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1.
Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts directional properties to the polycrystalline material. A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation density function on SO(3) from measured pole intensities on , which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into mathematical texture analysis. Wavelets on the two-dimensional sphere and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets on . A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship is developed.  相似文献   

2.
While crystallography conventionally presumes that a single crystal carries a unique crystallographic orientation, modern experimental techniques reveal that a single crystal may exhibit an orientation distribution. However, this distribution is largely concentrated; it is extremely concentrated when compared with orientation distributions of polycrystalline specimen. A case study of a deformation experiment with a single hematite crystal is presented, where the experimental deformation induced twining, which in turn changed a largely concentrated unimodal “parent” orientation distribution into a multimodal orientation distribution with a major mode resembling the parent mode and three minor modes corresponding to the progressive twining. The free and open source software MTEX for texture analysis was used to compute and visualize orientations density functions from both integral orientation measurements, i.e. neutron diffraction pole intensity data, and individual orientation measurements, i.e. electron back scatter diffraction data. Thus it is exemplified that MTEX is capable of analysing orientation data from largely concentrated orientation distributions.  相似文献   

3.
The concept of an ideal rock texture, in which crystals are distributed randomly in space, is proposed for use in general analysis of rock textures. The spatial correlation function for the ideal rock texture was examined and the function, a specific kind of spatial correlation function, is related to crystal size distribution and to some extent to crystal boundaries. The function is unity at distance zero, and monotonically decreases with increasing distance for the ideal texture. This behavior of the function is observed for any size distribution. In an ideal texture, the function is directly related to crystal size distribution and crystal shape. It is important in stereology because the crystal size distribution in three dimensions may be deduced from analyzing a function that is obtained from analyzing two-dimensional section images. Crystal shape is also related to the function. If crystals are concave in shape, or have inclusions of other phases, the function may show a hump or plateau when plotted against distance. However, the crystal shape effect cannot produce values smaller than zero. If values become negative, the texture is no longer considered ideal. The ideal textures for two model size distributions—step and delta functions—are considered. The rate of decrease of values is more strongly dependent on size distribution than on system dimension.  相似文献   

4.
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5.
The lattice preferred orientation (LPO) of an anorthosite (composed of andesine) sampled from a highly deformed anorthositic mylonite (Grenville Province, Quebec) was measured by TOF neutron diffraction and SEM-EBSD. The quantitative texture analysis of neutron data was accomplished by using the Rietveld texture analysis with the WIMV algorithm, implemented in the program package Materials Analysis Using Diffraction (MAUD). The texture calculations of the EBSD data were performed by using the program BEARTEX. Analyses from neutron and electron diffraction data gave similar results if EBSD data are smoothed to account for grain statistics. The principal pole figures show (010) roughly parallel to the rock foliation, (001) poles exhibiting a low angle (25°) to the pole to foliation, and (100) poles close to the Y-direction (perpendicular to the lineation and foliation pole). The [100] crystallographic direction shows a maximum in the lineation direction, [010] directions concentrate near the foliation pole. The geological deformation conditions and the constructed pole figure patterns indicate that the preferred orientation could be attributed to intracrystalline slip dominantly on (010) with [100] as slip direction. Elastic properties, calculated by averaging, document weak anisotropy that has implications for the seismic structure of the lower crust.  相似文献   

6.
Spherical harmonics in texture analysis   总被引：1，自引：0，他引：1  
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3 3 or hypersphere Ω4 4, respectively, they belong at least to the space of measurable and integrable functions 1(Ωd), d=3, 4, respectively.

Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of 1(Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.  相似文献   


7.
Pole figures of anorthosite mylonite (An 65) from San Juan Bautista, California, were determined with neutron diffraction using a 23 position sensitive detector. This novel technique enables us to deconvolute the complex diffraction spectrum of this triclinic mineral into fifteen separate peaks hkl which are measured simultaneously. All pole figures display strong preferred orientation with complicated triclinic distributions from which it appears that (001) poles are concentrated normal to the schistosity plane of the specimen. The triclinic mineral is well suited to discuss some fundamental issues of texture representation. If crystals are measured individually (e.g., on the U-stage), positive and negative ends of directions can be unequivocally identified and the whole sphere, rather than a hemisphere, is necessary to represent the distribution of positive axes. This is illustrated for a plagioclase-rich amphibolite from Ornö Huvud, Sweden.  相似文献   

8.
The deformation-related microstructure of an Indian Ocean zircon hosted in a gabbro deformed at amphibolite grade has been quantified by electron backscatter diffraction. Orientation mapping reveals progressive variations in intragrain crystallographic orientations that accommodate 20° of misorientation in the zircon crystal. These variations are manifested by discrete low-angle (<4°) boundaries that separate domains recording no resolvable orientation variation. The progressive nature of orientation change is documented by crystallographic pole figures which show systematic small circle distributions, and disorientation axes associated with 0.5–4° disorientation angles, which lie parallel to rational low index crystallographic axes. In the most distorted part of the grain (area A), this is the [100] crystal direction. A quaternion analysis of orientation correlations confirms the [100] rotation axis inferred by stereographic inspection, and reveals subtle orientation variations related to the local boundary structure. Microstructural characteristics and orientation data are consistent with the low-angle boundaries having a tilt boundary geometry with dislocation line [100]. This tilt boundary is most likely to have formed by accumulation of edge dislocations associated with a 〈001〉{100} slip system. Analysis of the energy associated with these dislocations suggest they are energetically more favorable than TEM verified 〈010〉{100} slip. Analysis of minor boundaries in area A indicates deformation by either (001) edge, or [100](100) and [001](100) screw dislocations. In other parts of the grain, cross slip on (111), and (112) planes seems likely. These data provide the first detailed microstructural analysis of naturally deformed zircon and indicate ductile crystal-plastic deformation of zircon by the formation and migration of dislocations into low-angle boundaries. Minimum estimates of dislocation density in the low-angle boundaries are of the order of ∼3.1010 cm−2. This value is sufficiently high to have a marked effect on the geochemical behavior of zircon, via enhanced bulk diffusion and increased dissolution rates. Therefore, crystal plasticity in zircon may have significant implications for the interpretation of radiometric ages, isotopic discordance and trace element mobility during high-grade metamorphism and melting of the crust.  相似文献   

9.
Over sixty syntectonic deformation experiments in uniaxial compression have been done on fine-grained limestones in the stability fields of calcite I, calcite II and aragonite. X-ray techniques and spherical harmonic analysis of the data were used to determine preferred orientation quantitatively, and inverse pole-figures were derived for these axially symmetric specimens. They display in most cases strong preferred orientation which varies as a function of the experimental conditions, mainly temperature and pressure. At temperatures below 350° C recrystallization is lacking and flattened grains indicate that translation, twin gliding and kinking have been the dominant deformation mechanisms. The inverse pole-figure shows a maximum at c with a shoulder towards or a second maximum at e. This is in agreement with preferred orientation observed in experimentally deformed Yule marble and can be explained as the product of dominant twin gliding on e and translation gliding on r (Turner et al., 1956). At high temperatures (900–1000° C) strong grain growth (from 4 to 50 microns) indicates that the fabric recrystallized. Grains are equidimensional and clear with a marble-like texture. The inverse pole-figure shows a single maximum at r, and c-axes are oriented in a small circle around the axis of compression, 1. Such a pattern of preferred orientation would be expected on thermodynamic grounds assuming that recrystallized grains will be oriented in such a way that the strain energy is a maximum (e.g. MacDonald, 1960). Decrease in confining pressure caused a decrease of the maximum at c and the formation of a secondary maximum at highangle positive rhombs in the inverse pole-figure. This can be interpreted as r translation dominating over e twinning. In all deformation experiments an equilibrium in preferred orientation was reached after 20 percent shortening. The strength of preferred orientation decreased with increasing temperature. Aragonite was produced within its hydrostatic stability field at temperatures above 500° C. Close to the phase boundary, coarse-grained textures showed preferred orientation with poles to (010) parallel to 1. At higher pressures the fabric is fine-grained and [001] is aligned parallel to 1. Evidence is given that the phase change from calcite to aragonite in these deformation experiments is a diffusive and not a martensitic transformation.Publication No. 1043, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California.  相似文献   

10.
This contribution describes the mathematical and numerical possibility to analyse heterogeneous data, e.g. experimental intensity data measured for many crystallographic but few sample directions, adaptively refined high resolution intensity data, or a mixture of diffraction intensity data and individual orientation data from scanning electron microscopy.These possibilities are put forward within the dual approach to texture analysis provided by the differential equation governing pole figures. The general solution of this differential equation is represented both in terms of spherical harmonics or characteristics. The resulting systems of equations are capable of considering such heterogeneous data as mentioned above.The eventual aim of this contribution is to show that (i) the mostly tacit ‘paradigm’ of texture analysis that additional pole figures can be calculated from experimental pole figures only by using a detour via the ODF is not correct, and (ii) any function satisfying the differential equation governing pole figures is the actual pole figure projection, or X-ray transform, of a common function defined in a higher dimensional space.Summarily, it is shown that the two dual approaches to texture analysis provided by the projection formula or the differential equation are equivalent, but put emphasis on different issues of the same problem.  相似文献   

11.
Microstructure-based finite element simulations were used to study the influence of grain shape fabric and crystal texture on thermoelastic responses related to marble degradation phenomena. Calcite was used as an illustrative example for studying extremes of shape preferred orientation (SPO) in shape fabric and lattice preferred orientation (LPO) in crystal texture. Three SPOs were analyzed: equiaxed grains, elongated grains, and a mixture of equiaxed and elongated grains. Three LPOs were considered: a random orientation distribution function and two degrees of strong directional crystal texture. Finally, the correlation between the direction of the LPO with respect to that of the SPO was examined. Results show that certain combinations of SPO, LPO, and their directional relationship have significant influence on the thermomechanical behavior of marble. For instance, while there is no major dependence of the elastic strain energy density and the maximum principal stress on SPO for randomly textured microstructures, there is a strong synergy between LPO and its directional relationship with respect to the SPO direction. Microcracking precursors, elastic strain energy density, and maximum principal stress, decrease when the crystalline c-axes have fiber texture perpendicular to the SPO direction, but increase significantly when the c-axes have fiber texture parallel to the SPO direction. Moreover, the microstructural variability increases dramatically for these latter configurations. In general, the influence of LPO was as expected, namely, the strain energy density and the maximum principal stress decreased with more crystal texture, apart from for the exception noted above. Spatial variations of these precursors indicated regions in the microstructure with a propensity for microcracking. Unexpectedly, important variables were the microstructural standard deviations of the spatial distributions of the microcracking indicators. These microstructural standard deviations were as large as or larger than the variables themselves. The elastic misfit-strain contributions to the coefficients of thermal expansion were also calculated, but their dependence was as expected.  相似文献   

12.
A generalized X-ray scattering factor model experimental electron density distribution has been generated for the orthosilicate forsterite, using an essentially extinction and absorption free set of single crystal diffraction data recorded with intense, high energy synchrotron X-ray radiation (E=100.6 keV). A refinement of the model converged with an R(F)=0.0061. An evaluation of the bond critical point, bcp, properties of the distribution at the (3, –1) stationary points for the SiO and MgO bonded interactions, yielded values that agree typically within ~5%, on average, with theoretical values generated with quantum chemical computational strategies, using relatively robust basis sets. On the basis of this result, the modeling of the experimental distribution is considered to be adequate. As the bcp properties increase in magnitude, the MgO and SiO bonds decrease in length as calculated for a number of rock forming silicates. As asserted by Coppens (X-ray charge densities and chemical bonding. Oxford University Press, Oxford, 1997), large negative 2(rc) values, characteristic of shared interactions involving first row atoms, may not be characteristic of closed shell covalent bonded interactions involving second row Si, P and S atoms bonded to O. This study adds new evidence to the overall relatively good agreement between theoretical bcp properties generated with computational quantum strategies, on the one hand, and experimental properties generated with single crystal high energy synchrotron diffraction data on the other. The similarity of results not only provides a basis for using computational strategies for studying and modeling structures, defects and the reactivity of representative structures, but it also provides a basis for improving our understanding of the crystal chemistry of earth materials and the character of the SiO bonded interaction.  相似文献   

13.
Samples of monomineralic quartz veins from the Simplon Fault Zone in southwest Switzerland and north Italy generally have asymmetric, single girdle c-axis patterns similar to textures measured from many other regions. Several samples have characteristically different textures, however, with a strong single c-axis maximum near the intermediate specimen axis Y (the direction within the foliation perpendicular to the lineation X) and a tendency for the other crystal directions to be weakly constrained in their orientation about this dominant c-axis maximum. This results in ‘streaked’ pole figure patterns, with an axis of rotation parallel to the c-axis maximum. These atypical samples also have a distinctive optical microstructure, with advanced recrystallization and grain growth resulting in a strong shape fabric (SB) oblique to the dominant regional foliation (SA), whereas typical samples have a strong SA fabric outlined by very elongate, only partially recrystallized, ribbon grains. The recrystallized grains of the atypical samples are themselves deformed and show strong undulose extinction and a core-mantle recrystallization structure. The streaked texture is likely to be a direct consequence of lattice bending and kinking during heterogeneous slip on the favoured first-order prism (10 0) (a) system, the heterogeneity itself being due to problems in maintaining coherence across grain boundaries when insufficient independent easy-slip systems are available for homogeneous strain by dislocation glide. Such bending would be particularly prevalent in very elongate, thin ribbon grains, resulting in high internal strain energy and promoting recrystallization. Thus both the texture and the microstructure could be significantly modified by later strain increments affecting quartz grains with an already developed, nearly single-crystal texture.  相似文献   

14.
Many of the observed features of zoning in magmatic phenocrysts may be due to the orientation of the section rather than inherent properties of the crystals. An ideal section for the studying of zoning in magmatic crystals has two characteristics: it goes through the center of the crystal, and is perpendicular to one or more crystal faces. Using a model zoned olivine crystal, it is possible to construct accurate zoning profiles for different types of section (centered, symmetrical and skewed). The probability of obtaining a random section which passes within x% of the center of a crystal is shown to be P=0.0x, while the probability that a random section will be within A degrees of perpendicular to a given plane is P=sin(A). A systematic approach to the study of zoned crystals is outlined. In particular, it is suggested that composition be plotted against distance cubed, in order to correct for the volume versus size problem. A method of determining if a given section goes through (or near) the center of a zoned crystal is also presented. The reasoning in this work applies to other types of magmatic crystals such as pyroxenes and plagioclase.  相似文献   

15.
Summary. This study relates textural properties to physical and mechanical properties of coarse grained sedimentary rocks of Permocarboniferous age. As an equivalent to rock texture the principle of geomechanical order is applied. The geomechanical order describes a rock as a function of its structural and compositional order which are derived from petrological analyses. Our results indicate that rock properties like density and porosity are stronger dependent on the structural order, while strength properties additionally depend on the compositional order. The ultrasonic wave velocity responds to both structural and compositional properties. These evidences imply that the geomechanical order is not an independent parameter but a variable function of structural or compositional features, which needs specification for correlation purposes to distinct physical and mechanical rock properties.  相似文献   

16.
The microstructure of a quartzite experimentally deformed and partially recrystallised at 900 °C, 1.2 GPa confining pressure and strain rate 10−6/s was investigated using orientation contrast and electron backscatter diffraction (EBSD). Boundaries between misoriented domains (grains or subgrains) were determined by image analysis of orientation contrast images. In each domain, EBSD measurements gave the complete quartz lattice orientation and enabled calculation of misorientation angles across every domain boundary. Results are analysed in terms of the boundary density, which for any range of misorientations is the boundary length for that range divided by image area. This allows a more direct comparison of misorientation statistics between different parts of a sample than does a treatment in terms of boundary number.The strain in the quartzite sample is heterogeneous. A 100×150 μm low-strain partially recrystallised subarea C was compared with a high-strain completely recrystallised subarea E. The density of high-angle (>10°) boundaries in E is roughly double that in C, reflecting the greater degree of recrystallisation. Low-angle boundaries in C and E are produced by subgrain rotation. In the low-angle range 0–10° boundary densities in both C and E show an exponential decrease with increasing misorientation. The densities scale with exp(−θ/λ) where λ is approximately 2° in C and 1° in E; in other words, E has a comparative dearth of boundaries in the 8–10° range. We explain this dearth in terms of mobile high-angle boundaries sweeping through and consuming low-angle boundaries as the latter increase misorientation through time. In E, the density of high-angle boundaries is larger than in C, so this sweeping would have been more efficient and could explain the relative paucity of 8–10° boundaries.The boundary density can be generalised to a directional property that gives the degree of anisotropy of the boundary network and its preferred orientation. Despite the imposed strain, the analysed samples show that boundaries are not, on average, strongly aligned. This is a function of the strong sinuosity of high-angle boundaries, caused by grain boundary migration. Low-angle boundaries might be expected, on average, to be aligned in relation to imposed strain but this is not found.Boundary densities and their generalisation in terms of directional properties provide objective measures of microstructure. In this study the patterns they show are interpreted in terms of combined subgrain rotation and migration recrystallisation, but it may be that other microstructural processes give distinctive patterns when analysed in this fashion.  相似文献   

17.
组构是指由岩石塑性变形导致多晶体的结晶学优势取向现象。组构的存在会增加岩石的各向异性,进而可能影响到岩石的后续变形。岩石组构包含了变形类型、运动学、变形环境、流变学特征等信息,因而成为显微构造学的重要内容。组构数值模拟是近年来得到重视的一种组构研究方法,它以晶体塑性理论为基础,利用计算机技术定量地模拟多晶岩石中组构的形成和演化。在晶体塑性理论中,晶体的塑性变形是由滑移系的剪切滑动导致的,由单晶塑性本构关系表征。多晶均匀化模型包括Sachs模型、Taylor模型、自洽模型和有限元模型,它们从不同角度描述了由单晶变形组成的多晶体变形。极图、反极图和取向分布函数被用来显示多晶体中各晶粒的空间取向。目前组构数值模拟在地学中的应用主要体现在各种单相和多相岩石的组构形成、重结晶作用下的组构形成、组构对地幔和地核地震波波速各向异性的影响等方面。  相似文献   

18.
The texture of digital rock images, as recorded, for instance, with borehole imaging devices, is shown to reflect different bedding types. Textural segmentation of borehole images, therefore, subdivides the recorded sequence into bedding units. We show that a textural segmentation algorithm based on the concept of texture energy achieves good results when compared with synthetic as well as real data in which petroleum geologists have performed zonations on cores. Texture energy involves filtering of the original image with a set of texture sensitive masks. The filtering is done as a finite convolution over the size of the masks. On the resulting images the variance is computed over a relatively large sliding window, which, in its practical implementation, covers the full width of the image. The resulting nine one-dimensional curves are then clustered hierarchically into a user-determined number of image texture or lithological bedding classes. Principal component analysis previous to clustering can be used to reduce redundancy in the data. A recurring and relatively ill-defined problem in this field are macro-textures, i.e., the cyclic interbedding of two or more bedding types. We show that sliding Fourier transforms and variable mask scale can successfully address the zonation of macro-textures. In general, the method gives best results with mask sizes equivalent to 2–4 centimeters, reflecting the length scale at which the investigated geological bedding seems to have its highest variation.  相似文献   

19.
The hydroxy groups of the crystal lattice of dioctahedral 2:1 phyllosilicates were investigated by means of quantum-mechanical calculation. The standard Kohn-Sham self-consistent density functional theory (DFT) method was applied using the generalized gradient approximation (GGA) with numerical atomic orbitals and double-zeta polarized functions as basis set. Isomorphous cation substitution of different cations in the octahedral and tetrahedral sheet was included along with several interlayer cations reproducing experimental crystal lattice parameters. The effect of these substitutions and the interlayer charge on the hydroxyl group properties was also studied. These structures represent different cation pairs among Al3+, Fe3+ and Mg2+ in the octahedral sheet of clays joined to OH groups. The geometrical disposition of the OH bond in the crystal lattice and the hydrogen bonds and other electrostatic interactions of this group were analyzed. The frequencies of different vibrational modes of the OH group [(OH), (OH) and (OH)] were calculated and compared with experimental data, finding a good agreement. These frequencies depend significantly on the nature of cations which are joined with, and the electrostatic interactions with, the interlayer cations. Besides, hydrogen-bonding interactions with tetrahedral oxygens are important for the vibrational properties of the OH groups; however, also the electrostatic interactions of these OH groups with the rest of tetrahedral oxygens within the tetrahedral cavity should be taken into account. The cation substitution effect on the vibration modes of the OH groups was analyzed reproducing the experimental behaviour.Dr. V. Botella passed away last February  相似文献   

20.
通过宝石学常规测试、显微硬度计、偏光显微镜观察、扫描电镜测试等方法,对韩国软玉的宝石学参数、结构特征进行了研究。研究表明,韩国产软玉相对密度为2.88～2.95,摩氏硬度为5.45～6.17。偏光显微镜下观察,韩国软玉的主要结构为显微-隐晶质变晶结构,常见交代假像结构、交代残蚀结构、碎裂结构,表明其重结晶作用不强烈。扫描电镜分析表明,韩国软玉的矿物颗粒大小不均,以纤维状为主,同时粗纤维状、柱状斑晶含量较高,纤维状透闪石定向性排列较明显。  相似文献   

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