Hf system

89 accepted literature values from 10 paper(s) (experimental 19, model 15, DFT 40, unspecified 15); 0 calculated phase diagram(s).

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Accepted values by evidence class
Evidence class	Values
experimental	19
model	15
DFT	40
unspecified	15

Accepted values by property group
Property group	Values
invariant reaction	8
formation	5
mixing / partial	18
crystal structure	58

Invariant reactions (literature)

Invariant reactions reported in the literature for the Hf system (8)
T (K)	Reaction / phases	Compositions (mole fraction)	Class	Source	Location
2073	polymorphic: βHf <-> αHf	βHf: ; αHf:	experimental	[1] Bittermann 1997 cites ref. 65Rud1	Table 1, p. 2, row 19 report
2050	polymorphic: βHf <-> αHf	βHf: ; αHf:	experimental	[1] Bittermann 1997 cites ref. 71Por	Table 1, p. 2, row 20 report
2043	polymorphic: βHf <-> αHf	βHf: ; αHf:	experimental	[2] Bittermann 1997 cites Rudy 1965	Table 1, p. 2, row 1 report
2016.15	bcc(Hf)->hcp(Hf)	bcc(Hf):	model	[3] Yang 2003	Table 3, p. 3, row 18 report
2016.15	bcc(Hf)->hcp(Hf)		experimental	[3] Yang 2003 cites Brukl 1968	Table 3, p. 3, row 19 report
2016	polymorphic: βHf <-> αHf	βHf: ; αHf:	model	[1] Bittermann 1997	Table 1, p. 2, row 21 report
2016	polymorphic: βHf <-> αHf	βHf: ; αHf:	unspecified	[2] Bittermann 1997 cites ref. 2	Table 1, p. 2, row 2 report
2016	polymorphic: βHf <-> αHf	βHf: ; αHf:	model	[2] Bittermann 1997	Table 1, p. 2, row 3 report

Formation enthalpies

Literature values in kJ/mol-atom where the per-atom basis is known. DFT columns: the lowest-energy entry at the same composition (Materials Project 2026.04.13, OQMD v1.8; different energy references, never averaged), from dft_parity.json.

Enthalpies of formation, Hf system (5)
Phase	Value	T (K)	Class	Source	Location
A3-Hf	0 kJ/mol (basis unstated)	0	DFT	[4] Berche 2016	Table 2, p. 4, row 2 report
λ	-38.22 kJ/mol-atom	1723	model	[5] Idbenali 2008	Table 2, p. 3, row 16 report
λ	-38 kJ/mol-atom ± 2.7	1723	experimental	[5] Idbenali 2008 cites Mahdouk 1995	Table 2, p. 3, row 13 report
λ	-23 kJ/mol-atom		model	[5] Idbenali 2008 cites F 1988	Table 2, p. 3, row 15 report
λ	-21 kJ/mol-atom		model	[5] Idbenali 2008 cites Colinet 1985 doi	Table 2, p. 3, row 14 report

Other properties

Mixing / partial (18)

Mixing / partial, Hf system
Property	Value	Phases / composition	Class	Source	Location
Enthalpy of mixing printed: ΔH^mix	-61.928 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 1 report
Enthalpy of mixing printed: ΔH^mix	-61.2715 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 2 report
Enthalpy of mixing printed: ΔH^mix	-107.768 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 8 report
Enthalpy of mixing printed: ΔH^mix	-108.075 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 4 report
Enthalpy of mixing printed: ΔH^mix	-144.356 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 10 report
Enthalpy of mixing printed: ΔH^mix	-107.818 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 6 report
Enthalpy of mixing printed: ΔH^mix	-146.428 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 9 report
Enthalpy of mixing printed: ΔH^mix	-109.187 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 5 report
Enthalpy of mixing printed: ΔH^mix	-109.481 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 3 report
Enthalpy of mixing printed: ΔH^mix	-109.23 kJ/mol-atom	α-Hf SQS	DFT	[6] Shin 2006	Table 6, p. 7, row 7 report
Enthalpy of mixing printed: ΔHmix	-176.866 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 12 report
Enthalpy of mixing printed: ΔHmix	-181.908 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 16 report
Enthalpy of mixing printed: ΔHmix	-307.1 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 15 report
Enthalpy of mixing printed: ΔHmix	-311.16 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 13 report
Enthalpy of mixing printed: ΔHmix	-139.345 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 10 report
Enthalpy of mixing printed: ΔHmix	-180.37 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 14 report
Enthalpy of mixing printed: ΔHmix	-227.299 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 9 report
Enthalpy of mixing printed: ΔHmix	-315.52 kJ/mol-atom	β-Hf	DFT	[6] Shin 2006	Table 7, p. 7, row 11 report

Crystal structure (58)

Crystal structure, Hf system
Property	Value	T (K)	Phases / composition	Class	Source	Location
Lattice a	3.192 Å		(αHf) alloy: Hf 1	unspecified	[7] Tang 2014	Table 4, p. 5, row 3 report
Lattice a	3.532 Å		(βHf) alloy: Hf 1	unspecified	[7] Tang 2014	Table 4, p. 5, row 5 report
Lattice a printed: a	3.2 Å	0	A3-Hf	DFT	[4] Berche 2016	Table 2, p. 4, row 2 report
Lattice a	3.537 Å		Hf (bcc)	DFT	[8] Lieser 2012	Table 1, p. 4, row 1 report
Lattice a	3.538 Å		Hf (bcc)	model	[8] Lieser 2012 cites Wang 2004 doi	Table 1, p. 4, row 3 report
Lattice a	3.2 Å		Hf (hcp)	model	[8] Lieser 2012 cites Wang 2004 doi	Table 1, p. 4, row 6 report
Lattice a	3.2 Å		Hf (hcp)	DFT	[8] Lieser 2012	Table 1, p. 4, row 4 report
Lattice a	5.6953 Å	0	Hf2Hf (C14) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 38 report
Lattice a	5.6953 Å		Hf2Hf (C14) alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 2, p. 3, row 7 report
Lattice a	8.1572 Å	0	Hf2Hf (C15) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 39 report
Lattice a	5.6926 Å		Hf2Hf (C36) alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 2, p. 3, row 14 report
Lattice a	5.6926 Å	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
Lattice a	3.1948 Å		NM HCP Hf alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 1, p. 3, row 4 report
Lattice a	3.1948 Å		NM HCP Hf alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 1, p. 3, row 9 report
Lattice a	3.197 Å	298.15	(αHf) alloy: Hf 1	experimental	[7] Tang 2014 cites Markin 1983	Table 4, p. 5, row 1 report
Lattice a	3.5 Å	298.15	(βHf) alloy: Hf 1	experimental	[7] Tang 2014 cites Duwez 1951 doi	Table 4, p. 5, row 4 report
Lattice a	3.61 Å	298.15	(βHf) alloy: Hf 1	unspecified	[2] Bittermann 1997 cites ref. 2	Table 2, p. 2, row 2 report
Lattice a	3.5 Å	298.15	Hf (bcc)	experimental	[8] Lieser 2012 cites Duwez 1951 doi	Table 1, p. 4, row 2 report
Lattice a	3.1952 Å	298.15	Hf (hcp)	experimental	[8] Lieser 2012 cites Duwez 1951 doi	Table 1, p. 4, row 5 report
Lattice a	3.23 Å	298.15	NM HCP Hf alloy: Hf 1	experimental	[9] Pavlů 2010 cites Villars 1991	Table 1, p. 3, row 3 report
Lattice a	3.195 Å	298.15	α(HfxZr1-x) α(HfxZr1-x): Hf 1	experimental	[10] Bittermann 2002 cites Russell 1953 doi	Table 1, p. 4, row 13 report
Lattice a	3.19 Å	298.15	α(HfxZr1-x) α(HfxZr1-x): Hf 1	experimental	[10] Bittermann 2002 cites Ming 1981 doi	Table 1, p. 4, row 8 report
Lattice a	0.31946 not_printed	298.15	αHf alloy: Hf 1	model	[1] Bittermann 1997 cites Massalski 1990	Table 2, p. 3, row 2 report
Lattice a	0.361 not_printed	298.15	βHf alloy: Hf 1	model	[1] Bittermann 1997 cites Massalski 1990	Table 2, p. 3, row 3 report
Lattice a	3.206 Å	1373.15	(αHf) alloy: Hf 1	experimental	[7] Tang 2014	Table 4, p. 5, row 2 report
Lattice a	3.1946 Å	1743 (<)	α(HfxZr1-x) α(HfxZr1-x): Hf 1	model	[10] Bittermann 2002 cites Massalski 1990	Table 1, p. 4, row 2 report
Lattice a	3.61 Å	1987	(βHf) alloy: Hf 1	model	[10] Bittermann 2002 cites Massalski 1990	Table 1, p. 4, row 15 report
Lattice c	5.046 Å		(αHf) alloy: Hf 1	unspecified	[7] Tang 2014	Table 4, p. 5, row 3 report
Lattice c printed: c	5.064 Å	0	A3-Hf	DFT	[4] Berche 2016	Table 2, p. 4, row 2 report
Lattice c	9.505 Å	0	Hf2Hf (C14) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 38 report
Lattice c	9.505 Å		Hf2Hf (C14) alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 2, p. 3, row 7 report
Lattice c	19.1581 Å		Hf2Hf (C36) alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 2, p. 3, row 14 report
Lattice c	19.1581 Å	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
Lattice c	5.0434 Å		NM HCP Hf alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 1, p. 3, row 4 report
Lattice c	5.0434 Å		NM HCP Hf alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 1, p. 3, row 9 report
Lattice c	5.058 Å	298.15	(αHf) alloy: Hf 1	experimental	[7] Tang 2014 cites Markin 1983	Table 4, p. 5, row 1 report
Lattice c	5.12 Å	298.15	NM HCP Hf alloy: Hf 1	experimental	[9] Pavlů 2010 cites Villars 1991	Table 1, p. 3, row 3 report
Lattice c	5.051 Å	298.15	α(HfxZr1-x) α(HfxZr1-x): Hf 1	experimental	[10] Bittermann 2002 cites Russell 1953 doi	Table 1, p. 4, row 13 report
Lattice c	5.067 Å	298.15	α(HfxZr1-x) α(HfxZr1-x): Hf 1	experimental	[10] Bittermann 2002 cites Ming 1981 doi	Table 1, p. 4, row 8 report
Lattice c	0.5051 not_printed	298.15	αHf alloy: Hf 1	model	[1] Bittermann 1997 cites Massalski 1990	Table 2, p. 3, row 2 report
Lattice c	5.085 Å	1373.15	(αHf) alloy: Hf 1	experimental	[7] Tang 2014	Table 4, p. 5, row 2 report
Lattice c	5.051 Å	1743 (<)	α(HfxZr1-x) α(HfxZr1-x): Hf 1	model	[10] Bittermann 2002 cites Massalski 1990	Table 1, p. 4, row 2 report
lattice 4e z	0.0999 not_printed	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
lattice 4f z	0.054 not_printed	0	Hf2Hf (C14) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 38 report
lattice 4f z 1	0.8487 not_printed	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
lattice 4f z 2	0.1302 not_printed	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
lattice 6h x	0.8267 not_printed	0	Hf2Hf (C14) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 38 report
lattice 6h x	0.1589 not_printed	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
lattice 6h y	0.6535 not_printed	0	Hf2Hf (C14) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 38 report
lattice 6h y	0.3177 not_printed	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
lattice c a	1.58 not_printed		Hf (hcp)	model	[8] Lieser 2012 cites Wang 2004 doi	Table 1, p. 4, row 6 report
lattice c a	1.58 not_printed		Hf (hcp)	DFT	[8] Lieser 2012	Table 1, p. 4, row 4 report
lattice c a	1.5787 not_printed		NM HCP Hf alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 1, p. 3, row 9 report
lattice c a	1.5827 not_printed	298.15	Hf (hcp)	experimental	[8] Lieser 2012 cites Duwez 1951 doi	Table 1, p. 4, row 5 report
lattice v atom	2.225 10^7 pm^3	0	Hf2Hf (C14) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 38 report
lattice v atom	2.26154 10^7 pm^3	0	Hf2Hf (C15) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 39 report
lattice v atom	2.24022 10^7 pm^3	0	Hf2Hf (C36) alloy: Hf 1	DFT	[9] Pavlů 2010	Table 2, p. 3, row 45 report
lattice v atom	2.22896 10^7 pm^3		NM HCP Hf alloy: Hf 1	unspecified	[9] Pavlů 2010	Table 1, p. 3, row 9 report

Sources

Reporting papers the values were read from (a value cited from another work names that work in its row).

H. Bittermann, P. Rogl, Critical assessment and thermodynamic calculation of the ternary system boron-hafnium-titanium (B-Hf-Ti), JPE 18, 24-47 (1997). doi:10.1007/bf02646757
H. Bittermann, P. Rogl, Critical assessment and thermodynamic calculation of the binary system hafnium-carbon (Hf-C), JPE 18, 344-356 (1997). doi:10.1007/s11669-997-0061-3
Y Yang, Y.A Chang, J.-C Zhao, B.P Bewlay, Thermodynamic modeling of the Nb–Hf–Si ternary system, Intermetallics 11, 407-415 (2003). doi:10.1016/s0966-9795(03)00021-9
A. Berche, J.C. Tédenac, P. Jund, Phase diagram and enthalpy of formation of Hf-Ni-Sn, Computational Materials Science 125, 271-277 (2016). doi:10.1016/j.commatsci.2016.08.042
M. Idbenali, N. Selhaoui, L. Bouirden, C. Servant, Thermodynamic assessment of the Fe–Hf binary system, Journal of Alloys and Compounds 456, 151-158 (2008). doi:10.1016/j.jallcom.2007.02.036
Dongwon Shin, Raymundo Arróyave, Zi-Kui Liu, Thermodynamic modeling of the Hf–Si–O system, Calphad 30, 375-386 (2006). doi:10.1016/j.calphad.2006.08.006
Ying Tang, Biao Hu, Jiong Wang, Yong Du, Kaiming Cheng, Dandan Liu et al., Experimental investigation and thermodynamic assessment of the Hf–Ge system, J Mater Sci 49, 1306-1316 (2014). doi:10.1007/s10853-013-7814-7
Alyson C. Lieser, Chelsey L. Zacherl, Arkapol Saengdeejing, Zi-Kui Liu, Laszlo J. Kecskes, First-principles calculations and thermodynamic re-modeling of the Hf–W system, Calphad 38, 92-99 (2012). doi:10.1016/j.calphad.2012.04.005
J. Pavlů, J. Vřešt’ál, M. Šob, Thermodynamic modeling of Laves phases in the Cr–Hf and Cr–Ti systems: Reassessment using first-principles results, Calphad 34, 215-221 (2010). doi:10.1016/j.calphad.2010.03.003
H. Bittermann, P. Rogl, Critical assessment and thermodynamic calculation of the ternary system C-Hf-Zr (Carbon-Zirconium-Hafnium), JPE 23, 218-235 (2002). doi:10.1361/105497102770331703

Please cite

R. Arróyave, J. Saal, D. Shin, ORCHID-Values: thermodynamic and phase-equilibrium values read from the literature (version 2026.10; Version 1, machine-extracted), Zenodo (2026). doi:10.5281/zenodo.23735569
R. Arróyave, J. Saal, D. Shin, ORCHID data: umbrella record of the ORCHID datasets (version 2026.10; Version 1, machine-extracted), Zenodo (2026). doi:10.5281/zenodo.23736065

Also cite the original source of every value you use (paper_citation / paper_doi, and cited_dois for values the paper cites from earlier work); B. Hallstedt, The SGTE collection of binary datasets, Calphad 89 (2025) 102833, https://doi.org/10.1016/j.calphad.2025.102833 (CC BY 4.0), and the original assessment named in each file; A. Jain et al., The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1 (2013) 011002, https://doi.org/10.1063/1.4812323 (CC BY 4.0); J. E. Saal et al., JOM 65 (2013) 1501, https://doi.org/10.1007/s11837-013-0755-4 and S. Kirklin et al., npj Comput. Mater. 1 (2015) 15010, https://doi.org/10.1038/npjcompumats.2015.10 (CC BY 4.0). Version 1, machine-extracted: values were read by language-model readers constrained to quote their source and checked automatically, and the release was then audited on the printed pages by adversarial audits, an independent second review of fit-facing records and a preliminary human review of a frozen sample. Flags such as accepted and ESPEI-ready record screening results, not certification; known issues are listed in the release notes.

@misc{orchid_literature_2026,
  author    = {Arr{\'o}yave, Raymundo and Saal, James and Shin, Dongwon},
  title     = {{ORCHID-Values: thermodynamic and phase-equilibrium values read from the literature}},
  version   = {2026.10},
  publisher = {Zenodo},
  year      = {2026},
  doi       = {10.5281/zenodo.23735569},
  url       = {https://doi.org/10.5281/zenodo.23735569},
  note      = {Version 1, machine-extracted}
}

@misc{orchid_data_2026,
  author    = {Arr{\'o}yave, Raymundo and Saal, James and Shin, Dongwon},
  title     = {{ORCHID data: umbrella record of the ORCHID datasets}},
  version   = {2026.10},
  publisher = {Zenodo},
  year      = {2026},
  doi       = {10.5281/zenodo.23736065},
  url       = {https://doi.org/10.5281/zenodo.23736065},
  note      = {Version 1, machine-extracted}
}