INFLUENCE OF STRAIN GRADIENTS IN CRYSTALLITES ON LINE PROFILES OF POWDER REFLECTIONS

K.H. Ehses, H. Thedens, Ch. Beck, R. Hempelmann

Universität des Saarlandes , D-66041 Saarbrücken, Germany.E-mail: kh.ehses@rz.uni-sb.de

Keywords: powder, nanocrystalline, strain

Observed lattice constant and strain increase with decreasing size of the crystallites for some nonmetallic nanocrystalline materials. We want to demonstrate that this behaviour occurs in perfect crystallites without introduction of special defects.

At the surface of crystallites the translation symmetry is broken. Simple pair potential calculations (equation 1) for a finite linear chain without periodic boundary conditions show that the distances between neighbouring atoms increase to the surface. The deformation e(x) depends on the power n of the long range attractive term in the potential and can be described suitably by a Lorentz-function (equation 2).

P(r,n) = a/r¹² -b/rⁿ ...........................................(1)

e(x) = es /(1+(x/he)²) .....................................(2),

where x defines the distance from the surface, es the strain at the surface, and he the half-width.

The corresponding displacements of atoms in the surface region influence the line profile of powder reflections. Displacement of the peak position, a broadening of the profile and an asymmetry occur simultaneously.

As model systems for the experimental verification of these effects we use perfect-crystalline non-agglomerated nanoparticles as can now be prepared using water droplets of inverse microemulsions as nanoreactors [1]. An example is nano-Y2O3 wich was synthesized with very narrow size distribution and with controlled volume-weighted particle diameters of 8, 10, 12, 15, and 25 nm.

Our X-ray diffraction results are in qualitative agreement with the above outlined linear chain theory.

1 H.Herrig, R.Hempelmann, Materials Letters 27 (1996) 287-292