X-ray refraction characterization of non-metallic materials

doi:10.1016/S0963-8695(00)00070-0

NDT & E International

Volume 34, Issue 4, 1 June 2001, Pages 297-302

https://doi.org/10.1016/S0963-8695(00)00070-0 Get rights and content

Abstract

Advanced materials require specific methods for their non-destructive characterization. X-ray refraction techniques determine the specific surfaces and interfaces of high performance ceramics, composites and other low density non-metallic materials down to nanometer dimensions. X-ray refraction occurs due to the interference of phase shifted X-rays in ultra small angle X-ray scattering at objects above 100 nm size. Applications to monolithic ceramics and ceramic composites are presented. The well localized mean pore size of ceramics at different stages of sintering and the crack growth of carbon fiber composites are measured non-destructively.

Introduction

The effect of X-ray refraction provides unconventional small angle X-ray scattering (SAXS) techniques which have been developed and applied to meet actual demands for improved non-destructive characterization of advanced materials.

Due to the short X-ray wavelength near 0.1 nm X-ray refraction reveals the inner surface and interface concentrations of nanometer dimensions. Sub-micron particles, cracks and pore sizes are easily determined by X-ray refractometry without destroying the structure by cutting or polishing for microscopic techniques.

Beyond this analytical potential for (integral) analysis, spatial resolution can be achieved when the sample is scanned across a narrow X-ray beam. As the scattered refraction intensity is much higher than in conventional wide angle X-ray scattering (WAXS) scanning is possible within relatively short time. In this case the technique is named ‘X-ray refraction topography’. It localizes the projection of inner surface concentrations or individual edges of surfaces and interfaces such as sub-micrometer pores or cracks. The spatial resolution can be better than 10 μm. The technique provides an extension of classical single crystal X-ray topography towards polycrystalline materials.

Although two-dimensional refraction topography provides an effective new probe for analyzing meso-structures of all kind of heterogeneous materials, it is sometimes interesting to have section images of transversal resolution as known from X-ray computer tomography in order to overcome the overlap of details by projection effects. Some experimental examples demonstrate the feasibility of X-ray refraction computer tomography.

Section snippets

Physics and instrumental

The physics of X-ray refraction is quite similar to the well-known refraction of light by optical lenses and prisms, which is governed by Snell's law [1]. However a major difference from optics is the deflection at very small angles, as the refractive index n of X-rays in matter is nearly one (Compton and Allison, 1935) [1]: $n=1−ε;ε∼ρλ^{2},$ where ε≅10⁻⁵ for glass/8 keV radiation. ε is the real part of the complex index of refraction, ρ the electron density and λ the X-ray wavelength. With n<1 the

Quantitative X-ray refraction

The angular intensity distribution I^∗_R(θ) of X-rays refracted by N spherical pores of radius R has been approximated by Hentschel et al. [3]: $I^{∗}_{R} (θ)=I_{A0} NR16ε^{2} /θ^{4},$ where I_A0 is the reduced intensity of the primary beam I₀ caused solely by the absorption of the sample due to the well-known absorption law I_A0=I₀e^−μd (μ: linear coefficient of absorption, d: thickness of the sample).

At a given scattering angle θ, fixed wavelength and electron density, the scattering intensity I^∗_R depends only on the

X-ray refractometry

X-ray refractometry determines the spatially averaged refraction intensities of samples. In the following discussion the resulting pore sizes of sintered glass ceramics are compared with those measured by (optical) microscopic image analysis, which is the standard method for materials with predominately sealed porosity. The micrographs of Fig. 4 show the pore formation of two sintered materials of the same porosity p=5%.

The samples obviously differ in their mean pore sizes. The micrograph on

X-ray refraction computer tomography

Although (two-dimensional) refraction topography provides an effective new probe for analyzing all kind of meso-structures of heterogeneous materials, it is sometimes interesting to have section images of transversal resolution in order to overcome the overlap of details by projections along the traversing beam path. For the purpose of density measurements by X-ray absorption the well-known technique of X-ray computer topography (CT) provides this feature. Beyond density investigations Fig. 11

Conclusions

X-ray refraction techniques provide new tools for the non-destructive investigation of the micro-structure of ceramics and other advanced materials. X-ray refractometry and X-ray refraction topography are well suited for characterizing changes in statistical and spatial pore size distributions during sintering of compacted powders, especially when microscopic analysis fails or is too exhaustive. X-ray refraction techniques image inner surface, interface and crack densities and agglomeration of

Karl-Wolfram Harbich, born in 1945, has studied physics at the Freie Universität Berlin, where he received his PhD in 1984. His postdoctoral activities have focussed on biophysics, especially membranes. Since 1989 he has collaborated with the BAM laboratory for ‘generalized X-ray topography’, where he is responsible for the development and application of new non-destructive X-ray techniques.

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Joerg V. Schors, born in 1962, has studied physics at the Technische Universität Berlin, where he received his master's degree in 1989. after which he collaborated with the BAM within the NDT X-ray division. Five years later he joined the X-ray topography laboratory, where his responsibilities are model calculations on new topographic applications and the management of European projects.

rer. nat. Manfred P. Hentschel, born in 1943, has studied physics at the Freie Universität Berlin, where he received his PhD in 1981. His postdoctoral activities have focussed on X-ray and neutron scattering of biomembranes and polymers. Since 1987 has collaborated with the BAM, where he is the head of the laboratory for ‘generalized X-ray topography’, where new imaging X-ray techniques are being developed for non-destructive characterization of advanced materials.

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