Anelasticity and microcreep in polycrystalline MgO at high temperature: an exploratory study

 The frequency dependence of the shear modulus and dissipation in polycrystalline MgO has been determined at high temperature using both microcreep (ɛ = 10⁻⁴) and seismic frequency forced-oscillation (ɛ = 10⁻⁵) measurements. The frequency-dependent and time-dependent data have been described in terms of the elastic, anelastic and viscous components of deformation using the Andrade model. The forced-oscillation measurements show that for temperatures above 700 °C the shear modulus begins to decrease dramatically and the modulus becomes frequency-dependent with increasing temperature. This is accompanied by an increase in dissipation, which also becomes frequency-dependent. The microcreep measurements resolve this frequency-dependent behaviour into an anelastic regime from 700–1050 °C, and a viscoelastic regime from 1100–1300 °C. At 1300 °C, the seismic frequency shear wave speed is ∼60% of the extrapolated low-temperature frequency-independent value, and the dissipation has risen to Q ⁻¹ = 10⁻¹ from 10⁻³ at temperatures below 600 °C. The mechanism by which this frequency-dependent rheology occurs appears to be diffusional creep, which produces viscous slip on the grain boundaries. It is proposed that the anelastic behaviour is due to viscous slip occurring on segments of grain boundaries, with the viscous deformation being accommodated by elastic distortion of adjacent unslipped regions of the grain boundary. At higher temperatures, slippage occurs across the entire grain boundary and viscoelastic behaviour begins to occur. Received: 11 April 2002 / Accepted: 9 January 2003 Acknowledgements Samples were precision-ground by Andrew Wilson, and polished sections prepared by Harri Kokkonen, who also did the SEM work. Uli Faul calculated the volume fraction of grain sizes. The density measurements were done by Lara Weston.     

Co and postseismic characteristics of Indian sub-continent in response to the 2004 Sumatra earthquake

The M_w 9.3 Sumatra earthquake of December 26, 2004 caused extensive coseismic displacements globally, measurements of which were made essentially using modern geodetic techniques. This earthquake induced considerable perturbation in stress distribution as far as ∼8000 km away from the epicenteral region, which is tending to relax to its normal rates as seen from postseismic transient deformation. The monitoring of crustal displacements from strategically located sites using GPS provides coseismic as well as postseismic deformation that facilitates the understanding of the fault geometry, elastic thickness, postseismic relaxation mechanisms, rheology and earthquake recurrence time interval.We investigated coseismic and postseismic GPS derived displacements in Indian region together with the GPS data collected from Andaman and Sumatra region. It is found that while EW displacements are significantly large in peninsular India, those in the region to the north of Central India Tectonic Zone (CITZ) are relatively small. We could delineate the postseismic transients from position time series and interpreted them in terms of viscoelastic relaxation. It is inferred that the postseismic deformation is characterized by a power-law viscoelastic flow in the mantle. In Indian peninsula region, the timescale parameter of the exponential decay (τ = 250 days) would require an extremely low viscosity for the upper mantle. Relying on the prevailing coseismic and postseismic displacement fields, the present study also reflects upon the contemporary litho-tectonics of the Indian sub-continent.     

基于分裂节点法的地震同震和震后形变数值模拟及其在汶川大地震中的应用

大地震导致的同震及震后效应,对于分析不同地震之间的相互影响及区域地震危险性等有着重要的作用.文中开发了模拟地震同震及震后效应的三维黏弹性有限元程序,通过计算走滑断层震例(概念性模型)引起的同震及震后效应,并与解析/半解析解进行对比,验证了程序的可靠性.同时基于概念性模型,分析了不同介质参数对同震及震后的地表变形的影响....     

Effect of the initial density and angular-velocity profiles of pre-stellar cores on the properties of young stellar objects

The physical properties of young stellar objects are studied as functions of the initial spatial distributions of the gas surface density Σ and angular velocity Ω in pre-stellar cores using numerical hydrodynamic simulations. Two limiting cases are considered: spatially homogeneous cores with Σ = const and Ω = const and centrally concentrated cores with radius-dependent densities Σ ∝ r ⁻¹ and Ω ∝ r ⁻¹. The degree of gravitational instability and protostellar disk fragmentation is mostly determined by the initial core mass and the ratio of the rotational to the gravitational energy, and depends only weakly on the initial spatial configuration of pre-stellar cores, except for the earliest stages of evolution, when models with spatially homogeneous cores can be more gravitationally unstable. The accretion of disk matter onto a protostar also depends weakly on the initial distributions of Σ and Ω, with matter from the collapsing core falling onto the disk at a rate that is slightly higher in models with spatially homogeneous cores. An appreciable dependence of the disk mass, disk radius, and the disk-to-protostar mass ratio on the initial density and angular velocity profiles of the parent core is found only for class 0 young objects; this relationship is not systematic in the later I and II stages of stellar evolution. The mass of the central protostar depends weakly on the initial core configuration in all three evolutionary stages.     

Viscoelastic behaviour of mica-based glass-ceramic aggregate

The present study deals with the small strain torsion deformation of MACOR glass-ceramic samples at high temperatures (450–850 °C) and over a range of low frequencies (20 Hz–5 mHz). The samples of MACOR ceramic consist of 55 vol% randomly oriented, sheet-like fluorophlogopite mica crystals (∼100–20 μm in planar size, 1–2 μm in thickness) and 45 vol% of isotropic alumino-borosilicate glass matrix. Measurements of the complex shear modulus show that the sample does not possess the relaxed shear viscosity even at temperatures above the glass transition temperature of the glass matrix. The maximum of the imaginary component G ^′′() of the shear modulus is ∼0.15 of the unrelaxed value G _∞, the relaxation strength Δ≈0.9. The activation energy of the peak of G ^′′() is ∼245 kJ mol⁻¹. Using this value of E _a , the data obtained at various frequencies and temperatures have been reduced to a master curve using the dimensionless variable ωτ, where ∼₀ exp(−E _a /RT). The internal friction Q⁻¹(ωτ) is ∝1/()^0.35−0.4 in the low-temperature high-frequency range (1); passes through a maximum at ∼1 and trends asymptotically to a value Q⁻¹∼0.25–0.30 at ≪1. The behaviour of Q ⁻¹(ωτ) differs from that of a Caputo body by the presence of the resolved peak which may be attributed to the slow mechanical relaxation of mica crystals due to rotation as well as flexing and bending modes of crystal deformation. Received: 26 June 1998 / Revised, accepted: 13 January 1999     

The limitations of three-dimensional kinematic vorticity analysis

The kinematic vorticity number (W_k) can be calculated for three-dimensional as well as two-dimensional geologic deformations. For steady-state deformations, W_k can be correlated to and analyzed in terms of finite strains. The analysis shows that assumptions commonly made for two-dimensional deformations are not applicable to three-dimensional deformations. A single W_k describes an infinite number of three-dimensional deformations. Further, even knowledge of flow apophyses orientation, instantaneous stretching axes orientation, and/or W_k are not sufficient to describe deformation. Three-dimensional deformations also require knowledge of the deformation ‘type’ or boundary conditions of deformation (e.g. transpression). Hence, in addition to being difficult to estimate, the value of knowing W_k for three-dimensional deformations is greatly reduced compared with plane strain. The most useful methods of determining W_k from naturally deformed rocks are presented.     

The study of the kinetics and the mechanism of dehydroxylation in muscovite by ESR on Fe3+

 Dehydroxylation of muscovite in the form of small lamellae at 923 <T <1173 K was studied by Electron Spin Resonance (ESR) on Fe³⁺. The kinetics of the process has been established to be described by the model of continuous nucleation on the large surface planes of the small plates. Determined by experimental data the rate constant of the process k is shown to be that of dehydroxylation itself. The activation energy obtained by data at T<1100 K is 97.5 KJ·mol⁻¹. The nonlinear dependence of ln(k) on 1/T is explained by the theory of transitions induced by the fluctuative preparation of a potential barrier as a result of thermal oscillations of ions in the lattice. At high temperatures the potential curve of the hydroxyl's proton is transformed so that it can overcome the barrier from one potential well to the other (from one hydroxyl site to the adjacent one). Such transformations of the curve can be caused by the oscillations of large structural clusters (∼1·10⁻²² kg) with the frequency ∼4.5·10¹² s⁻¹. Received: 3 August 1995 / Accepted: 13 April 1997     

On the Ratios between Elastic Modulus and Uniaxial Compressive Strength of Heterogeneous Carbonate Rocks

The ratios M _R = E/σ _c for 11 heterogeneous carbonate (dolomites, limestones and chalks) rock formations collected from different regions of Israel were examined. Sixty-eight uniaxial compressive tests were conducted on weak-to-strong (5 MPa < σ _c < 100 MPa) and very strong (σ _c > 100 MPa) rock samples exhibiting wide ranges of elastic modulus (E = 6100–82300 MPa), uniaxial compressive strength (σ _c = 14–273.9 MPa), Poisson's ratio (ν = 0.13–0.49), and dry bulk density (ρ = 1.7–2.7 g/cm³). The observed range of M _R = 60.9–1011.4 and mean value of M _R = 380.5 are compared with the results obtained by Deere (Rock mechanics in engineering practice, Wiley, London, pp 1–20, 1968) for limestones and dolomites, and the statistical analysis of M _R distribution is performed. Mutual relations between E, σ _c, ρ, M _R for all studied rocks, and separately for concrete rock formations are revealed. Linear multiple correlations between E on the one hand and σ _c and ρ on the other for Nekorot and Bina limestone and Aminadav dolomite are obtained. It is established that the elastic modulus and M _R in very strong carbonate samples are more correlated with ρ−σ _c combination and ε _a max, respectively, than in weak to strong samples. The relation between M _R and maximum axial strain (ε _a max) for all studied rock samples (weak-to-strong and very strong) is discussed.     

Fe(III) Reduction in the Presence of Catechol in Seawater

Fe(II)-Fe(III) redox behavior has been studied in the presence of catechol under different pH, ionic media, and organic compound concentrations. Catechol undergoes oxidation in oxic conditions producing semiquinone and quinone and reduces Fe(III) in natural solutions including seawater (SW). It is a pH-dependent process. Under darkness, the amount of Fe(II) generated is smaller and is related to less oxidation of catechol. The Fe(II) regeneration is higher at lower pH values both in SW with log k = 1.86 (M⁻¹ s⁻¹) at pH 7.3 and 0.26 (M⁻¹ s⁻¹) at pH 8.0, and in NaCl solutions with log k of 1.54 (M⁻¹ s⁻¹) at pH 7.3 and 0.57 (M⁻¹ s⁻¹) at pH 8.0. At higher pH values, rate constants are higher in NaCl solutions than in SW. This is due to the complexation of Mg(II) present in the media with the semiquinone that inhibits the formation of a second Fe(II) through the reaction of this intermediate with other center Fe(Cat)⁺.     

Deformability characteristics of a rock mass under true-triaxial stress compression

In this paper an experimental study was planned on rock mass model with three joint sets under triaxial and true-triaxial stress states to assess the influence of joint geometry and stress ratios on deformational behaviour of rock mass. The physical models were composed of three continuous orthogonal joint sets in which joint set-I was inclined at angle θ=0°, 20°, 40°, 60°, 80° and 90° with x-axis, joint set-II was produced at staggering s=0.5 and joint set-III was kept always vertical. Thus, rock mass models with medium interlocked smooth joints (ϕ _j =36.8°) were simulated under true triaxial compression (σ₁>σ₂>σ₃). Modulus of rock mass shows anisotropy with joint inclination θ which diminishes with increase in σ₂/σ₃ ratio. The rock mass at θ=60° shows the highest modulus enhancement (599.9%) whereas it is minimum (32.3%) at θ=90°. Further two empirical expressions for estimation of deformation modulus were suggested based on experimental results, which were developed by incorporating two basic concepts, e.g. Janbu’s coefficients and joint factor, J _f.     

Memory Effects in Rock Salt Under Triaxial Stress State and Their Use for Stress Measurement in a Rock Mass

Summary Regularities of memory effects in rock salt specimens under triaxial stress state were investigated. Each specimen was subjected to two loading cycles. The first cycle was axisymmetric triaxial compression (σ₁ >σ₂=σ₃). The second cycle was uniaxial compression in the direction of σ₁ of the first cycle. Distinct acoustic emission (AE) and deformation memory effects were observed in the second cycle at the stress value equal to a linear combination of the first cycle principal stresses given by σ₁− (k + 1) σ₃, where k is about 0.5–0.6 for rock salt. Anomalies in deformation curves were found to be more reliable than the AE methods in distinguishing memory symptoms. The necessary pre-requisite for memory formation in the first cycle was that σ₁ exceeded the elastic limit, corresponding to the given confining stress σ₃. Inflections in uniaxial stress versus axial strain and lateral strain curves, in the second cycle, were observed at equal stress values if in the first cycle σ₁ exceeded the elastic limit and memory-forming damage was induced. If there was no memory-forming damage, those inflections were seen at different stress values. This characteristic was used to distinguish between true memory effects and natural characteristic points in deformation curves derived from rock salt testing. A new memory symptom was established, namely a turn point in curve “uniaxial stress versus differential coefficient of lateral strains”. The results form a basis for application of the memory effects for stress measurement in rock salt masses.     

Elasticity of the pyrope (Mg3Al2Si3O12)-majorite (MgSiO3) garnets solid solution

Dense isotropic polycrystalline specimens of majorite-rich garnets (Py₁₀₀, Py₆₂Mj₃₈, Py₅₀Mj₅₀, Py₂₁Mj₇₉ and Mj₁₀₀) along the pyrope (Mg₃Al₂Si₃O₁₂ = Py₁₀₀)-majorite (MgSiO₃ = Mj₁₀₀) join were fabricated in a 2000-ton uniaxial split-sphere anvil apparatus (USSA-2000) at pressures from 10 to 18.5 GPa and temperatures from 1200 to 1850 °C, within their stability fields in runs of 2–4-h duration, using hot-pressing techniques developed by Gwanmesia et al. (1993). These specimens are single-phased, fine-grained (≤5 mm), free of microcracks, and have bulk densities greater than 99% of the corresponding single-crystal X-ray density. Elastic compressional (P) and shear (S) wave velocities were determined at room pressure and temperature for these polycrystalline garnet specimens by phase comparison ultrasonic interferometry. For Mj₁₀₀, the P and S wave velocities are within 1% of the Hashin-Shtrikman averages calculated from the single crystal elastic moduli measured by Brillouin spectroscopy. Both the elastic bulk modulus (K) and the shear modulus (G) decrease continuously with increasing majorite content from pyrope garnet (Py₁₀₀) to pure majorite garnet (Mj₁₀₀). The compositional dependence of K and G are given by K = 172.3 (40) − 0.085X, and G = 91.6 (10) − 0.038X, where X = mol% majorite), respectively, indicating that substitution of Si for Mg and Al decreases both K and G by about 5% along the solid solution series. Received: 25 March 1999 / Accepted: 12 July 1999     

Dissipative collapse of a magnetic flux rope with a force-free internal field

We have obtained new exact solutions describing the self-similar, uniform compression of twisted magnetic flux tubes (a magnetic flux rope) with a linear, force-free internal field with α = const in a resistive medium during the course of their dissipative evolution. Formally, the radius of the rope a decreases to zero over a finite time. This time turns out to be relatively short (several hours) for a rope with a radius of several hundred kilometers, if the helicity of the magnetic field in the rope is high: αa ≫ 1.     

Analysis of the behavior of large underground oil storage caverns in salt rock

The storage of petroleum products above ground surface has many constraints and limitations. A viable alternative is to excavate large underground spaces in rock to provide a safer way for oil storage. Soft rock formations such as salt domes provide suitable conditions from environmental and operational aspects. The potential for high volume storage and low permeability are among advantages of oil storage in caverns excavated in salt rocks. The complicated shape of oil storage caverns, complex behavior of salt rock, and boundary conditions associated with large underground openings are major challenges in the design of salt caverns excavated for oil storage purposes. In this study, the deformation mechanism and stability of salt caverns were investigated. A comprehensive 3D numerical study was carried out to investigate the effects of cavern size and depth, salt rock deformation modulus, and ground in‐situ stress regime on the behavior of large salt caverns. The stress field and deformation mechanisms were studied numerically aiming at shedding lights into the design aspects of salt caverns for oil storage. The analysis results show that the cavern safety factor is reduced as a function of cavern depth and storage volume. Also, with decrease in k (ratio of horizontal to vertical in‐situ stress), the stability of salt caverns will increase; however, with increase in salt rock young modulus, the sensitivity of cavern stability to k ratio is reduced. Copyright © 2016 John Wiley & Sons, Ltd.     

Unifying Batch-Dissolution Kinetics for Salts: Probing the Back Reaction for Gypsum and Calcite by Means of the Common-Ion Effect

Recent success in fitting the shrinking object model for dissolution kinetics to biogenic silica, silica gel, simple salts, sucrose and gypsum prompted this study of the effects of common ions upon gypsum dissolution kinetics. Middle-ground dissolutions were mainly studied, in which shrinkage of the surface area, S, is significant, and the system approaches, but does not reach, saturation, c _sat. Dissolution was monitored by conductimetry. At a constant ionic strength of 0.060 M, the net rate for gypsum dissolution is given by \textNet \textRate = k_\textb ·S ·(c_\textsat - c ) {\text{Net}}\,{\text{Rate}} = k_{\text{b}} \cdot S \cdot (c_{\text{sat}} - c ) , where k _b is a rate constant, and c can be expressed alternatively in terms of either [Ca²⁺], [SO₄ ²⁻] and [ε_±], that part of the electrolyte concentration contributed by gypsum dissolution, or as the equivalent total concentrations of these species, for example, [SO₄ ²⁻]_T. The presence of either calcium or sulphate as a common ion slows dissolution, and the effect of this upon c _sat, k _b and k _f, the forward rate constant, is discussed. Contrary to previous experience, it is emphasised that each fitting of the shrinking object model demands its own value of the Solubility of gypsum, c _sat, which can be derived from the Solubility Product. This experience with gypsum is aligned with previous work on calcite, to develop a unified approach to the batch dissolution of salts. It highlights serious deficiencies in the way earlier common-ion experiments were conceived and enacted, and in particular with the rate equation of Sj?berg (Geochim Cosmochim Acta 40:441–447, 1976) for calcite above a pH of 7. Common-ion experiments are shown to be crucially important for probing the back reaction to dissolutions and might be applied to the far bigger problem of silicate-mineral dissolution, where ‘non-linear kinetics’ are often observed.     

Fractal analysis of magnetite grains — implications for interpreting deformation mechanism

In the present study, the grain size (d) and shape of 225 magnetite grains, that crystallized at T>600°C in a syntectonic granite (Godhra Granite, India) are evaluated and implications of data to decipher deformation mechanism of magnetite are discussed. Fractal (ruler) dimension (D) analysis of magnetite grains is performed and it is demonstrated that they show fractal behaviour. Smaller magnetite grains tend to be more serrated than the larger ones, which is manifested in the higher fractal (ruler) dimension (D) of the former. Assuming a natural strain rate ranging between 10⁻¹⁰ s⁻¹ and 10⁻¹⁴ s⁻¹, the grain size data fall dominantly in the dislocation creep field of the existing deformation mechanism map of magnetite for 630°C. However, SEM-EBSD studies reveal that subgrains are absent in the magnetite grains and they did not undergo dislocation creep. Thus it is inferred that the shape of magnetite grains was not controlled by dislocation creep. It is concluded that the higher serration and increased fractal dimension of finer magnetite grains implies the importance of diffusion creep as an important deformation mechanism at high-T for magnetite in polymineralic rocks.     

Ri-μi/μm-Ci dependent oblateness of deformed pebbles in the Baraitha conglomerate,Central India and tectonic implications

Strain analysis of the Baraitha conglomerate is attempted by direct measurements on extracted pebbles and by micrometric analysis. The overall deformation is of flattening type, with thek value lower by more than half in the matrix than in the pebbles. The viscosity contrast between pebbles and matrix (μ _i/μ_m) is in the ratio of 2:1 and the bulk deformation appears to be strongly controlled by C_i (concentration of pebbles expressed as percentage). The total shortening (≃35%) in the Baraitha conglomerate is comparable with the shortening accomplished in the folding of the overlying Bijawar Group volcanosedimentary sequence. The bulk strain axesX _t, Y_t andZ _t, as determined from the analysis of the deformed conglomerate, are unsymmetrically oriented with reference to folds formed by oblique flexural-slip with neitherX _t norY _tcoincident with the fold hinges. The lack of transection of folds by cleavage again suggests flattening deformation. The extension in theY _tdirection is greater in the matrix than in the pebbles.     

High pressure behaviour of lead feldspar (PbAl2Si2O8)

An in situ high pressure powder diffraction study, using high-brilliance synchrotron radiation, on lead feldspar (PbAl₂Si₂O₈) was performed. Two samples, with Q _od=0.68 and 0.76, were loaded in a diamond anvil cell and were compressed up to 11 GPa. Up to P=7.1 GPa the only phase present is lead feldspar. In the range 7.1–9.4 GPa sudden changes in the position of the reflections suggest the transformation of lead feldspar to a new phase (probably feldspar-like). The absence of split that would be compatible with triclinic symmetry rules out the monoclinic-triclinic transition, that was reported for the structurally similar strontium feldspar. At P>9.4 GPa some new extra reflections not indexable in the feldspar cell are present as well. During decompression the lead feldspar was the only phase present at P<6 GPa. Peak enlargement was observed with pressure, probably preliminary to amorphization. However almost complete amorphization was observed only after fortuitous shock compression at ∼18 GPa; the crystallinity was recovered at room pressure after decompression. The bulk modulus for lead feldspar was K=71.0(9) and 67.6(1.2) GPa for the two samples, in the range reported for feldspars. The cell parameters show a compression pattern which is similar to that observed in anorthite, with Δa/a ₀>Δc/c ₀>Δb/b ₀; comparison with the high temperature behaviour shows that for lead feldspar the strain tensor with pressure is more isotropic and the deformation along a is less prominent. A turnover in the behaviour of the β angle with pressure suggests a change in the compression behaviour at P∼2 GPa. Rietveld refinement of the Pb coordinates was performed in a series of spectra with pressure ranging from 0.6 to 6.5 GPa. The combined analysis of cell parameters and Pb coordinates with pressure showed that the compression of the structure is mainly achieved by an approach of Pb atoms along a *. Received: 21 July 1998 / Revised, accepted: 13 October 1998     

Transport properties of low-sanidine single-crystals, glasses and melts at high temperature

Thermal diffusivity (D) was measured using laser-flash analysis from oriented single-crystal low-sanidine (K_0.92Na_0.08Al_0.99Fe³⁺ _0.005Si_2.95O₈), and three glasses near KAlSi₃O₈. Viscosity measurements of the three supercooled liquids, in the range 10^6.8 to 10^12.3 Pa s, confirm near-Arrhenian behavior, varying subtly with composition. For crystal and glass, D decreases with T, approaching a constant near 1,000 K: D _sat ∼ 0.65 ± 0.3 mm² s⁻¹ for bulk crystal and ∼0.53 ± 0.03 mm² s⁻¹ for the glass. A rapid decrease near 1,400 K is consistent with crossing the glass transition. Melt behavior is approximated by D = 0.475 ± 0.01 mm² s⁻¹. Thermal conductivity (k _lat) of glass, calculated using previous heat capacity (C _P) and new density data, increases with T because C _P strongly increases with T. For melt, k _lat reaches a plateau near 1.45 W m⁻¹ K⁻¹, and is always below k _lat of the crystal. Melting of potassium feldspars impedes heat transport, providing positive thermal feedback that may promote further melting in continental crust.