Functions describing preferred orientation in flat aggregates of flake-like clay minerals and in other axially symmetric fabrics
✍ Scribed by Friedrich Lippmann
- Publisher
- Springer
- Year
- 1970
- Tongue
- English
- Weight
- 1010 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0010-7999
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✦ Synopsis
The oriented aggregates of flake-like clay minerals, prepared in the laboratory for X-ray identification purposes, are axially symmetric fabrics, with the axis of symmetry or pole perpendicular the surface. The density of the vectors normal to the basal planes of the clay particles has its maximum at the pole. A given number of particles is considered, and the degree of orientation is assumed variable with one single parameter t, defined as maximum density over constant average density D. The decline of the basal vector density from the pole to the equator may then be described by a power of the cosine of the polar angle ~:
This formula yields a quantitative description of orientation patterns measured on artificial fabrics by means of X-ray diffraction and on the universal stage.
In some cases, the description may be refined by using a function composed of two additive cosine powers. The cosine power is by no means a mathematically unique solution but other possible functions are less versatile and yield no better fit with the experimental data. The Gauss distribution may be regarded as an approximation of (9) for very high degrees of orientation. * Herrn Prof. Dr. Wolf v. Engelhardt zum 60. Geburtstag gewidmet.