Experimental and theoretical bond critical point properties for model electron density distributions for earth materials

Generalized X-ray scattering factor model experimental electron density distributions and bond critical point, bcp, properties generated in recent studies for the earth materials stishovite, forsterite, fayalite and cuprite with high energy single crystal synchrotron X-ray diffraction data and those generated with high resolution diffraction data for coesite and senarmonite were found to be adequate and in relatively good agreement, ~5% on average, with those calculated with quantum chemical methods with relatively robust basis sets. High resolution low energy single crystal diffraction data, recorded for the molecular sieve AlPO₄-15, were also found to yield model electron density distribution values at the bcp points for the AlO and PO bonded interactions that are in relatively good to moderately good agreement with the theoretical values, but the Laplacian values of the distribution at the points for the two bonded interactions were found to be in relatively poor agreement. In several cases, experimental bcp properties, generated with conventional low energy X-ray diffraction data for several rock forming minerals, were found overall to be in poorer agreement with the theoretical properties. The overall agreement between theoretical bcp properties generated with computational quantum methods and experimental properties generated with synchrotron high energy radiation not only provides a basis for using computational strategies for studying and modeling structures and their electron density distributions, but it also provides a basis for improving our understanding of the crystal chemistry and bonded interactions for earth materials. Theoretical bond critical point properties generated with computational quantum methods are believed to rival the accuracy of those determined experimentally. As such the calculations provide a powerful and efficient method for evaluating electron density distributions and the bonded interactions for a wide range of earth materials.Dedicated to Professor Robert F. Stewart of Carnegie Mellon University on his retirement for his brilliant and original work modeling electron density distributions.     

Maximum entropy method: an unconventional approach to explore observables related to the electron density in phengites

The maximum entropy method (MEM) is used here to get an insight into the electron density [ρ(r)] of phengites 2M ₁ and 3T, paying special attention to the M1-formally empty site and charge distribution. Room temperature single crystal X-ray diffraction data have been used as experimental input for MEM. The results obtained by MEM have been compared with those from conventional structure refinement which, in turn, has provided the prior-electron density to start the entropy maximization process. MEM reveals a comparatively non-committal approach, able to produce information related to the M1-site fractional occupancy, and yields results consistent with those from the difference Fourier synthesis, but free of the uncertainties due to the abrupt truncation of the series. The charge distribution is investigated by means of the notion of ‘‘site basin’’, i.e., those site-centered volumes delimited by a surface such as ∇ρ·n = 0. In particular, we observe: (1) the overall partitioning of the basin total charge between cation and anion sites, and the interlayer site charge seems to depend on sample composition, and (2) the apical-oxygen plane total basin charge and hydroxyl basin charge are presumably related to the polytype. The MEM-determined electron density does not allow full exploration of the critical points for very complex structures as micas, insofar as conventional room temperature experimental diffraction data are used.     

Albite crystallographic preferred orientation and grain misorientation distribution in a low-grade mylonite: implications for granular flow

Crystallographic orientation data from pure albite domains in a low-grade sheared metagabbro from the Combin Zone of the western Italian Alps were measured by electron backscatter diffraction. Crystallographic preferred orientations (CPOs) in four high-strain domains are non-random and have a triclinic symmetry. The clusters of [100], [010] and [001] show an angular relationship that corresponds to that of the albite crystal lattice. However, the orientations of axis clusters to the kinematic axes vary from domain to domain. CPOs from a low-strain domain also show clustered axes with triclinic symmetry, but with more intense clustering than those in the high-strain domains. Grain misorientation distributions are presented both for the low-strain domain and one of the high-strain domains. In the high-strain domain, the distribution of misorientation angles between neighbouring grains displays a peak at about 70°. The equivalent distribution in the low-strain domain has a peak at 30°. For both domains, the misorientation axis distributions, between neighbouring and non-neighbouring grains, are random, except for some of axes with 160–180° misorientation that exhibit a slight concentration around [010]. The diversity of CPOs among the domains suggests that these CPOs could not be produced by dislocation creep. They are likely to have been inherited from plagioclase parents, as a result of host control on the nucleation of the new albite grains. These CPOs do not contain any direct information about the deformation kinematics. We interpret that deformation of these domains occurred by granular flow. Crystallographic axis dispersion due to grain boundary sliding (GBS) caused weakening of CPOs, modification of misorientation angle distributions and randomisation of misorientation axis distributions. The fact that a CPO can survive GBS even after a high strain indicates that CPO is not always a sensitive indicator of deformation mechanisms. Misorientation distribution may provide a complementary, and possibly a more sensitive indicator of deformation mechanisms.     

Preferred orientation of plagioclase—neutron diffraction and U-stage data

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.     

西准噶尔地区多源遥感信息的线性构造提取与定量分析

夹持在近东西向额尔齐斯断裂和天山走滑断裂系统之间的西准噶尔地区,经历了自晚古生代晚期以来长期复杂的陆内构造变形历史。线性构造的长度、方向以及空间分布能够反映构造变形的强度和样式,指示应力作用的方式。本文选取新疆西准噶尔地区为研究区,利用ASTER、Landsat等多源遥感数据通过彩色合成、主成分分析、波段比值和Sobel滤波等增强显示断裂构造在遥感影像上的空间分布和光谱信息,并利用Canny边缘检测与人工解译相结合的方法提取研究区内线性构造;运用地质统计学的原理和方法对提取出的线性构造进行定量分析。结果表明,研究区内依长度优选方位确定的主断裂走向为N50°～60°E,代表了区域一级构造即达拉布特断裂展布的方位;依线性构造数量优选方位确定的次级断裂走向为80°～90°(近东西向),代表了区域三级构造的方位;介于以上两者之间的线性构造,即数量与长度均适中的线性构造,代表了区域二级构造的方位。线性构造的区域分布,揭示了在南北向主压应力作用下,西准噶尔地区构造体系的组成与构造变形特征。由此说明,多源遥感信息提取的线性构造定量分析,对于区域断裂构造体系的厘定具有重要意义。     

Interlayer proton transfer in brucite under pressure by polarized IR spectroscopy to 5.3 GPa

In order to investigate the behaviour of proton in brucite under pressure, polarized IR absorption spectra and polarized absorbance distributions of (001) and (110) oriented single crystal of brucite under high pressure were measured by Fourier transform polarized infrared microspectroscopy with diamond anvil cell. A pressure-induced absorption peak at 3645 cm⁻¹ observed under pressures over 2.9 GPa was confirmed to be due to a secondarily formed OH dipole. Polarized absorbance distribution measured under pressure of (110) suggests that the secondary OH dipole is oriented 136.0° to c-axis under 5.3 GPa. Isotropic absorbance distribution of (001) suggests that the secondary OH dipole is disorderly trifurcated. Abrupt onset of the secondary peak and its reverse pleochroism suggest that the process of secondary OH dipole formation is due to proton transfer between layers in brucite. The calculated orientation of the secondary OH dipole consistent with the O-H···O′ angle revealed by neutron diffraction supports the existence of proton transfer along H···O′. The secondary OH dipole implies a new site of proton in brucite under pressure. Received: 6 March 1997 / Revised, accepted: 9 June 1997     

An examination of the elasticity of hot-pressed MgO

The elastic properties of polycrystalline as well as single crystal MgO have been measured extensively. New measurements on four hot-pressed magnesium oxide samples are presented and compared to existing data. Discrepancies are noted between the properties determined for the different polycrystalline MgO samples; the magnitude of these differences is as much as ±6% for the reported bulk modulus. X-ray and electron microscopy techniques were applied to the four hot-pressed specimens and revealed the presence of residual strains, plastic deformation and a preferred orientation of grains with respect to hot pressing directions. Scanning electron micrographs also indicated that a non-homogeneous pore distribution existed. The results suggest that the data obtained from polycrystalline materials may not truly reflect the intrinsic elasticity of the material but rather some combination of the elasticity of the material and the state of aggregation of the polycrystal.     

The petrological significance of misorientations between grains

Misorientation analysis quantifies microstructural features in tectonites, metamorphic and igneous rocks, and allows hypotheses on their formation to be tested. The misorientation between two lattices can be expressed by a rotation axis and rotation angle. For lattices with symmetry, it is conventional to take the minimum angle that enables one lattice to be rotated into the other. For a group of lattice measurements two types of misorientation distribution can be calculated. Selecting random pairs of grains gives the random-pair misorientation distribution. Selecting neighbouring pairs gives the neighbour-pair misorientation distribution. The forms of both distributions are visualised using histograms or cumulative frequency diagrams. They are strongly influenced by any overall crystallographic preferred orientation and by intrinsic crystal symmetry. In many rocks, the random-pair misorientation distribution and neighbour-pair misorientation distribution are statistically significantly different (quantified using the Kolmogorov-Smirnov test). Differences between the random-pair misorientation distribution and neighbour-pair misorientation distribution imply that adjacent grains have physically interacted or are inherited from a precursor microstructure. Interactions include (1) reduction in surface energy by lattice alignment. We show this may have occurred in garnet clusters in schist, and olivine in a cumulate. It is well-known in metals and may be a common geological process. (2) Nucleation, where those nuclei have influenced the orientation of adjacent nuclei. (3) Mechanical rotations of facetted grains in compacting crystal mushes, so that faces become parallel. (4) Growth twinning. Inheritance includes (1) subgrain rotation recrystallisation in tectonites deforming by crystal plastic processes. (2) Mechanical and transformation-related twinning. (3) Domainal microstructures, e.g. where grains have formed from a few large original grains, may give rise to spurious correlations when the orientation data cover more than one domain. With this proviso, misorientation analysis can be used to investigate many important microstructural processes.     

Dauphiné twinning and texture memory in polycrystalline quartz. Part 3: texture memory during phase transformation

Samples of quartz-bearing rocks were heated above the α (trigonal)–β (hexagonal) phase transformation of quartz (625–950°C) to explore changes in preferred orientation patterns. Textures were measured both in situ and ex situ with neutron, synchrotron X-ray and electron backscatter diffraction. The trigonal–hexagonal phase transformation does not change the orientation of c- and a-axes, but positive and negative rhombs become equal in the hexagonal β-phase. In naturally deformed quartzites measured by neutron diffraction a perfect texture memory was observed, i.e. crystals returned to the same trigonal orientation they started from, with no evidence of twin boundaries. Samples measured by electron back-scattered diffraction on surfaces show considerable twinning and memory loss after the phase transformation. In experimentally deformed quartz rocks, where twinning was induced mechanically before heating, the orientation memory is lost. A mechanical model can explain the memory loss but so far it does not account for the persistence of the memory in quartzites. Stresses imposed by neighboring grains remain a likely cause of texture memory in this mineral with a very high elastic anisotropy. If stresses are imposed experimentally the internal stresses are released during the phase transformation and the material returns to its original state prior to deformation. Similarly, on surfaces there are no tractions and thus texture memory is partially lost.     

Quantitative characterization of plastic deformation of zircon and geological implications

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.     

Structural characteristics of the halite fabric type ‘Kristallbrocken’ from the Zechstein Basin with regard to its development

The Kristallbrocken are a characteristic centimetre- to decimetre-sized, laminated halite fabric type occurring in the Stassfurt Formation in the Zechstein Basin. Up to now, the nature of the Kristallbrocken, i.e. if they are relics of fine-grained, polycrystalline halite beds or clasts of ‘single crystal-layers’, as well as the deformation mechanisms of this halite type, were not clear from the literature. Drill core material from the salt deposit Teutschenthal at the southern rim of the Zechstein Basin now allowed investigating less intensely deformed samples for the first time. The deformational behaviour of these Kristallbrocken ranges from brittle to ductile, which is evidenced by fractured Kristallbrocken on the one hand and weakly bent or even folded Kristallbrocken on the other hand. Local X-ray texture measurements demonstrated that the Kristallbrocken are definitely single crystals and that they can be regarded as relics of formerly larger ‘single crystal-layers’ of up to several dm² in size. The folded Kristallbrocken clearly display by their single grain texture characteristics that their crystal lattice is bent, which was most likely enabled by a kind of flexural-shear folding, and did not develop after deformation from a fine-grained aggregate by recrystallisation. Due to their monocrystallinity, their originally large size, and the solid inclusions forming the internal lamination, the Kristallbrocken have clearly stronger rheological properties than the surrounding fine- to coarse-grained polycrystalline rock salt, and thus also deform by fracturing.     

Thermal expansion along the NaAlSi2O6–NaFe3+Si2O6 and NaAlSi2O6–CaFe2+Si2O6 solid solutions

The high temperature volume and axial parameters for six C2/c clinopyroxenes along the NaAlSi₂O₆–NaFe³⁺Si₂O₆ and NaAlSi₂O₆–CaFe²⁺Si₂O₆ joins were determined from room T up to 800°C, using integrated diffraction profiles from in situ high temperature single crystal data collections. The thermal expansion coefficient was determined by fitting the experimental data according to the relation: ln(V/V ₀) = α(T − T ₀). The thermal expansion coefficient increases by about 15% along the jadeite–hedenbergite join, whereas it is almost constant between jadeite and aegirine. The increase is related to the Ca for Na substitution into the M2 site; the same behaviour was observed along the jadeite–diopside solid solution, which presents the same substitution at the M2 site. Strain tensor analysis shows that the major deformation with temperature occurs in all samples along the b axis; on the (010) plane the higher deformation occurs in jadeite and aegirine at a direction almost normal to the tetrahedral–octahedral planes, and in hedenbergite along the projection of the longer M2–O bonds. The orientation of the strain ellipsoid with temperature in hedenbergite is close to that observed with pressure in pyroxenes. Along the jadeite–aegirine join instead the high-temperature and high-pressure strain are differently oriented.     

Estimating the Mean Trace Length of Rock Discontinuities

Summary Rock discontinuities appear as traces on exposures such as natural outcrops or tunnel walls. Discontinuity size which has important effects on rock mass behavior is related to trace length.  This paper presents a technique for estimating mean trace length from the observations made on finite, circular sampling windows. The method takes sampling errors into account and it requires, like existing methods using rectangular sampling windows, that the numbers of discontinuities with both ends censored, with one end observed and one end censored, and with both ends observed be known. Knowledge of the lengths of the observed traces and the distribution of trace lengths is not required. A major advantage of the proposed method over the existing methods is that it does not need sampling data about the orientation of discontinuities, i.e. the proposed method is applicable to traces with arbitrary orientation distributions.  To check the validity of the proposed method, theoretical relations between the mean trace length and the mean diameter of circular discontinuities, respectively for lognormal and negative exponential distributions of the diameter of discontinuities, are derived. The proposed method is then applied to analyze data simulated with the FracMan code, and the predicted results are compared to the corresponding theoretical solutions. The results show that the proposed method is satisfactory. Comparisons of the predicted mean trace length with the mean of observed trace lengths show that it is important to consider sampling biases when estimating mean trace length.     

Function of distribution of clouds’ optical thickness over the West Siberian Plain

Results of measurements of optical thickness of clouds over the West Siberian Plain taken with the help of the MERIS spectrometer onboard the European satellite ENVISAT are analyzed. The observational data for two summer periods of 2008–2009 are considered. It is found that the distribution function of the clouds’ optical thickness averaged over the territory is best presented as the sum of three logonormal distributions. The contribution from each of them to the total envelope, values of optical thickness logarithms for mode centers, and values of variances are given. It is shown that the distribution parameters are almost unchanged with conditional division of the plain’s territory into four zones. The total number of the studied cases exceeds 10⁶.     

Fabric analysis of quartzites with negative magnetic susceptibility – Does AMS provide information of SPO or CPO of quartz?

We ask the question whether petrofabric data from anisotropy of magnetic susceptibility (AMS) analysis of deformed quartzites gives information about shape preferred orientation (SPO) or crystallographic preferred orientation (CPO) of quartz. Since quartz is diamagnetic and has a negative magnetic susceptibility, 11 samples of nearly pure quartzites with a negative magnetic susceptibility were chosen for this study. After performing AMS analysis, electron backscatter diffraction (EBSD) analysis was done in thin sections prepared parallel to the K₁K₃ plane of the AMS ellipsoid. Results show that in all the samples quartz SPO is sub-parallel to the orientation of the magnetic foliation. However, in most samples no clear correspondance is observed between quartz CPO and K₁ (magnetic lineation) direction. This is contrary to the parallelism observed between K₁ direction and orientation of quartz c-axis in the case of undeformed single quartz crystal. Pole figures of quartz indicate that quartz c-axis tends to be parallel to K₁ direction only in the case where intracrystalline deformation of quartz is accommodated by prism <c> slip. It is therefore established that AMS investigation of quartz from deformed rocks gives information of SPO. Thus, it is concluded that petrofabric information of quartzite obtained from AMS is a manifestation of its shape anisotropy and not crystallographic preferred orientation.     

Texture development of recrystallised quartz polycrystals unravelled by orientation and misorientation characteristics

The development of microstructures and textures (i.e. crystallographic preferred orientations) during recrystallisation of naturally deformed quartz polycrystals has been studied via electron diffraction techniques in the scanning electron microscope. In the investigated sample series of quartz-rich rocks originating from different deformation regimes, the microstructural and textural changes in quartz have been significantly influenced by dynamic recrystallisation. Based on microstructural observations paired with orientation and misorientation analyses down to the scale of grains and subgrains, criteria could be established which characterise the dominant recrystallisation process and its influence on texture development. It is shown that the texture development during dynamic recrystallisation is controlled by a differential activation of slip systems in grains of ‘soft’ and ‘hard’ orientations. The analyses provide further evidence that specific grain orientations are preferred during crystal plastic deformation, recrystallisation and grain growth. The influence of twinning after the Dauphiné law was also investigated. Observations of a progressive reduction in the population of Dauphiné-twin boundaries during recrystallisation and a penetrative deformation in both hosts and twins indicate a generation prior to deformation and recrystallisation. A mechanical origin for twinning and possible influence on texture development was therefore discarded.     

Plastic deformation of metamorphic pyrite: new evidence from electron-backscatter diffraction and forescatter orientation-contrast imaging

Application of new scanning electron microscope techniques to the study of deformed metamorphic pyrite reveals evidence for plastic deformation not readily recognised by more traditional methods. Specifically, use of forescatter solid-state detectors in conjunction with tilted polished specimens of pyritic ore produces high quality crystallographic orientation contrast images, which map the distribution of deformation domains within grains. Use of electron-backscatter diffraction allows quantification of the crystallographic misorientations shown by the orientation contrast images. Combination of these techniques shows that the pyrite studied deforms by slip on {100} and more rarely {110} systems. Slip is often associated with distributed rotation of up to 20° about <100> and more rarely <110> axes. Pyrites may have simple histories involving rotation about a single <100> axis, or more complex histories involving rotation about different <100> axes, and more rarely <110>, in different domains of the same pyrite grain, or sequential rotations about quite different systems, typically distributed rotation about <100> followed by discrete rotation about a non-crystallographic axis. Received: 25 June 1997 / Accepted: 14 May 1998     

Bayesian Mixture Modelling in Geochronology via Markov Chain Monte Carlo

In this paper we develop a generalized statistical methodology for characterizing geochronological data, represented by a distribution of single mineral ages. The main characteristics of such data are the heterogeneity and error associated with its collection. The former property means that mixture models are often appropriate for their analysis, in order to identify discrete age components in the overall distribution. We demonstrate that current methods (e.g., Sambridge and Compston, 1994) for analyzing such problems are not always suitable due to the restriction of the class of component densities that may be fitted to the data. This is of importance, when modelling geochronological data, as it is often the case that skewed and heavy tailed distributions will fit the data well. We concentrate on developing (Bayesian) mixture models with flexibility in the class of component densities, using Markov chain Monte Carlo (MCMC) methods to fit the models. Our method allows us to use any component density to fit the data, as well as returning a probability distribution for the number of components. Furthermore, rather than dealing with the observed ages, as in previous approaches, we make the inferences of components from the “true” ages, i.e., the ages had we been able to observe them without measurement error. We demonstrate our approach on two data sets: uranium-lead (U-Pb) zircon ages from the Khorat basin of northern Thailand and the Carrickalinga Head formation of southern Australia.     

Crystal Size Distributions Derived from 3D Datasets: Sample Size Versus Uncertainties

Crystal size distributions (CSD) are the most commonly studiedcharacter in quantitative textural investigations of igneousrocks. The quality of CSD depends fundamentally on the samplesize (i.e. total number of crystals). Here we use 3D X-ray tomographicdatasets of two early erupted Bishop Tuff pumice clasts (comprising849 and 446 quartz crystals) to investigate the effect of samplesize on the quality of the quartz size distributions. BecauseCSD are obtained using a counting procedure, uncertainties relatedto counting statistics can be used as minimum estimates of error.Given that most natural samples are characterized by a decreasingnumber of crystals with increasing crystal size, uncertaintiestend to increase markedly with crystal size, and the numberof small crystals to be counted grows very quickly with increasingsample size. Accordingly, with as few as 100 crystals in total,it is possible to properly estimate the population densitiesfor small size bins (20–80 µm). However, to obtainmeaningful estimates across four bin sizes (20–320 µm),at least 250 crystals, but preferably >400 crystals are needed.To minimize the total number of crystals counted, and keep theuncertainties on the larger size ranges within reasonable values,it becomes necessary to study multiple volumes at variable spatialresolution. KEY WORDS: crystal size distributions; quantitative petrography; texture; X-ray tomography