MODERN APPROACHES IN PROPERTY ANALYSIS OF POLYCRYSTALLINE TEXTURED MEDIA IN GEO- AND MATERIAL SCIENCE BY NEUTRON DIFFRACTION DATA Victor B. Yakovlev National Research University MIET, Moscow, Russia

Tectonic Blocks Anisotropic Polycrystalline Media Low Symmetry Isolated Inclusion Seismic Instrumentations Acoustic Emission Neutron Diffraction LEVELS OF DESCRIPTION IN GEOSCIENCE

KEY PROBLEMS TO DESCRIPTION OF POLYCRYSTALLINE ROCKS MACROLEVEL =c * ijkl (r) MICROLEVEL  ij (r)=c ijkl (r)  kl (r)  ij (r)=K ijkl (r)  ij (n)=K ijkl (n) TEXTURE FORMATION

EFFECTIVE CHARACTERISTICS AND RELATED PROBLEMS HISTORICAL BACKGROUND

STRUCTURE OF INHOMOGENEOUS MATERIALS Spatial geometric structure Matrix composite Polycrystals Sceletal Tissue Shape of inclusions Particulate Fiber Laminar Spatial arrangement Regular (periodic) Stochastic Orientation texture Nonisometric inclusions Crystallographic Linear size of inclusions Macro Micro Nano

GENERAL SINGULAR APPROXIMATION OF RANDOM FIELDS (1) (2) Equilibrium equation of inhomogeneous and comparison media Solution of (1) in terms of deformations (3) Introduce Green tensor as After transforms (4)

– integral tensor operator Direct evaluation leads to

PROBLEMS OF AVERAGING – Crystallographic ODF

ODF of polycrystalline Quartz

Plot 1 – Longitudinal wave in monocrystalline quartz Plot 2 – Voight approximation Plot 3 – averaged Hashin-Shtricman bounds Plot 4 – Reuss approximation Plot 5 – Transverse wave in monocrystalline quartz VELOCITIES OF THE LONGITUDINAL WAVE IN TEXTURED POLYCRYSTALLINE QUARTZ

Matrix 1052,5 Inclusion Symmetry Disk, Cubic 29,57 11,45 6,61 Hexagonal 33,3518,7614,198,954,669,58 Tetragonal 27,1033,779,5212,157,464,66 Sphere, Isotropic 22,01 10,10 5,96 Fiber, Cubic 26,47 10,29 5,68 Hexagonal 20,6034,999,8010,145,825,40 Tetragonal 28,9420,6010,5910,015,615,82 EFFECTIVE CHARACTERISTIC OF THE MATRIX REINFORCED COMPOSITE

1 – Cubic, 2 – Tetragonal, 3 – Hexagonal symmetry of effective properties Dependence of the anisotropy of the effective properties from

DISTRIBUTION OF STRESS FIELDS ON THE SURFACE OF THE CRYSTALLITE IN POLYCRYSTALLINE TEXTURED QUARTZ

Dependence of the operators of concentration of stresses and strains from the rotation in the olivine polycrystalline sample with effective characteristics DISTRIBUTION OF STRESS AND STRAIN FIELDS WITHIN THE CRYSTALLITE IN POLYCRYSTALLINE TEXTURED OLIVINE

PREFERED ORIENTATIONS OF CRYSTALLOGRAPHIC AXIS OF CRYSTALLITES IN OLIVINE ROCKS UNDER HYDROSTATIC PRESSURE Blue color designates concentration of crystallites with preferred orientations

MODELING OF DEFORMATION TEXTURE 1. Crystallites in the polycrystal orientate under external stress-strain condition 2. Local energy in preferred orientations of crystallites leads to minimum Mathematical formulation Algorithm of modeling 1. Split all Euler space on elementary volumes 2. All knots are crystallites with Euler coordinates 3. Evaluate local energy of crystallites 4. Rotate every crystallites on one step in decreasing energy direction 5. Repeat step 3 and 4

Relative local energy of quartz crystallites under external stress: axis, shift, hydrostatic pressure

PREFERED ORIENTATIONS OF CRYSTALLOGRAPHIC AXIS OF CRYSTALLITES IN OLIVINE ROCKS Experimental data (SKAT diffractometer) Model calculation after 8 iterations (external hydrostatic pressure)

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