Al3Zr2: enthalpy of formation

42 accepted literature formation-enthalpy value(s) (experimental 6, model 29, DFT 7); experimental median -46.96 kJ/mol-atom (n = 5); Materials Project -50.307 kJ/mol-atom (mp-aaaaacfa); OQMD -50.271 kJ/mol-atom (oqmd-10622).

Systems: Al–Zr

Literature values

Enthalpy of formation of Al3Zr2 reported in the literature (42)
Value	Phase as printed	T (K)	Class	Method	System	Source	Location
-59.6 kJ/mol-atom ± 2.4	Al3Zr2	298.15	experimental		Al–Zr	[1] Long 2020 cites Macia 2018	Table 4, p. 7, row 36 report
-55 kJ/mol-atom	Zr2Al3	298.15	experimental		Al–Zr	[2] T 2001 cites Kematick 1984	Table 2, p. 2, row 18 report
-55 unknown ± 4	Al3Zr2	298.15	experimental		Al–Zr	[3] Tamim 2018 cites Kuznetsov 1983	Table 3, p. 9, row 64 report
-46.96 kJ/mol-atom	Al3Zr2	298.15	experimental		Al–Zr	[4] Fischer 2015 cites Kematick 1984 doi	Table 2, p. 4, row 30 report
-46.94 kJ/mol-atom	Al3Zr2	298.15	experimental		Al–Zr	[5] Saunders 1986 cites ref. 36	Table 2, p. 5, row 5 report
55 kJ/mol-atom ± 4	Al3Zr2	298.15	experimental		Al–Zr	[1] Long 2020 cites Kematick 1984 doi	Table 4, p. 7, row 35 report
-57.664 kJ/mol-atom	Al3Zr2		model		Al–Zr	[1] Long 2020	Table 4, p. 7, row 30 report
-56.613 kJ/mol-atom	Al3Zr2		model	CALPHAD	Al–Zr	[1] Long 2020 cites Wang 2001 doi	Table 4, p. 7, row 40 report
-56.6 kJ/mol-atom	Zr2Al3		model		Al–Zr	[2] T 2001	Table 2, p. 2, row 20 report
-56.6 kJ/mol-atom	Al3Zr2	298.15	model	CALPHAD	Al–Zr	[4] Fischer 2015 cites Wang 2001 doi	Table 2, p. 4, row 33 report
-56.6 unknown	Al3Zr2		model	CALPHAD	Al–Zr	[3] Tamim 2018 cites Wang 2001 doi	Table 3, p. 9, row 67 report
-51.65 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Ghosh 2005 doi	Table 2, p. 4, row 36 report
-50.613 unknown	Al3Zr2		model		Al–Zr	[3] Tamim 2018	Table 3, p. 9, row 59 report
-50.27 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Saal 2013 doi	Table 2, p. 4, row 42 report
-50.12 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Mihalkovic 2011	Table 2, p. 4, row 38 report
-49.96 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Colinet 2013 doi	Table 2, p. 4, row 41 report
-49.9 kJ/mol-atom	Al3Zr2	298.15	model	CALPHAD	Al–Zr	[4] Fischer 2015	Table 2, p. 4, row 35 report
-49.9 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Harvey 2012 doi	Table 2, p. 4, row 40 report
-49.9 kJ/mol-atom	Al3Zr2	298.15	model	CALPHAD	Al–Zr	[4] Fischer 2015 cites Harvey 2012 doi	Table 2, p. 4, row 34 report
-49.899 kJ/mol-atom	Al3Zr2		model	CALPHAD	Al–Zr	[1] Long 2020 cites Fischer 2015 doi	Table 4, p. 7, row 41 report
-49.87 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Duan 2014 doi	Table 2, p. 4, row 43 report
-49.84 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Wang 2011 doi	Table 2, p. 4, row 39 report
-49.005 kJ/mol-atom	Al3Zr2		model	CALPHAD	Al–Zr	[1] Long 2020 cites Tamim 2018 doi	Table 4, p. 7, row 42 report
-49.005 unknown	Al3Zr2		model		Al–Zr	[3] Tamim 2018	Table 3, p. 9, row 60 report
-47.3 kJ/mol-atom	Al3Zr2		model	CALPHAD	Al–Zr	[1] Long 2020 cites Saunders 1986 doi	Table 4, p. 7, row 37 report
-47.3 kJ/mol-atom	Al3Zr2	1	model		Al–Zr	[5] Saunders 1986	Table 4, p. 8, row 10 report
-46.94 kJ/mol-atom	Al3Zr2		model	CALPHAD	Al–Zr	[1] Long 2020 cites Saunders 1989	Table 4, p. 7, row 38 report
-46.94 kJ/mol-atom	Al3Zr2	298.15	model	CALPHAD	Al–Zr	[4] Fischer 2015 cites Saunders 1989	Table 2, p. 4, row 32 report
-46.9 kJ/mol-atom	Zr2Al3		model		Al–Zr	[2] T 2001 cites Saunders 1989	Table 2, p. 2, row 19 report
-46.9 unknown	Al3Zr2		model	CALPHAD	Al–Zr	[3] Tamim 2018 cites Saunders 1988	Table 3, p. 9, row 65 report
-45.58 kJ/mol-atom	Al3Zr2		model		Al–Zr	[5] Saunders 1986	Table 2, p. 5, row 6 report
-45.47 kJ/mol-atom	Al3Zr2	298.15	model		Al–Zr	[4] Fischer 2015 cites Zhang 2010 doi	Table 2, p. 4, row 37 report
-45.2 kJ/mol-atom	Al3Zr2		model	CALPHAD	Al–Zr	[1] Long 2020 cites Murray 1992 doi	Table 4, p. 7, row 39 report
-45.2 kJ/mol-atom	Al3Zr2	298.15	model	CALPHAD	Al–Zr	[4] Fischer 2015 cites Murray 1992 doi	Table 2, p. 4, row 31 report
-45.2 unknown	Al3Zr2		model	CALPHAD	Al–Zr	[3] Tamim 2018 cites Murray 1992 doi	Table 3, p. 9, row 66 report
-51.649 kJ/mol-atom	Al3Zr2		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Ghosh 2005 doi	Table 4, p. 7, row 33 report
-51.649 unknown	Al3Zr2		DFT	ab initio	Al–Zr	[3] Tamim 2018 cites Ghosh 2005 doi	Table 3, p. 9, row 63 report
-49.867 kJ/mol-atom	Al3Zr2		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Duan 2013	Table 4, p. 7, row 31 report
-49.867 unknown	Al3Zr2		DFT	ab initio	Al–Zr	[3] Tamim 2018 cites Duan 2014 doi	Table 3, p. 9, row 61 report
-49.84 unknown	Al3Zr2		DFT	ab initio	Al–Zr	[3] Tamim 2018 cites Wang 2011 doi	Table 3, p. 9, row 62 report
-49.84 kJ/mol-atom	Al3Zr2		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Wang 2011 doi	Table 4, p. 7, row 32 report
-45.474 kJ/mol-atom	Al3Zr2		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Zhang 2010 doi	Table 4, p. 7, row 34 report

Uncertainty budget

Components kept separate, in the value's unit (literature SCHEMA.md, UNCERTAINTY_CALIBRATION.md): effective = max(sqrt(max(printed, reading, method)^2 + composition^2 + conversion^2), scatter). The method floor is the robust between-study scatter of the method class in ORCHID (calibrated) or a documented prior; printed values and printed uncertainties are unchanged.

Uncertainty budget of the literature values of Al3Zr2
Value	Unit	Printed	Reading	Method (class, basis)	Effective
-59.6	kJ/mol-atom	2.4	0.05	3.5 (unknown, calibrated)	3.5
-55	kJ/mol-atom		0.5	3.5 (unknown, calibrated)	3.5
-55	unknown	4	0.05	unit 'unknown' not convertible to kJ/mol-atom	4
-46.96	kJ/mol-atom		0.005	3.5 (unknown, calibrated)	3.5
-46.94	kJ/mol-atom		0.005	3.5 (unknown, calibrated)	3.5
55	kJ/mol-atom	4	0.05	3.5 (unknown, calibrated)	4
-57.664	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-56.613	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-56.6	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-56.6	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-56.6	unknown		0.05	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-51.65	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-50.613	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-50.27	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-50.12	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-49.96	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-49.9	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-49.9	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-49.9	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-49.899	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-49.87	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-49.84	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-49.005	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-49.005	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-47.3	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-47.3	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-46.94	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-46.94	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-46.9	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-46.9	unknown		0.05	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-45.58	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-45.47	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-45.2	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-45.2	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-45.2	unknown		0.05	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-51.649	kJ/mol-atom		5.000e-4	8.395 (dft, calibrated)	8.395
-51.649	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-49.867	kJ/mol-atom		5.000e-4	8.395 (dft, calibrated)	8.395
-49.867	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-49.84	unknown		0.005	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-49.84	kJ/mol-atom		0.005	8.395 (dft, calibrated)	8.395
-45.474	kJ/mol-atom		5.000e-4	8.395 (dft, calibrated)	8.395

DFT formation energies

Lowest-energy entries at this composition. Materials Project and OQMD use different energy references and are never averaged. 1 eV/atom = 96.485 kJ/mol-atom.

DFT formation energy of Al3Zr2
Source	Entry	kJ/mol-atom	eV/atom	Space group	E above hull (kJ/mol-atom)	E above hull (eV/atom)	Theoretical
Materials Project	mp-aaaaacfa	-50.307	-0.521393	Fdd2	0	0	no
OQMD	oqmd-10622	-50.271	-0.521025	Fdd2	0	0	no

DFT sources: A. Jain et al., Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1 (2013) 011002. doi:10.1063/1.4812323 (CC BY 4.0); J. E. Saal et al., JOM 65 (2013) 1501-1509; S. Kirklin et al., npj Comput. Mater. 1 (2015) 15010. doi:10.1007/s11837-013-0755-4 (CC BY 4.0);

Sources

Zhaohui Long, Dongyu Cui, Hongxing Hu, Zhi Li, Fucheng Yin, Touwen Fan, Thermodynamic Modeling of the Al-Li-Zr Ternary System, J. Phase Equilib. Diffus. 41, 623-641 (2020). doi:10.1007/s11669-020-00827-z
T. Wang, Z. Jin, J.-C. Zhao, J. Phase Equilib., 22, 544-51(2001). doi:10.1007/s12385-001-0072-4
Rkia Tamim, Kamal Mahdouk, Thermodynamic reassessment of the Al–Zr binary system, J Therm Anal Calorim 131, 1187-1200 (2018). doi:10.1007/s10973-017-6635-3
Evelyne Fischer, Catherine Colinet, An Updated Thermodynamic Modeling of the Al-Zr System, J. Phase Equilib. Diffus. 36, 404-413 (2015). doi:10.1007/s11669-015-0398-y
N. Saunders, V. G. Rivlin, Thermodynamic characterization of Al–Cr, Al–Zr, and Al–Cr–Zr alloy systems, Materials Science and Technology 2, 520-527 (1986). doi:10.1179/mst.1986.2.6.520

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-Parity: DFT-vs-experiment formation-enthalpy benchmark (version 2026.10; Version 1, machine-extracted), Zenodo (2026). doi:10.5281/zenodo.23735943
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); 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); G. Kim, S. V. Meschel, P. Nash, W. Chen, Experimental formation enthalpies for intermetallic phases and other inorganic compounds, Scientific Data 4 (2017) 170162, https://doi.org/10.1038/sdata.2017.162; 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. 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_dft_benchmark_2026,
  author    = {Arr{\'o}yave, Raymundo and Saal, James and Shin, Dongwon},
  title     = {{ORCHID-Parity: DFT-vs-experiment formation-enthalpy benchmark}},
  version   = {2026.10},
  publisher = {Zenodo},
  year      = {2026},
  doi       = {10.5281/zenodo.23735943},
  url       = {https://doi.org/10.5281/zenodo.23735943},
  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}
}