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On the development of the quantitative texture analysis and its application in solving problems of the Earth sciences

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Abstract

A history of texture analysis (TA) evolution is shown, beginning from the first experimental and theoretical attempts to find and characterize preferred orientations of crystal lattices of grains in real polycrystalline samples. Stages of formation of TA theoretical apparatus, its basic elements, and also application of its capabilities for quantitatively describing anisotropic properties of textured samples are discussed. Attention is also paid to the limitations and difficulties associated with the analysis. The application of the quantitative TA apparatus is demonstrated by example describing elastic properties of textured materials up to multiphase samples containing pores and cracks. A wide scope of TA includes the analysis based on neutron scattering which has been effectively developed at the Frank Laboratory of Neutron Physics. A practical opportunity to determine the bulk crystallographic textures of single-phase and multiphase materials is offered by the use of modern neutron diffractometers, including the SKAT diffractometer at the IBR-2 pulsed reactor. This is especially important for studying samples of natural rocks. The examples given show how the neutron scattering data for the quantitative TA are used in combination with other physical and petrological methods for solving fundamental problems of geology and geophysics based on the analysis of a structure and properties of the Earth’s lithosphere matter. The review includes a detailed list of references of original works concerning the TA elaboration, overview publications and monographs, and also information on the most popular TA-related software.

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References

  1. A. N. Nikitin and T. I. Ivankina, “Neutron diffractometry in geosciences,” Phys. Part. Nucl. 35, 193–224 (2004).

    Google Scholar 

  2. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957).

    MATH  Google Scholar 

  3. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (Nauka, Leningrad: 1975; World Scientific, Singapore, 1988).

    Google Scholar 

  4. E. S. Fedorov, Theodolite Method in Mineralogy and Petrography (Tipografiya A. Yakobsona, St. Petersburg, 1893) [in Russian].

    Google Scholar 

  5. L. I. Lukin, V. F. Chernyshev, and I. M. Kushnarev, Microstructural Analysis (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  6. H.-J. Bunge, Mathematische Methoden der Texturanalyse (Akademie, Berlin, 1969).

    Google Scholar 

  7. G. Wassermann and J. Grewen, Texturen Metallischer Werkstoffe (Springer, Berlin, 1962; Metallurgiya, Moscow, 1969).

    Google Scholar 

  8. A. S. Viglin, “Quantitative measure of texture of polycrystalline material. Texture function,” Fiz. Tverd. Tela 2, 2463–2476 (1960).

    MathSciNet  Google Scholar 

  9. R. J. Roe, “Description of crystallite orientation in polycrystalline materials. General solution to pole figure inversion,” J. Appl. Phys. 36, 2024–2031 (1965).

    ADS  Google Scholar 

  10. H.-J. Bunge, “Zur Darstellung allgemeiner Texturen,” Z. Metallkund. 56, 872–874 (1965).

    Google Scholar 

  11. S. Matthies, “On the reproducibility of the orientation distribution function from pole figures (ghost phenomena),” Phys. Stat. Sol. (b) 92, K135–138 (1979).

    ADS  Google Scholar 

  12. H.-J. Bunge, Texture Analysis in Materials Science (Butterworth, London, 1983).

    Google Scholar 

  13. S. Matthies, G. Vinel, and K. Helming, Standard Distributions in Texture Analysis (Akademie, Berlin, 1987).

    Google Scholar 

  14. T. I. Savjolova, “Calculation of domains of dependence for pole figures with an ultrahyperbolic equation,” Textures and Microstructures 23, 185–199 (1995).

    Google Scholar 

  15. T. I. Savelova, “On solution of an inverse diffraction problem,” Dokl. Akad. Nauk SSSR 266, 590–593 (1982).

    MathSciNet  Google Scholar 

  16. S. Matthies and C. Esling, “Comments to a publication of Savyolova T.I. concerning domains of dependence in pole figures,” Textures and Microstructures 30, 201–227 (1998).

    Google Scholar 

  17. A. Vadon, D. Ruer, and R. Baro, “The generalization and refinement of the vector method for the texture analysis of polycrystalline materials,” Adv. X-Ray Analysis 23, 349–360 (1980).

    Google Scholar 

  18. R. D. Williams, “Analytical methods for representing complex textures by biaxial pole figures,” J. Appl. Crystallogr. 40, 4329–4335 (1968).

    Google Scholar 

  19. J. Imhof, “An iteration procedure in the texture analysis,” Phys. Stat. Sol. (b) 119, 693–701 (1983).

    ADS  Google Scholar 

  20. S. Matthies and G. Vinel, “On the reproduction of the ODF of textured samples from reduced pole figures using the concept of conditional ghost correction,” Phys. Stat. Sol. (b) 112, K111–K120 (1982).

    ADS  Google Scholar 

  21. S. Matthies, “20 years WIMV, history, experience and contemporary developments,” Mater. Sci. Forum 408–412, 95–100 (2002).

    Google Scholar 

  22. S. Matthies, “Some remarks on theoretical developments in quantitative texture analysis and on the optimal calculation of harmonic quantities with high precision,” Textures and Microstructures 8–9, 115–129 (1988).

    Google Scholar 

  23. J. Pospiech, private communication, 1977.

  24. S. Matthies and J. Pospiech, “On the demonstration of the ghost effect in texture analysis,” Phys. Stat. Sol. (b) 97, 547–556 (1980).

    ADS  Google Scholar 

  25. S. Matthies, “On the reproducibility of the ODF of texture samples from pole figures. Part III: Relationship between the ODF and the reduced ODF f(g),” Kristall und Technik 15, 431–444 (1980).

    Google Scholar 

  26. M. Dahms and H.-J. Bunge, “Positivity method for the determination of complete ODFs,” Textures and Microstructures 10, 21–35 (1988).

    Google Scholar 

  27. P. Van Houtte, “The use of a quadratic form for the determination of non-negative texture functions,” Textures and Microstructures 6, 1–20 (1983).

    Google Scholar 

  28. P. Van Houtte, “A method for the generation of various ghost correction algorithms the example of the positivity method and the exponential method,” Textures and Microstructures 13, 199–212 (1991).

    Google Scholar 

  29. S. Matthies, “On the principle of conditional ghost correction and its realization in existing correction concepts,” Textures and Microstructures 14–18, 1–12 (1991).

    Google Scholar 

  30. H. Schaeben, “Entropy optimization in texture geometry. I. Methodology,” Phys. Stat. Sol. (b) 148, 63–72 (1988).

    ADS  Google Scholar 

  31. K. Pawlik, J. Pospiech, and K. Luecke, “The ODF approximation from pole figures with the aid of the ADC Method,” Textures and Microstructures 14–18, 105 (1991).

    Google Scholar 

  32. K. Helming and T. Eschner, “A new approach to texture analysis of multiphase materials using a texture component model,” Cryst. Res. Technol. 25, K203–K208 (1990).

    Google Scholar 

  33. M. Dahms, “Introduction of the phon-concept into pole figure inversion using the iterative series expansion method,” Textures and Microstructures 19, 169–174 (1992).

    Google Scholar 

  34. M. Dahms, “Final positivity correction in the harmonic method,” Textures and Microstructures 21, 61–69 (1993).

    Google Scholar 

  35. R. Hielscher, H. Schaeben, and D. Chateigner, “On the entropy to texture index relationships in quantitative texture analysis,” J. Appl. Crystallogr. 40, 371–375 (2007).

    Google Scholar 

  36. M. Junk, J. Budday, and T. Boehlke, “On the solvability of maximum entropy moment problems in texture analysis,” Math. Models Methods Appl. Sci. 22, 1250043 (2012).

    MathSciNet  Google Scholar 

  37. U. F. Kocks, C. N. Tomé, H. -R. Wenk, A. J. Beaudoin, and H. Mecking Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties (Cambridge University Press, Cambridge, 2000).

    Google Scholar 

  38. S. Matthies, K. Helming, and K. Kunze, “On the representation of orientation distributions in texture analysis by σ-sections,” Phys. Stat. Sol. (b) 157, 71–83 (1990); Phys. Stat. Sol. (b) 157, 489–507 (1990).

    ADS  Google Scholar 

  39. P. Neumann, “Representation of orientations of symmetrical objects by Rodrigues vectors,” Textures and Microstructures 14–18, 53–58 (1991).

    Google Scholar 

  40. J. J. Fundenberger, H. Schaeben, and K. G. Boogaart, “Visualization of patterns of preferred crystallographic orientation by ω-sections,” Mater. Sci. Forum 495–497, 289–294 (2005).

    Google Scholar 

  41. S. Matthies, “Standard functions in the texture analysis,” Phys. Stat. Sol. (b) 101(2), K111–K115 (1980).

    ADS  Google Scholar 

  42. R. H. Fisher, “Dispersion on a sphere,” Proc. R. Soc. London, Ser. A 217, 295–305 (1953).

    ADS  MATH  Google Scholar 

  43. T. Eschner, “Texture analysis by means of model functions,” Textures and Microstructures 21, 130–146 (1993).

    Google Scholar 

  44. S. Matthies, “Form effects in the description of the ODF of texturized materials by model components,” Phys. Stat. Sol. (b) 112(2), 705–716 (1982).

    ADS  Google Scholar 

  45. T. M. Ivanova and D. I. Nikolaev, “New standard function for quantitative texture analysis,” Phys. Stat. Sol. (b) 228, 825–836 (2001).

    ADS  Google Scholar 

  46. H. Schaeben, “A simple standard orientation density function: The hyperspherical de la Vallée Pousin kernel,” Phys. Stat. Sol. (b) 200, 367–376 (1997).

    ADS  Google Scholar 

  47. S. Matthies, K. Helming, T. Steinkopf, and K. Kunze, “Standard distributions for the case of fibre textures,” Phys. Stat. Sol. (b) 150, 262–277 (1988).

    Google Scholar 

  48. K. Kunze and H. Schaeben, “The Bingham distribution of quaternions and its spherical Radon transform in texture analysis,” Math. Geol. 36, 917–943 (2004).

    MathSciNet  Google Scholar 

  49. T. I. Savelova, “Preface,” in Novye metody issledovaniya tekstury polikristallicheskikh materialov (New Methods of Investigation of Texture of Polycrystalline Materials (Collection of articles from Textures and Microstructures journal)), Composed by I. I. Papirov (Metallurgiya, Moscow, 1985).

    Google Scholar 

  50. S. Matthies, M. Muller, and G. W. Vinel, “On the normal distribution in the orientation space,” Textures and Microstructures 10, 77–96 (1988).

    Google Scholar 

  51. D. J. Nikolaev and T. I. Savyolova, “Normal distribution on the rotation group SO(3),” Textures and Microstructures 29, 201–233 (1997).

    Google Scholar 

  52. H. -R. Wenk, S. Matthies, J. Donovan, and D. Chateigner, “BEARTEX: A Windows based program for quantitative texture analysis,” J. Appl. Crystallogr. 31, 262–269 (1998).

    Google Scholar 

  53. K. Pawlik and P. Ozga, LaboTex: The Texture Analysis Software, Göttinger Arbeiten zur Geologie und Palaeöntologie, SB4, 1999; http://www.labosoft.com.pl.

    Google Scholar 

  54. R. Hielscher and H. Schaeben, “A novel pole figure inversion method: Specification of the MTEX algorithm,” J. Appl. Crystallogr. 41, 1024–1037 (2008).

    Google Scholar 

  55. O. Engler and V. Randle, Texture Analysis: Macrotexture, Microtexture & Orientation Mapping (CRC Press, Boca Raton, 2010).

    Google Scholar 

  56. S. Matthies and F. Wagner, “On a 1/n law in texture related single orientation analysis,” Phys. Stat. Sol. (b) 196, K11–K15 (1996).

    ADS  Google Scholar 

  57. S. Matthies and F. Wagner, “Using sets of individual orientations for ODF determination,” in Proceedings of ICOTOM 12 (NRC Research Press, Montreal, 1999), pp. 40–45.

    Google Scholar 

  58. J. Pospiech, J. Jura, and G. Gottstein, “Statistical analysis of single grain orientation data generated from model textures,” in Proceedings of ICOTOM 10 (Trans. Tech. Publications, Clausthal, Germany, 1993), pp. 407–412.

    Google Scholar 

  59. S. Matthies and G. W. Vinel, “On some methodical developments concerning calculations performed directly in the orientation space,” in Proceedings of ICOTOM 10 (Trans. Tech. Publications, Clausthal, Germany, 1993), pp. 1641–1646.

    Google Scholar 

  60. K. G. Boogaart, “Statistics for Individual Crystallographic Orientation Measurements,” PhD Thesis, TU Freiberg (Shaker-Verlag, Aachen, 2001).

    Google Scholar 

  61. F. Bachmann, R. Hielscher, and H. Schaeben, “Texture analysis with MTEX-free and open source software toolbox,” Solid State Phenom. 160, 63–68 (2010).

    Google Scholar 

  62. S. Matthies, “The ODF-spectrum a new and comprehensive characterization of the degree of anisotropy of orientation distributions,” Mater. Sci. Forum 495–497, 331–336 (2005).

    Google Scholar 

  63. H. Schaeben, R. Hielscher, J. J. Fundenberger, D. Potts, and J. Prestin, “Orientation density function-controlled pole probability density function measurements: Automatic adapted control of texture goniometers,” J. Appl. Crystallogr. 40, 570–579 (2007).

    Google Scholar 

  64. A. Muecklich and P. Klimanek, “Experimental errors in quantitative texture analysis from pole figures,” Mater. Sci. Forum 157–162, 257–286 (1994).

    Google Scholar 

  65. V. V. Luzin and D. I. Nikolaev, “On the errors of experimental pole figures,” Textures and Microtextures 25, 121–128 (1996).

    Google Scholar 

  66. T. A. Lychagina and D. I. Nikolaev, “Investigation of experimental pole figure errors by simulation of individual spectra,” Crystallogr. Reports 52(5), 774–780 (2007).

    ADS  Google Scholar 

  67. F. Bachmann, H. Schaeben, and R. Hielscher, “Optimizing the experimental design of texture goniometry,” J. Appl. Crystallogr. 45, 1173–1181 (2012).

    Google Scholar 

  68. L. Lutterotti, S. Matthies, and H. -R. Wenk, “MAUD: A friendly JAVA Program for material analysis using diffraction,” IUCr Newsletter of the CPD 21, 14–15 (1999).

    Google Scholar 

  69. Texture Analysis and Modeling Package (Material Science and Technology Division. LANL, Los Alamos, USA, 1995). e-mail: popLA@lanl.gov.

  70. K. Helming, “Texture approximation by model components,” Material Structures 5(1), 3–9 (1998).

    Google Scholar 

  71. M. D. Vaudin, Ceramic Division. NIST. Gaithersburg. USA, 1999. e-mail: mark.vaudin@nist.gov.

    Google Scholar 

  72. D. Chateigner, Combined Analysis (ISTE-Wiley, London, 2010).

    Google Scholar 

  73. I. Salzmann and R. Resel, “STEREOPOLE: a software for the analysis of X-Ray diffraction pole figures with IDL,” J. Appl. Crystallogr. 37, 1029–1033 (2004).

    Google Scholar 

  74. TexTools. University of Montreal, Canada, 2005; http://www.resmat.com.

  75. A. Tewari, S. Suwas, D. Srivastava, I. Samajdar, and A. Haldar, Eds., Proceedings of ICOTOM 16 (Trans. Tech. Publications. Mumbai, India, 2012).

    Google Scholar 

  76. H. -J. Bunge, Ed., Theoretical Methods of Texture Analysis (DGM, Oberursel, Germany, 1987).

    Google Scholar 

  77. H. -J. Bunge and C. Esling, Eds., Advances and Applications of Quantitative Texture Analysis (DGM, Oberursel, Germany, 1991).

    Google Scholar 

  78. New Methods of Investigation of Texture of Polycrystalline Materials (Collection of articles from Textures and Microstructures journal), Composed by I.I. Papirov (Metallurgiya, Moscow, 1985).

  79. Ya. D. Vishnyakov, A. A. Babareku, S. A. Vladimirov, and I. V. Egiz, Theory of Texture Formation in Metals and Alloys (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  80. S. A. Berestova and Sh. M. Khananov, “On some ways of formation of structural-phenomenological theories in mechanics of a deformable solid,” Vestnik PGTU. Mekhanika, No. 4, 17–29 (2010).

    Google Scholar 

  81. W. Voigt, Lehrbuch der Kristallphysik (Teubner, Leipzig, 1928).

    MATH  Google Scholar 

  82. A. Reuss, Berechnung der Flieβsgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle Z. Angew. Math. Mech. 9, 49–58 (1929).

    MATH  Google Scholar 

  83. S. Matthies and M. Humbert, “On the principle of a geometric mean of even-rank symmetric tensors for textured polycrystals,” J. Appl. Crystallogr. 28(3), 254–266 (1995).

    Google Scholar 

  84. S. Matthies, “GEO-MIX-SELF calculations of the elastic properties of a textured graphite sample at different hydrostatic pressures,” J. Appl. Crystallogr. 45, 1–16 (2012).

    Google Scholar 

  85. K. S. Aleksandrov and L. A. Aizenberg, “A method for determining physical constants of polycrystal materials,” Dokl. Akad. Nauk SSSR 167, 1028–1031 (1966).

    Google Scholar 

  86. A. Moraviec, “Calculation of polycrystal elastic constants from single-crystal data,” Phys. Stat. Sol. (b) 154, 535–540 (1989).

    ADS  Google Scholar 

  87. R. Hill, “The elastic behaviour of a crystalline aggregate,” Proc. Phys. Soc. 65, 349–354 (1952).

    ADS  Google Scholar 

  88. S. Matthies, “On the combination of self-consistent and geometric mean elements for the calculation of the elastic properties of textured multi-phase samples,” Solid State Phenom. 160, 87–93 (2010).

    Google Scholar 

  89. Z. Hashin and S. Shtrikman, “Note on a variational approach to the theory of composite elastic materials,” J. Franklin Inst. 271(4), 336–41 (1961).

    Google Scholar 

  90. I. Fredholm, “Sur les équations de l’équilibre d’un corps élastique,” Acta Math. 23, 1–42 (1898).

    MathSciNet  Google Scholar 

  91. J. D. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion and related problems,” Proc. R. Soc. A 241(1226), 376–396 (1957).

    ADS  MATH  MathSciNet  Google Scholar 

  92. T. Mura, Micromechanics of Defects in Solids (Kluwer Academic Publishers, Dordrecht, 1991).

    Google Scholar 

  93. A. Einstein, “Eine neue Bestimmung der Moleküldimensionen,” Ann. Phys. (New York) 19, 289–306 (1906); Ann. Phys. (New York) 34, 591–592 (1911).

    ADS  MATH  Google Scholar 

  94. E. Kröner, “Berechnung der Elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls,” Z. Phys. 151(4), 504–518 (1958).

    ADS  Google Scholar 

  95. A. Moraviec, “The effective elastic constants of quasiisotropic polycrystalline materials composed of cubic phases,” Phys. Stat. Sol. A 155, 353–364 (1996).

    ADS  Google Scholar 

  96. S. Matthies and G. W. Vinel, “On the calculation of the Eshelby tensor and the beauty of our nature,” Solid State Phenom 105, 113–118 (2005).

    Google Scholar 

  97. T. D. Shermergor, Theory of Elasticity of Microinhomogeneous Media (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  98. I. O. Bayuk and E. M. Chesnokov, “Correlations between elastic and transport properties of porous cracked anisotropic media,” Phys. Chem. Earth 23(3), 361–366 (1998).

    Google Scholar 

  99. H.-R. Wenk, R. N. Vasin, H. Kern, S. Matthies, S. C. Vogel, and T. I. Ivankina, “Revisiting elastic anisotropy of biotite gneiss from the Outokumpu scientific drill hole based on new texture measurements and texture-based velocity calculations,” Tectonophysics 570–571, 123–134 (2012).

    Google Scholar 

  100. G. Simmons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (M.I.T. Press, Cambridge, Massachusetts, 1971).

    Google Scholar 

  101. S. Matthies, H. G. Priesmeyer, and M. R. Daymond, “On the diffractive determination of single crystal elastic constants using polycrystalline samples,” J. Appl. Crystallogr. 34(5), 585–601 (2001).

    Google Scholar 

  102. I. O. Bayuk, M. Ammerman, and E. M. Chesnokov, “Elastic moduli of anisotropic clay,” Geophysics 72(5), D107–D117 (2007).

    ADS  Google Scholar 

  103. M. Wang and N. Pan, “Elastic property of multiphase composites with random microstructures,” J. Comp. Phys. 228, 5978–5988 (2009).

    ADS  MATH  Google Scholar 

  104. M. A. Mazo, L. I. Manevitch, E. B. Gusarova, M. Yu. Shamaev, A. A. Berlin, N. K. Balabaev, and G. C. Rutledge, “Molecular dynamics simulation of thermomechanical properties of montmorillonite crystal. 3. Montmorillonite crystals with PEO oligomer intercalates,” J. Phys. Chem. B 112, 3597–3604 (2008).

    Google Scholar 

  105. B. Drach, I. Tsukrov, T. Gross, S. Dietrich, K. Weidenmann, R. Piat, and T. Boehlke, “Numerical modeling of carbon/carbon composites with nanotextured matrix and 3D pores of irregular shapes,” Intern. J. Solids Struct. 48, 2447–2457 (2011).

    Google Scholar 

  106. A. P. Roberts and E. J. Garboczi, “Elastic properties of model porous ceramics,” J. Amer. Ceram. Soc. 83, 3041–3048 (2000).

    Google Scholar 

  107. Y. J. Cho, V. J. Lee, S. K. Park, and Y. H. Park, “Effect of pore morphology on deformation behaviours in porous Al by FEM,” AEM 15, 166–169 (2013).

    MathSciNet  Google Scholar 

  108. I. C. Noyan and B. C. Jerome, Residual Stress: Measurement by Diffraction and Interpretation (Springer, New York, 1987).

    Google Scholar 

  109. A. S. Waghchaure, Residual Stress Analysis by Diffraction using High-Energy Synchrotron Radiation (Michigan Tech University, Houghton, 2010).

    Google Scholar 

  110. V. Hauk, Structural and Residual Stress Analysis by Nondestructive Methods (Elsevier, Amsterdam, 1997).

    MATH  Google Scholar 

  111. S. Matthies, “Moment pole figures in residual stress analysis,” Textures and Microstructures 25, 229–236 (1996).

    Google Scholar 

  112. C. M. Brakman, “Residual stresses in cubic materials with orthorhombic or monoclinic specimen symmetry: Influence of texture on ψ splitting and non-linear behavior,,” J. Appl. Crystallogr. 16, 325–340 (1986).

    Google Scholar 

  113. C. Schuman, V. Humbert, and C. Esling, “Determination of the residual stresses in a low carbon steel sheet using ODF,” Z. Metallkd. 85, 559–563 (1994).

    Google Scholar 

  114. P. Van Houtte and L. De Buyser, “The influence of crystallographic texture on diffraction measurements of residual stress,” Acta Metall. Mater. 41, 323–336 (1993).

    Google Scholar 

  115. N. C. Popa and D. Balzar, “Elastic strain and stress determination by Rietveld refinement: generalized treatment for textured polycrystals for all Laue classes,” J. Appl. Crystallogr. 34, 187–195 (2001).

    Google Scholar 

  116. H. M. Rietveld, “A profile refinement method for nuclear and magnetic structures,” J. Appl. Crystallogr. 2(2), 65 (1969).

    Google Scholar 

  117. S. Matthies, S. Merkel, H. R. Wenk, R. S. Hemley, and H. K. Mao, “Effect of texture on the determination of elasticity of polycrystalline ɛ-Iron from diffraction measurements,” Earth Planet. Sci. Lett. 194(1), 201–212 (2001).

    ADS  Google Scholar 

  118. B. Sander, “Zur Petrographisch-tektonischen Analyse,” Jahrb. Geol. Bundes Anstalt. A 23, 215–222 (1923).

    Google Scholar 

  119. H. -R. Wenk, H. Kern, W. Schaefer, and G. Will, “Comparison of neutron and X-Ray diffraction in texture analysis of deformed carbonate rocks,” J. Struct. Geol. 6, 687–692 (1984).

    ADS  Google Scholar 

  120. K. Ullemeyer, G. Braun, M. Dahms, J. H. Kruhl, N. Ø. Olesen, and S. Siegesmund, “Texture analysis of a muscovite-bearing quartzite: a comparison of some currently used techniques,” J. Struct. Geol. 22, 1541–1557 (2000).

    ADS  Google Scholar 

  121. K. Ullemeyer, P. Spalthoff, J. Heinitz, N. N. Isakov, A. N. Nikitin, and K. Weber, “The SKAT texture diffractometer at the pulsed reactor IBR-2 at Dubna: Experimental layout and first measurements,” Nucl. Instrum. Meth. Phys. Res. A412 80–88 (1998).

    ADS  Google Scholar 

  122. K. Walther, A. Frischbutter, C. Scheffzuek, M. Korobshenko, F. Levchanovski, A. Kirillov, N. Astachova, and S. Mureshkevich, “Epsilon-MDS-a neutron time-of-flight diffractometer for strain measurements,” Solid State Phenom. 105, 67–70 (2005).

    Google Scholar 

  123. H.-R. Wenk, L. Lutterotti, and S. Vogel, “Texture analysis with the new HIPPO TOF diffractometer,” Nucl. Instrum. Meth. Phys. Res. A515, 575–588 (2003).

    ADS  Google Scholar 

  124. A. Frischbutter, Ch. Janssen, Ch. Scheffzük, K. Walther, K. Ullemeyer, J. H. Behrmann, A. N. Nikitin, T. I. Ivankina, H. Kern, and B. Leiss, “Strain and texture measurements on geological samples using neutron diffraction at IBR-2, Joint Institute for Nuclear Research Dubna (Russia),” Phys. Part. Nucl. 37(Suppl. 7), S91–S128 (2007).

    Google Scholar 

  125. J. C. C. Mercier, “Olivine and pyroxenes,” in Preferred Orientation in Deformed Metals and Rocks: An Introduction to Modern Texture Analysis (Academic Press, Orlando. 407–430 (1985).

    Google Scholar 

  126. W. Skrotzki, A. Wedel, K. Weber, and W. F. Muller, “Microstructure and texture in lherzolites of the Balmuccia massif and their significance regarding the thermomechanical history,” Tectonophysics 179, 227–251 (1990).

    ADS  Google Scholar 

  127. S. Zhang and S. -Y. Karato, “Lattice preferred orientation of olivine aggregates deformed in simple shear,” Nature 375, 774–777 (1995).

    ADS  Google Scholar 

  128. D. Mainprice, “Seismic anisotropy of the deep Earth,” Treatise on Geophysics 2, 437–491 (2007).

    Google Scholar 

  129. A. Nicolas and N. I. Christensen, “Formation of anisotropy in upper mantle peridotites: A review,” in Composition, Structure and Dynamics of the Lithosphere-Asthenosphere System, Geodyn. Ser. 16, 111–123 (1987).

    Google Scholar 

  130. D. Mainprice, G. Barruol, and W. Ben Ismail, “The seismic anisotropy of the Earth’s mantle: From single crystal to polycrystal,” in Earth’s Deep Interior: Mineral Physics and Tomography from the Atomic to the Global Scale, Geophys. Monograph Ser, 117, 237–264 (2000).

    Google Scholar 

  131. L. Peselnick, J. P. Lockwood, and R. Stewart, “Anisotropic elastic velocities of some upper mantle xenoliths underlying the Sierra Nevada batholiths,” J. Geophys. Res. 82, 2005–2010 (1977).

    ADS  Google Scholar 

  132. D. Mainprice and P. G. Silver, “Interpretation of SKS-waves using samples from the subcontinental lithosphere,” Phys. Earth Planet. Inter. 78, 257 (1993).

    ADS  Google Scholar 

  133. S. Ji, X. Zhao, and D. Francis, “Calibration of shearwave splitting in the subcontinental upper mantle beneath active orogenic belts using ultramafic xenoliths from the Canadian Cordillera and Alaska,” Tectonophysics 239, 1–27 (1994).

    ADS  Google Scholar 

  134. B. Soedjatmiko and N. I. Christensen, “Seismic anisotropy under extended crust: evidence from upper mantle xenoliths, Cima Volcanic Field, California,” Tectonophysics 321, 279–296 (2000).

    ADS  Google Scholar 

  135. W. Ben Ismail and D. Mainprice, “An olivine fabric database: An overview of upper mantle fabrics and seismic anisotropy,” Tectonophysics 296, 145–157 (1998).

    ADS  Google Scholar 

  136. O. Engler, J. Jura, and S. Matthies, “Influence of number and arrangement of single orientation measurements on their statistical relevance,” in Proceedings of ICOTOM 12 (NRC Research Press, Montreal, 1999), pp. 68–73

    Google Scholar 

  137. T. Lokajicek, Z. Pros, K. Klima, A. N. Nikitin, and T. I. Ivankina, “Neutron diffraction and ultrasonic sounding: A tool for solid body investigation,” in Nondestructive Characterization of Material VIII (Plenum Press, New York, 1998) 529–533.

    Google Scholar 

  138. T. I. Ivankina, K. Klima, T. Lokajicek, A. N. Nikitin, and Z. Pros, “Study of anisotropy in an olivine xenolith using acoustic waves and neutron diffraction,” Izv., Phys. Solid Earth 35(5), 372–381 (1999).

    Google Scholar 

  139. A. N. Nikitin, T. I. Ivankina, D. E. Burilichev, K. Klima, T. Lokajicek, and Z. Pros, “Anisotropy and texture of olivine-bearing mantle rocks at high pressures,” Izv., Phys. Solid Earth 37(1), 59–72 (2001).

    Google Scholar 

  140. Z. Pros, “Investigation of anisotropy of elastic properties of rocks on spherical samples at high hydrostatic pressures,” in High Pressure and Temperature Studies of Physical Properties of Rocks and Minerals (Naukova Dumka, Kiev, 1977).

    Google Scholar 

  141. D. T. Griggs and J. D. Blacic, “The strength of quartz in the ductile regime,” Trans. Amer. Geophys. Union 45(1), 102–103 (1964).

    Google Scholar 

  142. H. G. Ave Lallemant and N. L. Carter, “Pressure dependence of quartz deformation lamellae orientations,” Amer. J. Sci. 270, 218–235 (1971).

    Google Scholar 

  143. J. Hofmann, “Das Quarzteilgefuge von Metamorphiten und Anatexiten, Dargestellt am Beispiel des Osterzgebirges (DDR),” Freiberger Forschungshefte C 297 107 (1974).

    Google Scholar 

  144. V. N. Kozhevnikov, Conditions for Formation of Structural-Metamorphic Parageneses in Precambrian Complexes (Nauka, Leningrad, 1982) [in Russian].

    Google Scholar 

  145. A. N. Kazakov, Dynamical Analysis of Microstructural Orientations of Minerals (Nauka, Leningrad, 1987) [in Russian].

    Google Scholar 

  146. A. N. Nikitin, E. I. Rusakova, and T. T. Ivankina, “To theory of formation of piezoelectric textures in rocks,” Izv. Akad. Nauk SSSR, Fiz. Zem., No. 6, 49 (1989).

    Google Scholar 

  147. H. -R. Wenk and J. Pannetier, “Texture development in deformed granodiorites from the Santa Rosa mylonite zone, Southern California,” J. Struct. Geol. 12, 177–184 (1990).

    ADS  Google Scholar 

  148. A. N. Nikitin and T. I. Ivankina, “On the possible mechanisms of the formation of piezoelectric active rocks with crystallographic textures,” Textures and Microstructures 25, 33–43 (1995).

    Google Scholar 

  149. A. N. Nikitin, T. I. Ivankina, K. Ullemeyier, and R. N. Vasin, “Similar quartz crystallographic textures in rocks of continental Earth’s crust (by neutron diffraction data): I. Quartz textures in monomineral rocks,” Crystallogr. Reports 53(5), 812–818 (2008).

    ADS  Google Scholar 

  150. A. N. Nikitin, T. I. Ivankina, K. Ullemeyier, and R. N. Vasin, “Similar quartz crystallographic textures in rocks of continental Earth’s crust (by neutron diffraction data): II. Quartz textures in monophase rocks,” Crystallogr. Reports 53(5), 819–827 (2008).

    ADS  Google Scholar 

  151. A. N. Nikitin, T. I. Ivankina, K. Ullemeyier, and R. N. Vasin, “Similar quartz crystallographic textures in rocks of continental earth’s crust (by neutron diffraction data): III. Relation of quartz texture types with means and conditions of texture formation,” Crystallogr. Reports 53(5), 828–836 (2008).

    ADS  Google Scholar 

  152. W. Schäfer, “Neutron diffraction applied to geological texture and stress analysis,” Eur. J. Mineral. 14, 263–289 (2002).

    Google Scholar 

  153. H.-R. Wenk, Preferred Orientation in Deformed Metals and Rocks: An Introduction to Modern Texture Analysis (Academic Press, Orlando, 1985).

    Google Scholar 

  154. H. -R. Wenk, “Neutron scattering in Earth sciences. Reviews in mineralogy and geochemistry,” Mineral. Soc. America 63, 620 (2006).

    Google Scholar 

  155. V. A. Kalinin, M. V. Rodkin, and I. S. Tomashevskaya, Geodynamic Effects of Physicochemical Transformations in a Solid Medium (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  156. T. I. Ivankina, A. N. Nikitin, T. Lokajicek, Z. Pros, K. Klima, and K. Ullemeyer, “Textures and elastic anisotropies of amphibolites from the Kola borehole,” in Proceedings of the ICOTOM 12 (NRC Research Press, Montreal, 1999), Vol. 2, 1587–1592.

    Google Scholar 

  157. A. N. Nikitin, T. I. Ivankina, K. Ullemeyer, T. Lokajicek, Z. Pros, K. Klima, Yu. P. Smirnov, and Yu. I. Kusnetzov, “Texture-controlled elastic anisotropy of amphibolites from the Kola Superdeep Borehole SG-3 at high pressure,” Izv., Phys. Solid Earth 37(1), 37–45 (2001).

    Google Scholar 

  158. K. V. Lobanov, V. I. Kazansky, A. V. Kuznetsov, A. V. Zharikov, A. N. Nikitin, T. I. Ivankina, and N. V. Zamyatina, “Correlation of Archean rocks from the Kola Superdeep Borehole and their analogues from the surface: Evidence from structural-petrological, petrophysical, and neutron diffraction data,” Petrology 10(1), 23–38 (2002).

    Google Scholar 

  159. T. I. Ivankina, A. N. Nikitin, N. V. Zamyatina, V. I. Kazanskii, K. V. Lobanov, and A. V. Zharikov, “Neutron diffraction texture analysis of anisotropy in Archean amphibolites and gneisses from the Kola super-deep borehole,” Izv., Phys. Solid Earth 40(4), 334–346 (2004).

    Google Scholar 

  160. T. I. Ivankina, K. Klima, A. L. Kulakovskii, T. Lokajicek, Yu. A. Morozov, A. N. Nikitin, and Z. Pros, “Study of the structure of geospace of the Kola Superdeep Borehole using methods of ultrasonic, neutronography, and microstructural analysis of rocks,” in Sb. nauch. tr. Geofizicheskie issledovaniya IFZ RAN (Proc. of Geophysical Research of the Institute of Physics of the Earth, Russian Academy of Sciences) (IFZ RAN, Moscow, 2005), No. 1, 88–107 [in Russian].

    Google Scholar 

  161. T. I. Ivankina, H. M. Kern, and A. N. Nikitin, “Directional dependence of P- and S-wave propagation and polarization in foliated rocks from the Kola superdeep well: Evidence from laboratory measurements and calculations based on TOF neutron diffraction,” Tectonophysics 407, 25–42 (2005).

    ADS  Google Scholar 

  162. K. Helming and T. Eschner, “A new approach to texture analysis of multiphase materials using a texture component model,” Cryst. Res. Technol. 25, K203–K208 (1990).

    Google Scholar 

  163. S. Siegesmund, “The significance of rock fabrics for the geological interpretation of geophysical anisotropics,” Geotektonische Forschungen 85, 1–123 (1996).

    Google Scholar 

  164. T. I. Ivankina, H. Kern, and A. N. Nikitin, “Neutron texture measurements and 3D velocity calculations on strongly foliated biotite gneisses from the Outokumpu Deep Drill Hole,” in Outokumpu Deep Drill Project, Second International Workshop. Report Q10.2/2007/29, Ed. by I.T. Kukkonen (Southern Finland Office, Marine Geology and Geophysics, Espoo, Finland, 2007), 47–50.

    Google Scholar 

  165. H. Kern, K. Mengel, K. W. Strauss, T. I. Ivankina, A. N. Nikitin, and I. T. Kukkonen, “Elastic wave velocities, chemistry and modal mineralogy of crustal rocks sampled by the Outokumpu scientific drill hole: Evidence from lab measurements and modeling,” Phys. Earth Planet. Inter. 175, 151–166 (2009).

    ADS  Google Scholar 

  166. H. Kern, T. I. Ivankina, A. N. Nikitin, T. Lokajicek, and Z. Pros, “The Effect of oriented microcracks and crystallographic and shape preferred orientation on bulk elastic anisotropy of a strongly foliated biotite gneiss,” Tectonophysics 457(3–4), 143–149 (2008).

    ADS  Google Scholar 

  167. G. I. Petrashen’, Wave Propagation in Anisotropic Elastic Media (Nauka, Leningrad, 1980) [in Russian].

    Google Scholar 

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  1. Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    T. I. Ivankina & S. Matthies

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Dedicated to Memory of Professor A.N. Nikitin

Original Russian Text © T.I. Ivankina, S. Matthies, 2015, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2015, Vol. 46, No. 3.

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Ivankina, T.I., Matthies, S. On the development of the quantitative texture analysis and its application in solving problems of the Earth sciences. Phys. Part. Nuclei 46, 366–423 (2015). https://doi.org/10.1134/S1063779615030077

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