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It is shown that to determine the quantitative phase composition of n samples each of which contains n phases it is sufficient to obtain a set of n 2 intensities values of analytical lines, I~j, where 1 < i < n is the phase number in a sample of number 1

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Preferred orientation of clay particles in various clay mounts was measured with an X-ray texture diffractometer. Pole distributions are approximately symmetrical about the normal to the sample. Particle orientation is characterized by standard deviations ranging from 7 ~ for thin sedimented layers, to 20 ~ and more for dry-pressed samples, the latter showing less dependence on particle size. The orientation of the reflecting particles may span a considerable angular range affecting the intensities of diffraction peaks observed on contemporary powder diffractometers, even those with moderate axial divergence. A theory based on the diffractometer geometry was developed to calculate the effect of particle orientation. Results are presented as modified Lorentz factors for orientations deduced from experimental observations. In qualitative X-ray diffractometry of clays, preference must be given to preparation techniques which ensure a high degree of preferred orientation and therefore strong enhancement of basal reflections. In quantitative X-ray diffractometry, the main factor is the reproducibility of particle orientation, and suction and dry pressing are promising methods of sample preparation. X-ray diffraction (XRD) is the main tool for the identification and quantitative analysis of clay minerals. Although effective techniques for randomizing clay particle orientation have been developed (Smith et aL, 1978), oriented clay mounts are commonly used as they enhance the diagnostically important basal reflections. Techniques used in sample preparation are (in order of increasing preferred orientation of the clay particles): dry pressing, suction on a millipore filter, smearing on a glass slide, gravity sedimentation, and centrifuge-assisted sedimentation (Gibbs, 1965). In conventional diffractometers with Bragg-Brentano parafocusing geometry, reflections occur only from the crystallographic planes approximately parallel to the sample plane. Consequently, if the 001 crystallographic plane is oriented predominantly parallel to the sample plane, enhancement of the corresponding 00l reflections for the clay sample is achieved. If "point" geometry is used (where the X-ray tube focus and the detector slit can be regarded as points), the degree of intensity enhancement will be equal for all 001 diffraction peaks of a given mineral. However, contemporary diffractometers do not use point geometry but "line" geometry with the X-ray focus and detector slit extended in the axial direction. The axial divergence of the incident and diffracted beams, although restricted by the Soller slits and monochromators, remains significant and exerts a strong influence on XRD by partially oriented samples. The main phenomenon is that some of the particles