Al3Zr4: enthalpy of formation

24 accepted literature formation-enthalpy value(s) (model 17, DFT 7); Materials Project -44.408 kJ/mol-atom (mp-aaaaaswm); OQMD -44.415 kJ/mol-atom (oqmd-27981).

Systems: Al–Zr

Literature values

Enthalpy of formation of Al3Zr4 reported in the literature (24)
Value	Phase as printed	T (K)	Class	Method	System	Source	Location
-58.5 unknown	Al3Zr4		model	CALPHAD	Al–Zr	[1] Tamim 2018 cites Wang 2001 doi	Table 3, p. 9, row 40 report
-58.5 kJ/mol-atom	Al3Zr4	298.15	model	CALPHAD	Al–Zr	[2] Fischer 2015 cites Wang 2001 doi	Table 2, p. 4, row 70 report
-58.5 kJ/mol-atom	Zr4Al3		model		Al–Zr	[3] T 2001	Table 2, p. 2, row 11 report
-58.48 kJ/mol-atom	Al3Zr4		model	CALPHAD	Al–Zr	[4] Long 2020 cites Wang 2001 doi	Table 4, p. 7, row 73 report
-52.138 kJ/mol-atom	Al3Zr4		model		Al–Zr	[4] Long 2020	Table 4, p. 7, row 68 report
-47.56 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Ghosh 2005 doi	Table 2, p. 4, row 72 report
-46.3 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Mihalkovic 2011	Table 2, p. 4, row 74 report
-46.21 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Wang 2011 doi	Table 2, p. 4, row 75 report
-45.708 unknown	Al3Zr4		model		Al–Zr	[1] Tamim 2018	Table 3, p. 9, row 35 report
-44.57 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Duan 2014 doi	Table 2, p. 4, row 78 report
-44.54 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Colinet 2013 doi	Table 2, p. 4, row 76 report
-44.38 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Saal 2013 doi	Table 2, p. 4, row 77 report
-42.925 unknown	Al3Zr4		model		Al–Zr	[1] Tamim 2018	Table 3, p. 9, row 36 report
-42.925 kJ/mol-atom	Al3Zr4		model	CALPHAD	Al–Zr	[4] Long 2020 cites Tamim 2018 doi	Table 4, p. 7, row 75 report
-41.18 kJ/mol-atom	Al3Zr4	298.15	model	CALPHAD	Al–Zr	[2] Fischer 2015	Table 2, p. 4, row 71 report
-40.894 kJ/mol-atom	Al3Zr4		model	CALPHAD	Al–Zr	[4] Long 2020 cites Fischer 2015 doi	Table 4, p. 7, row 74 report
-39 kJ/mol-atom	Al3Zr4	298.15	model		Al–Zr	[2] Fischer 2015 cites Zhang 2010 doi	Table 2, p. 4, row 73 report
-47.555 unknown	Al3Zr4		DFT	ab initio	Al–Zr	[1] Tamim 2018 cites Ghosh 2005 doi	Table 3, p. 9, row 39 report
-47.555 kJ/mol-atom	Al3Zr4		DFT	Ab-initio	Al–Zr	[4] Long 2020 cites Ghosh 2005 doi	Table 4, p. 7, row 71 report
-46.21 unknown	Al3Zr4		DFT	ab initio	Al–Zr	[1] Tamim 2018 cites Wang 2011 doi	Table 3, p. 9, row 38 report
-46.21 kJ/mol-atom	Al3Zr4		DFT	Ab-initio	Al–Zr	[4] Long 2020 cites Wang 2011 doi	Table 4, p. 7, row 70 report
-44.875 unknown	Al3Zr4		DFT	ab initio	Al–Zr	[1] Tamim 2018 cites Duan 2014 doi	Table 3, p. 9, row 37 report
-44.875 kJ/mol-atom	Al3Zr4		DFT	Ab-initio	Al–Zr	[4] Long 2020 cites Duan 2013	Table 4, p. 7, row 69 report
-39 kJ/mol-atom	Al3Zr4		DFT	Ab-initio	Al–Zr	[4] Long 2020 cites Zhang 2010 doi	Table 4, p. 7, row 72 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 Al3Zr4
Value	Unit	Reading	Method (class, basis)	Effective
-58.5	unknown	0.05	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-58.5	kJ/mol-atom	0.05	3.9 (model_calculated, calibrated)	3.9
-58.5	kJ/mol-atom	0.05	3.9 (model_calculated, calibrated)	3.9
-58.48	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-52.138	kJ/mol-atom	5.000e-4	3.9 (model_calculated, calibrated)	3.9
-47.56	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-46.3	kJ/mol-atom	0.05	3.9 (model_calculated, calibrated)	3.9
-46.21	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-45.708	unknown	5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-44.57	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-44.54	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-44.38	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-42.925	unknown	5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-42.925	kJ/mol-atom	5.000e-4	3.9 (model_calculated, calibrated)	3.9
-41.18	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-40.894	kJ/mol-atom	5.000e-4	3.9 (model_calculated, calibrated)	3.9
-39	kJ/mol-atom	0.05	3.9 (model_calculated, calibrated)	3.9
-47.555	unknown	5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-47.555	kJ/mol-atom	5.000e-4	8.395 (dft, calibrated)	8.395
-46.21	unknown	0.005	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-46.21	kJ/mol-atom	0.005	8.395 (dft, calibrated)	8.395
-44.875	unknown	5.000e-4	unit 'unknown' not convertible to kJ/mol-atom	unit 'unknown' not convertible to kJ/mol-atom
-44.875	kJ/mol-atom	5.000e-4	8.395 (dft, calibrated)	8.395
-39	kJ/mol-atom	0.05	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 Al3Zr4
Source	Entry	kJ/mol-atom	eV/atom	Space group	E above hull (kJ/mol-atom)	E above hull (eV/atom)	Theoretical
Materials Project	mp-aaaaaswm	-44.408	-0.460261	P6/mmm	0	0	no
OQMD	oqmd-27981	-44.415	-0.460326	P6/mmm	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

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
T. Wang, Z. Jin, J.-C. Zhao, J. Phase Equilib., 22, 544-51(2001). doi:10.1007/s12385-001-0072-4
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

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}
}