X-ray diffraction study of crystallite size-distribution and strain in carbon blacks
- PDF / 196,661 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 75 Downloads / 172 Views
X-ray diffraction study of crystallite size-distribution and strain in carbon blacks T. Ungár, J. Gubicza, G. Ribárik and T. W. Zerda1 Department of General Physics, Eötvös University Budapest, H-1518, P.O.B. 32 Budapest, Hungary 1 Department of Physics, Texas Christian University, Fort Worth, TX, U.S.A. ABSTRACT The crystallite size and size-distribution in carbon blacks in the presence of strain are determined by recently developed procedure of X-ray diffraction peak profile analysis. The Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain peak profiles. Strain anisotropy is accounted for by expressing the mean square strain in terms of average dislocation contrast factors. Crystallite shape anisotropy is modelled by ellipsoids incorporated into the size profile function. To make the fitting procedure faster, the Fourier transform of the size profile is given as an analitical function. The method is applied to carbon blacks treated at different preassures and temperatures. The microstructure is characterised in terms of crystallite size distribution, dislocation density, and crystallite shape anisotropy.
INTRODUCION X-ray diffraction peak profile analysis is a widely used method for the determination of crystallite size and lattice defect structure in crystalline materials. The evaluation procedures are based on the diffraction order dependence of size and strain. In the simplest case, the size is independent and the strain is dependent on the diffraction order. Both dependencies become, however complicated if the shape or strain are anisotropic. Shape anisotropy can be modelled by cylindrical or flat bodies [1], strain anisotropy can be accounted for either by a phenomenological model of anisotropic elastic constants [2] or by the anisotropic strain fields of dislocations [3,4]. In the absence of strain, the crystallite size-distribution has recently been suggested to be determined by the whole profile fitting by using theoretically calculated size profiles [5]. The strain profile in dislocated crystals has been derived by Wilkens in the form of Forier transforms [6]. In the present work a procedure is described in which the Fourier coefficients of the experimentally determined physical peak profiles are fitted by the Fourier transforms of ab initio size and strain profiles. The only fitting parameters are well established physical parameters characteristic of the microstructure: (i) m and σ, the median and the variance of the log-normal crystallite size distribution function, (ii) ρ and M, the density and the arrangement parameter of dislocations and (iii) q or A and B, the parameters describing the average dislocation contrast factors in cubic or hexagonal crystals, respectively. In the case of the shape anisotropy a further fitting parameter can be introduced to characterize, for example, the ellipticity of the crystallite shape. This procedure will be applied to representative carbon blacks. A more detailed accou
Data Loading...
