Correct preparation of specimens is the crucial problem for any
experimental procedure including diffraction experiments. Starting from
fundamental principles of diffraction on polycrystalline samples, the
ideal sample consists of crystals or crystal fragments oriented completely
at random. In this case loci of end points of individual reciprocal
vectors Hhkl are on the surfaces of concentric spheres and orientation of
samples is independent on direction of primary beam. In this way the
diffraction conditions are always fulfilled without change of sample
orientation (only radius of Ewald sphere is the limiting factor). An
absolute random orientation of particles can exist only if shape of
particles is spherical.
real samples preferred orientation of particles is always present and thus
measured intensities of diffractions are incorrect. Treatment of this
problem depends on precision of information required. It can be neglected
in routine identification procedure of common phases. In the case of using
the data for quantitative phase analyses and for Rietveld refinement
procedures, correction of intensities to influence of preferred
orientation is necessary. Preferred orientation can be easy recognized on
powder diffraction photographs and on texture goniometer outputs. On
standard diffractometer records, information about this phenomenon is
completely hidden. To correct intensity data, the most frequent approach
is an empirical one, based on trial-and-error method: first we consider
that preferred orientation is parallel to (100), next to (010) and so
on... It can be and it is often successful.
Unfortunately, if more than one
type of preferred orientation is present, this approach is almost useless.
general, it is possible to distinguish four types of polycrystalline
Specimens formed by euhedral crystals of appropriate size (within the
interval 1 - 10 _m). This type of polycrystalline samples is represented
by some thin layers, clay minerals, natural as well as synthetic zeolites.
Because number of crystal faces in this type of specimens is strongly
limited, preferred orientation is always present, and the morphology of
crystals is the decisive phenomenon.
Specimens with dominant morphological features others than crystal faces.
As example can be frequently used quantitative phase analyses of amphibole
and chryzotile asbestos mixtures in building materials.
Specimens, where suitable size of crystal fragments is obtained by
grinding of coarse crystals in agate mortar. This kind of powdered samples
consists of crystal fragments which shape is primary influenced by
cleavage. If cleavage is perfect (galena PbS, fluorite CaF2; cubic system,
point-group symmetry m3m, excellent cleavage parallel to (100), calcite
CaCO3; trigonal system, point-group symmetry 32/m preferred orientation
parallel to (1011)), crystal fragments are always of the same shape (in
examples mentioned here are cubes and rombohedrons, respectively). For
these reasons, preferred orientation drastically influences intensities of
individual diffractions, like in preceded type. On the other hand, minimum
degree of preferred orientation can be obtained from materials having no
cleavage and thus crystal fragments have irregular shape (garnets,
datolite CaB(SiO4)(OH), etc.).
4. In fine-grained metallic samples formed by anhedral crystals, textures
are the function of preparation and further processing of material (sheet
textures of rolled materials, fiber textures of wires).
Very often there are compact samples or
powders which cannot be prepared without texture or it cannot be neglected
absolutely. The term texture is characterized by an inhomogeneous
distribution of crystal orientations of a lot of grains or crystallites
(mostly more than 100000 in the considered volume). That means, that with
regard to the normal direction of the sample some directions occur over
proportionally. One typical example is the well-known fiber texture, where
the fiber axis corresponds to a small-indexed lattice direction, mostly.
Perpendicular to this direction no further preferred orientations exist.
This special and simple texture will be observed on crystals with fibrous
(or plated - but than the direction is described by a small-indexed
reciprocal lattice vector) habit which can be directed more or less during
However, an observed texture can be much
more complicate than usually assumes, especially for low-symmetry
crystals. Therefore, for a mathematical description one needs as much as
possible complete distributions of multiplicities for different lattice
planes, which must be derived from measured spatial intensity
If one speaks about preferred orientations, one assumes a very simple
texture for the given sample. This will be described by only one texture
component, where its axis or normal direction corresponds to the sample
normal. Usually, it is nothing known about any distribution of
multiplicity, because only a single powder pattern has been measured. In
maximum only the sample has been rotated around its normal for a better
statistic. Then, only the existence of singular deviations between
theoretical and experimental reflection intensities let suppose an
occurrence of texture components, which must be considered during the
comparison of theoretical and experimental curve.
This is an equation which has been developed by MARCH in 1932 and will be
used in many Rietveld programs. Mainly it is useful for the description of
the preferred orientations of axial crystals
Diffraction pattern is almost always
affected by various preferred orientation.
powder diffraction pattern of Muscovite with various degrees preferred
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