First-Principles Study of the Structural Stability and Electronic and Elastic Properties of Helium in α-Zirconium

Table 2

Vacancy formation energies (in eV) for a single He atom positioned in different sites. All the configurations are found to be stable, except O, which is unstable and transfers to BO. 𝐸^𝑓_v represents the formation energy of a Zr vacancy and 𝐸^′𝑓_s represents the formation energy of a substitutional He atom in a preexisting Zr vacancy.

	𝐸^𝑓v	𝐸^𝑓s	𝐸^′𝑓s	𝐸^𝑓T	𝐸^𝑓O	𝐸^𝑓BT	𝐸^𝑓BO
36-atom cell	1.97	3.30	1.33	2.67	/	3.01	2.42
54-atom cell	1.95	3.20	1.25	2.64	/	2.99	2.40
𝛼-Zr [25]	—	—	—	3.08	3.19	—	—
Er [34]	—	2.59	—	1.73	1.98	—	—
Sc [35]	—	2.98	—	1.74	2.06	1.76	1.97
Ti [2]	—	3.65	1.70	2.82	3.04	—	2.69