Relative Partial Molar Free Energy Research Articles

Swelling Stress of Bentonite: Thermodynamics of Interlayer Water in K-Montmorillonite in Consideration of Alteration

The buffer material that makes up the geological disposal system of high-level waste swells by contact with groundwater and seals space with rock mass and fractures in rock mass. The buffer material has a function of mechanical buffer with rock pressure, and swelling stress is important in this case. The alteration of bentonite may occur due to the initial replacement of cations (Na+ ions) in the interlayer with K+ ions upon contact with groundwater, but there are no studies on the swelling stress of K-bentonite. In this study, the author prepared K-montmorillonite samples and obtained thermodynamic data on interlayer water as a function of water content using a relative humidity method. The swelling stress was analyzed based on a thermodynamic model developed in earlier studies and compared with measured data. The activity and the relative partial molar Gibbs free energy of porewater decreased with decreasing water content in the region, below approximately 15%. This behavior significantly differs from that of other ions, such as Na. The swelling stress calculated based on the thermodynamic model and date occurred in the region of high density of 1.9 Mg/m3 with montmorillonite partial density. It was indicated for the first time that K-bentonite scarcely swells under realistic design conditions.

Electrochemical behavior and separation of dysprosium from molten NaCl-KCl eutectic by co-reduction with aluminum

To electrolytically separate dysprosium from spent fuel, the electrochemical behavior of Dy3+ and its co-reduction process with Al3+ on inert Mo electrode in molten NaCl-KCl eutectic was systematically investigated employing a series of electrochemical methods. Dy3+ ions were directly reduced to dysprosium metal on inert Mo electrode through one step with three electrons exchanged. The reduction of Dy3+ was considered to be a quasi-reversible process, and the deposition of dysprosium on Mo follows the progressive nucleation mode. However, the co-reduction of Dy3+ with Al3+ on the Mo electrode allows the reduction of Dy3+ at more positive potentials because of the formation of Dy-Al intermetallics. The electromotive force method was then adopted to determine the thermodynamic properties of the Dy-Al intermetallics, such as the relative partial molar Gibbs free energy and the activity of dysprosium, and the standard formation Gibbs energy for Dy-Al intermetallics. Finally, potentiostatic electrolysis was conducted to extract Dy-Al alloys from the NaCl-KCl-0.40mol%DyCl3-0.56mol%AlCl3 melts. The XRD and FE-SEM/EDS analyses indicated that DyAl3, DyAl2 and DyAl intermetallics and metallic Al were generated in the products by electrolysis at −1.8 V, while the dysprosium-rich phases of DyAl2 and DyAl were produced as electrolysis at −2.0 V. The electrochemical separation of dysprosium from molten NaCl-KCl eutectic on inert Mo electrode was proved to be practically feasible by co-reduction with aluminum.

A Thermodynamic Analysis on the Effect of Salinity on Interlayer Space of Na-Montmorillonite

ABSTRACTBentonite is used as one of the materials for engineered barrier systems in a radioactive waste repository. Since the major clay mineral constituent of bentonite is montmorillonite, its physico-chemical properties are important. Basal spacing of water-saturated Na-montmorillonite is reported to decrease with increasing Na-montmorillonite density. This paper presents a thermodynamic model to calculate change in the interlayer space of Na-montmorillonite based on the relative partial molar Gibbs free energy (dG) of interlayer water as contacted with a solution of an arbitrary salinity (NaCl concentration). Directly change in montmorillonite density (ρdm) against salinity was calculated by the thermodynamic model. The dG of interlayer water as contacted with a solution of an arbitrary salinity can be calculated by dG = dGH2O+ dGS (dGH2O: relative partial molar Gibbs free energy of interlayer water, dGS: that of water in a solution of an arbitrary salinity). The author previously reported an empirical correlation of dGH2O vs. water content for Na-montmorillonite. The dependence of ρdm on salinity was calculated by replacing dGH2O in the empirical correlation with dG. ρdm increased with salinity. Concretely, initially the ρdm-values of 0.5 and 1.0 Mg/m3 increased to 1.05 and 1.16 Mg/m3 under 0.5 m-NaCl, respectively. Interlayer space vs. salinity was estimated based on the measured results of basal spacing vs. ρdm by XRD and the average density of montmorillonite vs. salinity calculated by this model.

Thermodynamic model on swelling of bentonite buffer and backfill materials

Smectite (montmorillonite) is the major clay mineral constituent of the bentonite buffer and the backfill materials which would be used for geological disposal of a high-level radioactive waste. Swelling pressure of bentonite occurring in the permeation process of moisture was modelled on the basis of thermodynamic theory and data of water sorption by smectite. The activity ( a H 2 O ) of water on smectite surface was measured by a vapor pressure method as a function of water content (0–83%) and temperature (15–40 °C) at smectite densities of 0.6 and 0.9 Mg/m 3. From experimented results, the relative partial molar Gibbs free energy ( Δ G H 2 O ) of water was determined at 25 °C. Purified Na-smectite, of which all interlayer cations were completely exchanged with Na + ions and soluble salts were removed in advance, was used. The a H 2 O and Δ G H 2 O of water decreased with water content when water content is lower than about 40%, which is consistent with the behaviour of Kunipia-F bentonite, for which smectite content was approximately 100 wt.%. Water affected from the surface of smectite was deduced to be up to a distance of approximately two water layers on the average (corresponding to four water layers in the interlayer) from the specific surface area of smectite (ca. 800 m 2/g) and the correlation between a H 2 O (or Δ G H 2 O ) and water content. Swelling pressure against smectite partial density under saturated condition was estimated from the difference ( Δ G H 2 O ) in the chemical potentials of water in equilibrium state between free water and water-saturated smectite, and compared to data measured for various samples of bentonites and different silica sand amounts. The calculated swelling pressures were in good agreement with the measured data for smectite partial density ranging between 0.7 and 2.1 Mg/m 3, covering then most of bentonites and dry densities of compacted bentonites by considering smectite content.

Measurements on the Thermodynamic Properties of Porewater in Sandstone by Vapor Pressure Method

The thermodynamic properties of porewater in sandstone were obtained as a function of water content and temperature by vapor pressure method. The activity, the relative partial molar Gibbs free energy (Δ HH2O), the relative partial molar enthalpy (Δ SH2O) and the relative partial molar entropy (ΔSH2O) of the porewater were determined at 298.15 K. The activity decreased with decreasing water content in the region where water content is about 1.5%, and drastically decreased in the region where water content is about 0.5%. No clear dependencies of Δ H 2O and Δ SH2O on water content were found. Synthesizing the correlations of the activity, Δ GH2O, Δ H H2O and Δ S H2O with water content and the enthalpy and entropy of fusion for ice, the porewater at the surface of the solid was found to have a low chemical potential compared with free water, and dissimilar with the structure of ice. Correlating the activity and Δ GH2 O with water content, the specific surface area of sandstone and the porosity, the porewater is deduced to be weakly affected up to a distance of approximately 3 nm from the surface of the solid. However, as the porewater approaches a distance of approximately 1.1nm from the solid surface, the effect from the solid surface abruptly becomes strong. This is deduced to be the effects of hydrogen bond at the solid surface and hydration to cations corresponding to the CEC.

Electrical Conductivity and Thermoelectric Power of Uranium Dioxide

The electrical conductivity and thermoelectric power of an uranium dioxide single crystal were measured between 908 and 1697 K and for PO2 included between 10−24 atm and the boundary UO2+x/U4O9. For T<1273 K and near stoichiometry, the electrical conductivity versus PO2 shows a plateau characteristic of an extrinsic regime. For T≥1273 K, the conductivity exhibits a minimum. The Seebeck coefficient Q̄UO2 also exhibits a behavior change when the temperature is increased. For T<1200 K, Q̄UO2 remains positive whatever the values of PO2. For T>1200 K, Q̄UO2 changes from negative to positive values when PO2 increases. This set of results shows that the stoichiometric oxide presents a p extrinsic to intrinsic transition near 1273 K. At T≤1273 K, the extrinsic conductivity values versus temperature confirm that the mobility of the holes occurs by a small polaron process, with an activation energy of 0.17 eV. At T>1273 K, the electrical conductivity minima are characteristic of a p→n transition. A band gap energy of 2.0 eV has been calculated from the temperature dependence of these conductivity minima values. Furthermore, this set of results has allowed us to determine the relative oxygen partial molar free energy of stoichiometric UO2.

Measurements on the Thermodynamic Properties of Porewater in Sandstone by Vapor Pressure Method

The thermodynamic properties of porewater in sandstone were obtained as a function of water content and temperature by vapor pressure method. The activity, the relative partial molar Gibbs free energy (Δ HH2O), the relative partial molar enthalpy (Δ SH2O) and the relative partial molar entropy (ΔSH2O) of the porewater were determined at 298.15 K. The activity decreased with decreasing water content in the region where water content is about 1.5%, and drastically decreased in the region where water content is about 0.5%. No clear dependencies of Δ H 2O and Δ SH2O on water content were found. Synthesizing the correlations of the activity, Δ GH2O, Δ H H2O and Δ S H2O with water content and the enthalpy and entropy of fusion for ice, the porewater at the surface of the solid was found to have a low chemical potential compared with free water, and dissimilar with the structure of ice. Correlating the activity and Δ GH2 O with water content, the specific surface area of sandstone and the porosity, the porewater is deduced to be weakly affected up to a distance of approximately 3 nm from the surface of the solid. However, as the porewater approaches a distance of approximately 1.1nm from the solid surface, the effect from the solid surface abruptly becomes strong. This is deduced to be the effects of hydrogen bond at the solid surface and hydration to cations corresponding to the CEC.

Thermodynamic Properties of Water in Compacted Bentonite Under External Pressure-free Conditions

AbstractIn an attempt to determine the thermodynamic properties of water in bentonite, the vapor pressure of water in compacted bentonite was measured as functions of water content and temperature, under external pressure-free conditions. The relative partial molar Gibbs free energy ΔGH2O, enthalpy ΔHH2Oand entropy ΔSH2O of tne waler in bentonite were determined at temperature of 298.15K. The interlayer distance of montmorillonite in bentonite was also measured by X-ray diffraction.It is probable that one fourth of the total water included in the bentonite at water content of 20.3wt% and dry density of 1.76 × 103kg/m3 is nearly free water; the water is not regarded as dilute electrolytic solution but the solution with higher ionic strength. Another one fourth of the water in the bentonite at the water content is bound water; the partial molar entropy of the bound water referred to pure water is from a half to whole of solidification entropy of pure water. The remainder is regarded as intermediately bound water.

Thermodynamic studies of La(Fe xAl 1−x) 13 alloys

The Invar alloy La(Fe xAl x−1) 13 with NaZn 13-type cubic structure was prepared. Using single crystals of CaF 2 as solid electrolyte, the activity and the relative partial molar Gibbs free energy of lanthanum in La(Fe xAl 1−x) 13 alloys were determined by the e.m.f. method over the temperature range 983–1085 K. The melting point and the phase transition temperature of two La(Fe xAl 1−x) 13 alloys were measured by differential thermal analysis. The average molar heat capacity was measured using a high temperature microcalorimeter in the temperature range 416–610 K.

Phase relation in BaBiO 3− x by coulometric titration

The electromotive force (EMF) of the solid electrolyte galvanic cell: Pt, O 2(BaBiO 3− x )|YSZ|O 2(air), Pt has been measured in the temperature range of 975–1300 K. The oxygen content in BaBiO 3− x was controlled by coulometric titration. The relative partial molar free energy of oxygen (Δ [ovbar|G] o2) was determinedfrom the EMF. Three distinct phases (I, II and III) were observed for 0≦ x<0.5. The relative partial molar enthalpy (Δ[ovbar|H] o2) and entropy (Δ[ovbar|S] o2) of oxygen were calculated from the temperature dependence of the Δ[ovbar|G] o2. The value of Δ[ovbar|H] o2 decreased in phase I and increased in phase II with an increase in x. In phase II, the change of Δ[ovbar|S] o2 agreed well with that of the configurational entropy, Δ[ovbar|S] o2(conf), which was calculated assuming the following defect reaction: 1 2 O 2 + V .. O + Bi X O + Bi .. Bi .

Oxygen pressures over LaMnO 3+x

Equilibrium oxygen partial pressures over non-stoichiometric lanthanum manganite, LaMnO 3+x, have been determined by a gravimetric method at 1188–1370 K. Relative partial molar free energy, entropy and enthalpy of solution of oxygen in this phase were derived. The variation of the relative partial molar entropy of oxygen with the composition in the non-stoichiometric LaMnO 3+x phase was calculated and discussed in relation to the metal vacancy model.

Physico‐chemical Properties of Sols and Gels of Na‐montmorillonite with and without Adsorbed Hydrous Aluminum Oxide

AbstractSodium‐montmorillonite was prepared with and without adsorbed hydrous aluminum oxide and called Na/Al‐clay and Na‐clay, respectively. The two clays were mixed with 10‐4N NaCl solution in different proportions. Measurements of shear stress at different shear rates showed that the clay content at which gelation began, as indicated by an increase in viscosity and the initiation of non‐Newtonian and hysteretic behavior, was lower for the Na/Al‐clay than for the Na‐clay (∼ 2% clay vs. 4% clay). Theoretical considerations indicated that both strong and weak bonds were present in the gels but only weak bonds were present in the sols.Specific heat capacities of the mixtures were determined in a Calvet microcalorimeter and were found to differ from those calculated from the known proportions and specific heat capacities of clay and water. Differences were greater for the Na/Al‐ than for the Na‐clay. A detailed analysis indicated that these differences could be attributed to clay‐water interaction.EMF measurements, made with sodium glass and Ag/AgCl electrodes, showed that the relative partial molar free energy of NaCl changed with clay content in somewhat different ways for the Na/Al‐ and Na‐clay mixtures. The changes were correlated with changes in other properties of the mixtures. It was concluded that adsorbed hydrous aluminum oxide does influence the physico‐chemical properties of sols and gels of Na‐montmorillonite.

Effect of the Sol‐Gel Transformation in Clay‐Water Systems on Biological Activity: II. Sodium Uptake by Corn Seedlings

AbstractHomoionic Na‐ and K‐ clay were prepared from the &lt; 2µ fraction of Wyoming bentonite. The Na‐ clay separately, or combined with the K‐clay, was mixed with water to produce clay‐water systems having different clay contents. These systems were extruded through a hypodermic needle to orient the particles within them. Thereafter, some of them were disturbed by tapping their containers on the laboratory bench. Then the following quantities were measured on all or part of them: viscosity, relative partial molar free energy, (F̄ − F̄°), of NaCl, KCl and HCl, and water tension. It was found that the viscosity, the (F̄ − F̄°) of HCl, and the water tension were decreased by disturbing the clay systems, whereas, the (F̄ − F̄°) of both NaCl and KCl were increased. The physical significance of these changes was discussed.Samples of the Na‐ clay systems were mixed with 22Na and extruded around the radicles of corn seedlings (Zea mays L.). Then Na+ uptake was determined by analyzing the seedlings for 22Na. It was found that Na+ uptake increased curvilinearly with Na‐ clay content in the range 0–4% clay and then leveled off. In the curvilinear range, Na+ uptake was directly proportional to the (F̄ − F̄°) of NaCl. Combined samples of Na‐ and K‐ clay were also mixed with 22Na and extruded around the radicles of corn seedlings. The K‐ clay was used to maintain consistency and yet dilute the Na‐ clay enough so that the seedlings would respond to changes in the (F̄ − F̄°) of NaCl. As before, some of the systems were disturbed by tapping. It was found that Na+ uptake was greater from the disturbed than from the undisturbed systems. And since the disturbance also increased the (F̄ − F̄°) of NaCl, it was concluded that Na+ uptake depended on this quantity.

Some thermodynamic relationships for soils at or below the freezing point: 1. Freezing point depression and heat capacity

An extended equation was derived relating the relative partial molar free energy of water in a soil to its freezing point depression and relative partial molar heat content. The equation was used to prepare a table from which each of these three quantities can be ascertained if the other two are known. The table was used with experimental data to obtain a curve of freezing point depression versus water content for Na‐Wyoming bentonite. Provided the activity of the liquid water in the clay is a single‐valued function of the liquid water content, and that the ice has the properties of pure bulk ice, this curve also represents the relationship between freezing point depression and unfrozen water in the partially frozen clay. An equation for the heat capacity of a partially frozen soil was also derived. This equation was employed to calculate the heat capacities of the clay at different water contents and sub‐zero temperatures. A comparison of the calculated unfrozen water contents and heat capacities of the partially frozen Na‐Wyoming bentonite with the available experimental data indicated satisfactory agreement, especially as regards the unfrozen water contents.

Statistical model of partially ordered defects in a hypostoichiometric metal oxide

A statistical model is proposed to account for partial ordering of anion vacancies and reduced cations in a hypostoichiometric fluorite-type metal oxide. Both defect assemblages are considered to be divided into many subgroups, each corresponding to a specific repulsion energy level. The analysis provides approximate expressions for the relative partial molar entropy, enthalpy and free energy of oxygen in the solid, and gives the variation of these quantities with defect concentration. The resulting curves exhibit irregularities that become increasingly pronounced with falling temperature and mark the precipitation of a series of new phases from the original fluorite structure.

Effect of Gelation on the Properties of Water in Clay Systems

AbstractParticle size distributions in samples of Belle Fourche, Wyoming, Aberdeen, Utah, and Cheto bentonite were obtained by a centrifugation technique. From these distributions and the clay density the number of particles per gram was calculated for the different samples. Then the clays were mixed in different proportions with water and the clay concentrations required for thixotropy were determined. It was found that a smooth curve was obtained when the clay concentration required for thixotropy was plotted against the number of particles per gram of clay. A smooth curve was also obtained when the clay concentration at the upper plastic limit was plotted against the number of particles per gram of clay.In each suspension the water tension at the upper plastic limit was measured at several temperatures. From the resulting data, the relative partial molar free energy, entropy and heat content of the water were calculated. In all cases the values were negative, suggesting that the water in the suspension had more order than pure bulk water.When the water tension was measured in different suspensions of Aberdeen and Cheto bentonite it was found that the tension remained zero until the clay concentration was sufficient to allow gelation of the suspension. Thereafter, the tension increased rapidly with clay concentration. Consequently, it was concluded that the sol-gel transformation was accompanied by a change in the energy status of the included water. This conclusion was supported by reference to other investigations in which changes in water properties were noted on gelation.

High-Temperature Electrochemical Study of Uranium Oxides in the UO2-U3O8 Region.

Electromotive force measurements on galvanic cells involving solid electrolytes were made at temperatures of 800 to 1200 deg C in order to obtain standard thermodynamic data for the mixing of UO2and oxygen gas. Due to purely anionic conductivity of the electrolyte, a direct evaluation of the relative partial molar free energy of oxygen in uranium oxide as a function of the O/U atomic ratio and temperature was possible. As a result, values for the partial molar heat and entropy of mixing and the corresponding relative integral quantities were calculated for the whole composition and temperature range investigated. Nonstoichiometry in the homogeneous UO2+xphase is discussed. The solubility of oxygen in this phase was found to be higher than previously known.

Electrochemical Measurements of Elevated-Temperature Thermodynamic Properties of Certain Iron and Manganese Oxide Mixtures

Measurements have been made in the temperature range 750° to 1050°C. of the temperature dependence of the electromotive force of the solid-electrolyte galvanic cells and from these data the variation with temperature of the relative partial molar free energy of oxygen on the right side of the foregoing cells was calculated. In the case of the first of these cells, a favorable comparison was made between the present values of this thermodynamic quantity and those predicted from published thermodynamic data for this oxide mixture. The lack of gas equilibria data for the manganese oxide mixture prevented such a comparison in the second instance, however, and there were substantial discrepancies between the present values of the relative partial molar free energy of oxygen and those obtained from published calorimetric data. This disparity in results was rationalized on the basis of possible differences in the metal-oxygen ratio for the manganese oxide specimens measured by the two different techniques.

Thermodynamics of liquid Mg-Bi alloys

Thermodynamic studies on liquid Mg-Bi alloys have been carried out using the e.m.f. method. A cell is described, suitable for measuring Mg activities in this system. Values of the excess partial molar free energy, the relative partial molar free energy, entropy, and enthalpy are listed along with the corresponding integral quantities. The results are compared with previous vapor pressure and calorimetric measurements as well as investigations of the phase diagram. Wagner's interpretation in terms of electronic constitution is consistent with the present data.