Kinetic rate laws derived from order parameter theory III: Al,Si ordering in sanidine

The time dependence of the ordering and disordering of Al and Si in sanidine is described within the framework of the kinetic rate laws developed in papers I and II of this series. It was found that the relevant order parameter Q _t is homogeneous and non-conserved. The rate law is:

Kinetic rate laws derived from order parameter theory IV: Kinetics of Al,Si disordering in Na-feldspars

The kinetic rate laws of Al-Si disordering under dry conditions (T = 1353K, 1253 K, 1223 K, 1183 K) and in the presence of water (p = 1 kbar, T = 1023 K, 1073 K, 1103 K) were studied both experimentally and theoretically. A gradual change of the degree of order was found under dry conditions. For intermediate degrees of order broad distributions of the order parameter Q _od occur. The variations of Q _od are correlated with structural modulations as observed in the transmission electron microscope. The time evolution of the mean value of Q _od can be well described by the rate law: $$\frac{{dQ_{od} }}{{dt}} = - \frac{\gamma }{{RT}}\exp \sum\limits_{i = 1}^n {X_i^2 } \left[ {\frac{{ - (G_a^0 + \varepsilon (\Delta Q_{od} )^2 )}}{{RT}}} \right]\frac{{dG}}{{dQ_{od} }}$$ with the excess Gibbs energy G and G _a ⁰ = 433.8 kJ/mol, ?= -27.4 kJ/mol, γ = 1.687 · 10¹⁴ h ^?1. Under wet conditions, two processes were found which occur simultaneously. Firstly, some material renucleated with the equilibrium degree of order. Secondly, the bulk of the material transformed following the same rate law as under dry conditions but with the reduced activation energy G _a ⁰ = 332.0 kJ/mol and ? = -43.0 kJ/ mol, γ = 1.047 · 10¹³ h^?1. The applicability of the kinetic theory is discussed and some ideas for the analysis of geological observations are evolved.     

Kinetic rate laws as derived from order parameter theory V: Computer simulations of ordering processes using a soft ising model

The kinetic and equilibrium behaviour of order/disorder systems and related processes are simulated using an Ising spin model in which the coupling between spins occurs via local strain in a harmonic lattice. The equilibrium states are found to be well described by a mean field Landau-type Gibbs free energy. The ordering kinetics laws follow the rate law:

Kinetic rate laws as derived from order parameter theory II: Interpretation of experimental data by laplace-transformation,the relaxation spectrum,and kinetic gradient coupling between two order parameters

A unifying theory of kinetic rate laws, based on order parameter theory, is presented. The time evolution of the average order parameter is described by $$\langle Q\rangle \propto \smallint P(x)e^{^{^{^{^{^{^{ - xt} } } } } } } dx = L(P)$$ where t is the time, x is the effective inverse susceptibility, and L indicates the Laplace transformation. The probability function P(x) can be determined from experimental data by inverse Laplace transformation. Five models are presented:

1. Polynomial distributions of P(x) lead to Taylor expansions of 〈Q〉 as $$\langle Q\rangle = \frac{{\rho _1 }}{t} + \frac{{\rho _2 }}{{t^2 }} + ...$$
2. Gaussian distributions (e.g. due to defects) lead to a rate law $$\langle Q\rangle = e^{ - x_0 t} e^{^{^{^{^{\frac{1}{2}\Gamma t^2 } } } } } erfc\left( {\sqrt {\frac{\Gamma }{2}} t} \right)$$ where x ₀ is the most probable inverse time constant, Γ is the Gaussian line width and erfc is the complement error integral.
3. Maxwell distributions of P are equivalent to the rate law 〈Q〉∝e^?k√t .
4. Pseudo spin glasses possess a logarithmic rate law 〈Q〉∝lnt.
5. Power laws with P(x)=x ^a lead to a rate law: ln〈Q〉=-(α + 1) ln t.

The power spectra of Q are shown for Gaussian distributions and pseudo spin glasses. The mechanism of kinetic gradient coupling between two order parameters is evaluated.     

Composite flow laws derived from high temperature experimental data on limestone and marble

An interesting feature of recently published experimental data on high temperature deformation of Solnhofen limestone and Carrara marble is that it is not possible, for either rock, to fit isothermal points on a log strain-rate vs. log stress plot to a single straight line as required for a flow law of the familiar form e = Aexp(- H/RT)σⁿ. Instead for Solnhofen limestone the data can be well fitted to two straight line segments suggesting a change from power law with high stress exponent (at high stress) to power law with low stress exponent at low stress. However, the constant strain-rate data are even better fitted by a single composite flow law formed by addition of the two power laws; a single flow law operates throughout but the strain-rate contributions of the two components change in response to changing stress. Published microstructural evidence supports this composite flow law approach.For Carrara marble constant data provides much poorer control and it is possible to propose several composite flow laws (formed by addition of two or three separate power-law components) all of which provide reasonable correspondence with the data. Stress relaxation data is then used both to test these flow models and to suggest others. Flow models that are broadly compatible with constant and stress relaxation data can then be tested against microstructural measurements.It is suggested that, by treating a set of composite flow laws as alternative hypotheses to be tested against all available data, a more realistic Theological model will result. Composite flow laws have the major advantage of being able to represent a smooth transition from one dominant deformation mechanism to another irrespective of how wide the transition zone may be.     

X-ray diffraction study of the orientational order/disorder transition in NaNO3: Evidence for order parameter coupling

The orientational ordering transition R \(R\bar 3m - R\bar 3c\) in NaNO₃ near 552 K has been investigated using x-ray diffraction techniques. NaNO₃ is a model system for CaCO₃ and other minerals with orientational disorder of triangular molecules in a simple NaCl-type matrix. The temperature evolution of the integrated intensities of the superlattice reflection \(\bar 1\) 23 and the fundamental reflection 110 are discussed in terms of Landau theory of two coupled order parameters. It is shown that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T > T _tr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO ₃ ^- disorder, and a second order parameter linked with the spontaneous strain of this phase transition.     

蒙特卡洛方法与逆冲构造变形速率的限定

变形速率是衡量构造活动强弱的重要参数, 对其准确限定一直是构造地貌、活动构造研究的重点。以河流地貌作为参考面限定构造变形速率是目前研究中最常用的手段。基于近年来的研究体会和具体的研究案例分析认为, 虽然目前已能获得可靠的变形量和地貌年龄数据, 但若想获得合理、可靠的变形速率, 需要关注这两类数据之间的匹配关系与由其构建的断裂滑动历史的合理性。相较于通过位错量与构造变形时间的比值, 或利用两者进行线性回归的方法来限定变形速率, 从模拟合理的断裂滑动历史的角度出发, 蒙特卡洛方法可有效减小变形速率估计的不确定性, 使变形速率估计更加合理, 从而为地震风险评价等提供可靠的基础资料。

     

Size and shape characteristics of drumlins,derived from a large sample,and associated scaling laws

Ice sheets flowing across a sedimentary bed usually produce a landscape of blister-like landforms streamlined in the direction of the ice flow and with each bump of the order of 10² to 10³ m in length and 10¹ m in relief. Such landforms, known as drumlins, have mystified investigators for over a hundred years. A satisfactory explanation for their formation, and thus an appreciation of their glaciological significance, has remained elusive. A recent advance has been in numerical modelling of the land-forming process. In anticipation of future modelling endeavours, this paper is motivated by the requirement for robust data on drumlin size and shape for model testing.From a systematic programme of drumlin mapping from digital elevation models and satellite images of Britain and Ireland, we used a geographic information system to compile a range of statistics on length L, width W, and elongation ratio E (where E = L/W) for a large sample. Mean L, is found to be 629 m (n = 58,983), mean W is 209 m and mean E is 2.9 (n = 37,043). Most drumlins are between 250 and 1000 metres in length; between 120 and 300 metres in width; and between 1.7 and 4.1 times as long as they are wide. Analysis of such data and plots of drumlin width against length reveals some new insights. All frequency distributions are unimodal from which we infer that the geomorphological label of ‘drumlin’ is fair in that this is a true single population of landforms, rather than an amalgam of different landform types. Drumlin size shows a clear minimum bound of around 100 m (horizontal). Maybe drumlins are generated at many scales and this is the minimum, or this value may be an indication of the fundamental scale of bump generation (‘proto-drumlins’) prior to them growing and elongating. A relationship between drumlin width and length is found (with r² = 0.48) and that is approximately W = 7 L ^1/2 when measured in metres. A surprising and sharply-defined line bounds the data cloud plotted in E–W–L space, and records a scale-dependent maximum elongation limit (approximated by E_max = L^1/3, when L measured in metres). For a given length, for some reason as yet unknown, drumlins do not exceed the elongation ratio defined by this scaling law. We also report and compare our statistics to an amalgamated sample (25,907 drumlins) of measures derived from around 50 published investigations. Any theory must be able to explain the drumlin statistics and fundamental scaling properties reported herein and they thus provide powerful tests for drumlin modelling.     

Semi-two-dimensional numerical model for river morphological change prediction: theory and concepts

This paper presents a new numerical model for river morphological predictions. This tool predicts vertical and lateral cross-section variations for alluvial rivers, which is an important task in predicting the associated hazard zone after a flood event. The Model for the HYdraulics of SEdiments in Rivers, version 1.0 (MHYSER 1.0) is a semi-two-dimensional model using the stream tubes concept to achieve lateral variations of velocity, flow stresses, and sediment transport rates. Each stream tube has the same conveyance as the other ones. In MHYSER 1.0, the uncoupled approach is used to solve the set of conservation equations. After the backwater calculation, the river is divided into a finite number of stream tubes of equal conveyances. The sediment routing and bed adjustments calculations are accomplished separately along each stream tube taking into account lateral mass exchanges. The determination of depth and width adjustments is based on the minimum stream power theory. Moreover, MHYSER 1.0 offers two options to treat riverbank stability. The first one is based on the angle of repose. The bank slope should not be allowed to increase beyond a certain critical value supplied to MHYSER 1.0. The second one is based on the modified Bishop’s method to determine a safety factor evaluating the potential risk of a landslide along the river bank.     

The phase diagram calcite-aragonite as derived from the crystallographic properties

A general method to calculate phase diagrams from the fundamental crystallographic properties has been suggested, using the calcite-aragonite reaction as an example. This procedure requires the measurement of the phonon spectra at different temperatures and pressures, calculation of a reasonable Grüneisen parameter to obtain C _p values from the C _v values and the consideration of the order—disorder phenomena and its contribution to the Gibb's energy. The remarkable agreement seen between the calculated diagram and that determined experimentally speaks for the reliability of this method.     

Crustal structure of Japan as derived from explosion seismic data

Crustal structures of Japan were investigated under the Upper Mantle Project in three profiles, Kurayosi-Hanabusa, western Japan; Atumi-Noto, central Japan; Kesennuma-Oga, northeastern Japan. These investigations have revealed that the crust of Japan is of continental type. The variation of the crustal structure reflects the topography, especially the water depth; so the thinning of the crust occurs near the shore where the water depth increases rapidly. The velocity below the Mohorovi?i? discontinuity is smaller than 8.0 km/sec, but it is possible that a deeper layer with a velocity of over 8.0 km/sec may exist. The basaltic layer in central Japan, if existing at all, must be thin.     

Quantification of mineral dissolution rates and applicability of rate laws: Laboratory studies of mill tailings

Reliable quantification of mineral weathering rates is a key to assess many environmental problems. In this study, the authors address the applicability of pure mineral laboratory rate laws for dissolution of mill tailings samples. Mass-normalised sulfide and aluminosilicate mineral dissolution rates, determined in oxygenated batch experiments, were found to be different between two samples from the same ∼50-year-old, carbonate-depleted mill tailings deposit. Consideration of difference in particle surface area and mineralogy between the samples resolved most of this discrepancy in rates. While the mineral surface area normalised dissolution rates of pyrite in a freshly crushed pure pyrite specimen and a sulfide concentrate derived from the tailings were within the range of abiotic literature rates of oxidation by dissolved molecular O₂, as were rates of sphalerite and chalcopyrite dissolution in the tailings, dissolution rates of pyrite and aluminosilicates in the tailings generally differed from literature values. This discrepancy, obtained using a consistent experimental method and scale, is suggested to be related to difficulties in quantifying individual mineral reactive surface area in a mixture of minerals of greatly varying particle size, possibly due to factors such as dependence of surface area-normalised mineral dissolution rates on particle size and time, or to non-proportionality between rates and BET surface area.     

Kinetic study of the kaolinite-mullite reaction sequence. Part I: Kaolinite dehydroxylation

The decomposition reaction of kaolinite has been investigated as a function of the defectivity of the starting material and the temperature of reaction. Time resolved energy-dispersive powder diffraction patterns have been measured using synchrotron radiation, both under a constant heating rate (heating rates from 10 to 100° C/min) and in isothermal conditions (in the temperature range 500 to 700° C). The apparent activation energy of the dehydroxylation process is different for kaolinites exhibiting a different degree of stacking fault density. The results of the analysis of the kinetic data indicate that the starting reaction mechanism is controlled by diffusion in the kaolinite particle. The diffusion process is dependent on the defective nature of both kaolinite and metakaolinite. At high temperatures, and at higher heating rates, the reaction mechanism changes and the resistance in the boundary layer outside the crystallites becomes the rate-limiting factor, and nucleation begins within the reacting particle. During the final stage of the dehydroxylation process the reaction is limited by heat or mass transfer, and this might be interpreted by the limited diffusion between the unreacted kaolinite domains and the metakaolinite matrix.     

Transformation in territorial concepts: from nation building to concessions

The transition to globalization, socio-cultural fragmentation and an era of peace all constrain Zionism to a restructuring in its territorial perspectives. In the nation-building era, Zionism made the territory the focus of Zionist activity, which necessitated seizing territory, controlling it, and creating an affinity and attachment and a bond of identity between the nation and the territory. Pure colonization as a central strategy for realizing these national goals originated mainly from the unique historical circumstances of Zionism and from the adoption of an ethno-national ideology. This also led to the Palestinian-Jewish conflict that concentrated on the control of territory. The national economy regime that influenced Israel in different ways also served the territorial ideology to a great degree. Peace borders will require Israel to cooperate closely with Jordan, Palestine, Syria and Lebanon in managing resources, external influences and additional common interests. The peace economy will integrate with the multi-national economy. Furthermore, in the reality of peace, Israel will have to abandon the internal colonization of areas populated by Israeli Arab citizens and give greater legitimation to their more prominent inclusion the Israeli identity. It will also become difficult for any elite group to dictate the national agenda to other marginal groups, such as Israeli Arabs, and Sephardic or Orthodox Jews, each group creates for itself considerable degree of autonomy in its own territory. In the main, the national periphery divides into an Israeli Arab periphery beside the periphery of the traditionally religious Sephardic Jews. The ultra-Orthodox Jews take control of increasingly larger Israeli space and expanding the horizons of their public involvement beyond their traditional ghettos. Each group creates for itself a different symbolic space with differing views concerning the limits of Israeli sovereignty.     

Thermodynamics of sodium feldspar I: Order parameter treatment and strain induced coupling effects

The thermodynamic behaviour of Na-rich feld-spars is derived from a Landau-type free energy expression which contains two order parameters. One order parameter describes the structural distortion during the displacive phase transition between monalbite and analbite, the other the Al, Si order. The structural phase transition \(C2/m - C\bar 1\) in sodium feldspar under thermal equilibrium is due to both order parameters and is accompanied by a crossover between a thermal regime with low Al, Si order (high-albite) and a thermal regime with high Al, Si order (low-albite). The crossover is a smooth function of temperature. Simple formulae are given for the calculation of thermodynamic potentials for thermal equilibrium and for metastable phases with temperature independent Al, Si order.     

Cation order in olivines: Evidence from vibrational spectra

A simple theory is developed which relates cation ordering in the olivine structure to compositional trends in the vibrational spectra of olivines. Quantitative results for (Mg, Mn) and (Fe, Mn) olivines indicate that Mn²⁺ favors the M2 site relative to both Mg²⁺ and Fe²⁺.     

Inverse methods and kinetic models of hydrocarbon generation: I. Theoretical considerations

Several different proposed models of thermocatalytic cracking of kerogen to hydrocarbons are exhibited. The specific models are then combined into a single generic, encompassing framework. For laboratory pyrolysis measurements of kerogen degradation and of thermal generation of hydrocarbons, inverse methods are used to show how to determine the relevant distributions of kinetic parameters consistent with the measured data.