Table 1 The calculated values of all the energies related to diffusion and forming of an impurity atom in B1-TiN for all 3d and selected 4d and 5d impurities.

Impurity	\(E_{imp}^f \,\mathrm {(eV)}\)	\(E_{bind} \,\mathrm {(eV)}\)	\(E_{net}^f \,\mathrm {(eV)}\)	\(E_m \,\mathrm {(eV)}\)	\(Q\ \,\mathrm {(eV)}\)
3d
Sc	− 0.27	− 1.63	1.48	3.68	5.17
Ti	0.00	0.00	3.11	4.03	7.14
V	1.50	2.60	5.72	3.77	9.48
Cr	2.86	− 1.31	1.81	2.76	4.57
Mn	3.74	− 3.67	− 0.55	1.47	0.92
Fe	3.92	0.03	3.15	1.53	4.68
Co	4.03	− 2.61	0.50	0.74	1.25
Ni	4.60	− 9.04	− 5.92	0.39	− 5.53
Cu	4.63	− 0.07	3.04	0.29	3.34
Zn	4.14	− 2.29	0.82	0.90	1.73
4d
Y	1.40	− 1.42	1.69	3.32	5.00
Zr	0.36	− 2.48	0.64	4.37	5.00
Nb	1.33	11.90	15.02	4.82	19.84
Mo	2.88	8.66	11.78	4.60	16.38
Pd	6.28	− 7.84	− 4.73	0.45	− 4.28
Ag	6.93	− 0.21	2.90	0.48	3.39
5d
Hf	0.07	14.05	17.17	4.63	21.80
Ta	1.41	2.15	5.27	5.12	10.39
W	− 3.19	− 0.31	2.81	4.95	7.75

Note that the impurity formation energy, \(E^f_{imp}\), is in eV/(impurity atom), \(E_{bind}\) and \(E_{net}^f\) in eV/(vacancy-impurity pair). And the \(E^f_{net}\) for all the species is \(E_{bind}\), scaled by the formation energy of single Ti vacancy(\(E^f\)) as per the Eq. (6). The value calculated for \(E^f\) is 3.11 eV/atom.

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