Typical experimental situations of texture measurements are demonstrated involving failure to take into
account some physical factors responsible for an inadequate texture description or imaginary texture
changes. Among these factors there are inevitable texture inhomogeneities, inhomogeneous distribution
of defects in deformed metal materials and resulting inhomogeneous lattice perfection by their heat
treatment. It is shown that a formal approach to texture analysis does not allow to reveal a number
of important regularities of structure formation.

Yu. Perlovich

Some Physical Errors of X-Ray Texture Measurements

The results of several years (1980&#x2013;1994) field observations of rock joints at the former USSR territory
are integrated. New methods of data processing and interpretation are proposed and developed. With
the local data set for an exposure we connect the symmetric positively defined second order tensor
J characterizing the density and relative position of joint systems as well as their orientation in space.
The complete set of tensors J for any region depicted in appropriate manner gives the integral &#x201C;portrait&#x201D;
of tectonic fracturing of the region. The regular changes of such integral characteristics for Great
Caucasus as an example are determined.

T. P. Belousov

Sh. A. Mukhamediev

S. F. Kurtasov

Joints Orientation Distributions in Sedimentary Rocks

The mathematical problems, in the field of texture analysis, which remain still unsolved are briefly
discussed. The importance of the positivity condition and its use in the harmonic method are then
explained.

F. Wagner

The Use of the Positivity Method to Approximate the Complete O.D.F.

Up to now Texture investigations of phyllosilicates were restricted to pole density measurements of
the (001) basal plane. Because of the tabular grain shape parallel to the basal plane an axial symmetry
of the texture is assumed usually. This assumption was proved for four mica bearing samples by
calculating the ODF from neutron diffraction data. Beside the mica-texture the textures of the other
major fractions like quartz and feldspar were determined to detect correlation between them. The
textures are explained by components. Each component is characterised by a preferred orientation or
fibre axis, a corresponding spreading and an intensity I&#x2BF; describing the volume fraction of all crystallites
belonging to the component. The presented component method can be applied to any crystal symmetry
and to polyphase materials with overlapped pole figures.

K. Helming

D. Schmidt

K. Ullemeyer

Preferred Orientations of Mica Bearing Rocks Described by Texture Components

Statistical methods for calculating the effective static and dynamic characteristics of textured
microheterogeneous materials such as polycrystals, composites and rocks are considered. Effective static
characteristics based on the example of the elastic modules tensor are analyzed. Effective dynamic
characteristics based on the example of the dielectric permeability tensor in calculating the scattering
factor, phase and group velocities of the propagation of plane electromagnetic waves are presented.

T. D. Shermergor

Statistical Methods for Property Calculation of Textured Materials

In texture analysis there are several instances when mathematical methods of spherical interpolation
or approximation are required. Ad hoc adaptions of univariate or bivariate methods to the topology
of spherical manifolds usually fail in one way or another. Therefore, this contribution will provide
a brief survey of genuinely spherical methods.

H. Schaeben

A Brief Survey of Spherical Interpolation and Approximation Methods for Texture Analysis

Pole figures are represented as the sum of solutions of two ultrahyperbolic differential equations. We
derive the domains of dependence for pole figures and apply the method of continuation to solve the
ultrahyperbolic equations.

T. I. Savyolova

Determination of Domains of Dependence Through the Solution of an Ultrahyperbolic Differential Equation

Although the smoothing of experimental pole-density data modifies the primary data set, the effect
of such a procedure on the Orientation Distribution Function and on the interpretation of the texture
was not considered until recently. The influence of smoothing on texture reproduction will be derived
for the case, that the Orientation Distribution Function is approximated by a linear combination of
normal distributions (ideal orientation components) and smoothing is carried out with normal
distributions, too. The characteristic component parameters are well-suited to indicate changes of the
Orientation Distribution Function. The observed texture variations as a consequence of smoothing lead
to the conclusion, that moderate smoothing does not falsifythe texture. Several possibilities to control
the effect of smoothing will be discussed. Based on the visual comparison of smoothed and unsmoothed
pole-figures it is argued, that even extreme smoothing may be useful for some purposes.

D. I. Nikolayev

The Effect of Smoothing on ODF Reproduction

A method of calculating the tensor operator of the electroelastic field concentration in the vicinity of
two kinds of inhomogeneities (pores and crystalline inclusions) is developed. It is assumed that the
shape of inhomogeneities is an ellipsoid. The materials of the matrix and/or inclusions have
piezoelectric properties. Effective piezoelectric properties of textured polycrystalline media are
calculated by means of the general singularity approximation of the theory of random fields. Methods
for the analysis of the operators of electroelastic field concentration on the surface of the inclusion are
used. The influence of the ellipsoidal pore shape on the tensor operators of electroelastic field
concentration is considered. Data are shown in figures.

V. B. Yakovlev

Electroelastic Field Concentration on Elliptical Pores in Textured Media

Invariants of the tomographic projection operator of texture goniometry and counterexamples provide
a unified view of existing methods to resolve the corresponding inverse problem and may be instructive
to develop novel approaches.

A Unified View of Methods to Resolve the Inverse Problem of Texture Goniometry

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Texture, Stress, and Microstructure

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