Number of diffracting grains and preferential orientation

As we have said, the diffracted integrated intensity is proportional to the quantity per volume of the phase. However, in a polyciystalline sample irradiated with a 

2 This type of study can also be achieved with neutron diffraction. The method is the same as the one we will describe, but neutron diffraction studies are, of course, much more cumbersome to implement than those involving X-ray diffraction. Note that the volume studied in neutron diffraction is much larger than in X-ray diffraction, which is why it can be used to study the core of bulky samples. 

The last two films illustrate the influence of the multiplicity factor on the diffraction arcs. For a highly symmetrical crystal (which is the case for NaCl), the multiplicity factor of each peak is high, meaning that the number of families of planes that contribute to a given peak is larger than when symmetry is low (which is 

In the previous sections, we discussed the influence of the number of crystals in the sample. The orientations of the crystals were assumed to be random, and obviously, this factor comes into play. Theoretically, quantitative analyses by X-ray diffraction are conducted on samples comprised of a very large number of micrometric crystals without any preferential orientation. This latter condition is sometimes difficult to meet, since it can be sometimes complicated to give the crystals in the sample a random orientation. This effect often occurs when crystals have an anisotropic shape. Clays are an extreme example of this behavior [BRI 80]. Their layered stracture naturally causes a preferential orientation along the (001) planes. Some authors pLO 55, SMI 79, HIL 99] have used atomization methods to produce polycrystalhne particles in which the clay crystals have a random orientation. Another approach consists of quantifying the preferential orientation and to take it into accoimt when calculating the proportions of the phases in the sample. We will not be giving arty details on this method, since it requires considerable skill in the production of pattern and data analysis. It is always better not to have a preferential orientation. 

The diffraction pattern of a phase which is obtained with a sample that contains several of them is not exactly what would be obtained if the sample contained only the phase in question. The intensity of the X-ray beam diffracted by the grains of the phase we are focusing on is modified by the absorption from the matrix surrounding these grains. Since the phases in the matrix have different absorption coefficients, 

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