluminium-phase (nal) and an extra end-member in mw.

Phase	Warr (2021)	Model	em	End-members
plg	Pl	plg_SB21	2	an · ab
sp	Spl	sp_SB21	2	sp · hc
ol	Ol	ol_SB21	2	fo · fa
wa	Wds	wa_SB21	2	mgwa · fewa
ri	Rwd	ri_SB21	2	mgri · feri
opx	Opx	opx_SB21	4	en · fs · mgts · odi
cpx	Cpx	cpx_SB21	5	di · he · cen · cats · jd
hpcpx	hpcpx	hpcpx_SB21	2	hpcen · hpcfs
ak	Aki	ak_SB21	3	mgak · feak · co
gtmj	Grt	gtmj_SB21	5	py · alm · gr · mgmj · jdmj
pv	pv	pv_SB21	3	mgpv · fepv · alpv
ppv	ppv	ppv_SB21	3	mppv · fppv · appv
cf	cf	cf_SB21	3	mgcf · fecf · nacf
mw	mw	mw_SB21	3	pe · wu · anao
nal	nal	nal_SB21	3	mnal · fnal · nnal

Pure phases: neph · ky · st · coe · qtz · capv · co

Activities: aMgO · aFeO · aAl2O3

== Mantle SB24

Stixrude & Lithgow-Bertelloni (2024). Expanded solid solutions throughout; new iron polymorphs and high-pressure phases as pure phases.

Phase	Warr (2021)	Model	em	End-members
plg	Pl	plg_SB24	2	an · ab
sp	Spl	sp_SB24	4	sp · hc · smag · picr
ol	Ol	ol_SB24	2	fo · fa
wa	Wds	wa_SB24	2	mgwa · fewa
ri	Rwd	ri_SB24	2	mgri · feri
opx	Opx	opx_SB24	4	en · fs · mgts · odi
cpx	Cpx	cpx_SB24	6	di · he · cen · cats · jd · acm
hpcpx	hpcpx	hpcpx_SB24	2	mgc2 · fec2
ak	Aki	ak_SB24	5	mgak · feak · co · hem · esk
gtmj	Grt	gtmj_SB24	7	py · alm · gr · mgmj · jdmj · knor · andr
pv	pv	pv_SB24	7	mgpv · fepv · alpv · hepv · hlpv · fapv · crpv
ppv	ppv	ppv_SB24	5	mppv · fppv · appv · hppv · cppv
cf	cf	cf_SB24	5	mgcf · fecf · nacf · hmag · crcf
mw	mw	mw_SB24	5	pe · wu · wuls · mag · anao
nal	nal	nal_SB24	3	mnal · fnal · nnal

Pure phases: neph · ky · st · coe · qtz · capv · O2 · fea · fee · feg · apbo · wo · lppv · pwo

Buffers: qfm · qif · mw · iw · hm    Activities: aMgO · aFeO · aAl2O3 · aO2

== Global (all)

Phase	Warr (2021)	Model	em	End-members
liq_S26	liq	liq_S26	14	q3L · sl1L · wo1L · fo2L · fa2L · neL · hmL · ekL · tiL · kjL · anL · ab1L · enL · kfL
liq_G16	liq	liq_G16	9	q4L · abL · kspL · wo1L · sl1L · fa2L · fo2L · h2oL · anoL
liq_W14	liq	liq_W14	8	q4L · abL · kspL · anL · slL · fo2L · fa2L · h2oL
liq_G25w	liq	liq_G25w	12	q4L · slL · wo1L · fo2L · fa2L · jdL · hmL · ekL · tiL · kjL · ctL · h2o1L
fsp_H22	Fsp	fsp_H22	3	ab · an · san
fsp_H22op	Fsp	fsp_H22	4	ab · an · san · op
g_W24	Grt	g_W24	6	py · alm · gr · andr · knom · tig
g_W14	Grt	g_W14	5	py · alm · spss · gr · kho
g_H18	Grt	g_H18	2	py · alm
g_T21	Grt	g_T21	6	py · alm · gr · andr · knr · tig
opx_W24	Opx	opx_W24	9	en · fs · fm · odi · mgts · cren · obuf · mess · ojd
opx_W14	Opx	opx_W14	7	en · fs · fm · mgts · fopx · mnopx · odi
opx_T21	Opx	opx_T21	9	en · fs · fm · odi · mgts · cren · obuf · mess · ojd
ol_H18	Ol	ol_H18	4	mnt · fa · fo · cfm
ol_H11	Ol	ol_H11	2	fo · fa
ilm_W24	Ilm	ilm_W24	5	oilm · dilm · hm · ogk · dgk
ilm_W00	Ilm	ilm_W00	3	oilm · dilm · dhem
ilm_T21	Ilm	ilm_T21	5	oilm · dilm · hm · ogk · dgk
spl_T21	Spl	spl_T21	7	nsp · isp · nhc · ihc · nmt · imt · pcr
spl_W02	Spl	spl_W02	3	herc · sp · usp
bi_G25	Bt	bi_G25	6	phl · annm · obi · eas · tbi · fbi
bi_W14	Bt	bi_W14	7	phl · annm · obi · east · tbi · fbi · mmbi
cd_G25	Crd	cd_G25	3	crd · fcrd · hcrd
cd_W14	Crd	cd_W14	4	crd · fcrd · hcrd · mncd
fl_G25	fl	fl_G25	11	qfL · slfL · wofL · fofL · fafL · jdfL · hmfL · ekfL · tifL · kjfL · H2O
fl_EF21	fl	fl_EF21	2	H2 · H2O
fl_H03	fl	fl_H03	2	H2O · CO2
ep_H11	Ep	ep_H11	3	cz · ep · fep
ma_W14	Mrg	ma_W14	6	mut · celt · fcelt · pat · ma · fmu
mu_W14	Ms	mu_W14	6	mut · cel · fcel · pat · ma · fmu
sa_W14	Spr	sa_W14	5	spr4 · spr5 · fspm · spro · ospr
st_W14	St	st_W14	5	mstm · fst · mnstm · msto · mstt
chl_W14	Chl	chl_W14	8	clin · afchl · ames · daph · ochl1 · ochl4 · f3clin · mmchl
ctd_W14	Cld	ctd_W14	4	mctd · fctd · mnct · ctdo
sp_W02	Spl	sp_W02	4	herc · sp · mt · usp
mt_W00	Mag	mt_W00	3	imt · dmt · usp
ilmm_W14	Ilm	ilmm_W14	4	oilm · dilm · dhem · geik
amp_G16	Amp	amp_G16	11	tr · tsm · prgm · glm · cumm · grnm · a · b · mrb · kprg · tts
dio_G16	Cpx	dio_G16	7	jd · di · hed · acmm · om · cfm · jac
aug_G16	Aug	aug_G16	8	di · cenh · cfs · jdm · acmm · ocats · dcats · fmc
abc_H11	Ab	abc_H11	2	abm · anm
ta_EF21	Tlc	ta_EF21	6	ta · fta · tao · tats · ota · tap
oamp_D07	oamp	oamp_D07	9	anth · ged · ompa · omgl · otr · fanth · omrb · amoa · amob
DEW_S24	DEW	DEW_S24	107	107 aqueous species — see the DEW section below
cpx_W24	Cpx	cpx_W24	10	di · cfs · cats · crdi · cess · cbuf · jd · cen · cfm · kjd
cpx_T21	Cpx	cpx_T21	10	di · cfs · cats · crdi · cess · cbuf · jd · cen · cfm · kjd
fper	Fper	fper	2	per · wu
lct_W24	Lct	lct_W24	2	nlc · klc
mel_W24	Mel	mel_W24	5	geh · ak · fak · nml · fge
nph_W24	Nph	nph_W24	6	neN · neS · neK · neO · neC · neF
kals_W24	Kls	kals_W24	2	nks · kls
br_E13	Brc	br_E13	2	br · fbr
ch_EF21	Chu	ch_EF21	2	chum · chuf
atg_EF21	Atg	atg_EF21	5	atgf · fatg · atgo · aatg · oatg
spi_W02	Spl	spi_W02	3	herc · sp · mt
po_E10	Po	po_E10	2	trov · trot
anth_D07	Ath	anth_D07	5	anth · gedf · fant · a · b
occm_F11	occm	occm_F11	5	cc · odo · mag · sid · oank
carp_W14	Cph	carp_W14	2	mcar · fcar
plc_B05	Pl	plc_B05	3	ab · an · san
ilmmn_W14	Ilm	ilmmn_W14	5	oilm · dilm · dhem · geik · pnt
scp_K04	Scp	scp_K04	3	me · coma · mizz

Pure phases: q · crst · trd · coe · stv · law · ky · sill · and · ru · sph · O2 · H2O · ab · zo · cor · pyr · hem · gph · ne · prl · mpm · pre

Buffers: qfm · mw · qif · nno · hm · iw · cco    Activities: aH2O · aO2 · aMgO · aFeO · aAl2O3 · aTiO2

all contains both W14 ilmenite-hematite variants: ilmm_W14 (4 end-members, from mb) and ilmmn_W14 (with the Mn end-member pnt, from mp/mpe). With MnO = 0 they are equivalent.

• The two fsp_H22 rows share the same internal citation tag despite differing endmember counts (a known, pre-existing data labelling quirk carried over from the source databases, not introduced by all) - distinguish them by endmember count/list in practice.

:::

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Deep Earth Water (DEW) aqueous fluid model

Unlike every other phase in MAGEMin, the DEW phase is not a solid solution. It is an ionic aqueous-fluid speciation model: charged and neutral species such as Na+, K+, H+, OH-, H4SiO4, CO2, CH4, and larger organic or complex species. Their molalities and activity coefficients are solved self-consistently at the system's pressure, temperature and oxide chemical potentials, following the Deep Earth Water (DEW) model.

Availability

Database	Phase name	Model	Species
mbe	DEW	DEW_S24	32
ume	DEW	DEW_S24	100
mpe	DEW	DEW_S24	102
all	DEW_S24	DEW_S24	107

MAGEMin holds a 120-species table taken from DEW2019. Each database only keeps the species whose formula can be written with that database's oxides, which is why the number of species differs between databases.

There is no separate activation flag. The DEW phase is a normal solution phase that takes part in the Gibbs energy minimization whenever it is in the chosen database's phase list. It can be excluded the same way as any other phase (remove_phases/rm_list=, or select_phases/pp_list=/ss_list=, see MAGEMin_C.jl: options).

Formulation

The fluid is described by solute species (molality , charge ) dissolved in water . The formulation has five parts:

1. standard-state Gibbs energy of every species;

2. properties of the solvent;

3. activity model;

4. equilibrium speciation at the system's oxide chemical potentials;

5. Gibbs energy of the fluid phase in the minimization.

Composition and formation reactions

Each species carries two sets of stoichiometric coefficients:

• its composition in the oxide components of the database. The O component takes up the charge: a cation carries a negative O coefficient and an anion a positive one. For example:

• its formation reaction from the oxide components, water and H+, used in the mass-action equation below:

The two are consistent through   . A species is kept only if all its fall on oxides of the database.

Standard-state Gibbs energy of the species

The standard-state Gibbs energy of each species, , follows the revised Helgeson-Kirkham-Flowers (HKF) equation of state (Tanger & Helgeson, 1988; Shock et al., 1992), with the DEW2019 parameters. is in bar and in K, with   K,   bar,   K and   bar:

Here , , , and are the species parameters, is the dielectric constant of water, and     and     K⁻¹ are the reference values.

The Born coefficient is constant ( ) for neutral species. For charged species it varies with and through the solvent function :

with   J Å mol⁻¹ and   Å.

The result is converted from the SUPCRT convention (Gibbs energy of formation from the elements) to the convention of the Holland & Powell dataset (apparent Gibbs energy, as used for all other phases):

where is the entropy of the elements of oxide at . By convention   (and  ).

Properties of the solvent

The standard-state Gibbs energy of water and its density (g cm⁻³) are taken from the H₂O endmember of the selected thermodynamic dataset (Pitzer & Sterner, 1994 equation of state), so that the solvent is consistent with the other phases of the database.

The dielectric constant blends the Johnson & Norton (1991) model, used at low pressure, with the Sverjensky et al. (2014) model, used at high pressure. The two are weighted around 5 kbar:

with

where is the temperature in °C. A weight below 0.001 is set to zero.

The solvent function of Shock et al. (1992) enters the Born coefficient. It is zero for   g cm⁻³ and otherwise

where the correction only applies for   kbar and    °C.

The Debye-Hückel parameters are

Activity model

The ionic strength and total solute molality are

The activity coefficients follow the extended Debye-Hückel (B-dot) equation of Helgeson (1969), with the same ion size   Å and   kg mol⁻¹ for every species. The term converts from the mole-fraction to the molality scale:

where   kg mol⁻¹. therefore only depends on , and neutral species have   .

The activity of water follows from the Gibbs-Duhem relation (osmotic coefficient) of the same model:

The chemical potentials are then

Equilibrium speciation

Let be the chemical potentials of the oxide components, given by the current G-hyperplane of the minimization. At equilibrium, the chemical potential of each species equals that of its formation reaction:

which gives the molality of each species (mass action):

The chemical potential of H+ is not fixed by the oxide components. It is the extra unknown set by electroneutrality:

Because and depend on all the molalities (through and ), these   equations are non-linear and are solved iteratively (see Speciation solver). The pH is .

Gibbs energy of the fluid phase

The speciation is converted to mole fractions, water included, with    mol kg⁻¹:

The molar Gibbs energy of the fluid and its composition in oxide components are

In the minimization, the fluid is handled like a solution phase whose endmembers are the species and water. Its driving force is evaluated with the standard states shifted by the G-hyperplane,  . Unlike other solution phases, its composition is not found by a local optimization (NLopt): at each iteration of the minimization it is given directly by the speciation above for the current . If the speciation does not converge, the phase is set to pure water and rejected for that iteration. A converged speciation is also rejected if its charge residual exceeds .

Speciation solver

The speciation equations can have several self-consistent solutions. MAGEMin therefore solves them from several initial values of   and keeps the converged solution with the lowest . The inner solver is selected with --DEW_solve_algorithm (C command line only, see MAGEMin command-line reference):

Value	Method
4 (default)	Newton method on   and (see below). Starts from  , then ; if neither converges, falls back to algorithm 2
2	Fixed-point (Picard) iteration: and are updated from the current molalities, then the charge balance is solved for by a Newton step safeguarded by bisection, and the molalities are recomputed by mass action. Eight starts,
1	As 0, with the new molalities mixed with the previous ones,      . is halved when the charge residual does not decrease and relaxed back otherwise; this targets high ionic strength (high P-T), where plain Picard iteration oscillates
0	As 2, with plain bracketed bisection for (original solver)

The Picard variants stop when  , or after 1000 iterations or 100 iterations without improvement.

The Newton method (algorithm 4) solves the residuals

with the activity coefficients and included in the residual. Since and only depend on the molalities through and , the Jacobian is the identity plus a rank-2 correction. The Newton step is therefore obtained in operations with the Sherman-Morrison-Woodbury formula; the derivatives with respect to and are evaluated by finite differences. A backtracking line search on   is used, with steps limited to   and  . The solve has converged when   and   (at most 50 iterations).

All algorithms converge to the same equilibrium conditions; they differ in robustness and cost.

During the minimization, the speciation of a given P-T point is solved many times with slowly changing . After the first full multi-start solve of a point, later iterations first try a single solve started from the previous solution (warm start). The warm-started result is only accepted if its is not higher than that of the full multi-start solution; otherwise the full multi-start is run again. Warm starting is reset at every new point and can be disabled with --warm_start=0.

Output

In MAGEMin_C.jl, the DEW entry of out.SS_vec gives, besides the usual fields, the molality (molality) and activity (activity) of every species, the fluid's pH, the charge residual (chargeResidual), the total solute molality (sumMolality) and the chemical potential of water (G_water).

Controlling DEW species in MAGEMin_C.jl

Individual species can be removed from the calculation with exclude_DEW_species. It raises the reference Gibbs energy of the named species by a large penalty (default 1.0e6 kJ/mol), so they are never stable. It returns a gbase override to pass to the minimization functions. filter_DEW_species = true only trims the output: species with a negligible fraction (≤ 1e-40) are dropped from the DEW phase's endmember list.

using MAGEMin_C
Xoxides = ["SiO2"; "Al2O3"; "CaO"; "MgO"; "FeO"; "K2O"; "Na2O"; "TiO2"; "O"; "MnO"; "Cr2O3"; "H2O"; "CO2"; "S"];
X       = [0.62212, 0.1122, 0.0, 0.03486, 0.05557, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.17525, 0.0, 0.0];

excl    = exclude_DEW_species("all", ["H6Si2O7"])
data    = Initialize_MAGEMin("all", verbose=false, solver=0)
out     = single_point_minimization(10.0, 400.0, data; X=X, Xoxides=Xoxides, sys_in="mol",
                                    gbase=excl, filter_DEW_species=true)
Finalize_MAGEMin(data)

Here the DEW_S24 phase of the result lists 19 species instead of 107, and H6Si2O7 is absent.

Note

• exclude_DEW_species only works for databases that contain a DEW phase (mbe, ume, mpe, all).

• Species indices are resolved from the database's full oxide list. When the minimization uses a reduced set of oxides, check the result (out.SS_vec[i].emNames) to make sure the right species was excluded.

References

• Sverjensky, D. A., Harrison, B., & Azzolini, D. (2014). Water in the deep Earth: The dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200 °C. Geochimica et Cosmochimica Acta, 129, 125–145. doi: 10.1016/j.gca.2013.12.019 - the dielectric-constant / activity-coefficient methodology the model is built on.

• Huang, F., & Sverjensky, D. A. (2019). Extended Deep Earth Water Model for predicting major element mantle metasomatism. Geochimica et Cosmochimica Acta, 254, 192–230. doi: 10.1016/j.gca.2019.03.036 - the "DEW2019" species-parameter update the species table is drawn from.

• dewcommunity.org - the DEW community's reference site (spreadsheet releases, documentation).

Species list

The 107 species of DEW_S24 in the all database (the mbe, ume and mpe databases use the subset compatible with their oxides):

Show all 107 DEW_S24 species

Al(OH)3 · Al(OH)4- · Al(OH)Si(OH)- · Al+3 · C2H5COOH · CH3CH2COO- · CH3COO- · CH3COOH · CO2 · CO3-2 · Ca(H3SiO4)+ · Ca(HCO3)+ · Ca(HCOO)+ · Ca(OH)+ · Ca+2 · CaCO3 · CaO · CaSO4 · Co · Cr+2 · Cr+3 · Cr2O7-2 · CrO4-2 · Fe(CH3COO)+ · Fe(H3SiO4)+ · Fe(HCOO)+ · Fe(OH)+ · Fe(OH)2 · Fe(OH)3- · Fe+2 · Fe+3 · FeC4H6O4 · H+ · H2 · H2CO3 · H2S · H3SiO4- · H4SiO4 · H6Si2O7 · H8Si3O10 · HCO3- · HCOO- · HCOOH · HCrO4- · HS- · HSO3- · HSO4- · HSO5- · H_SUCCINa · K+ · KOH · KSO4- · Mg(H3SiO4)+ · Mg(HCO3)+ · Mg(OH)+ · Mg(OH)2 · Mg+2 · MgCO3 · MgSO4 · MgSiC+ · Mn+2 · MnO4- · MnO4-2 · MnSO4 · Na(AC) · Na(AC)2- · Na+ · NaCO3- · NaHCO3 · NaHSiO3 · NaOH · O2 · OH- · S2-2 · S2O3-2 · S2O4-2 · S2O5-2 · S2O6-2 · S2O8-2 · S3- · S3-2 · S3O6-2 · S4-2 · S4O6-2 · S5-2 · S3O6-2 · SO2 · SO3-2 · SO4-2 · benzene · ethane · ethanol · ethylene · glutarate- · glutaric · glycolate- · glycolic · hexane · isobutane · lactate- · lactic · methane · methanol · propane · propanol · toluene · H2O

Trace-element partitioning models

OL fixed Kd database

The OL model uses a fixed set of empirical mineral/melt partition coefficients compiled by O. Laurent (2012). Kd values are tabulated as geometric-mean estimates subdivided into three melt SiO₂ ranges. Phase abbreviations used throughout:

Abbreviation	Phase	Warr (2021)
cpx	clinopyroxene	Cpx
pl	plagioclase	Pl
g	garnet	Grt
opx	orthopyroxene	Opx
ol	olivine	Ol
amp	amphibole	Amp
bi	biotite	Bt
afs	alkali feldspar	Afs
mu	muscovite	Ms
ttn	titanite (sphene)	Ttn
ap	apatite	Ap
zrc	zircon	Zrn
ep	epidote	Ep
all	allanite	Aln
mgt	magnetite	Mag
ru	rutile	Rt
FeTiOx	Fe-Ti oxide	-
sp	spinel	Spl
cd	cordierite	Crd
q	quartz	Qz
and	andalusite	And
sill	sillimanite	Sil

Note

Phases marked - are not present in that compositional range. Values of 1e-5 indicate nominally incompatible or effectively zero partitioning.

Mafic compositions

Element	cpx	pl	g	opx	ol	amp	bi	afs	mu	ttn	ap	zrc	ep	all	mgt	ru	FeTiOx	sp	cd	and	sill	q
La	0.632	0.387	0.100	0.158	0.0671	0.559	1.265	0.141	1e-5	6.00	13.2	1.26	2.05	1549	1.02	0.0354	3.35	0.00245	0.0742	1e-5	1e-5	0.00316
Ce	1.095	0.285	0.237	0.240	0.0775	1.000	0.949	0.0866	1e-5	7.42	21.2	3.46	2.44	1225	1.000	0.0458	2.83	0.00387	0.0849	1e-5	1e-5	0.00316
Pr	1.483	0.221	0.461	0.290	0.0917	1.597	0.791	0.0548	1e-5	8.83	30.6	2.00	2.85	1006	1.061	0.0495	2.58	0.00600	0.0990	1e-5	1e-5	0.00316
Nd	1.936	0.158	0.866	0.354	0.106	2.646	0.791	0.0316	1e-5	10.2	40.3	2.83	3.34	794	1.095	0.0566	2.51	0.00812	0.120	1e-5	1e-5	0.00316
Sm	2.324	0.126	1.937	0.424	0.122	3.464	0.632	0.0187	1e-5	10.95	47.4	7.75	4.22	447	1.095	0.0566	2.37	0.0116	0.173	1e-5	1e-5	0.00316
Eu	2.775	2.739	1.581	0.316	0.141	3.464	0.316	3.873	1e-5	8.06	21.2	2.24	3.78	98.0	0.949	0.00112	0.632	0.0106	0.0316	1e-5	1e-5	0.00316
Gd	3.062	0.116	6.124	0.583	0.132	4.743	0.512	0.0187	1e-5	10.2	52.9	20.5	4.67	255	1.183	0.0355	2.37	0.0145	0.403	1e-5	1e-5	0.00316
Tb	3.464	0.102	11.18	0.725	0.155	5.374	0.522	0.0167	1e-5	9.30	52.9	28.5	4.58	170	1.183	0.0278	1.90	0.0150	0.671	1e-5	1e-5	0.00316
Dy	3.578	0.0949	22.36	0.849	0.175	5.422	0.520	0.0200	1e-5	7.88	45.8	44.2	4.50	118	1.107	0.0257	1.58	0.0150	1.146	1e-5	1e-5	0.00316
Y	3.240	0.100	25.5	0.775	0.126	5.745	0.775	0.0316	1e-5	6.00	38.7	67.1	4.30	95.4	0.949	0.0707	0.447	0.0158	0.987	1e-5	1e-5	0.00316
Ho	3.354	0.0775	32.4	0.925	0.194	5.244	0.539	0.0200	1e-5	6.56	37.1	73.5	4.12	84.9	1.025	0.0242	1.58	0.0141	1.581	1e-5	1e-5	0.00316
Er	3.186	0.0693	41.2	1.000	0.232	4.970	0.555	0.0224	1e-5	5.17	30.0	110	3.78	63.2	0.866	0.0218	1.58	0.0133	2.291	1e-5	1e-5	0.00316
Tm	3.074	0.0574	44.7	1.162	0.277	4.500	0.557	0.0235	1e-5	3.73	22.9	140	3.34	43.3	0.866	0.0185	1.42	0.0130	2.806	1e-5	1e-5	0.00316
Yb	2.898	0.0524	44.7	1.275	0.316	3.742	0.559	0.0234	1e-5	2.57	15.8	173	2.96	26.8	0.707	0.0173	1.26	0.0124	3.162	1e-5	1e-5	0.00316
Lu	2.775	0.0447	37.4	1.549	0.387	2.958	0.559	0.0245	1e-5	1.67	12.5	224	2.62	17.7	0.548	0.0158	1.26	0.0116	3.518	1e-5	1e-5	0.00316
Sc	26.46	0.0316	22.36	22.36	0.447	14.14	9.220	0.0316	1e-5	2.24	0.316	63.2	0.0001	57.0	8.660	0.316	4.47	0.316	2.236	1e-5	1e-5	0.00316
Rb	0.0316	0.126	0.00791	0.0158	0.0224	0.0548	4.000	0.949	1e-5	0.400	0.00316	0.632	0.0045	0.0632	0.0224	0.0118	0.0224	0.00548	0.106	1e-5	1e-5	0.00316
Ba	0.122	0.632	0.0173	0.0500	0.0300	0.190	6.708	9.487	1e-5	1.37	0.274	0.632	0.408	3.46	0.0224	0.0100	0.0224	0.00224	0.0224	1e-5	1e-5	0.00316
Sr	0.335	4.472	0.0224	0.0447	0.132	0.387	0.224	3.873	1e-5	2.24	7.07	4.47	2.00	1.00	0.0265	0.0707	0.194	0.00346	0.187	1e-5	1e-5	0.00316
Pb	0.224	0.671	0.0316	0.0894	0.158	0.632	0.316	0.949	1e-5	0.224	0.158	0.100	0.500	0.316	0.548	0.0316	0.447	0.000316	0.0316	1e-5	1e-5	0.00316
Th	0.141	0.0548	0.0775	0.158	0.0200	0.212	0.316	0.0145	1e-5	0.224	1.00	18.0	156	424	0.221	0.335	0.387	0.00791	0.194	1e-5	1e-5	0.00316
U	0.155	0.100	0.158	0.158	0.0155	0.822	0.316	0.0158	1e-5	0.200	0.949	31.6	1.29	20.0	0.447	0.335	0.387	0.0132	0.632	1e-5	1e-5	0.00316
Zr	0.387	0.0894	0.447	0.0548	0.0253	0.632	0.632	0.0194	1e-5	1.34	0.387	949	0.100	0.173	0.671	3.46	1.58	0.0791	0.0612	1e-5	1e-5	0.00316
Hf	0.548	0.0671	0.707	0.0949	0.0285	0.707	0.632	0.0158	1e-5	1.73	0.387	949	10.0	12.2	0.707	5.29	1.58	0.100	0.0775	1e-5	1e-5	0.00316
Ta	0.155	0.0671	0.0707	0.316	0.0335	0.400	1.897	0.00707	1e-5	8.66	0.0316	22.4	0.226	2.74	2.121	27.4	44.7	0.0707	0.0316	1e-5	1e-5	0.00316
Nb	0.110	0.100	0.0316	0.253	0.0312	2.000	6.325	0.0447	1e-5	3.46	0.0316	22.4	0.226	0.447	1.673	61.2	28.3	0.0707	0.0316	1e-5	1e-5	0.00316
V	4.743	0.158	4.472	3.162	0.245	6.708	3.162	0.224	1e-5	5.48	0.316	0.100	0.100	1.00	36.06	47.4	31.6	8.37	0.447	1e-5	1e-5	0.00316

Intermediate compositions

Phases and, sill, mu and ep are absent in this range.

Element	cpx	pl	g	opx	ol	amp	bi	afs	ttn	ap	zrc	all	mgt	ru	FeTiOx	sp	cd	q
La	0.132	0.200	0.0265	0.00894	0.00274	0.335	0.0592	0.112	6.00	3.87	1.26	1414	0.141	0.0112	0.0224	0.00245	0.0742	0.00316
Ce	0.212	0.155	0.0520	0.0205	0.00490	0.412	0.0600	0.0671	7.42	7.07	3.46	1175	0.190	0.0141	0.0306	0.00387	0.0849	0.00316
Pr	0.291	0.122	0.102	0.0363	0.00791	0.574	0.0649	0.0447	8.83	11.1	2.00	949	0.235	0.0157	0.0367	0.00600	0.0990	0.00316
Nd	0.402	0.106	0.206	0.0574	0.0116	0.866	0.0671	0.0300	10.2	15.0	2.83	612	0.267	0.0172	0.0412	0.00812	0.120	0.00316
Sm	0.500	0.0775	0.433	0.0812	0.0153	1.369	0.0707	0.0212	10.95	17.3	7.75	300	0.300	0.0185	0.0548	0.0116	0.173	0.00316
Eu	0.693	1.118	0.500	0.114	0.0188	1.000	0.132	3.354	8.06	11.2	2.24	34.6	0.255	0.000632	0.0447	0.0106	0.0316	0.00316
Gd	0.726	0.0447	1.581	0.157	0.0228	1.803	0.0742	0.0167	10.2	18.4	20.5	116	0.324	0.0195	0.0791	0.0145	0.403	0.00316
Tb	0.849	0.0367	3.162	0.208	0.0271	2.214	0.0775	0.0150	9.30	17.9	28.5	58.3	0.312	0.0205	0.0900	0.0150	0.671	0.00316
Dy	0.954	0.0300	5.454	0.256	0.0324	2.291	0.0794	0.0145	7.88	15.7	44.2	31.6	0.302	0.0222	0.0990	0.0150	1.146	0.00316
Y	1.095	0.0292	6.124	0.283	0.0346	2.121	0.112	0.0255	6.00	12.2	67.1	31.6	0.335	0.0274	0.0707	0.0158	0.987	0.00316
Ho	1.063	0.0257	8.292	0.311	0.0370	2.086	0.0775	0.0162	6.56	13.4	73.5	19.0	0.268	0.0240	0.102	0.0141	1.581	0.00316
Er	1.141	0.0212	9.899	0.351	0.0400	1.817	0.0748	0.0190	5.17	11.2	110	13.4	0.246	0.0265	0.112	0.0133	2.291	0.00316
Tm	1.182	0.0182	10.06	0.400	0.0440	1.517	0.0735	0.0200	3.73	8.94	140	10.2	0.235	0.0291	0.117	0.0130	2.806	0.00316
Yb	1.186	0.0170	9.354	0.458	0.0474	1.407	0.0727	0.0232	2.57	6.71	173	7.75	0.224	0.0315	0.117	0.0124	3.162	0.00316
Lu	1.183	0.0155	7.746	0.500	0.0529	1.304	0.0707	0.0274	1.67	4.47	224	6.71	0.212	0.0335	0.110	0.0116	3.518	0.00316
Sc	7.746	0.0316	3.162	5.477	0.433	10.00	9.220	0.0200	2.24	0.316	63.2	57.0	3.162	0.274	1.73	0.316	2.236	0.00316
Rb	0.0316	0.0447	0.00837	0.0245	0.0132	0.122	3.162	0.949	0.400	0.00316	0.632	0.0632	0.0387	0.0100	0.00316	0.00548	0.106	0.00316
Ba	0.0548	0.387	0.0155	0.0316	0.0122	0.224	5.477	5.477	1.37	0.0791	0.632	3.46	0.158	0.00866	0.00447	0.00224	0.0224	0.00316
Sr	0.287	2.449	0.0173	0.0194	0.0100	0.274	0.235	2.236	2.24	1.94	4.47	1.00	0.0224	0.0316	0.00632	0.00346	0.187	0.00316
Pb	0.316	0.500	0.0316	0.112	0.0187	0.224	0.0316	0.224	0.224	0.316	0.100	1.00	0.316	0.0274	0.0158	0.000316	0.0316	0.00316
Th	0.0707	0.0316	0.0474	0.100	0.0155	0.141	0.0474	0.0173	0.224	0.791	18.0	324	0.0935	0.162	0.0158	0.00791	0.194	0.00316
U	0.0447	0.0548	0.0935	0.0316	0.0224	0.100	0.0707	0.0274	0.200	0.387	31.6	13.2	0.132	0.200	0.0237	0.0132	0.632	0.00316
Zr	0.235	0.0224	0.548	0.0346	0.0387	0.400	0.229	0.0224	1.34	0.194	949	0.173	0.221	2.24	1.22	0.0791	0.0612	0.00316
Hf	0.312	0.0324	0.387	0.0548	0.0224	0.548	0.316	0.0224	1.73	0.0707	949	11.2	0.158	3.74	1.50	0.100	0.0775	0.00316
Ta	0.0707	0.0447	0.0500	0.0671	0.0274	0.274	0.316	0.00316	8.66	0.00707	22.4	0.837	0.122	22.4	6.71	0.0707	0.0316	0.00316
Nb	0.112	0.0612	0.0265	0.0500	0.0194	0.559	0.474	0.0158	3.46	0.00354	22.4	0.837	0.137	33.5	4.47	0.0707	0.0316	0.00316
V	1.936	0.158	2.646	1.500	0.164	5.477	3.162	0.112	5.48	0.224	0.100	1.00	22.36	3.16	11.2	8.37	0.447	0.00316

Felsic compositions

Phases and, sill and mu are absent in this range; ep reappears.

Element	cpx	pl	g	opx	ol	amp	bi	afs	ttn	ap	zrc	ep	all	mgt	ru	FeTiOx	sp	cd	q
La	0.0474	0.112	0.00894	0.000837	0.000224	0.0725	0.0145	0.112	6.00	3.87	1.26	2.05	1414	0.0126	0.0112	0.0224	0.00245	0.0742	0.00316
Ce	0.0866	0.0894	0.0219	0.00265	0.000447	0.145	0.0190	0.0671	7.42	7.07	0.100	2.44	1175	0.0274	0.0141	0.0306	0.00387	0.0849	0.00316
Pr	0.145	0.0714	0.0566	0.00548	0.000935	0.235	0.0245	0.0447	8.83	11.1	2.00	2.89	949	0.0474	0.0157	0.0367	0.00600	0.0990	0.00316
Nd	0.216	0.0592	0.122	0.0110	0.00158	0.346	0.0312	0.0300	10.2	15.0	2.83	3.78	612	0.0624	0.0172	0.0412	0.00812	0.120	0.00316
Sm	0.302	0.0490	0.265	0.0180	0.00251	0.447	0.0387	0.0212	10.95	17.3	7.75	4.22	300	0.0725	0.0185	0.0548	0.0116	0.173	0.00316
Eu	0.387	0.707	0.424	0.0224	0.00316	0.524	0.0418	3.354	8.06	11.2	2.24	3.78	34.6	0.0361	0.000632	0.0447	0.0106	0.0316	0.00316
Gd	0.461	0.0387	0.822	0.0324	0.00424	0.590	0.0447	0.0167	10.2	18.4	20.5	4.67	116	0.0775	0.0195	0.0791	0.0145	0.403	0.00316
Tb	0.522	0.0338	1.323	0.0412	0.00629	0.635	0.0520	0.0150	9.30	17.9	28.5	4.59	58.3	0.0703	0.0205	0.0900	0.0150	0.671	0.00316
Dy	0.551	0.0300	1.936	0.0500	0.00908	0.669	0.0592	0.0145	7.88	15.7	44.2	4.50	31.6	0.0666	0.0222	0.0990	0.0150	1.146	0.00316
Y	0.600	0.0357	2.324	0.0671	0.00775	0.612	0.0663	0.0255	6.00	12.2	67.1	4.30	31.6	0.0592	0.0274	0.0707	0.0158	0.987	0.00316
Ho	0.586	0.0267	2.550	0.0620	0.0132	0.681	0.0693	0.0162	6.56	13.4	73.5	4.14	19.0	0.0620	0.0240	0.102	0.0141	1.581	0.00316
Er	0.608	0.0241	3.122	0.0735	0.0194	0.648	0.0748	0.0190	5.17	11.2	110	3.78	13.4	0.0566	0.0265	0.112	0.0133	2.291	0.00316
Tm	0.608	0.0222	3.518	0.0917	0.0242	0.604	0.0794	0.0200	3.73	8.94	140	3.37	10.2	0.0548	0.0291	0.117	0.0130	2.806	0.00316
Yb	0.586	0.0203	4.023	0.107	0.0274	0.536	0.0820	0.0232	2.57	6.71	173	2.96	7.75	0.0500	0.0315	0.117	0.0124	3.162	0.00316
Lu	0.560	0.0179	4.472	0.120	0.0283	0.458	0.0866	0.0274	1.67	4.47	224	2.55	6.71	0.0447	0.0335	0.110	0.0116	3.518	0.00316
Sc	4.743	0.0316	3.742	1.225	0.287	3.873	9.220	0.0200	2.24	0.316	63.2	0.0001	57.0	1.414	0.274	1.73	0.316	2.236	0.00316
Rb	0.00949	0.0548	0.000866	0.00548	0.00224	0.224	2.000	0.949	0.400	0.00316	0.632	0.0045	0.0632	0.0158	0.0100	0.00316	0.00548	0.106	0.00316
Ba	0.00500	0.335	0.000387	0.00173	0.00224	0.312	4.472	5.477	1.37	0.0791	0.632	0.408	3.46	0.0158	0.00866	0.00447	0.00224	0.0224	0.00316
Sr	0.122	1.658	0.0132	0.0141	0.000110	0.300	0.235	2.236	2.24	1.94	4.47	2.00	1.00	0.0122	0.0316	0.00632	0.00346	0.187	0.00316
Pb	0.0224	0.592	0.0122	0.0200	0.000194	0.0632	0.0316	0.224	0.224	0.316	0.316	0.500	1.00	0.0592	0.0274	0.0158	0.000316	0.0316	0.00316
Th	0.00935	0.100	0.00200	0.000316	0.000707	0.0141	0.0474	0.0173	0.224	0.791	18.0	156	324	0.0387	0.162	0.0158	0.00791	0.194	0.00316
U	0.00707	0.0632	0.00612	0.000500	0.000707	0.0194	0.0707	0.0274	0.200	0.387	31.6	1.29	13.2	0.0387	0.200	0.0237	0.0132	0.632	0.00316
Zr	0.0707	0.0100	0.300	0.0292	0.00316	0.335	0.0548	0.0224	1.34	0.194	949	0.100	0.173	0.151	2.24	1.22	0.0791	0.0612	0.00316
Hf	0.187	0.0155	0.252	0.0548	0.00548	0.391	0.0548	0.0224	1.73	0.0707	949	10.0	11.2	0.200	3.74	1.50	0.100	0.0775	0.00316
Ta	0.0180	0.0447	0.0180	0.00632	0.00500	0.221	0.187	0.00316	8.66	0.00707	22.4	0.226	0.837	0.100	22.4	6.71	0.0707	0.0316	0.00316
Nb	0.00894	0.0447	0.0132	0.00346	0.00274	0.158	0.274	0.0158	3.46	0.00354	22.4	0.226	0.837	0.100	33.5	4.47	0.0707	0.0316	0.00316
V	1.581	0.0671	2.449	1.000	0.0775	4.899	3.162	0.112	5.48	0.224	0.100	0.100	1.00	6.32	3.16	11.2	8.37	0.447	0.00316

---

Yak25 fixed Kd database

Fixed mineral/melt partition coefficients from Yakymchuk, Gareau & Williams (2025), Table S1, compiled after Bédard (2006), Taylor et al. (2015), Bea et al. (1994), Stepanov et al. (2012) and Yakymchuk et al. (2018). Selected with get_Yak25_KDs_database().

Zr and P₂O₅ carry no Kd in any phase (shown as –): following the paper's own treatment they are controlled by the zircon and apatite saturation fronts rather than partitioned into the silicate assemblage, so they are handled by the saturation models rather than by a Nernst coefficient. See Saturation models.

Element	g	pl	afs	opx	cd	FeTiOx	ru	sp	smt	zrc	fapt	mnz	q	sa	sill	ky
La	0.03	0.358	1.01	0.0003	0.06	0.015	0.0057	0.015	0.015	0.6	12	517	0.0001	0.0001	0.0001	0.0001
Ce	0.03	0.339	0.86	0.0007	0.07	0.012	0.0065	0.016	0.016	0.9	15	505	0.0001	0.0001	0.0001	0.0001
Pr	0.07	0.316	0.87	0.0014	0.09	0.011	0.0073	0.018	0.018	0.9	17	530	0.0001	0.0001	0.0001	0.0001
Nd	0.2	0.289	0.51	0.0028	0.09	0.01	0.0082	0.026	0.026	1.4	19	538	0.0001	0.0001	0.0001	0.0001
Sm	1.6	0.237	0.42	0.0085	0.1	0.009	0.0954	0.024	0.024	4.2	20	493	0.0001	0.0001	0.0001	0.0001
Eu	1.6	2.17	2.32	0.68	0.01	0.01	0.00037	0.025	0.025	2.6	13	414	0.0001	0.0001	0.0001	0.0001
Gd	5	0.192	0.6	0.02	0.29	0.011	0.0106	0.018	0.018	8	20	419	0.0001	0.0001	0.0001	0.0001
Y	34.55	0.138	0.5	0.054	0.72	0.037	0.0118	0.018	0.018	19.3	17.5	130	0.0001	0.0001	0.0001	0.0001
Th	0.0075	0.095	0.3	0.13	0.1	0.09	0.2	0.02	0.02	62	23	5000	0.0001	0.0001	0.0001	0.0001
U	0.024	0.091	1.98	0.089	1.61	0.09	0.2	0.02	0.02	298	25	22	0.0001	0.0001	0.0001	0.0001
Zr	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–
P2O5	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–

References

• Yakymchuk, C., Gareau, J., & Williams, M. (2025). Location, location, location: monazite behaviour during UHT metamorphism and melt crystallization. Journal of Metamorphic Geology, 44(2), 158–175.

• Bédard, J. H. (2006). Trace element partitioning in plagioclase feldspar. Geochimica et Cosmochimica Acta, 70(14), 3717–3742.

• Bea, F., Pereira, M. D., & Stroh, A. (1994). Mineral/leucosome trace-element partitioning in a peraluminous migmatite (a laser ablation-ICP-MS study). Chemical Geology, 117(1–4), 291–312.

• Stepanov, A. S., Hermann, J., Rubatto, D., & Rapp, R. P. (2012). Experimental study of monazite/melt partitioning with implications for the REE, Th and U geochemistry of crustal rocks. Chemical Geology, 300–301, 200–220.

• Taylor, R. J. M., Clark, C., Harley, S. L., Kylander-Clark, A. R. C., Hacker, B. R., & Kinny, P. D. (2015). Interpreting granulite facies events through rare earth element partitioning arrays. Journal of Metamorphic Geology, 33(7), 763–781.

• Yakymchuk, C., Kirkland, C. L., & Clark, C. (2018). Th/U ratios in metamorphic zircon. Journal of Metamorphic Geology, 36(6), 715–737.

CO lattice strain model

The CO model (ported from TEPM v02.02, Cornet 2017) computes mineral/melt Kd values from first principles using the Brice (1975) lattice strain partitioning equation. Unlike OL, all Kd values are fully predictive and depend on the mineral composition, melt composition, temperature and pressure at each P-T node.

Elements and output order

Twenty-eight elements are predicted in the following fixed order:

Group	Elements
LILE 1+	Cs · Rb · K
LILE 2+	Ba · Sr
REE + Y + Sc	La · Ce · Pr · Nd · Sm · Eu · Gd · Tb · Dy · Y · Ho · Er · Tm · Yb · Lu · Sc
HFSE 4+	Ti · Hf · Zr
Actinides	U · Th
HFSE 5+	Ta · Nb

Brice lattice strain equation

The partition coefficient of an element i entering a crystallographic site of optimal-fit radius r₀ is:

where:

$$D_0$$
- peak partition coefficient at the optimal ionic radius $r_0$

• • Young's modulus of the crystallographic site [GPa]
• • ionic radius of element i in the relevant coordination (Shannon, 1976)
• • optimal-fit radius of the site
• • temperature [K]
• • gas constant (8.3145 J mol⁻¹ K⁻¹)
• • Avogadro's number

A second variant ("mixed Brice") separates the elastic radius from the fixed reference cation radius when the peak is anchored to a cation with a known :

Mineral-specific models

Mineral site fractions are derived from the oxide wt% composition following Thermocalc a-x conventions:

Mineral	TC model	Reference for site fractions
cpx	cpx_G23	Green et al. (2025, after Holland et al. 2018)
garnet (g)	g_G23	Green et al. (2025, after Holland et al. 2018)
opx	opx_G23	Green et al. (2025, after Holland et al. 2018)
olivine (ol)	ol_H18	Holland et al. (2018)
feldspar (pl, afs)	fsp_H21	Holland et al. (2021)
amphibole (amp)	hb_G16	Green et al. (2016)

Clinopyroxene (cpx)

Element group	Model reference	Key parameters
REE 3+ (M2 site, 8-fold)	Sun & Liang (2012)	, from M2 Al content; from , , H₂O in melt
Sc	Hill et al. (2011)	, , , melt index
LILE 1+ (M2, mixed Brice)	Blundy & Wood (1994)	,  , ref =
LILE 2+ (M2, mixed Brice)	Blundy & Wood (1994)	,  , ref =
Ti (M1 site)	Hill et al. (2011)	, , , ,
HFSE 4+ (M1, mixed Brice)	Corgne et al. (2005)	, from , , ; ref =
HFSE 5+	-	Fixed regressions:  ;
Actinides U, Th (M2)	Blundy & Wood (2003)	from Mg-site exchange; from Brice relative to Th

Garnet (g)

Element group	Model reference	Key parameters
REE 3+ (X site, 8-fold)	van Westrenen & Draper (2007), Sun & Liang (2013)	, from ; from , ,
Sc	Adam & Green (2006)	Fixed:
LILE 1+	-	(fixed); , from , ,
LILE 2+ (X site, mixed Brice)	-	, ref =
Ti	-	Empirical regression to melt polymerisation index
HFSE 4+ (X or Y site)	-	Dual-site model when   ; mixed Brice with or as
HFSE 5+	Adam & Green (2006)	Fixed:  ,
Actinides	Salters & Longhi (1999)	from melt Fe+Mg+Si;

Orthopyroxene (opx)

Element group	Model reference	Key parameters
REE 3+ (M2 site, 8-fold)	Bédard (2007)	, from , ; from , ,
Sc	Frei et al. (2009)	Regression to ,
LILE 1+	Bédard (2007)	Regressions to melt SiO₂, Al₂O₃, MgO, FeO, Mg#
LILE 2+ (M2, mixed Brice)	Wood & Blundy (2013)	, ref =
HFSE 4+ (M1 site)	Frei et al. (2009)	, , from , , , ,
HFSE 5+	Bédard (2007)	, from
Actinides	Bédard (2007)	Regressions to Mg# and melt FeO, MgO

Plagioclase (pl) / alkali feldspar (afs)

Element group	Model reference	Key parameters
REE 3+ (A site, mixed Brice)	Dohmen & Blundy (2014)	, from ; anchored to
Sc	Dohmen & Blundy (2014)	Regression to melt MgO
LILE 1+ (A site, mixed Brice)	Dohmen & Blundy (2014)	, from ; ref =
LILE 2+ (A site, mixed Brice)	Dohmen & Blundy (2014)	from , ; ref =
HFSE 4+ (Ti, Zr, Hf)	Dohmen & Blundy (2014)	Regressions to melt SiO₂ and
HFSE 5+ (Ta, Nb)	Dohmen & Blundy (2014)	Regressions to melt SiO₂, MgO,
Actinides (U, Th)	Dohmen & Blundy (2014)	Regressions to

Olivine (ol)

Element group	Model reference	Key parameters
REE 3+ + Sc (M site, 8-fold)	Yao et al. (2012)	Å,   GPa; from melt Al₂O₃,
LILE 1+	Bédard (2005)	Fixed value if melt MgO > 1.11 wt%, otherwise 0.035
LILE 2+	Bédard (2005)	Brice with   Å,   GPa, ref =
HFSE 4+ (Ti, Hf, Zr)	Bédard (2005)	Piecewise regressions to melt SiO₂, MgO and Mg#
HFSE 5+ (Ta, Nb)	Bédard (2005)	Piecewise regressions to melt MgO
Actinides (U, Th)	Bédard (2005)	Piecewise regressions to melt MgO

Amphibole (amp)

Element group	Model reference	Key parameters
REE 3+ (M4 site, empirical)	Tiepolo et al. (2007)	Regression to melt SiO₂ via polymerisation index
Sc	Tiepolo et al. (2007)	Regression to polymerisation index
LILE 1+ (A site, Brice)	Dalpe & Baker (2000)	12-fold coordination;   Å,   GPa,
LILE 2+ (Ba, Sr)	Dalpe & Baker (2000)	from Brice; from regression to
HFSE 4+ (Ti, Hf, Zr)	Tiepolo et al. (2007)	Piecewise: regression for SiO₂ < 65 wt%; Brice otherwise
HFSE 5+ (Ta, Nb)	Tiepolo et al. (2007)	Piecewise: regression for SiO₂ < 56 wt%; Brice otherwise
Actinides (U, Th)	Tiepolo et al. (2007)	Regression to polymerisation index

References

• Shannon, R. D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica A, 32(5), 751–767.

• Brice, J. C. (1975). Some thermodynamic aspects of the growth of strained crystals. Journal of Crystal Growth, 28(2), 249–253.

• Blundy, J., & Wood, B. (1994). Prediction of crystal–melt partition coefficients from elastic moduli. Nature, 372, 452–454.

• Blundy, J., & Wood, B. (2003). Mineral-melt partitioning of uranium, thorium and their daughters. Reviews in Mineralogy and Geochemistry, 52(1), 59–123.

• Bédard, J. H. (2005). Partitioning coefficients between olivine and silicate melts. Lithos, 83(3–4), 394–419.

• Bédard, J. H. (2007). Trace element partitioning coefficients between silicate melts and orthopyroxene: Parameterizations of D variations. Chemical Geology, 244(1–2), 263–303.

• Adam, J., & Green, T. (2006). Trace element partitioning between mica- and amphibole-bearing garnet lherzolite and hydrous basanitic melt. Contributions to Mineralogy and Petrology, 152, 1–17.

• Dalpe, C., & Baker, D. R. (2000). Experimental investigation of large-ion-lithophile-element-, high-field-strength-element- and rare-earth-element-partitioning between calcic amphibole and basaltic melt. Contributions to Mineralogy and Petrology, 140, 233–250.

• Tiepolo, M., Oberti, R., Zanetti, A., Vannucci, R., & Foley, S. F. (2007). Trace-element partitioning between amphibole and silicate melt. Reviews in Mineralogy and Geochemistry, 67(1), 417–452.

• Corgne, A., Liebske, C., Wood, B. J., Rubie, D. C., & Frost, D. J. (2005). Silicate perovskite-melt partitioning of trace elements and geochemical signature of a deep perovskitic reservoir. Geochimica et Cosmochimica Acta, 69(2), 485–496.

• Dohmen, R., & Blundy, J. (2014). A predictive thermodynamic model for element partitioning between plagioclase and melt as a function of pressure, temperature and composition. American Journal of Science, 314(9), 1319–1372.

• Frei, D., Liebscher, A., Franz, G., Wunder, B., Klemme, S., & Blundy, J. (2009). Trace element partitioning between orthopyroxene and anhydrous silicate melt on the lherzolite solidus from 1.1 to 3.2 GPa and 1230 to 1535 °C. Contributions to Mineralogy and Petrology, 157, 473–490.

• Hill, E., Blundy, J. D., & Wood, B. J. (2011). Clinopyroxene-melt trace-element partitioning and the development of a predictive model for HFSE and Sc. Contributions to Mineralogy and Petrology, 161, 423–438.

• Salters, V. J. M., & Longhi, J. (1999). Trace element partitioning during the initial stages of melting beneath mid-ocean ridges. Earth and Planetary Science Letters, 166(1–2), 15–30.

• Sun, C., & Liang, Y. (2012). Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat. Earth and Planetary Science Letters, 327–328, 9–19.

• Sun, C., & Liang, Y. (2013). The importance of crystal chemistry and lattice strain in controlling REE partitioning between garnet and melt. Earth and Planetary Science Letters, 368, 64–75.

• van Westrenen, W., & Draper, D. S. (2007). Quantifying garnet-melt trace element partitioning using lattice-strain theory. Contributions to Mineralogy and Petrology, 154, 483–497.

• Wood, B. J., & Blundy, J. D. (2013). Trace element partitioning under crustal and uppermost mantle conditions. In Treatise on Geochemistry (2nd ed., vol. 3, pp. 421–448). Elsevier.

• Yao, L., Sun, C., & Liang, Y. (2012). A parameterized model for REE distribution between low-Ca pyroxene and basaltic melts. Contributions to Mineralogy and Petrology, 164, 261–280.