Nonuniversal structure of point defects in face-centered cubic metals

Using ab initio density function theory calculations, we have determined the structure of self-interstitial atom (SIA) defects in the most commonly occurring face-centered cubic (FCC) metals. The most stable SIA defects in Al, Ca, Ni, Cu, Pd, and Ag are the $\langle 100\rangle$ dumbbells whereas octahedral SIA configurations have the lowest energy in Pt, Rh, and Th. The relative stability of defect configurations in Sr, Ir, Au, and Pb is less well defined, and calculations suggest that an SIA defect has the $\langle 100\rangle$ dumbbell structure in Sr and Ir, a $\langle 110\rangle$ crowdion/dumbbell structure in Au, and that it adopts an octahedral configuration in Pb. The occurrence of octahedral and $\langle 110\rangle$ crowdion/dumbbell SIA configurations implies that defects diffuse one-dimensionally. This is fundamentally different from the three-dimensional translation-rotation migration characterizing the mobility of a $\langle 100\rangle$ dumbbell. Elastic fields of point defects are defined by their elastic dipole tensors, which we compute for all the defect configurations. The magnetism of a $\langle 100\rangle$ dumbbell in ferromagnetic nickel appears to have little effect on the structure of the defect. The variation of energy and elastic field of an SIA defect in copper is explored in detail as a function of its structural transformation along the migration pathway.

Figure 1

Schematic sketches of self-interstitial atom defect structures in face-centered cubic metals. In all the cases illustrated in this figure, a simulation cell contains one extra atom, and hence the corresponding atomic configuration represents a single-atom SIA defect. All the atoms shown in the sketches are identical, and colors highlight the symmetry of a particular defect structure. Empty spheres, where appropriate, indicate positions of unoccupied ideal lattice sites. Letters d or c refer to a dumbbell or crowdion configuration.

Figure 2

Relaxation volumes of vacancies, expressed in atomic volume units ${\mathrm{\Omega }}_0$, in Cu, Cu_pv, Ag, Ir, Pt, Au, Pb, and Th, calculated using exchange-correlation PBE and PBEsol functionals with and without spin-orbit coupling (SOC).

Figure 3

Formation energies of various self-interstitial atom (SIA) defect configurations in Al, Ca, and Ni. In each case, the energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 4

Formation energies of various self-interstitial atom (SIA) defect configurations in Cu. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 5

Formation energies of various self-interstitial atom (SIA) defect configurations in Cu_pv. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 6

Formation energies of various self-interstitial atom (SIA) defect configurations in Sr, Rh, and Pd. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 7

Formation energies of various self-interstitial atom (SIA) defect configurations in Ag. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 8

Formation energies of various self-interstitial atom (SIA) defect configurations in Ir. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 9

Formation energies of various self-interstitial atom (SIA) defect configurations in Pt. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 10

Formation energies of various self-interstitial atom (SIA) defect configurations in Au. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 11

Formation energies of various self-interstitial atom (SIA) defect configurations in Pb. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 12

Formation energies of various self-interstitial atom (SIA) defect configurations in Th. The energy of a $\langle 100\rangle$ dumbbell is used as a reference, and the curves show the difference between the energy of a given defect configuration and that of a $\langle 100\rangle$ dumbbell.

Figure 13

Two-dimensional plots of the electron charge density difference in Al (top), Cu (middle), and Pb (bottom), computed for a $\langle 100\rangle$ dumbbell configuration in a $\left\{010\right\}$ plane. Electron charge density difference is defined as the fully convergent electron density derived from ab initio simulations minus the superposition of atomic charge densities.

Figure 14

Two-dimensional plots of the electron charge density difference in Al (top), Cu (middle), and Pb (bottom), computed for a $\langle 100\rangle$ dumbbell configuration in a $\left\{011\right\}$ plane.

Figure 15

Two-dimensional plots of electron charge density difference in Al (top), Cu (middle), and Pb (bottom), computed for an octahedral site interstitial configuration in a $\left\{010\right\}$ plane.

Figure 16

Two-dimensional plots of electron charge density difference in Al (top), Cu (middle), and Pb (bottom), computed for an octahedral site interstitial configuration in a $\left\{011\right\}$ plane.

Figure 17

Schematic illustration of the three-dimensional translation-rotation pathway of migration of a $\langle 100\rangle$ dumbbell from a [100] configuration to a [010] configuration in an FCC crystal.

Figure 18

Schematic illustration of the one-dimensional pathway of migration of an octahedral site interstitial defect in an FCC crystal.

Figure 19

Schematic illustration of one-dimensional migration of a $\langle 110\rangle$ crowdion/dumbbell in an FCC crystal.

Figure 20

Relaxation volumes of the $\langle 100\rangle$ dumbbell and octahedral site interstitial defects, given in atomic volume units ${\mathrm{\Omega }}_0$, in Cu, Cu_pv, Ag, Ir, Pt, Au, Pb, and Th, calculated using exchange-correlation PBE and PBEsol functionals with and without spin-orbit coupling (SOC).

Figure 21

Two-dimensional plots of magnetization density in nickel, computed for a $\langle 100\rangle$ dumbbell configuration in (top) $\left\{010\right\}$ and (bottom) $\left\{011\right\}$ planes.

Figure 22

Two-dimensional plots of electron charge density difference in nickel computed for a $\langle 100\rangle$ dumbbell configuration in (top) $\left\{010\right\}$ and (bottom) $\left\{011\right\}$ planes.

Figure 23

Energy and magnetic moment of a nickel atom plotted as a function of the FCC lattice constant in a perfect crystal structure.

Figure 24

Variation of the formation energy of a $\langle 100\rangle$ dumbbell in Cu along the migration pathway of the defect.

Figure 25

Variation of elements of elastic dipole tensor of a $\langle 100\rangle$ dumbbell in Cu along the migration pathway from a [100] to a [010] configuration.

Figure 26

Variation of elements of the relaxation volume tensor of a $\langle 100\rangle$ dumbbell in Cu along the migration pathway from a [100] to a [010] configuration.

Figure 27

Variation of the relaxation volume of a $\langle 100\rangle$ dumbbell in Cu along its migration pathway.