On Equilibrium Constants for Aqueous Geochemical Reactions in Water Unsaturated Soils and Sediments

Usually, equilibrium constants for aqueous geochemical reactions in the unsaturated zone are assumed to be equal to those for free water solutions (at atmospheric pressure) considered in classical water chemistry. This paper shows that high negative pressures in pore water may essentially change these constants in dry soils and sediments. The influence of negative capillary pressures on equilibrium constants for some important reactions occurring in the upper part of the unsaturated zone is analyzed. It is shown that values of these constants at low water contents may differ from those normally used by orders of magnitude. Sediment drying usually decreases the equilibrium constant for salt dissolution-precipitation reactions (makes precipitation easier) and for silicate weathering (delays it), whilst in the case of dedolomitization, orthoclase-albite transition and some types of cation exchange the equilibrium constant grows and these processes in dry soils and sediments have to be enhanced. This revised version was published online in July 2006 with corrections to the Cover Date.     

地热系统中矿物-流体化学平衡的计算

在热勘探过程中 ,建立在水 -岩平衡基础上的地热温标方法 ,常被用来评价地下热储温度。本文采用多矿物平衡图解法和Na -K -Mg三角图解法 ,研究西藏高温及江西中低温地热流体的平衡状态 ,从而为地热温标的选择提供了理论依据。     

Monazite-Xenotime-Garnet Equilibrium in Metapelites and a New Monazite-Garnet Thermometer

Prograde suites of pelitic rocks were examined with electronmicroprobe and laser ablation inductively coupled plasma massspectrometry to determine the systematics of element partitioningbetween coexisting monazite, xenotime, and garnet. Monazitegrains that grew in equilibrium with xenotime are enriched inY and Dy compared with monazite that grew in xenotime-absentassemblages. Y and heavy rare earth element contents of monazitecoexisting with xenotime increase with rising temperature. Monazite–xenotimeY–Gd and Y–Dy partitioning is systematic withina metamorphic grade, and increases slightly with increasingmetamorphic grade, suggesting that monazite–xenotime pairsapproached partitioning equilibrium. Garnet and monazite inboth xenotime-bearing and xenotime-absent assemblages show astrong ( R² = 0·94) systematic relationship between inversetemperature and ln(K_Eq) for the net-transfer equilibrium YAG+ OH-Ap + (25/4)Qtz = (5/4)Grs + (5/4)An + 3YPO₄-Mnz + 1/2H₂O,suggesting that garnet and monazite crystallized in compositionalequilibrium. The following temperature–K_Eq relationshipfor the equilibrium above has been derived:      

稳定同位素交换反应平衡常数与平衡分馏因子的关系——过量因子的实质及计算方法

理论计算稳定同位素平衡分馏因子(α),是以计算平衡常数K为桥梁,但是K与α之间并非简单的指数关系,二者之间还存在一个较为神秘的过量因子X(excess factor)。然而,几乎所有的理论计算工作都直接忽略了过量因子,并没有人详细研究过过量因子的实质及其可以被忽略的条件,因此,针对这个现状,本文从最基础的理论推导开始,精确推导了α和K之间的关系,并得到了过量因子的具体表达式,同时也给出了β因子(一种物质与其理想气态原子之间的平衡分馏因子)和同位素约化配分函数比(RPFR)之间的具体关系式。本文还以石膏与溶液中硫酸根之间的硫和氧同位素的分馏为实例,具体展示了过量因子产生的原因和计算方法,也提供了精确的石膏和硫酸根之间的硫和氧同位素的平衡分馏参数。     

含钾水盐体系介稳相关系研究

针对西藏扎布耶盐湖卤水组成,采用等温蒸发法分别研究了含钾四元体系Na+,K+//Cl-,B4O27--H2O308.15K、五元体系K+//Cl-,CO23-,SO42-,B4O72--H2O273.15K下的介稳相关系。分别测定了上述体系308.15K、273.15K时介稳平衡液相组成及密度、pH值。根据实验数据绘制了相应的介稳相图、水图。结果表明,本文研究的两个体系均为简单共饱型,无复盐和固溶体生成。其中,四元体系介稳相图由2个共饱点,5条单变量曲线,4个结晶区组成。平衡固相分别为Na2B4O7.10H2O、K2B4O7.4H2O、NaCl和KCl。对比四元体系308.15K和273.15K下的介稳相图发现,平衡固相盐的种类及结晶形式均没有发生变化,但结晶区大小产生变化:在308.15K下,Na2B4O7.10H2O结晶区变小,K2B4O7.4H2O结晶区变大。五元体系投影图中有1个共饱点、3条单变量曲线和3个结晶相区。结晶相区分别为K2CO3.3/2H2O、K2SO4和KCl。K2CO3.3/2H2O结晶区面积最小,K2SO4结晶区面积最大。K2CO3对KCl有较强的盐析作用。     

Equilibrium of a star cluster in the tidal field of the Galaxy

The tensor virial theorem is used to analyze the conditions for the existence of an equilibrium cluster moving in a circular orbit in a stationary axisymmetric galaxy. A general necessary condition is derived, which, for uniform models, coincides with the Bok stability condition. Generalized Mineur ellipsoids are constructed for nonuniform systems with anisotropic velocity distributions. The Hill stability of the cluster is analyzed.     

冰川物质平衡线的估算方法

冰川物质平衡线高度(ELA)与气候变化, 特别是与气温和降水的变化关系密切, 是重建古气候和反映冰川积累和消融变化的重要代用指标.直接观测方法可以获得较为精准的ELA, 但不能大范围展开.因此, ELA的间接估算方法, 如赫斯法(Hess)、 积累区面积比率法(AAR)、 面积–高程平衡率法(AABR)、 末端至冰斗后壁比率法(THAR)、 终碛到最高峰高差比率法(TSAM)、 侧碛最大高度法(MELM)、 冰斗底部高程法(CF)、 冰川作用阈值法(GT)等, 得到了广泛的发展与应用.然而, 由于受到雪崩或风吹雪补给、 表碛覆盖、 冰川类型和形态等因素的影响, 单一使用某种方法易受到算法本身的限制, 误差较大, 需综合考虑各种算法的适用性和选取参数的差异, 以提高计算的精度, 同时也要考虑到后期构造抬升等的影响.     

恒河-雅鲁藏布江流域雪线场的建立及其环境意义

利用冰川编目最新数据资料,计算恒河-雅鲁藏布江冰川平均高度(H_me)与测量雪线(ELA_h)之间的回归方程,发现冰川系统越大,样本数越多,则相关性越好,从而建立大系统的回归方程计算系统内所有冰川样点的计算雪线高度(ELA_hc).对所求得的ELAhc采用10’×10’的格网覆盖区域,对格网内样点的经纬度和计算雪线高度进行算术平均,用Kriging插值生成一定间隔的雪线分布图,即雪线高度场.把所得结果与该区域已有研究对比,发现它除具有共同的基本规律外,还更能体现出西藏南部雪线场的详尽分布规律,如全流域从下游向上游按照平均雪线高度的大小可以分为4个区,不同区域的雪线分布反映了影响区域雪线分布的主导因素.此方法可应用于其它已进行冰川编目的地区,也可建立不同尺度的温度场、积累场、降水场等冰川特征值场.     

天然气输送管线中水合物形成的边界条件

运用水合物形成的热力学相平衡模拟计算方法及根据输气管线中的天然气组成，确定了青海和甘肃输气管线中水合物形成的边界条件，提出预防水合物堵塞的热力学方法。在青海和甘肃输气管线工作压力约为2．5～4．11MPa的范围内，水合物形成最低温度约为1～5℃。在-7～5℃时，在体系中加入甲醇或增加盐度可有效地控制管线中水合物的形成。在低于-7℃的条件下，盐度和甲醇的联合应用，才能有效抑制输气管线中水合物的形成。在温度低于0℃和压力为2．5～4．11MPa的水合物热力学稳定范围内，降低输气管线中的水含量可有效地控制水合物形成而产生的堵塞。     

Equilibrium coexistence of three amphiboles

Electron probe and wet chemical analyses of amphibole pairs from the sillimanite zone of central Massachusetts and adjacent New Hampshire indicated that for a particular metamorphic grade there should be a restricted composition range in which three amphiboles can coexist stably. An unequivocal example of such an equilibrium three amphibole rock has been found in the sillimanite-orthoclase zone. It contains a colorless primitive clinoamphibole, space group P2₁/m, optically and chemically like cummingtonite with blue-green hornblende exsolution lamellae on (100) and (¯101) of the host; blue-green hornblende, space group C2/m, with primitive cummingtonite exsolution lamellae on (100) and (¯101) of the host; and pale pinkish tan anthophyllite, space group Pnma, that is free of visible exsolution lamellae but is a submicroscopic intergrowth of two orthorhombic amphiboles. Mutual contacts and coarse, oriented intergrowths of two and three host amphiboles indicate the three grew as an equilibrium assemblage prior to exsolution. Electron probe analyses at mutual three-amphibole contacts showed little variation in the composition of each amphibole. Analyses believed to represent most closely the primary amphibole compositions gave atomic proportions on the basis of 23 oxygens per formula unit as follows: for primitive cummingtonite (Na_0.02Ca_0.21 ^– Mn_0.06Fe²⁺ _2.28Mg_4.12Al_0.28) (Al_0.17Si_7.83), for hornblende (Na_0.35Ca_1.56Mn_0.02Fe_1.71Mg_2.85Al_0.92) (Al_1.37Si_6.63), and for anthophyllite (Na_0.10Ca_0.06Mn_0.06Fe_2.25Mg_4.11Al_0.47) (Al_0.47Si_7.53). The reflections violating C-symmetry, on X-ray single crystal photographs of the primitive cummingtonite, are weak and diffuse, and suggest a partial inversion from a C-centered to a primitive clinoamphibole. Single crystal photographs of the anthophyllite show split reflections indicating it is an intergrowth of about 80% anthophyllite and about 20% gedrite which differ in their b crystallographic dimensions. Split reflections are characteristic of all analyzed orthorhombic amphiboles so far examined from Massachusetts and New Hampshire except the most aluminous gedrites, and the relative intensity of the gedrite reflections is roughly proportional to the degree of Na and Al substitution. Thin sections of a few of these anthophyllite specimens show lamellae parallel to (010) that are just resolved with a high power objective.Publication approved by the Director, U.S. Geological Survey.     

山地冰川平衡线高度作为气候变化代用指标的讨论

对以平衡线高度作为气候变化代用指标的理论依据进行了讨论,依据天山乌鲁木齐河源1号冰川的大量观测资料,建立和完善现代冰川平衡线高度与气候统计关系,从传统方法以区域范围内气候因子为参数改造为以冰川范围内气候因子为参数,通过检验认为改造后的公式比较合理.将公式外推到小冰期第二次冰进时的1号冰川,并运用侧碛垄最大高度法确定了小冰期第二次冰进时冰川的平衡线高度,给出了该次冰进时气候条件的半定量推算结果.证明利用山地冰川平衡线高度作为气候变化的代用指标,并且对气候状况进行半定量推断是可行的.     

Analysis of Equilibrium in Garnet-Biotite-Sillimanite Gneisses from Quebec

An analysis is presented of equilibrium in six specimens ofgarnet—biotite—sillimanite—plagioclase—potashfeldspar—quartz ... gneiss from a metamorphic terrainin south-western Quebec. A nearly uniform Ti content of biotite may be accounted forby an equilibrium (a) involving biotite, sillimanite, quartz,garnet, potash feldspar, and H₂O. The nature of the distributionof Fe and Mg between garnet and biotite may be accounted forby another equilibrium (b) involving the same mineral suite,or by a simple exchange equilibrium (c) involving only garnetand biotite. The distribution of Mn between garnet and biotiteis accounted for by an exchange equilibrium (d). A nearly uniformvalue of the ratio Ca content of plagioclase/Ca content of garnetmay be accounted for by an equilibrium (e) involving plagioclase,garnet, sillimanite, and quartz. A proposed equilibrium (f)involving biotite, quartz, ilmenite, potash feldspar, sillimanite,and H₂O conflicts with equilibrium (a) and was evidently notestablished in the gneisses. The factors governing the Ca contentof biotite remain largely unknown. Some of these equilibria form potential indicators of relativegeologic temperature, pressure, and chemical potential of H₂O.     

若尔盖铀矿田铀镭平衡特征分析

为了充分了解若尔盖铀矿田铀镭平衡系数的各种规律,该文对若尔盖铀矿田大量的铀镭平衡数据进行了计算、统计,并从平衡系数的频率分布形态、与矿体的埋深关系及与矿体在走向上的规律进行了分析和总结。     

Reactions involving hydration of orthopyroxene in anorthosite-gabbro

Hydration of orthopyroxene (En₆₀) in contact with plagioclase (An₃₆) leads to oronas of the type orthopyroxene-cummingtonite-edenite + quartz-edenitic hornblende. The compositions of the minerals involved indicate that kyanite needles in the adjacent plagioclases form as part of the reaction: orthopyroxene (En₆₀) + plagioclase (An₃₆) + H₂O→ cummingtonite + edenite/edenitic hornblende + plagioclase (< An₃₆) + kyanite + quartz. The reaction proceedings consumption first of the orthopyroxene and later of the cummingtonite to produce a corona structure consisting of a core of intergrown edenite and quartz surrounded by edenitic hornblende. Corona evolution of this type is controlled by diffusion.     

Reactions in Amphibolite, Greenschist and Blueschist

Mineral assemblages in which chlorite [CHL], epidote [EPI],clinoamphibole [AMP], plagioclase [PLG] and quartz [QTZ] aremajor phases are characteristic of many low-grade mafic schists.The possible heterogeneous reactions in such an assemblage maybe separated into two types, exchange reactions and net-transferreactions. Only the latter alter significantly the modal proportionsof the minerals. A set of linearly independent reactions defines a reaction spaceof as many dimensions as there are independent reactions. Thespace defined by the net-transfer reactions alone is a sub-spacethat can be portrayed in three dimensions for the above assemblage.A procedure is presented herein that gives a set of independentreactions that may be taken as basis reactions for definingsuch a reaction space. All other reactions that can be writtenfor this assemblage, as well as observed whole-rock reactions,can be portrayed as vectors in these reaction spaces. Thesevectors connect the region (mineral facies) accessible to theabove assemblage. The whole-rock reactions of Laird (1980) relatinggreenschist, blueschist and various low-grade amphibolites fromVermont, provide informative examples, as do the whole-rockexperiments of Liou et al. (1974). Although reaction spaces apply to both equilibrium and disequilibriumassemblages the reactions selected as basis vectors correspondone-for-one to the chemical conditions for equilibrium thatmust obtain in any fully equilibrated assemblage. The set selectedis one that provides maximum sensitivity for geothermometric,geobarometric and geohygrometric purposes.     

The Role of One- and Two-Electron Transfer Reactions in Forming Thermodynamically Unstable Intermediates as Barriers in Multi-Electron Redox Reactions

In the aquatic geochemical literature, a redox half-reaction is normally written for a multi-electron process (n > 2); e.g., sulfide oxidation to sulfate. When coupling two multi-electron half-reactions, thermodynamic calculations indicate possible reactivity, and the coupled half-reactions are considered favorable even when there is a known barrier to reactivity. Thermodynamic calculations should be done for one or two-electron transfer steps and then compared with known reactivity to determine the rate controlling step in a reaction pathway. Here, thermodynamic calculations are presented for selected reactions for compounds of C, O, N, S, Fe, Mn and Cu. Calculations predict reactivity barriers and agree with one previous analysis showing the first step in reducing O₂ to O₂ ^? with Fe²⁺ and Mn²⁺ is rate limiting. Similar problems occur for the first electron transfer step in these metals reducing NO₃ ^?, but if reactive oxygen species form or if two-electron transfer steps with O atom transfer occur, reactivity becomes favorable. H₂S and NH₄ ⁺ oxidation in a one-electron transfer step by O₂ is also not favorable unless activation of oxygen can occur. H₂S oxidation by Cu²⁺, Fe(III) and Mn(III, IV) phases in two-electron transfer steps is favorable but not in one-electron steps indicating that (nano)particles with bands of orbitals are needed to accept two electrons from H₂S. NH₄ ⁺ oxidation by Fe(III) and Mn(III, IV) phases is generally not favorable for both one- and two-electron transfer steps, but their reaction with hydroxylamine and hydrazine to form N₂O and N₂, respectively, is favorable. The anammox reaction using hydroxylamine via nitrite reduction is the most favorable for NH₄ ⁺ oxidation. Other chemical processes including photosynthesis and chemosynthesis are considered for these element–element transformations.     

Equilibrium thermodynamics of Al/Si ordering in anorthite

Variations in the equilibrium degree of Al/Si order in anorthite have been investigated experimentally over the temperature range 800-1535° C. Spontaneous strain measurements give the temperature dependence of the macroscopic order parameter, Q, defined with respect to the \(C\bar 1 \rightleftharpoons I\bar 1\) phase transition, while high temperature solution calorimetric data allow the relationship between Q and excess enthalpy, H, to be determined. The thermodynamic behaviour can be described by a Landau expansion in one order parameter if the transition is first order in character, with an equilibrium transition temperature, T _tr, of ～2595 K and a jump in Q from 0 to ～0.65 at T_tr. The coefficients in this Landau expansion have been allowed to vary with composition, using Q=1 at 0 K for pure anorthite as a reference point for the order parameter. Published data for H and Q at different compositions allow the calibration of the additional parameters such that the free energy due to the \(C\bar 1 \rightleftharpoons I\bar 1\) transition in anorthite-rich plagioclase feldspars may be expressed (in cal. mole^-1) as: \(\begin{gathered}G = \tfrac{1}{2} \cdot 9(T - 2283 + 2525X_{Ab} )Q^2 \\ {\text{ + }}\tfrac{1}{4}( - 26642 + 121100X_{Ab} )Q^4 \\ {\text{ + }}\tfrac{1}{6}(47395 - 98663X_{Ab} )Q^6 \\ \end{gathered}\) where X _Ab is the mole fraction of albite component. The nature of the transition changes from first order in pure anorthite through tricritical at ～An₇₈ to second order, with increasing albite content. The magnitude of the free energy of \()\) ordering reduces markedly as X _Ab increases. At ～700° C incommensurate ordering in crystals with compositions ～An₅₀–An₇₀ needs to have an associated free energy reduction of only a few hundred calories to provide a more stable structure. These results, together with a simple mixing model for the disordered ( \()\) ) solid solution, an assumed tricritical model for the incommensurate ordering and published data for ordering in albite have been used to calculate a set of possible free energy relations for the plagioclase system. The incommensurate structure should appear on the equilibrium phase diagram, but its apparent stability with respect to the assemblage albite plus anorthite at low temperatures depends on the values assigned to the mixing parameters of the $$$$ solid solution.     

Numerical Modelling of Dissolving and Driving Exploitation of Potash Salt in the Qarhan Playa ? A Coupled Model of Reactive Solute Transport and Chemical Equilibrium in a Multi-component Underground Brine System

Firstly, the macroscopic chemical equilibrium state of a series of chemical reactions between intercrystal brine and its media salt layer （salt deposit） in Qarhan Salt Lake was studied by using the Pitzer theory. The concept of macroscopic solubility product and its relation with accumulated ore dissolving ratio were presented, which are used in the numerical model of dissolving and driving exploitation of potassium salt in Qarhan Salt Lake. And secondly, with a model forming idea of transport model for reacting solutes in the multi-component fresh groundwater system in porous media being a reference, a two-dimensional transport model coupled with a series of chemical reactions in a multi-component brine porous system （salt deposits） was developed by using the Pitzer theory. Meanwhile, the model was applied to model potassium/magnesium transport in Qarhan Salt Lake in order to study the transfer law of solid and liquid phases in the dissolving and driving process and to design the optimal injection/abstraction strategy for dissolving and capturing maximum Potassium/ Magnesium in the mining of salt deposits in Qarhan Salt Lake.