Tech Note 109

Preferred Orientation

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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.

In 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.


Theoretical consideration

In general, it is possible to distinguish four types of polycrystalline specimens:

1. 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.

2. 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.

3. 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 the preparation.

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 distributions.
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

Why important

Diffraction pattern is almost always affected by various preferred orientation.


An example

Text Box: O1=1
Calculated powder diffraction pattern of Muscovite with various degrees preferred orientation (00L)

Text Box: O1=0.2
Text Box: O1=0.8



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TN-101 Ab initio Structure Determination XRD.US initio structure determination.htm
TN-102  Expert Witness XRD.US witness.htm
TN-103  Grazing Incidence Diffraction XRD.US incidence diffraction.htm
TN-104  High Temperature Diffraction XRD.US temperature diffraction.htm
TN-105  Neutron Diffraction XRD.US diffraction.htm
TN-106  Percentage Crystallinity XRD.US crystallinity.htm
TN-107  Phase Identification XRD.US identification.htm
TN-108  Precision Lattice Parameters XRD.US lattice parameters.htm
TN-109  Preferred Orientation XRD.US orientation.htm
TN-1010  Quantitative Phase Analysis XRD.US phase analysis.htm
TN-1011  Residual Stress XRD.US stress.htm
TN-1012  Retained Austenite XRD.US austenite.htm
TN-1013  Rietveld Structure Refinement XRD.US structure refinement.htm
TN-1014 Crystallite size, size distribution and strain XRD.US and strain analysis.htm
TN-1015 Synchrotron Diffraction XRD.US diffraction.htm




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