Modeling of Positron Annihilation

Phil Sterne and John Pask

Methods: Finite Element Method

Collaborators: Positron and Surface Science Group

Positron annihilation experiments are a sensitive probe of atomic-scale defects in materials. Positrons are very sensitive to vacancy-type defects which act as traps, localizing the positron in a vacancy or vacancy cluster. Since positrons provide information only about the environment in which they annihilate, they are a selective probe of the atomic environment around defects. This selectivity is determined by the distribution of the positron in the defect, so detailed quantum-mechanical calculations are required to interpret positron annihilation data correctly.

Since positrons are quantum-mechanical particles like electrons, but with positive charge, we use methods based on electronic structure calculations to compute the positron wavefunction. We originally developed a first-principles approach for calculating positron lifetimes and momentum densities based on the Linear Muffin-Tin Orbital Method [1]. This was useful for small periodic systems consisting of a few tens of atoms in the unit cell, large enough to treat a vacancy in a simple elemental metal, but too small for many systems of interest containing more complicated defects. Recently we developed a new approach for positron calculations [2] based on a finite-element method [3,4]. This new approach provides positron distributions and positron lifetimes for systems ranging in size from one atom to many thousands of atoms per unit cell. The finite element-based calculations now enable us to calculate the properties of large realistic defect structures, including those obtained from molecular dynamics simulations.

The figure shows calculated positron distributions for three different systems. Figure 1(a) shows a surface of constant positron density around a stacking fault tetrahedron in copper. Stacking fault tetrahedra are common defects in irradiated copper. The general tetrahedral structure of the defect is evident from the figure, and the finer structure shows the exclusion of the positron from the region around the atomic nuclei. The effects of thermal noise on the atomic distribution, which was taken from a finite-temperature molecular dynamics simulation, also contribute to the distortion of the constant-density surface. This calculation on a system of 836 atoms illustrates our ability to couple defect structures produced by atomistic modeling approaches with positron theory to produce explicit predictions of positron annihilation data. This combination of positron experiment and theory provides an important validation step for checking the defect types, distributions and concentrations predicted in first-principles-based atomistic simulations.

The positron distribution in crystalline fullerene C60 is shown in figure 1(b). The positron resides in the interstitial region and avoids the interior of the fullerene balls. Two sets of experiments confirm that the positron is indeed in the interstitial region, and not inside the fullerene molecules. First, the positron lifetime changes abruptly at the C60 orientational transition temperature, and the size of the lifetime change is consistent with the observed change in lattice constant associated with the transition [5]. Second, when C60 is doped with lithium atoms which fill these interstitial positions, the positron is repelled by the lithium nucleus and redistributes around the interstitial region, changing both the lifetime and the overlap of the positron with different parts of the cell [2]. This illustrates the positron's sensitivity to different parts of the unit cell and emphasizes the importance of quantum mechanical calculations in predicting and interpreting the experimental data.

Figure 1(c) shows the positron distribution on a plane through a copper precipitate in iron. Copper has a higher positron affinity than iron, so positrons are attracted to the copper precipitates and localize in that region, in much the same way that positrons localize in vacancy clusters. However, in contrast to vacancy cluster trapping, the positrons in the copper precipitate are excluded from the atomic cores by the strong coulomb repulsion from the nucleus, resulting in the highly structured positron density shown in the diagram. The positron's sensitivity to copper precipitates has been confirmed experimentally in studies of reactor pressure vessel steels, where the formation of coherent nanometer-sized copper precipitates is an important embrittling mechanism. Positrons therefore provide a uniquely sensitive probe of this nanoscale precipitate, enabling us to determine both the chemical composition and the magnetic structure of the precipitate.[6]

References

1. P.A. Sterne and J.H Kaiser, "First-Principles Calculation of Positron Lifetimes in Solids ," Phys. Rev. B 43, 13892 (1991).
2. P.A. Sterne, J.E. Pask, and B.M. Klein, "Calculation of positron observables using a finite-element-based approach ," Applied Surface Science 149, 1 (2001).
3. J.E. Pask, B.M. Klein, P.A. Sterne, and C.Y. Fong, "Finite-element methods in electronic-structure theory ," Computer Physics Communications 135, 1 (2001).
4. J.E. Pask, B.M. Klein, C.Y. Fong, and P.A. Sterne, "Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach ," Phys. Rev. B 59, 12352 (1999).
5. J.D. Dykes, W.D. Mosley, P.A. Sterne, J.Z. Liu, R.N. Shelton, and R.H. Howell, "Investigation of the electronic charge distribution in the octahedral sites of C60 through the 260K orientational phase transition ," Chem. Phys. Lett. 232, 22 (1995).
6. P. Asoka-Kumar, B.D. Wirth, P.A. Sterne, G.R. Odette and R.H. Howell, "Composition and magnetic character of nanometer Cu-precipitates in reactor pressure vessel steels: Implications for nuclear power plant lifetime extension ," Philos. Mag. Lett. 82, 609 (2002).

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