## electron scattering

Amorphous solids and glasses are produced and studied in the "collaborative research centre SFB 408" at the university of Bonn. Such solids do not exhibit any long range structural order of the atoms. When irradiated by electrons, these materials produce diffuse scattering patterns in which the scattered intensity falls off with increasing scattering angle. The diffuse appearance of the scattering patterns reflects the missing order in amorphous solids. Nevertheless, information on the existing structural elements can be gained from electron scattering experiments.

Experimental: Electron scattering experiments are performed using a transmission electron microscope with a field emission source, Philips CM300FEG, at an accelaration voltage of 297 kV. The scattering patterns are recorded with the Gatan imaging electron energy filter (GIF) which is attached to the microscope column. The main function of the energy filter in this application is to exclude inelastically scattered electrons so that only the intensity of elastically scattered electrons is acquired. Energy filtering is of particular importance for materials containing light elements (B, C, N, O, Si) since their cross sections for inelastic scattering processes are larger than those for elastic scattering events. The patterns of only elastically scattered electrons are recorded on the CCD camera of the GIF.

We have designed and implemented a method to acquire scattering patterns up to scattering angles of 55 mrad by the acquisition of several overlapping regions of the scattered intensity. This is technically realised by precisely displacing the whole scattering pattern over the chip of the camera, which in turn is achieved by defined tilting of the electron beam in the experiment.

Interpretation: A scattering diagram has to be calculated from the two dimensional pattern of the scattered intensity (data reduction). For doing this the acquired parts of the scattered intensity distribution have to be merged together to obtain the complete scattering pattern. Then the scattered intensity is integrated along an arc of a circle of equal scattering length q (= modulus of the scattering vector) to yield a scattering diagram with low noise. The scattering diagram I(q) (= intensity as a function of the scattering length) can be calculated from basic equations of the kinematic scattering theory by assuming an isotropically scattering material. The background of the scattered intensity contains a part which corresponds to the intensity from isolated or free atoms, i.e. it is the weighted sum of the squares of the atomic scattering factors of the constituting elements. The background can be calculated or numerically fitted and is subtracted from I(q) to give the reduced interference function i(q). That function contains information on preferred scattering angles. In real space the structural information is given by the pair distribution function (PDF) as defined by

g(r)=4π.r.(ρ(r)-ρ(0))

Finally, the PDF or g(r) is calculated from i(q) by Fourier transformation.

The definition of the PDF shows that it represents the difference between the local density ρ(r), as measured for all atoms as a function of the distance r around them and then averaged over all atoms, and the macroscopic density ρ(0) of the material. Hence, maxima in the PDF correspond to preferred distances between atom pairs while minima indicate distances that are rarely found between the atoms. In principle, the height of a maximum in the PDF can be used to determine the number of atoms at that distance on the shell of a sphere around an ad-atom, e.g. for neighbouring atoms the coordination number of a specific atom can be calculated. However, this is not yet possible in the general case of electron scattering because for this the scattering diagram should be corrected for multiple elastic scattering in the irradiated specimen. This is the topic of ongoing work.

In our studies the resolution limit which can be reached in the pair distribution function is 20 pm. The position of the maxima in the PDF and hence the distances between atoms can be determined to a relative accuracy of 2%. The distances found in the PDF allow us to draw conclusions on the existing structural elements and their connectivity in an amorphous network. As an example, the PDF of the amorphous ceramic material with chemical composition Si3B3N7 is shown below. The maximum at 1.43 Å clearly corresponds to the distance between boron and nitrogen in trigonal planar BN3 units, whereas the maximum at 1.71 Å corresponds unambiguously to the distance between silicon and nitrogen in tetragonally coordinated SiN4 units. With this, the basic structural elements of the ceramic are already identified.

Fig. 1: PDF of the amorphous ceramic Si_{3}B_{3}N_{7}