Al4Zr5: enthalpy of formation

39 accepted literature formation-enthalpy value(s) (experimental 5, model 27, DFT 7); experimental median -47.8 kJ/mol-atom (n = 4); Materials Project -40.375 kJ/mol-atom (mp-aaabgmiw); OQMD -40.389 kJ/mol-atom (oqmd-27980).

Systems: Al–Zr

Literature values

Enthalpy of formation of Al4Zr5 reported in the literature (39)
Value	Phase as printed	T (K)	Class	Method	System	Source	Location
-52 kJ/mol-atom ± 4	Al4Zr5	298.15	experimental		Al–Zr	[1] Long 2020 cites Kematick 1984 doi	Table 4, p. 7, row 61 report
-52 unknown ± 4	Al4Zr5	298.15	experimental		Al–Zr	[2] Tamim 2018 cites Kematick 1984 doi	Table 3, p. 9, row 46 report
-52 kJ/mol-atom	Zr5Al4	298.15	experimental		Al–Zr	[3] T 2001 cites Kematick 1984	Table 2, p. 2, row 12 report
-43.6 kJ/mol-atom	Al4Zr5	298.15	experimental		Al–Zr	[4] Saunders 1986 cites ref. 36	Table 2, p. 5, row 9 report
-43.59 kJ/mol-atom	Al4Zr5	298.15	experimental		Al–Zr	[5] Fischer 2015 cites Kematick 1984 doi	Table 2, p. 4, row 58 report
-55.424 kJ/mol-atom	Al4Zr5		model	CALPHAD	Al–Zr	[1] Long 2020 cites Wang 2001 doi	Table 4, p. 7, row 65 report
-55.4 kJ/mol-atom	Zr5Al4		model		Al–Zr	[3] T 2001	Table 2, p. 2, row 14 report
-55.4 unknown	Al4Zr5		model	CALPHAD	Al–Zr	[2] Tamim 2018 cites Wang 2001 doi	Table 3, p. 9, row 49 report
-55.4 kJ/mol-atom	Al4Zr5	298.15	model	CALPHAD	Al–Zr	[5] Fischer 2015 cites Wang 2001 doi	Table 2, p. 4, row 61 report
-49.419 kJ/mol-atom	Al4Zr5		model		Al–Zr	[1] Long 2020	Table 4, p. 7, row 56 report
-45.597 kJ/mol-atom	Al4Zr5	1	model		Al–Zr	[4] Saunders 1986	Table 4, p. 8, row 12 report
-45.597 kJ/mol-atom	Al4Zr5		model	CALPHAD	Al–Zr	[1] Long 2020 cites Saunders 1986 doi	Table 4, p. 7, row 62 report
-43.717 unknown	Al4Zr5		model		Al–Zr	[2] Tamim 2018	Table 3, p. 9, row 41 report
-43.2 kJ/mol-atom	Al4Zr5		model		Al–Zr	[4] Saunders 1986	Table 2, p. 5, row 10 report
-43.13 kJ/mol-atom	Al4Zr5	298.15	model	CALPHAD	Al–Zr	[5] Fischer 2015 cites Murray 1992 doi	Table 2, p. 4, row 59 report
-43.127 kJ/mol-atom	Al4Zr5		model	CALPHAD	Al–Zr	[1] Long 2020 cites Murray 1992 doi	Table 4, p. 7, row 64 report
-43.127 unknown	Al4Zr5		model	CALPHAD	Al–Zr	[2] Tamim 2018 cites Murray 1992 doi	Table 3, p. 9, row 48 report
-42 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Ghosh 2005 doi	Table 2, p. 4, row 63 report
-41.371 kJ/mol-atom	Al4Zr5		model	CALPHAD	Al–Zr	[1] Long 2020 cites Tamim 2018 doi	Table 4, p. 7, row 67 report
-41.371 unknown	Al4Zr5		model		Al–Zr	[2] Tamim 2018	Table 3, p. 9, row 42 report
-41 kJ/mol-atom	Al4Zr5	298.15	model	CALPHAD	Al–Zr	[5] Fischer 2015 cites Saunders 1989	Table 2, p. 4, row 60 report
-41 kJ/mol-atom	Zr5Al4		model		Al–Zr	[3] T 2001 cites Saunders 1989	Table 2, p. 2, row 13 report
-41 unknown	Al4Zr5		model	CALPHAD	Al–Zr	[2] Tamim 2018 cites Saunders 1988	Table 3, p. 9, row 47 report
-41 kJ/mol-atom	Al4Zr5		model	CALPHAD	Al–Zr	[1] Long 2020 cites Saunders 1989	Table 4, p. 7, row 63 report
-40.5 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Mihalkovic 2011	Table 2, p. 4, row 65 report
-40.43 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Saal 2013 doi	Table 2, p. 4, row 68 report
-40.35 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Colinet 2013 doi	Table 2, p. 4, row 67 report
-40.18 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Duan 2014 doi	Table 2, p. 4, row 69 report
-40.06 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Wang 2011 doi	Table 2, p. 4, row 66 report
-38.725 kJ/mol-atom	Al4Zr5		model	CALPHAD	Al–Zr	[1] Long 2020 cites Fischer 2015 doi	Table 4, p. 7, row 66 report
-38.66 kJ/mol-atom	Al4Zr5	298.15	model	CALPHAD	Al–Zr	[5] Fischer 2015	Table 2, p. 4, row 62 report
-35.21 kJ/mol-atom	Al4Zr5	298.15	model		Al–Zr	[5] Fischer 2015 cites Zhang 2010 doi	Table 2, p. 4, row 64 report
-42.002 kJ/mol-atom	Al4Zr5		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Ghosh 2005 doi	Table 4, p. 7, row 59 report
-42.002 unknown	Al4Zr5		DFT	ab initio	Al–Zr	[2] Tamim 2018 cites Ghosh 2005 doi	Table 3, p. 9, row 45 report
-40.175 unknown	Al4Zr5		DFT	ab initio	Al–Zr	[2] Tamim 2018 cites Duan 2014 doi	Table 3, p. 9, row 43 report
-40.175 kJ/mol-atom	Al4Zr5		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Duan 2013	Table 4, p. 7, row 57 report
-40.06 kJ/mol-atom	Al4Zr5		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Wang 2011 doi	Table 4, p. 7, row 58 report
-40.06 unknown	Al4Zr5		DFT	ab initio	Al–Zr	[2] Tamim 2018 cites Wang 2011 doi	Table 3, p. 9, row 44 report
-35.208 kJ/mol-atom	Al4Zr5		DFT	Ab-initio	Al–Zr	[1] Long 2020 cites Zhang 2010 doi	Table 4, p. 7, row 60 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 Al4Zr5
Value	Unit	Printed	Reading	Method (class, basis)	Effective
-52	kJ/mol-atom	4	0.05	3.5 (unknown, calibrated)	4
-52	unknown	4	0.05	unit 'unknown' not convertible to kJ/mol-atom	4
-52	kJ/mol-atom		0.5	3.5 (unknown, calibrated)	3.5
-43.6	kJ/mol-atom		0.05	3.5 (unknown, calibrated)	3.5
-43.59	kJ/mol-atom		0.005	3.5 (unknown, calibrated)	3.5
-55.424	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-55.4	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-55.4	unknown		0.05	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-55.4	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-49.419	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-45.597	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-45.597	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-43.717	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-43.2	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-43.13	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-43.127	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-43.127	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-42	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-41.371	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-41.371	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-41	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-41	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-41	unknown		0.05	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-41	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-40.5	kJ/mol-atom		0.05	3.9 (model_calculated, calibrated)	3.9
-40.43	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-40.35	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-40.18	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-40.06	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-38.725	kJ/mol-atom		5.000e-4	3.9 (model_calculated, calibrated)	3.9
-38.66	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-35.21	kJ/mol-atom		0.005	3.9 (model_calculated, calibrated)	3.9
-42.002	kJ/mol-atom		5.000e-4	8.395 (dft, calibrated)	8.395
-42.002	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-40.175	unknown		5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-40.175	kJ/mol-atom		5.000e-4	8.395 (dft, calibrated)	8.395
-40.06	kJ/mol-atom		0.005	8.395 (dft, calibrated)	8.395
-40.06	unknown		0.005	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-35.208	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 Al4Zr5
Source	Entry	kJ/mol-atom	eV/atom	Space group	E above hull (kJ/mol-atom)	E above hull (eV/atom)	Theoretical
Materials Project	mp-aaabgmiw	-40.375	-0.418458	P6_3/mcm	4.5795	0.0475	no
OQMD	oqmd-27980	-40.389	-0.418601	P63/mcm	4.5681	0.0473	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
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
T. Wang, Z. Jin, J.-C. Zhao, J. Phase Equilib., 22, 544-51(2001). doi:10.1007/s12385-001-0072-4
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
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

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}
}