To understand the properties of a material detailed knowledge about its atomistic structure is of great importance. Often, one is interested in the change of atom configurations as a consequence of external manipulation, for instance the elastic reaction and the nucleation of lattice dislocations caused by an external load. X-ray and neutron diffraction experiments yield information in the reciprocal space which allows for an investigation in position space, for example the grain size and the different moments (mean, variance) of the distribution of lattice parameters. The data analysis usually exhibits large scatter. In contrast to that, atomistic simulations of the material or process under investigation by molecular dynamics simulation (MD) yield precise information in terms of coordinates in position space of every single atom, which typically number between 10⁵ –- 10⁷. A comparative discussion is problematic because it is not clear in what extent the quite different data sets from experiment and simulation are comparable. The method “virtual x-ray diffraction” which we developed establishes a meaningful comparison in these cases.

Starting with MD atom coordinates, we calculate as realistic as possible virtual” diffraction patterns, and we analyse them by use of the same evaluation algorithms as in a laboratory experiment. The results so far validate a method to determine grain size and microstrain in nanocrystalline metals, and they prove that the typical occurrence of microstrain does not – as it is mostly assumed – indicate the existence of lattice dislocations. Instead of that, the strain of the crystal lattice at small grain sizes originates from compatibility constraints of the packing of small crystalline objects with quantised length. Ongoing investigations of the DFG research group 714 “Plasticity of nanocrystalline metals” extend over virtual and real diffraction experiments of nanocrystalline materials in-situ under load.

Selected Publications:

J. Markmann, V. Yamakov and J. Weissmüller
Validating Grain Size Analysis from X-Ray Line Broadening: A Virtual Experiment
Scripta Mater. 59 (2008) 15

A. Stukowski, J. Markmann, J. Weissmüller and K. Albe
Atomistic origin of microstrain broadening in diffraction data of nanocrystalline solids
Acta Mater. 57 (2009) 1648

J. Markmann, D. Bachurin, L. Shao, P. Gumbsch and J. Weissmüller
Microstrain in nanocrystalline solids under load by virtual diffraction
Europhys. Lett. 89 (2010) 66002

Cross-section through a nanocrys- talline palladium sample generated by molecular dynamics simulation. The atoms (circles) are coloured according to the local strain of the surrounding crystalline lattice. Atoms in the core of the grain boundaries were omitted. Note the considerable microstrain in spite of the lack of lattice dislocations.

Intensity vs. scattering angle in a virtual (upper curve) and in an experimental (lower curve) x-ray diffraction pattern of nanocrystalline Pd. The comparison yields a method to describe the repre- sentativeness of the atom configuration of the computer simulation for the real structure of the experimentally inves- tigated material.

Microstrain vs. grain size, comparison of a Williamson-Hall analysis of the virtual diffraction pattern with a direct determi- nation by analysis of atom displace- ments.