Victor B. Yakovlev National Research University MIET, Moscow , Russia yakovlev@miee.ru

1. 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 yakovlev@miee.ru

2. LEVELS OF DESCRIPTION IN GEOSCIENCE Seismic Instrumentations Acoustic Emission Neutron Diffraction

3. KEY PROBLEMS TO DESCRIPTION OF POLYCRYSTALLINE ROCKS MACROLEVEL <ij(r)>=c*ijkl(r)<kl(r)> TEXTURE ij(r)=Kijkl(r)<kl(r)> ij(n)=Kijkl(n)<kl(r)> TEXTURE FORMATION MICROLEVEL ij(r)=cijkl(r)kl(r)

4. EFFECTIVE CHARACTERISTICS AND RELATED PROBLEMS HISTORICAL BACKGROUND

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

7. – integral tensor operator Direct evaluation leads to

8. PROBLEMS OF AVERAGING 1. 2. – Crystallographic ODF 3. 4.

9. ODF of polycrystalline Quartz

10. VELOCITIES OF THE LONGITUDINAL WAVE IN TEXTURED 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

11. EFFECTIVE CHARACTERISTIC OF THE MATRIX REINFORCED COMPOSITE

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

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

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

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

16. 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

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

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

19. Thank for your attention!