Coherence of nanocrystalline particles to X-rays

David Rafaja ¹⁾, Volker Klemm ¹⁾, Gerhard Schreiber ¹⁾, Michael Knapp ²⁾ and Michal Šíma ³⁾

¹Institute of Physical Metallurgy, TU Bergakademie Freiberg, Gustav-Zeuner-Str. 5, D-09599 Freiberg, Germany

²Institute of Materials Science, TU Darmstadt, Petersenstr. 23, D-64287 Darmstadt, Germany

³SHM, Nový Malín 266, CZ – 788 03 Nový Malín, Czech Republic

In the kinematical diffraction theory, individual crystallites are defined as coherent domains and their coherence to X-rays is neglected. This assumption is certainly correct for large crystallites (larger than some tens of nanometers), which are represented by narrow points in the reciprocal space. On the contrary, this assumption may be incorrect in nanocrystalline materials (smaller than 10 nm) with broad and overlapping reciprocal space points, where a partial coherence of the adjacent crystallites can be anticipated. In X-ray diffraction (XRD) experiments, partly coherent crystallites seem larger because they cannot be distinguished from each other. The partial coherence combined with a slightly different orientation and with a shift of adjacent crystallites causes an additional diffraction line broadening, which is increasing with increasing size of the diffraction vector. Such a diffraction line broadening is then misleadingly interpreted as microstrain. The above phenomena were described theoretically considering that the overlap of the reciprocal space points from adjacent crystallites can serve as a measure of their coherence in the direct space. It was shown that the degree of coherence of the nanocrystalline particles depends on their size as well as on their mutual orientation. The experimental evidence of the coherence of the nanocrystalline particles to X-rays was provided by the comparison of the crystallite size obtained from XRD and from the transmission electron microscopy with high resolution (HRTEM). The experimental results were obtained on the Ti_1-xAl_xN thin films with different chemical and phase compositions, which were deposited by the arc sputtering from two targets (Ti and Al) in working atmosphere containing nitrogen. In these samples, HRTEM yielded the crystallite size of 35 – 50 Å; the crystallite size obtained from XRD was 35 – 200 Å depending on the degree of coherence of the neighbouring crystallites. The coherence of the adjacent crystallites varied with the degree of the preferred orientation of crystallites and with the phase composition of the samples (cubic ternary solid solution (Ti,Al)N and hexagonal AlN).