Heat capacities and entropies of silicate liquids and glasses

The heat capacities of several dozen silicate glasses and liquids composed of SiO₂, TiO₂, Al₂O₃, Fe₂O₃, FeO, MgO, CaO, BaO, Li₂O, Na₂O, K₂O, and Rb₂O have been measured by differential scanning and drop calorimetry. These results have been combined with data from the literature to fit C _pas a function of composition. A model assuming ideal mixing (linear combination) of partial molar heat capacities of oxide components (each of which is independent of composition), reproduces the glass data within error. The assumption of constancy of ¯C _p,iis less accurate for the liquids, but data are not sufficient to adequately constrain a more complex model. For liquids containing alkali metal and alkaline earth oxides, heat capacities are systematically greater in liquids with high field strength network modifying cations. Entropies of fusion (per g-atom) and changes of configurational entropy with temperature, are similarly affected by composition. Both smaller cation size and greater charge are therefore inferred to lead to greater development of new structural configurations with increasing temperature in silicate liquids.     

Heat capacities of Fe2O3-bearing silicate liquids

Direct measurements of liquid heat capacity, using a Setaram HT1500 calorimeter in step-scanning mode, have been made in air on six compositions in the Na₂O-FeO-Fe₂O₃-SiO₂ system, two in the CaO-FeO-Fe₂O₃-SiO₂ system and four of natural composition (basanite, andesite, dacite, and peralkaline rhyolite). The fitted standard deviations on our heat capacity measurements range from 0.6 to 3.6%. Step-scanning calorimetry is particularly useful when applied to iron-bearing silicate liquids because: (1) measurements are made over a small temperature interval (10K) through which the ferric-ferrous ratio of the liquid remains essentially constant during a single measurement; (2) the sample is held in equilibrium with an atmosphere that can be controlled; (3) heat capacity is measured directly and not derived from the slope of enthalpy measurements with temperature. Liquid compositions in the sodic and calcic systems were chosen because they contain large concentrations of Fe₂O₃ (up to 19 mol%), and their equilibrium ferric-ferrous ratios were known at every temperature of measurement. These measurement have been combined with heat capacity (Cp) data in the literature on iron-free silicate liquids to fit Cp as a function of composition. A model assuming no excess heat capacity (linear combination of partial molar heat capacities of oxide components) reproduces the liquid data within error (±2.2% on average). The derived partial molar heat capacity of the Fe₂O₃ component is 240.9 ±7.9 J/g.f.w.-K, with a standard error reduced by more than a factor of two from that in earlier studies. The model equation, based primarily on simple, synthetic compositions, predicts the heat capacity of the four magmatic liquids within 1.8% on average.     

Tschermak Substitution in Low- and Middle-grade Pelitic Schists

In low- and middle-grade pelitic metamorphic rocks, the extentsof Tschermak substitution in muscovite, chlorite and biotitechange regularly with bulk-rock composition and external conditions.This paper gives a theoretical analysis of the changes. From equipotential lines for Al₂O₃ plotted on AFM diagrams,we have derived a series of Thompson-type muscovite compositiondiagrams, which show how the celadonite content of muscovitevaries with the associated ferromagnesian minerals or with thebulk-rock composition under constant external conditions. Thedistribution coefficient of the exchange reaction for Tschermaksubstitution between muscovite and chlorite varies greatly notonly with temperature but also with the extent of this substitutionin the two minerals because of their strong deviation from ideality.Muscovites with a high celadonite content (phengites) occurin low-temperature rocks in any of the high-, medium- and low-pressuretypes of metamorphism, probably because the exchange equilibriumfor Tschermak substitution between muscovite and chlorite isnot sensitive to pressure. When both Mg-Fe and Tschermak substitutionoccur in muscovite and some other silicates, a metapelite containingthree AFM phases together with muscovite and quartz has at leasttwo independent net-transfer reactions that take place sideby side with changing external conditions. The mass balancerequirement in the rock is imposed on a linear combination ofthe two reaction equations, leading to a constraint on the stoichiometricequations among phase components and the progressive compositionalchanges of muscovite, chlorite and biotite. From such a viewpoint,we examine reactions and progressive mineralogical changes inmetapelites, beginning with K-feldspar-bearing low-grade metapeliticrocks, in which biotite appears by reaction of K-feldspar withchlorite at a temperature lower than that of the biotite isograddefined for K-feldspar-free pelitic rocks. When both Mg-Fe and Tschermak substitution occur in muscoviteand some other silicates, a metapelite containing three AFMphases together with muscovite and quartz has at least two independentnet-transfer reactions that take place side by side with changingexternal conditions. The mass balance requirement in the rockis imposed on a linear combination of the two reaction equations,leading to a constraint on the stoichiometric equations amongphase components and the progressive compositional changes ofmuscovite, chlorite and biotite. From such a viewpoint, we examinereactions and progressive mineralogical changes in metapelites,beginning with K-feldspar-bearing low-grade metapelitic rocks,in which biotite appears by reaction of K-feldspar with chloriteat a temperature lower than that of the biotite isoerad definedfor K-feldsoar-free oelitic rocks. The equations for the reactions that produce biotite or biotite? garnet in K-feldspar-free metapelites have been derived. Combinedwith the composition relations of coexisting muscovite, chlorite,biotite and garnet, they lead to the inference that progressof these reactions with rising temperature causes a decreaseof the celadonite content of muscovite, the antigorite contentof chlorite and the phlogopite content of biotite in the metapelitesof the chlorite, biotite and lower garnet zones, and that thistrend may not continue into the staurolite zone. This inferencehas been verified by examination of the analytical data of mineralsin four progressive metamorphic terranes covering the high-,medium- and low-pressure types. The composition of chlorite is buffered by the garnet-producingreaction so that chlorites in garnet-bearing metamorphic rocksdevelop (Mg ? Fe)/Al₂ ratios close to that of almandine at elevatedtemperatures. The maximum possible celadonite content in muscoviteunder given external conditions is realized in K-feldspar-bearingrocks, and decreases with rising temperature.     

Thermodynamic properties of chlorite CCa-2. Heat capacities, heat contents and entropies

The heat capacities of the international reference clay mineral chlorite CCa-2 from Flagstaff Hill, California, were measured by low temperature adiabatic calorimetry and differential scanning calorimetry, from 5 to 520 K (at 1 bar). The studied chlorite is a Fe-bearing trioctahedral chlorite with an intermediary composition between ideal clinochlore (Si₃Al)(Mg₅Al)O₁₀(OH)₈ and chamosite (Si₃Al)(Fe₅Al)O₁₀(OH)₈. Only few TiO₂ impurities were detected in the natural chlorite sample CCa-2. Its structural formula, obtained after subtracting the remaining TiO₂ impurities, is (Si_2.633Al_1.367)(Al_1.116Mg_2.952Mn_0.012Ca_0.011)O₁₀(OH)₈. From the heat capacity results, the entropy, standard entropy of formation and heat content of the chlorite were deduced. At 298.15 K, the heat capacity of the chlorite is 547.02 (±0.27) J mol⁻¹ K⁻¹ and the molar entropy is 469.4 (±2.9) J mol⁻¹ K⁻¹. The standard molar entropy of formation of the clay mineral from the elements is −2169.4 (±4.0) J mol⁻¹ K⁻¹.     

Tschermak fractionation in calc-alkaline magmas: the Eocene Sabzevar volcanism (NE Iran)

Calc-alkaline arc magmatism at convergent plate margins is volumetrically dominated by metaluminous andesites. Many studies highlighted the importance of differentiation via fractionation processes of arc magmas, but only in the last decades, it has been demonstrated that not all rock-forming minerals may affect the evolution of calc-alkaline suites. In particular, a major role exerted by Al-rich hornblende amphibole as fractionating mineral phase has been documented in many volcanic arc settings. The aim of this work is to understand the role of the Tschermak molecule (CaAlAlSiO₆) hosted in the hornblende and plagioclase fractionation assemblage in driving magma differentiation in calc-alkaline magmatic suites. We explore this issue by applying replenishment–fractional crystallization (RFC) and rare earth element–Rayleigh fractional crystallization (REE-FC) modeling to the Sabzevar Eocene (ca. 45–47 Ma) calc-alkaline volcanism of NE Central Iran, where hornblende-controlled fractionation has been demonstrated. Major element mass balance modeling indicates RFC dominated by a fractionating assemblage made of Hbl_52.0–52.5 + Pl_44.1–44.2 + Ttn_3.3–3.9 (phases are expressed on total crystallized assemblage). REE-FC modeling shows, instead, a lower degree of fractionation with respect to RFC models that is interpreted as due to hornblende and plagioclase resorption by the residual melt. Calculations demonstrate that fractionation of the Tschermak molecule can readily produce dacite and rhyolite magmas starting from a calc-alkaline andesite source (FC = ca. 30 %). In particular, the Tschermak molecule controls both the heavy rare earth elements (HREE) and light rare earth element (LREE) budgets in calc-alkaline differentiation trends.     

Heat capacities of aqueous sodium hydroxide/aluminate mixtures and prediction of the solubility constant of boehmite up to 300 °C

A modified commercial (Setaram C80) calorimeter has been used to measure the isobaric volumetric heat capacities of concentrated alkaline sodium aluminate solutions at ionic strengths from 1 to 6 mol kg⁻¹, with up to 40 mol.% substitution of hydroxide by aluminate, at temperatures from 50 to 300 °C and a pressure of 10 MPa. Apparent molar heat capacities for the mixtures, C_p?, derived from these data were found to depend linearly on the aluminate substitution level, i.e., they followed Young’s rule. These quantities were used to estimate the apparent molar heat capacities of pure, hypothetical sodium aluminate solutions, C_p? (‘NaAl(OH)₄’(aq)). Slopes of the Young’s rule plots were invariant with ionic strength at a given temperature but depended linearly on temperature. The heat capacities of ternary aqueous sodium hydroxide/aluminate mixtures could therefore be modelled using only two parameters in addition to those needed for the correlation of C_p? (NaOH(aq)) reported previously from these laboratories. An assessment of the standard thermodynamic quantities for boehmite, gibbsite and the aluminate ion yielded a set of recommended values that, together with the present heat capacity data, accurately predicts the solubility of gibbsite and boehmite at temperatures up to 300 °C.     

Heat capacities of aqueous solutions of sodium hydroxide and water ionization up to 300 °C at 10 MPa

A commercial (Setaram C80) calorimeter has been modified to measure the heat capacities of highly caustic solutions at temperatures up to 300 °C and pressures up to 20 MPa. The improvements have allowed more accurate determination of the isobaric volumetric heat capacities of chemically aggressive liquids at high temperatures. Test measurements with aqueous solutions of sodium chloride showed a reproducibility of about ±0.1%, with an accuracy of ∼0.3% or better, over the whole temperature range. Heat capacities of aqueous solutions of sodium hydroxide at concentrations from 0.5 to 8 mol/kg were measured at temperatures from 50 to 300 °C and a pressure of 10 MPa. Apparent molar isobaric heat capacities of NaOH(aq) were calculated using densities determined previously for the same solutions by vibrating-tube densimetry. Standard state (infinite dilution) partial molar isobaric heat capacities of NaOH(aq) were obtained by extrapolation using an extended Redlich-Meyer equation. Values of the standard heat capacity change for the ionization of water up to 300 °C were derived by combining the present results with the literature data for HCl(aq) and NaCl(aq).     

地基承载力经验公式的变异性分析

应用随机场理论,研究了地基承载力表、CPT等地基承载力经验公式的变异性分析方法,提出经验公式确定地基承载力的变异性是由经验公式本身的不确定性和土性参数的不确定性组成,提出了考虑土性参数自相关性的地基承载力经验公式的变异性分析方法,通过对编制CPT确定地基承载力经验公式资料的计算分析,得出CPT确定地基承载力的变异系数在0.1~0.135之间。     

倾斜荷载下群桩承载特性理论分析

倾斜荷载是海洋、输变线塔等桩基工程的最主要荷载形式之一。然而现行规范中有关该问题的计算方法相对并不成熟。将桩身划分为自由段和嵌固段,建立桩基单元体的挠曲微分方程;基于群桩p-y曲线法计算水平荷载下群桩承载特性;考虑桩-土相对滑移和竖向力引起的二阶弯矩(P-(35))效应,基于剪切位移法计算竖向荷载下桩-土相互作用;编制相应程序,以迭代法计算获得荷载-位移曲线、桩身弯矩分布规律曲线等。分析验证了所建立的理论计算方法的准确性和可靠性。相关研究成果拓展了工程设计中倾斜荷载作用下桩基承载特性计算方法,为工程设计与计算提供参考依据。     

红黏土地基承载力和变形参数的空间分布特征分析

为了获得红黏土地基承载力和变形参数在横向和垂向上的定量数据及分析它们的变化规律,选取厦门至成都高速公路湖南省郴州段典型横纵断面上的红黏土地层作为试验点,采用平板载荷试验、旁压试验等技术手段进行了原位测试。试验结果表明：红黏土地基承载力和变形模量在横向较小的范围内呈现较大幅度的变化,在垂向上则呈现先增大再减小的变化趋势,与红黏土赋存厚度、地形地貌、含水率等相关;旁压试验所测得的承载力特征值和平板载荷试验测得的承载力特征值之间存在一定的差异性;旁压模量与变形模量可以通过结构性系数联系起来,所得的结构性系数与Menard根据大量黏土试验资料对比所得到的结论较为一致。     

Thermodynamic properties of anhydrous smectite MX-80, illite IMt-2 and mixed-layer illite-smectite ISCz-1 as determined by calorimetric methods. Part I: Heat capacities, heat contents and entropies

The heat capacities of the anhydrous international reference clay minerals, smectite MX-80, illite IMt-2 and mixed-layer illite-smectite ISCz-1, were measured by low temperature adiabatic calorimetry and differential scanning calorimetry, from 6 to 520 K (at 1 bar). The samples were chemically purified and Na-saturated. Dehydrated clay fractions <2 μm were studied. The structural formulae of the corresponding clay minerals, obtained after subtracting the remaining impurities, are K_0.026Na_0.435Ca_0.010(Si_3.612Al_0.388) (Al_1.593Mg_0.228Ti_0.011)O₁₀(OH)₂ for smectite MX-80, K_0.762Na_0.044(Si_3.387Al_0.613) (Al_1.427Mg_0.241O₁₀(OH)₂ for illite IMt-2 and K_0.530Na_0.135(Si_3.565Al_0.435)(Al_1.709Mg_0.218Ti_0.005)O₁₀(OH)₂for mixed-layer ISCz-1. From the heat capacity values, we determined the molar entropies, standard entropies of formation and heat contents of these minerals. The following values were obtained at 298.15 K and 1 bar:

	(J mol−1 K−1)	S0 (J mol−1 K−1)
Smectite MX-80	326.13 ± 0.10	280.56 ± 0.16
Illite IMt-2	328.21 ± 0.10	295.05 ± 0.17
Mixed-layer ISCz-1	320.79 ± 0.10	281.62 ± 0.15

Full-size table

     

The influence of design and operating variables on the capacities of hydrocyclone classifiers

An extensive test programme has been conducted on 10.2-, 25.4- and 38.1-cm “Krebs” hydrocyclones in order to study the effects of some design and operating variables on their volume capacities.For a given pressure the capacity of a cyclone was found to rise sharply with the addition of solid particles to water until the solids content was about 15% by weight. Further increase in solids caused a decrease in throughput. The effect of vortex finder diameter on the throughput was found to be non-linear. A general equation which relates inlet and outlet diameters, operating pressure and feed solids content to the volume capacity is presented. This equation is independent of hydrocyclone diameter.     

基于库容分区运用的水库群生态调度模型

在不影响防洪、供水等现有利益格局的前提下,通过改善水库调度方式、发挥库群联合调控作用,提高生态供水保证率,是当前中国北方缺水地区流域水资源管理中的重大科学问题。把河流生态系统作为一个独立用水户,制订多用户分区运用水库群调度模拟规则,同时考虑调度方案对生态与发电的影响,建立水资源系统仿真模型,结合保证各用户供水保证率最大且尽可能均衡的目标函数,构建基于库容分区运用的水库群生态调度模型。将模型应用于海河流域滦河水系,提出了现状供水条件下潘家口、大黑汀和桃林口三大水库联合调度方案,绘制了水库群分区运用调度图,评价了调度方案对水力发电和下游生态系统的影响。结果表明,所提出的模型有效,水库群生态调度方案较之现行调度,可在不降低兴利和防洪效益的前提下,将河流生态系统供水保证率由46.9%提高到93.8%,生态水文改变度指标改善明显。     

Equilibrium thermodynamics of multiply substituted isotopologues of molecular gases

Isotopologues of molecular gases containing more than one rare isotope (multiply substituted isotopologues) can be analyzed with high precision (1σ <0.1‰), despite their low natural abundances (∼ ppm to ppt in air), and can constrain geochemical budgets of natural systems. We derive a method for calculating abundances of all such species in a thermodynamically equilibrated population of isotopologues, and present results of these calculations for O₂, CO, N₂, NO, CO₂, and N₂O between 1000 and 193 to 77 K. In most cases, multiply substituted isotopologues are predicted to be enriched relative to stochastic (random) distributions by ca. 1 to 2‰ at earth-surface temperatures. This deviation, defined as Δ_i for isotopologue i, generally increases linearly with 1/T at temperatures ≤ 500 K. An exception is N₂O, which shows complex temperature dependences and 10’s of per-mill enrichments or depletions of abundances for some isotopologues. These calculations provide a basis for discriminating between fractionations controlled by equilibrium thermodynamics and other sorts of isotopic fractionations in the budgets of atmospheric gases. Moreover, because abundances of multiply substituted isotopologues in thermodynamically equilibrated populations of molecules vary systematically with temperature, they can be used as geothermometers. Such thermometers are unusual in that they involve homogeneous rather than heterogeneous equilibria (e.g., isotopic distribution in gaseous CO₂ alone, rather than difference in isotopic composition between CO₂ and coexisting water). Also, multiple independent thermometers exist for all molecules having more than one multiply substituted isotopologue (e.g., thermometers based on abundances of ¹⁸O¹³C¹⁶O and ¹⁸O¹²C¹⁸O are independent); thus, temperatures estimated by this method can be tested for internal consistency.     

Applicability of CPT-based methods in predicting toe bearing capacities of driven piles in sand

This paper presents a study on applicability of predicting toe bearing capacities from cone penetration test (CPT) for PHC (pretensioned spun high-strength concrete) driven piles into deep sandy deposits in the Nakdong River deltaic area west of Busan City in South Korea. Using toe bearing capacities obtained from pile driving analyzer (PDA) tests as reference values, which were reliably calibrated by on-site O-cell tests, the applicability of the CPT-based methods was evaluated using a statistical rank index (RI). A total of 82 piezocone penetration test soundings and 190 PDA test piles were used for reliability analysis in this study. Three correction steps were applied to obtain reliable PDA and CPT data sets before ranking is carried out. The RI index is combined from four criteria: (1) the best-fit line, (2) the arithmetic mean and standard deviation, (3) the cumulative probabilities, and (4) the log-normal and histogram distributions. Based on these criteria the performance of some SPT-based methods in the literature is evaluated.     

Study of compressive loading capacities of helical piles using torque method and induced settlements

Torque is a most widely used method to estimate the load capacities of helical piles because of its simplicity and minimal costs. This research attempts to investigate the torque method by incorporating settlements and involves its comparison with bearing equations which have also been used to estimate the capacities of helical piles. The test program consisted of installation of seven helical piles including a static axial compression test to estimate the corresponding settlements. The compression test was conducted on the seventh pile which is referred to as the test pile. The load movement curve of the test pile is used to predict the settlement of each pile corresponding to the ultimate load calculated using torque method. In addition, few methods to interpret the load movement curve have been discussed. This research would pave way to yield more reliable results using torque method and could lead to the large-scale usage of helical piles.     

筒型基础水平向和抗倾承载力的极限分析上限解

海上风电是我国近年来重点发展的能源形式之一,大直径宽浅式筒型基础作为一种新型海上风电基础,具有更好的抗倾覆承载能力,更加适用于我国近海软黏土较多的土质特点;并可以实现岸边预制、海上基础?塔筒?风机整体浮运与安装,具有良好的经济效益。为更好地掌握宽浅式筒型基础的承载特性,针对海上风电基础承受水平向与倾覆荷载较大的特点,开展了数值分析对筒型基础的单向极限承载性能进行研究,得到水平向以及抗倾极限承载力和对应的承载模式;并基于筒型基础的承载模式,建立相应的破坏机动场和速度场,结合虚功方程和内部能量损耗率函数,采用数学软件编程求解了宽浅式筒型基础水平向和抗倾承载力的极限分析上限解,计算结果与数值结果的吻合程度良好。     

地源热泵土壤源换热器的施工技术

地源热泵（Ground Source Heat Pump，GSHP）作为最有发展潜力的热泵技术在各级政府的积极推窑下发壁迅速，但由于地源换热器施工安装成本高，技术的发展遇到了很大的阻力。探讨了土壤源换热器施工技术和土壤源换热器的热平衡问题，力图提高土源换热器施工技术，降低地源热泵成本，促进该技术的推广应用。