# Al3Zr4: enthalpy of formation

> Enthalpy of formation of Al3Zr4: 24 literature value(s) with sources, pages and quotes and DFT values (Materials Project / OQMD), from ORCHID.

HTML: https://data.orchid-project.org/compounds/Al3Zr4.html · Markdown: https://data.orchid-project.org/compounds/Al3Zr4.md

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](https://data.orchid-project.org/systems/AL-ZR.html)

## Literature values

Table: Enthalpy of formation of Al3Zr4 reported in the literature (24)

| Value | Phase as printed | T (K) | Class | Method | System | Source | Location | Quote |
|---:|---|---:|---|---|---|---|---|---|
| -58.5 unknown | Al3Zr4 |  | model | CALPHAD | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [1] Tamim 2018; _cites Wang 2001_ [doi](https://doi.org/10.1007/s11669-001-0072-4) | Table 3, p. 9, row 40; `ORC-O2WCIV7JEN.0679a0` |  |
| -58.5 kJ/mol-atom | Al3Zr4 | 298.15 | model | CALPHAD | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Wang 2001_ [doi](https://doi.org/10.1007/s11669-001-0072-4) | Table 2, p. 4, row 70; `ORC-PW7OFDPHMG` |  |
| -58.5 kJ/mol-atom | Zr4Al3 |  | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [3] T 2001 | Table 2, p. 2, row 11; `ORC-ZEMQSSSNL5` |  |
| -58.48 kJ/mol-atom | Al3Zr4 |  | model | CALPHAD | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Wang 2001_ [doi](https://doi.org/10.1007/s11669-001-0072-4) | Table 4, p. 7, row 73; `ORC-4FZB6UC6GR.790619` |  |
| -52.138 kJ/mol-atom | Al3Zr4 |  | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020 | Table 4, p. 7, row 68; `ORC-VKGC3AJ4FD.b25bb8` |  |
| -47.56 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Ghosh 2005_ [doi](https://doi.org/10.1016/j.actamat.2005.03.028) | Table 2, p. 4, row 72; `ORC-CCBQMROEQU` |  |
| -46.3 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Mihalkovic 2011_ | Table 2, p. 4, row 74; `ORC-EJQPJLZMFV` |  |
| -46.21 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Wang 2011_ [doi](https://doi.org/10.1016/j.calphad.2011.09.009) | Table 2, p. 4, row 75; `ORC-MIPPUF44PQ` |  |
| -45.708 unknown | Al3Zr4 |  | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [1] Tamim 2018 | Table 3, p. 9, row 35; `ORC-MNK4SUPTCR.24d12b` |  |
| -44.57 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Duan 2014_ [doi](https://doi.org/10.1016/j.jallcom.2013.12.079) | Table 2, p. 4, row 78; `ORC-5SEEN2EMNP` |  |
| -44.54 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Colinet 2013_ [doi](https://doi.org/10.1016/j.jssc.2013.07.017) | Table 2, p. 4, row 76; `ORC-XHKLQR7IDW` |  |
| -44.38 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Saal 2013_ [doi](https://doi.org/10.1007/s11837-013-0755-4) | Table 2, p. 4, row 77; `ORC-2R6GLFN6K4` |  |
| -42.925 unknown | Al3Zr4 |  | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [1] Tamim 2018 | Table 3, p. 9, row 36; `ORC-2OCXGDBMQ4.199c0e` |  |
| -42.925 kJ/mol-atom | Al3Zr4 |  | model | CALPHAD | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Tamim 2018_ [doi](https://doi.org/10.1007/s10973-017-6635-3) | Table 4, p. 7, row 75; `ORC-O227QFO6IU.889002` |  |
| -41.18 kJ/mol-atom | Al3Zr4 | 298.15 | model | CALPHAD | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015 | Table 2, p. 4, row 71; `ORC-354MIDSXP4` |  |
| -40.894 kJ/mol-atom | Al3Zr4 |  | model | CALPHAD | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Fischer 2015_ [doi](https://doi.org/10.1007/s11669-015-0398-y) | Table 4, p. 7, row 74; `ORC-BKOHOFVXNS.016c60` |  |
| -39 kJ/mol-atom | Al3Zr4 | 298.15 | model |  | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [2] Fischer 2015; _cites Zhang 2010_ [doi](https://doi.org/10.1557/jmr.2010.0227) | Table 2, p. 4, row 73; `ORC-UWLQCOYVCW` |  |
| -47.555 unknown | Al3Zr4 |  | DFT | ab initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [1] Tamim 2018; _cites Ghosh 2005_ [doi](https://doi.org/10.1016/j.actamat.2005.03.028) | Table 3, p. 9, row 39; `ORC-2E45LO2IT3.1cb312` |  |
| -47.555 kJ/mol-atom | Al3Zr4 |  | DFT | Ab-initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Ghosh 2005_ [doi](https://doi.org/10.1016/j.actamat.2005.03.028) | Table 4, p. 7, row 71; `ORC-WPA4T4W7DL.024908` |  |
| -46.21 unknown | Al3Zr4 |  | DFT | ab initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [1] Tamim 2018; _cites Wang 2011_ [doi](https://doi.org/10.1016/j.calphad.2011.09.009) | Table 3, p. 9, row 38; `ORC-G62KXAVQGT.25f5aa` |  |
| -46.21 kJ/mol-atom | Al3Zr4 |  | DFT | Ab-initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Wang 2011_ [doi](https://doi.org/10.1016/j.calphad.2011.09.009) | Table 4, p. 7, row 70; `ORC-MHSN5IZBWH.d8e39e` |  |
| -44.875 unknown | Al3Zr4 |  | DFT | ab initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [1] Tamim 2018; _cites Duan 2014_ [doi](https://doi.org/10.1016/j.jallcom.2013.12.079) | Table 3, p. 9, row 37; `ORC-4D5QIQUO6E.2db728` |  |
| -44.875 kJ/mol-atom | Al3Zr4 |  | DFT | Ab-initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Duan 2013_ | Table 4, p. 7, row 69; `ORC-4NTPY7BXKI.16c28f` |  |
| -39 kJ/mol-atom | Al3Zr4 |  | DFT | Ab-initio | [Al–Zr](https://data.orchid-project.org/systems/AL-ZR.html) | [4] Long 2020; _cites Zhang 2010_ [doi](https://doi.org/10.1557/jmr.2010.0227) | Table 4, p. 7, row 72; `ORC-MICVBHLBGD.1a16df` |  |

### Uncertainty budget

Components kept separate, in the value's unit (literature [SCHEMA.md](https://data.orchid-project.org/literature/SCHEMA.md), [UNCERTAINTY_CALIBRATION.md](https://data.orchid-project.org/literature/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.

Table: Uncertainty budget of the literature values of Al3Zr4

| Value | Unit | Printed | Reading | Method (class, basis) | Composition | Scatter | Conversion | 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.

Table: 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](https://doi.org/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](https://doi.org/10.1007/s11837-013-0755-4) (CC BY 4.0); 

## Sources

1. 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](https://doi.org/10.1007/s10973-017-6635-3)
2. 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](https://doi.org/10.1007/s11669-015-0398-y)
3. T. Wang, Z. Jin, J.-C. Zhao, J. Phase Equilib., 22, 544-51(2001). [doi:10.1007/s12385-001-0072-4](https://doi.org/10.1007/s12385-001-0072-4)
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](https://doi.org/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). https://doi.org/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). https://doi.org/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). https://doi.org/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.

```bibtex
@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}
}
```

---

Derived data CC BY 4.0 ([licence](https://creativecommons.org/licenses/by/4.0/)): cite ORCHID ([CITATION.cff](https://data.orchid-project.org/CITATION.cff)) and the original sources. Quotes are short excerpts kept so that each value can be checked; they remain under the publishers' copyright and are not relicensed. Source papers, page images and full text are not redistributed. Field reference: [SCHEMA.md](https://data.orchid-project.org/literature/SCHEMA.md). Machine-readable guide: [llms.txt](https://data.orchid-project.org/llms.txt). Found an error? The report link of a value (Markdown: its id, ORC-..., in the Location column) opens a pre-filled GitHub issue, https://github.com/orchid-calphad/orchid-data/issues/new?template=report-value-error.yml&record_id=\<id>, carrying only the record id, source and value; [how to contribute](https://orchid-project.org/contribute/).