X-ray scattering on highly perturbed carbon nanomaterials

Milan Dopita1*and Zdeněk Matěj2

1Institute of Materials Science, Technical University of Freiberg, Gustav-Zeuner-Strasse 5, Freiberg, D-09599, Germany

2Max IV Laboratory, Lund University, Ole Römers väg 1, 223 63 Lund, Sweden

*dopita@gmail.com

Simulations of scattered intensity distributions from two and three dimensional carbon structures of different shapes and sizes were done using the general Debye scattering equation [1]. The influence of the lattice defects typical for the turbostratic structure, i.e. random fluctuations in the parallel layer spacings, random lateral translations of graphitic layers, the curvatures of layers and mutual disorientations of individual parallel layers around the layers normal direction, on the resulting simulated scattered intensities were studied and discussed [2]. The microstructure-induced changes in the line broadening, in the shape parameter in the Scherrer formula and in the lattice parameters determined from the positions of the X-ray diffraction lines are discussed in particular. The set of presented Scherrer parameters allows the calculation of the cluster sizes along and normal to the basal planes from the measured X-ray scattering. The applicability of the Warren-Bodenstein’s approach [3] and paracrystalline model [4, 5] for description of scattering on turbostratic carbon structures was proven. Intensity distributions simulated using both approaches were compared to those obtained using the general Debye scattering equation.

A computer program adopting Warren-Bodenstein’s approach and paracrystalline model allowing fitting of whole measured scattering powder patterns was written. The program enables refinement of physical parameters of turbostratic carbon materials, i.e. the mean lattice parameters a0, c0, the mean cluster sizes parallel and perpendicular to the graphitic planes La and Lc, their distributions as well as the mean square atomic displacements áua2ñ and áuc2ñ. A series of high melting coal-tar synthetic pitch specimens, annealed at different temperatures, was prepared and investigated [6]. In studied samples we observed the increase of the clusters sizes, changes in the mean lattice parameters a0, c0, and decay of disorder with increasing annealing temperature.

The generalized Warren-Bodenstein’s method describing the scattering on turbostratic carbon was implemented into the Rietveld program MStruct [7] allowing fitting of measured scattered intensity distribution from mixtures of crystalline materials with turbostratic carbon, refinement of essential microstructural parameters and quantitative phase analysis.

 

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Text Box: Figure 1. Model of turbostratic carbon cluster of cylindrical shape (a). Calculated coherently scattered intensity contribution from cylindrical turbostratic carbon cluster with diameter La = 10 Å; number of parallel layers varied between 1 and 15 (b). Measured and refined x-ray scattering patterns from mixture of crystalline Al2O3 and turbostratic carbon (25 wt. %) sample (c).

 

1.         P. Debye, Ann Phys, 351, 6, (1915), 809.

2.         M. Dopita, M. Rudolph, A. Salomon, M. Emmel, C. G. Aneziris & D. Rafaja, Adv. Eng. Maters., 15, (2013) 1280.

3.         B. E. Warren & P. Bodenstein, Acta. Cryst., 18, (1965), 282.

4.         S. Hendricks and E. Teller, J Chem Phys, 10, (1942), 147.

5.         R. Hosemann, Zeit Phys, 128, (1950), 465.

6.         M. Dopita, M. Emmel, A. Salomon, M. Rudolph, Z. Matěj, C. G. Aneziris, D. Rafaja, Carbon 81, (2015), 272.

7.         Z. Matěj, A. Kadlecová, M. Janeček, L. Matějová, M. Dopita, R. Kužel, Powder Diffraction, 29, S2, (2014), S35.

The authors would like to thank the German Research Foundation (DFG) for supporting the subproject A05, which is a part of the Collaborative Research Centre 920 (CRC 920) “Multi-Functional Filters for Metal Melt Filtration - A Contribution towards Zero Defect Materials”.