Texture and anisotropy

INSTITUTE OF PHYSICS PUBLISHING

REPORTS ON PROGRESS IN PHYSICS

Rep. Prog. Phys. 67 (2004) 1367–1428

PII: S0034-4885(04)25222-8

Texture and anisotropy H-R Wenk1 and P Van Houtte2 1

Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA 2 Department of MTM, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium E-mail: [email protected] Received 17 February 2004 Published 5 July 2004 Online at stacks.iop.org/RoPP/67/1367 doi:10.1088/0034-4885/67/8/R02

Abstract A large number of polycrystalline materials, both manmade and natural, display preferred orientation of crystallites. Such alignment has a profound effect on anisotropy of physical properties. Preferred orientation or texture forms during growth or deformation and is modified during recrystallization or phase transformations and theories exist to predict its origin. Different methods are applied to characterize orientation patterns and determine the orientation distribution, most of them relying on diffraction. Conventionally x-ray polefigure goniometers are used. More recently single orientation measurements are performed with electron microscopes, both SEM and TEM. For special applications, particularly texture analysis at non-ambient conditions, neutron diffraction and synchrotron x-rays have distinct advantages. The review emphasizes such new possibilities. A second section surveys important texture types in a variety of materials with emphasis on technologically important systems and in rocks that contribute to anisotropy in the earth. In the former group are metals, structural ceramics and thin films. Seismic anisotropy is present in the crust (mainly due to phyllosilicate alignment), the upper mantle (olivine), the lower mantle (perovskite and magnesiowuestite) and the inner core (ε-iron) and due to alignment by plastic deformation. There is new interest in the texturing of biological materials such as bones and shells. Preferred orientation is not restricted to inorganic substances but is also present in polymers that are not discussed in this review.

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Contents

1. Introduction 2. Measurements of textures 2.1. Overview 2.2. X-ray pole-figure goniometer 2.3. Synchrotron x-rays 2.4. Neutron diffraction 2.5. Transmission electron microscope 2.6. Scanning electron microscope 2.7. Comparison of methods 3. Data analysis 3.1. Orientation distributions and texture representations 3.2. From pole figures to ODF 3.3. Use of diffraction spectra 3.4. Statistical considerations of single orientation measurements 3.5. From textures to elastic anisotropy 4. Polycrystal plasticity simulations 4.1. General comments 4.2. Deformation 4.3. Recrystallization 5. Important texture types in metals 5.1. Fcc metals 5.2. Bcc metals 5.3. Hcp metals 5.4. Phase transformations 6. Ceramic textures 6.1. Bulk ceramics 6.1.1. α-alumina (Al2 O3 ) 6.1.2. Silicon nitride (Si3 N4 ) 6.1.3. Zirconia (ZrO2 ) 6.1.4. Ceramic matrix composites 6.1.5. Bulk high-temperature superconductors 6.2. Thin films and coatings 6.2.1. Silicon and diamond 6.2.2. Nitride, carbide and oxide coatings 6.2.3. Epitaxial films 7. Textures in minerals and rocks 7.1. Calcite (CaCO3 ) 7.2. Quartz (SiO2 ) 7.3. Olivine (Mg2 SiO4 ) 7.4. Sheet silicates

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7.5. Ice (H2 O) 7.6. Halite (NaCl) and periclase (MgO) 7.7. Polymineralic rocks 7.8. Cement minerals 7.9. Earth structure 7.10. Textures as indicators of strain history 7.11. Anisotropy in the deep earth 8. Textures in mineralized biological materials 8.1. Nacre of mollusc shells (aragonite) 8.2. Bones (apatite) 9. Conclusions References

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1. Introduction Preferred orientation of crystallites (or texture) is an intrinsic feature of metals, ceramics, polymers and rocks and has an influence on physical properties such as strength, electrical conductivity, piezoelectricity, magnetic susceptibility, light refraction and wave propagation, particularly in the anisotropy of these properties. The directional characteristics of many polycrystalline materials were first recognized not in metals but in rocks and were described as ‘texture’ (d’Halloy 1833). In the 20th century texture research was largely pursued by metallurgists but recently it has gained importance in ceramics (e.g. high temperature superconductors), polymers, and regained interest in the earth sciences. The reason for the latter is that seismologists have discovered anisotropic wave propagation in large sectors of the earth’s interior and a likely cause is preferred orientation of crystals that developed by deformation during the earth’s long history. This review will highlight some aspects of textures with focus on new approaches and methods, as well as relevant problems. Metallurgists and ceramicists are engaged in texture research to develop materials with favourable properties. In contrast, geologists and geophysicists are using textures to interpret the past. The rationale is thus reversed. In metallurgy specimens are readily available for analysis, and theories can be tested with experiments. Deep-earth materials do not occur on the surface and many are unstable at ambient conditions. Also, many geological conditions are outside the realm of experiments, particularly the slow strain rates and highly heterogeneous nature of rock formations. Yet, in spite of these differences, methods and approaches are remarkably similar, even though the objects of interest vary greatly in dimension. This review is intended to provide a brief introduction for physical scientists, not for texture experts. Some of the important issues are highlighted with examples, and we refer new researchers in the field of texture and anisotropy to important publications. Since the classic books on metallurgy (e.g. Wassermann and Grewen (1962), Dillamore and Roberts (1965), Hatherly and Hutchinson (1979)) and geology (e.g. Sander (1950), Turner and Weiss (1963)), there have been newer books (e.g. Bunge (1982), Wenk (1985), Kocks et al (2000)), numerous journal articles and particularly research papers in the tri-annual proceedings of the International Conferences of Textures of Materials (ICOTOM). These publications need to be consulted for details. Textures in polymers, though important, are only mentioned peripherally (see, e.g. G’Sell et al (1999)). While preparing this review we noticed that almost half of the references are in physics journals and fifteen in Nature and Science, illustrating that texture and anisotropy are subjects of core physics as well as of general interest. We try to give a balanced account of recent progress in texture research; however, in this broad field it was hard to avoid some emphasis on our own specialities, particularly in the selection of examples which were more readily available. We do not suggest that these are in any way more important. 2. Measurements of textures 2.1. Overview Interpretation of textures has to rely on a quantitative description of orientation characteristics. Two types of preferred orientations are distinguished: the lattice preferred orientation (LPO) or ‘texture’ (also ‘preferred crystallographic orientation’) and the shape preferred orientation (or ‘preferred morphological orientation’). Both can be correlated, such as in sheet silicates with a flaky morphology in schists, or fibres in fibre-reinforced ceramics. In many cases they

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are not. In a rolled cubic metal the grain shape depends on the deformation rather than on the crystallography. Many methods have been used to determine preferred orientation. Optical methods have been extensively applied by geologists, using the petrographic microscope equipped with a universal stage to measure the orientation of morphological and optical directions in individual grains (e.g. Phillips (1971)). Metallurgists have used a reflected light microscope to determine the orientation of cleavages and etch pits (e.g. Nauer-Gerhardt and Bunge (1986)). With advances in image analysis, shape preferred orientation can be determined quantitatively and automatically with stereological techniques. Optical methods of LPO measurements of some minerals have also been automated (Heilbronner and Pauli 1993). Today diffraction techniques are most widely used to measure crystallographic preferred orientation (e.g. Bunge (1986), Kocks et al (2000)). X-ray diffraction with a pole-figure goniometer is a routine method. For some applications synchrotron x-rays provide unique opportunities. Neutron diffraction offers some distinct advantages, particularly for large bulk samples. Electron diffraction using the transmission (TEM) or scanning electron microscope (SEM) is gaining interest, because it permits one to correlate microstructures, neighbour relations and texture. There are two distinct ways to measure orientations. One way is to average over a large volume of a polycrystalline aggregate. A pole figure collects signals from many crystals and spatial information is lost (e.g. misorientations with neighbours), but also some orientation relations (such as how x, y, and z-axes of individual crystals correlate). The second method is to measure orientations of individual crystals. In that case orientations and the orientation distribution can be determined unambiguously and, if a map of the microstructure is available, the location of a grain can be determined and relationships with neighbours can be evaluated. But compared to the bulk methods, the statistics of such measurements are limited. 2.2. X-ray pole-figure goniometer X-ray diffraction was first employed by Wever (1924) to investigate preferred orientation in metals, but only with the introduction of the pole-figure goniometer and use of electronic detectors did it become a quantitative method (Schulz 1949). Bragg’s Law for monochromatic radiation is applied. The principle is simple: in order to determine the orientation of a given lattice plane, hkl, of a single crystallite, the detector is first set to the proper Bragg angle, 2θ of the diffraction peak of interest, then the sample is rotated in a goniometer until the lattice plane hkl is in the reflection condition (i.e. the normal to the lattice plane or diffraction vector is the bisectrix between incident and diffracted beam) (see figure 1). In the case of a polycrystalline sample, the intensity recorded at a certain sample orientation is proportional to the volume fraction of crystallites with their lattice planes in reflection geometry. Determination of texture can be done on a sample of large thickness and a plane surface on which x-rays are reflected, or on a thin slab which is penetrated by x-rays. Because of defocusing effects as the flat sample surface is inclined against the beam, variations in the irradiated volume and absorption intensity corrections are necessary, particularly in reflection geometry. In reflection geometry only incomplete pole figures can be measured, usually to a pole distance of 80˚ from the sample surface normal. 2.3. Synchrotron x-rays Conventional x-ray tubes produce a broad beam of relatively low intensity (∼1 mm). A powerful new tool for texture research is synchrotron radiation. In a synchrotron a very

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Figure 1. Geometry of a pole-figure goniometer equipped with Soller slits and monochromator. Bragg’s Law applies to lattice planes. The sample is rotated about an axis perpendicular to the surface.

Figure 2. Synchrotron x-ray diffraction image of a sheet of rolled copper with Debye rings recorded with a CCD camera at ESRF. Intensity variations immediately display the presence of texture.

fine-focused high-intensity beam of x-rays with monochromatic or continuous wavelengths can be produced. The unique advantages of high intensity, small beam size (