A. Appendix, where Al atoms are located in 2b (1/3, 2/3, 0) and X in 2b (1/3, 2/3, u), the zincblende structure (ZB, cF8, space group f43m) where Al atoms are in 4a (0, 0, 0) and X in 4c (1/4, 1/4, 1/4) and the NaCI structure (cF8, space group Fm3m) where Al atoms are in 4a (0, 0, 0) and X in 4b (0.5, 0.5, 0.5). We also reported results for additional structures: (i) the corundum A)z04 structure (hR10, space group R3c), Aluminum al/oys Finally, we conducted additional calculations on several Al-X alloys: the wurtzite (WZ, hP4, space group P6 3 mc)

, The NaCI structure corresponds to an fcc structure in which ail octahedral sites are occupied. The AIX zincblende is an fcc-AI where half of the tetrahedral sites are occupied. Table A.1 summarizes these results. DFT results are in excellent agreement with experi mental values (lattice parameters and Wyckoff positions) for AIN wurtzite

D. Tanguy, Y. Wang, and D. Connétable, Stability of vacancy-hydrogen clusters in nickel from first principles calculations, Acta Mater, vol.78, pp.135-143, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01169788

Y. Wang, D. Connétable, and D. Tanguy, Influence of trap connectivity on h diffusion: vacancy trapping, Acta Mater, vol.103, pp.334-340, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01564913

C. Barouh, T. Schuler, C. Fu, and M. Nastar, Interaction between vacancies and interstitial solutes (c, n, and o) in a-fe: from electronic structure to thermo dynamics, Phys. Rev. B, vol.90, p.54112, 2014.

T. Schuler, C. Barouh, M. Nastar, and C. Fu, Equilibrium vacancy concentration driven by undetectable impurities, Phys. Rev. Lett, vol.115, p.15501, 2015.

D. Tanguy, H effects in al-mg, al-zn-mg alloys, and al: experiments, contin uum, and atomistic modeling, Corrosion, vol.72, issue.2, pp.297-313, 2016.

A. Sieverts, The absorption of gases by metals, Z. Metallkd, vol.21, pp.37-46, 1929.

D. Connétable, M. David, A. Prillieux, D. Young, and D. Monceau, Impact of the clusterization on the solubility of oxygen and vacancy concentration in nickel: a multi-scale approach, J. Alloys Compd, vol.708, pp.1063-1072, 2017.

R. Nazarov, T. Hickel, and . Neugebauer, Ab initio study of h-vacancy interactions in fcc metals: implications for the formation of superabundant vacancies, Phys. Rev. B, vol.89, p.144108, 2014.

G. Lu and E. Kaxiras, Hydrogen embrittlement of aluminum: the crucial role of vacancies, Phys. Rev. Lett, vol.94, p.155501, 2005.

M. Ji, C. Wang, K. Ho, S. Adhikari, and K. R. Hebert, Statistical model of defects in al-h system, Phys. Rev. B, vol.81, p.24105, 2010.

X. Yang, F. Zu, and . Gao, Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum, Phys. B Condens. Matter, vol.403, issue.17, pp.2719-2724

M. David and D. Connétable, Diffusion of interstitials in metallic systems, illus tration of a complex study case: aluminum, j. Phys. Condens. Matter, vol.29, issue.45, p.455703, 2017.

H. A. Wriedt, The al-n (aluminum-nitrogen) system, Bull. Alloy Phase Dia grams, vol.7, pp.329-333, 1986.

H. A. Wriedt, The al-o (aluminum-oxygen) system, Bull, Alloy Phase Diagrams, vol.6, issue.6, pp.548-553, 1985.

B. Grashchenko, V. Darovskii, T. Khandzhyan, and . Ses, Alyumin. Magnievyi. Inst, vol.90

H. Okamoto, Al-c (aluminum-carbon), J. Phase Equil, vol.13, issue.1, pp.97-98, 1992.

A. San-martin and F. Manchester, The al-h (aluminum-hydrogen) system, Phase Equil, vol.13, issue.1, pp.17-21, 1992.

H. Duschanek and P. Rogl, The al-b (aluminum-boron) system, j. Phase Equil, vol.15, pp.543-552, 1994.

G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B, vol.47, p.558, 1993.

K. Perdew, M. Burke, and . Emzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett, vol.78, p.1396, 1997.

G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, vol.59, p.1758, 1999.

H. J. Monkhorst and . Pack, Special points for the brilluoin zone integrations, Phys. Rev. B, vol.13, p.5188, 1976.

A. Togo, F. Oba, and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and ca, Phys. Rev. B, vol.78, p.134106, 2008.

D. Connétable, E. Andrieu, and D. Monceau, First-principles nickel database: en ergetics of impurities and defects, Comput. Mater. Sei, vol.101, pp.77-87, 2015.

C. Wolverton, V. Ozolins, and M. Asta, Hydrogen in aluminum: first-principles calculations of structure and thermodynamics, Phys. Rev. B, vol.69, p.144109, 2004.

A. Glensk, B. Grabowski, T. Hickel, and J. Neugebauer, Breakdown of the arrhenius law in describing vacancy formation energies: the importance of local anharmonicity revealed by Ab initio thermodynamics, Phys. Rev. X, vol.4, p.11018, 2014.

H. Wang, D. Rodney, D. Xu, R. Yanga, and P. Veyssière, Pentavacancy as the key nucleus for vacancy clustering in aluminum, Phys. Rev. B, vol.84, p.220103, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00664746

J. Dai and Y. Song, Influence of h, c, n and o impurities on the stability of mg and al from first-principles calculations, Model. Simulat. Mater. Sei. Eng, vol.21, issue.5, p.55014, 2013.

E. Clouet, S. Garruchet, H. Nguyen, M. Perez, and C. Becquart, Dislocation inter action with in alpha-fe: a comparison between atomic simulations and elas ticity theory, Acta Mater, vol.56, pp.3450-3460, 2008.

D. Connétable, Y. Wang, and D. Tanguy, Segregation of hydrogen to defects in nickel using first-principle calculations: the case of self-interstitials and cav ities, J. Alloys Compd, vol.614, pp.211-220, 2014.

C. Domain, C. S. Becquart, and . Foct, Ab initio study of foreign interstitial atom ( c,n) interactions with intrinsic point defects in o:-fe, Phys. Rev. B, vol.69, p.144112, 2004.

Y. Wang, D. Connétable, and D. Tanguy, Hydrogen influence on diffusion in nickel from first-principles calculations, Phys. Rev. B, vol.91, p.94106, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01167264

B. Callmer, An accurate refinement of the /J-rhombohedral boron structure, Acta Crystallogr. Sect. B, vol.33, issue.6, pp.1951-1954, 1977.

C. Kittel, Introduction to Solid State Physics, 1996.

P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban et al., Space Groups (173) P63-(166) R-3m Al4c3: Datasheet from Landolt-bômstein-Group iii Condensed Matter, vol.5, 2007.