Investigation of Interatomic Solid State Potentials

Timo Hauschild (1,2), M. Jentschel (2), K.-H. Heinig (1), H. G. Börner (2)


Reliable interatomic potentials are needed for computer simulations that become a more and more powerful tool in materials sciences. As many ion beam and plasma techniques operate at energies up to several hundreds of eV, a suitable potential in this energy region is vital. The Crystal-GRID technique is a unique method for the study of interatomic potentials in the energy range of 10 to 1000 eV. It is based on the direct observation of collisions within the bulk material.

Interatomic potentials have been well investigated for energies near the equilibrium (phonons) and high energies (several keV). However, there are no other methods so far yielding information about the intermediate region without being largely influenced by surface properties.

Gamma Ray Induced Doppler broadening (GRID)

During the last decade the GRID technique has been developed at the Institut Laue-Langevin (ILL) in Grenoble. It has been successfully applied to nuclear level lifetime measurements. A description of the method can be found in [BorJol93].

The use of single-crystalline samples for GRID experiments was proposed in 1992 [HeiJan92]. This special application, called ``Crystal-GRID'', allows to perform several measurements with the same material by aligning different crystal directions with respect to the optical axis of the spectrometer. Thereby information can be accumulated allowing to find the nuclear level lifetime and to improve the interatomic solid state potentials at the same time. Using standard GRID with powder targets, the nuclear level lifetime has to be known in order to extract information about the slowing down of the nuclei in the solid. In recent works [Jen96, Jen96a, Koc99, Str99] the general applicability of the new method to the study of interatomic potentials has been proven.

GRID - the Physics behind

In a thermal neutron capture reaction the binding energy of a neutron is freeded and deposited in the nucleus, leading to a highly excited nucleus. The deexcitation takes place via a gamma cascade. The emission of a first, primary photon entails a recoil of the still excited nucleus due to the conservation of momentum (initial velocity: 0.1 to 2 Angstrom/fs, initial kinetic energy: 100 to 1000 eV). The direction of the initial recoil is arbitrary. The further motion of the recoiling nucleus is governed by the collisions with the neighboring lattice atoms. Its trajectory is defined by the crystal structure and the interatomic forces,  i.e. by the interatomic solid state potential. Due to the regular arrangement of the atoms in ctrystals, the ensemble of trajectories form an unisotropic pattern (see first figure).

A few tens of femtoseconds later, a second photon is emitted by the recoiling atom. It is observed by the spectrometer. Its measured energy (in the laboratory system) is Doppler shifted as the emitting atom is moving. In a measurement a large number of secondary photons is observed, giving rise to a Doppler broadened photon energy spectrum (see second figure).  This spectrum is fine structured due to the anisotropy of the crystal. The maximum Doppler shift is some hundreds of eV. The very small shifts in energy can be measured with the ultra-high resolving gamma spectrometers (GAMS) at the ILL in Grenoble.

Studying Interatomic Potentials

The slowing down of the nuclei can be simulated using Molecular Dynamics (MD) simulations. Thereby energy spectra for any orientation of the crystal can be calculated. By fitting these predictions to the experimental data and varying potential parameters, new interatomic potentials can be extracted. The most recent result is the Crystal-GRID potential for Zn-S. It has been obtained by switching from the well-known KrC potential to a Stillinger-Weber type of potential and varying the spline parameters (see third figure).


  1. Institute of Ion Beam Physics and Materials Research (Helmholtz-Zentrum Dresden-Rossendorf)
  2. Institut Laue-Langevin (Grenoble, France)


[BorJol93] H. G. Börner(2) and J. Jolie, "Sub-picosecond lifetime measurements by gamma ray induced Doppler broadening", J. Phys. G: Nucl. Part. Phys. 19 (1993) 217-248.
[HeiJan92] K.-H. Heinig(1) and D. Janssen(1), "The fine structure of Doppler profiles in MD channeling calculation", ILL Internal Report 92HGB16T (1992).
[Jen96] M. Jentschel(1,2), K. H. Heinig(1), H. G. Börner(2), J. Jolie and E. G. Kessler, "Atomic collision cascades studied with the Crystal-GRID method", Nucl. Ins. Meth. B115 (1996) 446-451.
[Jen96a] M. Jentschel(1,2), H. G. Börner(2) and C. Doll(2), "New applications of the GRID-technique in nuclear and solid state physics", in: G. L. Molnar, T. Belgya, Zs. Revay, Proc. of the CGS9, Budapest , Springer, Vol. 2 (1996) 755-768.
[Koc99] T. Koch(1,2), K.-H. Heinig(1), M. Jentschel(2), H. G. Börner(2), "Study of interatomic potentials in ZnS - Crystal-GRID experiments versus ab initio calculations"; NIST J Research (1999).
[Str99] N. Stritt, J. Jolie, M. Jentschel(2), H. G. Börner(2) and C. Doll(2), "Investigation of the interatomic potential using the crystal gamma-ray-induced Doppler-broadening method on oriented Ni single crystals", Phys. Rev. B 59 (1999) 6762-6773.