BiEr: enthalpy of formation

22 accepted literature formation-enthalpy value(s) (experimental 10, model 7, DFT 5); experimental median -103 kJ/mol-atom (n = 10); Materials Project -77.511 kJ/mol-atom (mp-aaaabikb); OQMD -80.472 kJ/mol-atom (oqmd-1926318).

Systems: Bi–Er

Literature values

Enthalpy of formation of BiEr reported in the literature (22)
Value	Phase as printed	T (K)	Class	Method	System	Source	Location
-109 kJ/mol-atom	BiEr	298.15	experimental		Bi–Er	[1] Wang 2013 cites Petrashkevich 1976	Table 4, p. 4, row 6 report
-109 kJ/mol-atom	ErBi	298.15	experimental		Bi–Er	[2] Wang 2017 cites Petrashkevich 1976	Table 9, p. 7, row 2 report
-109 kJ/mol-atom	α-ErBi	298.15	experimental	EMF	Bi–Er	[3] Bennoui 2022 cites Petrashkevich 1976	Table 2, p. 5, row 12 report
-103 kJ/mol-atom	ErBi	298.15	experimental		Bi–Er	[2] Wang 2017 cites Yamshchikov 1979	Table 9, p. 7, row 4 report
-103 kJ/mol-atom	BiEr	298.15	experimental		Bi–Er	[1] Wang 2013 cites Yamshchikov 1979	Table 4, p. 4, row 7 report
-103 kJ/mol-atom	α-ErBi	298.15	experimental	EMF	Bi–Er	[3] Bennoui 2022 cites Yamshchikov 1979	Table 2, p. 5, row 11 report
-101.3 kJ/mol-atom	α-ErBi	298.15	experimental	EMF	Bi–Er	[3] Bennoui 2022 cites Sidorko 2011 doi	Table 2, p. 5, row 14 report
-90 kJ/mol-atom	α-ErBi	298.15	experimental	Calorimetry	Bi–Er	[3] Bennoui 2022 cites Borzone 1993 doi	Table 2, p. 5, row 13 report
-90 kJ/mol-atom	BiEr	298.15	experimental		Bi–Er	[1] Wang 2013 cites Borzone 1993 doi	Table 4, p. 4, row 5 report
-90 kJ/mol-atom	ErBi	298.15	experimental		Bi–Er	[2] Wang 2017 cites Borzone 1993 doi	Table 9, p. 7, row 3 report
-83.62 kJ/mol-atom	α-ErBi		model	CALPHAD	Bi–Er	[3] Bennoui 2022 cites Wang 2013 doi	Table 2, p. 5, row 9 report
-80.35 kJ/mol-atom	α-ErBi		model	CALPHAD	Bi–Er	[3] Bennoui 2022 cites Wang 2017 doi	Table 2, p. 5, row 10 report
-80.35 kJ/mol-atom	ErBi		model		Bi–Er	[2] Wang 2017	Table 9, p. 7, row 5 report
-79.131 kJ/mol-atom	α-ErBi		model	CALPHAD	Bi–Er	[3] Bennoui 2022	Table 2, p. 5, row 5 report
-75 kJ/mol-atom	BiEr	0	model	Miedima model	Bi–Er	[1] Wang 2013 cites Colinet 1984 doi	Table 4, p. 4, row 9 report
-75 kJ/mol-atom	ErBi		model		Bi–Er	[2] Wang 2017 cites Colinet 1984 doi	Table 9, p. 7, row 1 report
-75 kJ/mol-atom	α-ErBi		model	Miedema model	Bi–Er	[3] Bennoui 2022 cites Colinet 1984 doi	Table 2, p. 5, row 15 report
-82.069 kJ/mol-atom	α-ErBi	0	DFT	DFT	Bi–Er	[3] Bennoui 2022 cites Wang 2013 doi	Table 2, p. 5, row 8 report
-82.069 kJ/mol-atom	BiEr	0	DFT	first-principles	Bi–Er	[1] Wang 2013	Table 4, p. 4, row 8 report
-80.274 kJ/mol-atom	α-ErBi		DFT	DFT	Bi–Er	[3] Bennoui 2022 cites Kirklin 2015 doi	Table 2, p. 5, row 6 report
-80.005 kJ/mol-atom	α-ErBi	0	DFT	DFT	Bi–Er	[3] Bennoui 2022	Table 2, p. 5, row 4 report
-77.576 kJ/mol-atom	α-ErBi		DFT	DFT	Bi–Er	[3] Bennoui 2022 cites Jain 2013 doi	Table 2, p. 5, row 7 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 BiEr
Value	Unit	Reading	Method (class, basis)	Effective
-109	kJ/mol-atom	5.000e-4	3.5 (unknown, calibrated)	3.5
-109	kJ/mol-atom	0.5	3.5 (unknown, calibrated)	3.5
-109	kJ/mol-atom	0.05	4.6 (emf, cleaned_below_threshold)	4.6
-103	kJ/mol-atom	0.5	3.5 (unknown, calibrated)	3.5
-103	kJ/mol-atom	5.000e-4	3.5 (unknown, calibrated)	3.5
-103	kJ/mol-atom	0.05	4.6 (emf, cleaned_below_threshold)	4.6
-101.3	kJ/mol-atom	0.05	4.6 (emf, cleaned_below_threshold)	4.6
-90	kJ/mol-atom	0.05	3.2 (solution_reaction_calorimetry, calibrated)	3.2
-90	kJ/mol-atom	5.000e-4	3.5 (unknown, calibrated)	3.5
-90	kJ/mol-atom	0.5	3.5 (unknown, calibrated)	3.5
-83.62	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-80.35	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-80.35	kJ/mol-atom	0.005	3.9 (model_calculated, calibrated)	3.9
-79.131	kJ/mol-atom	5.000e-4	3.9 (model_calculated, calibrated)	3.9
-75	kJ/mol-atom	5.000e-4	3.9 (model_calculated, calibrated)	3.9
-75	kJ/mol-atom	0.5	3.9 (model_calculated, calibrated)	3.9
-75	kJ/mol-atom	0.05	3.9 (model_calculated, calibrated)	3.9
-82.069	kJ/mol-atom	5.000e-4	8.395 (dft, calibrated)	8.395
-82.069	kJ/mol-atom	5.000e-4	8.395 (dft, calibrated)	8.395
-80.274	kJ/mol-atom	5.000e-4	8.395 (dft, calibrated)	8.395
-80.005	kJ/mol-atom	5.000e-4	8.395 (dft, calibrated)	8.395
-77.576	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 BiEr
Source	Entry	kJ/mol-atom	eV/atom	Space group	E above hull (kJ/mol-atom)	E above hull (eV/atom)	Theoretical
Materials Project	mp-aaaabikb	-77.511	-0.803348	Fm-3m	0	0	no
OQMD	oqmd-1926318	-80.472	-0.834035	P-3m1	0	0	yes

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

Jinsan Wang, Changrong Li, Cuiping Guo, Zhenmin Du, Bo Wu, Thermodynamic assessment of the Bi–Er and the Bi–Dy systems, Thermochimica Acta 566, 44-49 (2013). doi:10.1016/j.tca.2013.05.024
Yafei Wang, Wentao Zhou, Shaoqiang Guo, Jinsuo Zhang, Thermodynamic properties of fission products (Pr, Ce, Er) in liquid bismuth by thermodynamic assessment, Journal of Nuclear Materials 495, 181-191 (2017). doi:10.1016/j.jnucmat.2017.08.016
S. Bennoui, Y. Djaballah, V. Vassiliev, A. Belgacem-Bouzida, Thermodynamic Study of Er-Bi and Er-Te Systems by Combination of First-Principles Calculations and the CALPHAD Method, J. Phase Equilib. Diffus. 43, 126-138 (2022). doi:10.1007/s11669-022-00947-8

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}
}