Table 2 The calculated unrelaxed surface energies (E_s), vacancy formation energies (\({E}_{{{\rm{v}}}}^{{{\rm{f}}}}\)), interstitial formation energies (\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\)), and unstable (γ_usf) and stable stacking fault energies (γ_sf), as well as grain boundary energies of low Miller index tilt boundaries for FCC Ni using DP-Ni, in comparison with DFT results, available experimental data, and selected interatomic potentials

E_s{111} (J/m²)

1.919

1.958

1.636

1.815

1.630

1.938

E_s{221} (J/m²)

2.210

2.259

1.924

2.164

1.965

2.230

E_s{110} (J/m²)

2.343

2.357

2.056

2.367

2.172

2.356

E_s{211} (J/m²)

2.279

2.323

1.970

2.222

2.021

2.280

E_s{210} (J/m²)

2.463

2.488

2.181

2.526

2.321

2.472

E_s{100} (J/m²)

2.239

2.223

1.884

2.220

2.088

2.254

\({E}_{{{\rm{v}}}}^{{{\rm{f}}}}\) (eV)

1.424

1.400–1.800^b

1.236

1.598

1.539

1.509 (1.41)

1.465 (1.49)

\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\langle 100\rangle\) dumbbell (eV)

4.048

-

4.184

4.885^c

4.253

4.531

4.118

\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\langle 111\rangle\) dumbbell (eV)

4.664

-

4.892

6.920

4.765

5.508

4.751

\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\langle 110\rangle\) dumbbell (eV)

4.828

-

4.614

5.786

4.664

5.103

4.769

\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\) Crowdion (eV)

4.826

-

4.614

5.114

4.669

5.112

4.788

\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\) Octahedral (eV)

4.229

-

4.421

⊛

4.465

⊛

4.460

\({E}_{{{\rm{i}}}}^{{{\rm{f}}}}\) Tetrahedral (eV)

4.670

-

4.986

6.920

5.085

5.508

⊛

γ_usf 〈110〉 (mJ/m²)

766.6

-

801.6

924.3

746.9

898.2

789.9

γ_usf 〈112〉 (mJ/m²)

280.4

-

301.9

365.6

285.4

423.6

275.5

γ_sf 〈112〉 (mJ/m²)

135.9

125^d

126.8

125.2

−26.9

60.0

52.2

\(\Sigma 3\,[1\bar{1}0](111)\) (mJ/m²)

68.03

-

63.50

63.46

−13.45

30.09

26.53

\(\Sigma 3\,[1\bar{1}0](112)\) (mJ/m²)

896.03

-

893.67

1064.03

782.53

960.66

908.44

\(\Sigma 5\,[100](0\bar{2}1)\) (mJ/m²)

1288.75

-

1310.72

1564.08

1372.11

1421.66

1339.00

\(\Sigma 7\,[\bar{1}\bar{1}\bar{1}](3\bar{2}\bar{1})\) (mJ/m²)

1234.31

-

1212.57

1471.91

1210.14

1395.51

1286.36

\(\Sigma 9\,[\bar{1}10](22\bar{1})\) (mJ/m²)

1120.58

-

1103.69

1368.13

1148.89

1258.83

1157.30

\(\Sigma 11\,[1\bar{1}0](113)\) (mJ/m²)

454.23

-

440.81

531.15

420.36

518.89

464.21