A COMPARISON OF METHODS FOR PARTICLE SIZE DETERMINATION

Marian Cernansky¹, Vaclav Holy², Jiri Kub¹ and Josef Kubena²

¹Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 180 40 Praha 8, Czech Republic
²Department of Solid State Physics, Faculty of Sciences, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic

Keywords: X-ray diffraction, directional distribution, particle size

Usually, the particle size is determined from the breadths of diffraction line profiles measured on a powder diffractometer. Focusing arrangements are utilized very often to enhance the intensity. On the other hand, the application of focusing complicates the exact interpretation of measured data. It is questionable whether the measured distribution of the diffracted radiation is just the right directional distribution required by the theory of particle size determination. Equally, the elimination of the instrumental distortion is usually rather difficult.

Therefore, we have suggested and realized measurements of directional distributions both of the diffracted and transmitted beams by a triple-axis diffractometer. A sample (in position of the second crystal) is irradiated by nearly monochromatic and nearly parallel beam originating by the diffraction on a plane crystal monochromator (the first crystal). The directional distribution of the diffracted or the transmitted wave is measured by the analyser (the third crystal). The device distortion -- the instrumental function -- can be easily calculated applying the dynamical theory of diffraction.

A plane monochromatic wave incident upon a small diffracting crystal produces a divergent diffracted wave (diffuse X-ray scattering). Information about the shape and size of the crystal can be obtained from the distribution of the scattered intensity in the reciprocal space. The close proximity of a point hkl in the reciprocal space describes diffuse scattering in the diffraction hkl. The distribution of intensity around the origin 000 of the reciprocal lattice is characteristic of the diffuse scattering in the transmitted nondiffracted wave.

The diffuse scattering in the transmitted wave originates by two different mechanisms. The first mechanism is based on inhomogenities of the electron density of the sample (i.e. changes of the refractive index) and refers to the classical small angle scattering. The second mechanism is caused by the primary extinction in crystals. If some small crystal of a polycrystalline sample is in the diffraction position, the wave transmitted by this crystal is weakened due to primary extinction of X-rays. It disturbs the perfect geometric planes of the transmitted waves and the diffuse scattering of X-rays is observed.

The first mechanism predominates in powder samples, where there is an appreciable difference between the refractive index of grains and spaces among them. This mechanism does not occur in the compact polycrystalline samples, because whole measured volume of the sample has approximately the same refractive index. In these samples the second mechanism appears sensitive to the size of coherently scattering regions.

As long as we know, this effect has not been utilized so far for the particle size determination. The practical advantage of this effect lies in the practical independence of the measured diffuse scattering on the structure of the crystal -- internal strains, dislocation structure etc. It is more sensitive rather to large particles, while the conventional powder diffractometry has the more remarkable effects from small particles. Conventional powder diffraction methods result in rather smaller values then the method of the diffuse scattering in the transmitted wave for the sample containing particles of different sizes. Samples, containing fractions of different particle sizes, complicate, too, the comparison of conventional powder diffractometry with the method of diffuse scattering in the diffracted beam, as measured by triple-axis diffractometer.

This research was funded by the Grant Agency of the Czech Republic under grant No. 202/96/1685 and this support is gratefully acknowledged. The authors are grateful to HMZ a.s., Bruntal and Pramet Sumperk for powders of metallic materials.