Relative Chemical Potential Research Articles

Thermodynamics of hydrogen absorption by PdSb and PdBi alloys

The thermodynamic parameters for absorption of hydrogen by PdSb and PdBi solid solution alloys containing up to 10.0 at.% Sb and Bi have been determined from measurements of pressure-composition isotherms at temperatures between 273 and 433 K and hydrogen pressures up to 1000 Torr. The hydrogen-free Pd lattice is expanded by additions of Sb and Bi, and at the same alloy composition the lattice expansion of PdBi alloys is larger than that of PdSb alloys. The dilute phase solubilities in both alloys, as relected by the relative chemical potential of dissolved hydrogen at infinite dilution, Δ μ H 0, increases with increasing Sb and Bi contents; where the solubilities in PdBi alloys are larger than those in PdSb alloys. The relative partial molar enthalpy, ΔH H 0, at infinite dilution in both alloy systems increases in exothermicity with increasing Sb and Bi contents, and at the same solute metal content, the ΔH H 0, values for PdBi alloys are more exothermic. The standard free energy change, ΔG plat 0, for β-hydride formation in PdBi alloys decreases with Bi content, whereas the ΔG plat 0 value for PdSb alloys increases with Sb content, although only by a small amount, despite the fact that the alloys have expanded lattices compared to Pd. The higher pressure solubilities in both alloys decrease with increase of the solute metal contents.

Calorimetric enthalpies for palladium - hydrogen (deuterium) systems at H(D) contents up to about [H]([D])/[Pd] = 0.86

The enthalpies for the reaction of gaseous hydrogen and deuterium with palladium have been measured as a function of [H]/[Pd] and [D]/[Pd] atomic ratios up to 0.865 and 0.85, respectively, in the temperature range 298 - 194.5 K using a differential-heat-flow low-temperature calorimeter; pressure - concentration isotherms have been measured simultaneously. The calorimetric two-phase enthalpies for the Pd - H and Pd - D systems at 298 K are and , and the corresponding entropies determined from the calorimetric enthalpies and the absorption plateau pressures are and . These - and -values are in agreement with the previously reported values and also with values determined in the literature from van't Hoff plots of the plateau pressures. The calorimetrically determined enthalpies for solution in the -phase regions of both systems become less exothermic in an almost linear fashion with increasing H(D) content, independently of temperature. At the same H(D) content, the -values for the Pd - H system are slightly more exothermic than the -values for the Pd - D system. Enthalpies of almost the same magnitude are obtained from the desorption data. The corresponding entropies, for solution in the -phase region of both systems have a tendency to decrease gradually with increase in H(D) content independently of temperature; however, there is no marked difference between the magnitudes of the -values of the two systems. The dependences of the calorimetric enthalpies for hydrogen (deuterium) solution on H and D contents in the ranges and can be expressed by the temperature-independent relations , and . The variations in -values with H(D) content are in agreement with that calculated from van't Hoff plots of the previously reported relative chemical potentials of hydrogen and deuterium at low temperatures. The present calorimetric data determined by gas-phase measurements do not offer support for the generation of any `excess heat' up to [D]/[Pd] = 0.85, beyond that which is expected from the chemical reaction because the values determined calorimetrically are almost the same as those derived from van't Hoff plots.

Bismuth activities in a lead-doped bismut-2223 superconductor

Observations are reported on the thermal decomposition of a Pb doped Bi 2Sr 2Ca 2Cu 3O y (Bi-2223) sample. Experimental methods include differential thermal analysis (DTA), thermogravimetric analysis (TGA) using a vacuum balance, and vapor-pressure measurements by Knudsen effusion using (1) mass spectrometry, (2) a vacuum balance, and (3) an external balance for mass transport detection. DTA performed under N 2 showed endothermic peaks at 722°C and 864°C. TGA under vacuum showed mass loss beginning at 700°C with a peak at 750°C. Mass spectrometry showed that O 2(g) was lost from the sample at temperatures between ca. 650°C and 675°C. It was concluded that the DTA peak at 722°C, the mass loss in TGA, and the O 2 loss by mass spectrometry were all associated with a change in oxidation state of Cu from +2 to +1. Vapor pressures of Bi(g) from the Bi-2223 superconductor samples yielded the activity of Bi in the Bi-2223 phase as 0.073 ± 0.016 and the relative chemical potential of Bi in the Bi-2223 phase of −17.4 ± 1.4 kJ/mol at 800 K.

Thermodynamic Properties for Solution of Hydrogen in Palladium‐Based Binary Alloys

AbstractThe thermodynamic parameters for solution of hydrogen at infinite dilution and the (a+B) plateau thermodynamic properties for hydrogen absorption at moderate temperatures for a series of Pd‐based f.c.c binary alloys with relatively low solute metal content have been correlated from the viewpoint of whether the alloy lattice is expanded or contracted to parent Pd lattice. Newly determined data for Pd‐Zn, Pd‐Sb, Pd‐Bi, Pd‐Cr, Pd‐Mo and Pd‐Mn alloys are included. When alloys with solute metals in the same groups are compared, the lattice parameters of Pd binary alloys with the 4 d and 5 d transition elements are, in general, larger than those with the 3 d elements. The relative partial molar enthalpy, ΔH0H, at infinite dilution becomes more exothermic with an increase of lattice parameter for the lattice‐expanded alloys with the exception of Pd‐Pt alloys. Conversely, for contracted alloys, with the exceptions of Pd‐Li, Pd‐Zn, Pd‐Al and low Ti content Pd‐Ti alloys, the enthalpy becomes less exothermic with increasing lattice contraction. The dilute phase solubility at the same temperature as reflected by the relative chemical potential of dissolved hydrogen at infinite dilution, Δμ0H, increases with increasing lattice expansion for the expanded alloys, with the exceptions of Pd‐Pt and Pd‐Nb (Ta), whereas for the contracted alloys, the solubility decreases with increasing lattice contraction, with the exception of the Pd‐Li alloys. The standard free energy change, ΔG0plat' for B‐hydride formation in the expanded alloys decreases with increase of lattice expansion with the exceptions of the Pd‐Pt, Pd‐Zr, Pd‐Sb, Pd‐Nb(Ta) and Pd‐Mn alloys. For the contracted alloys, the B‐hydride becomes less stable with increasing lattice contraction except for the Pd‐Li alloys. The isobaric hydrogen solubilities in Pd alloys at relatively high pressures may be attributed to the influence of the solute metal atoms on the Pd band structure and to the exclusion of H from site occupation due to solute atoms in the nearest neighbor shells; both of these effects are independent of the lattice expansion and contraction.

The temperature-composition phase diagram and the miscibility gap of Hg1-xCdxTe solid solutions by dynamic mass-loss measurements

The dynamic mass-loss technique has been employed to measure Hg partial pressures over Te-saturated Hg1-xCdxTe solid solutions with x = 0.40, 0.54, and 0.70 in the 10-1 to 10-4 atm range. The relative chemical potentials of HgTe in Hg1-xCdxTe solid solutions have been calculated using the measured Hg partial pressures at temperatures below 413°C, and fitted into an analytical expression. A Gibbs-Duhem integration yielded the relative chemical potentials of CdTe. By combining the relative chemical potentials of the binary components HgTe and CdTe, an expression for the Gibbs free energy of mixing was derived. The binodal (miscibility gap) and spinodal curves of the Hg1-xCdxTe solid solutions have been established with the critical temperature and composition of 221°C and Hg0.40Cd0.60Te.

THE EFFECTS OF DRILLING FLUID-SHALE INTERACTIONS ON WELLBORE STABILITY

Wellbore instability, experienced mainly in shale sections, has resulted in significant drilling delays and suspension of wells in major Australian petroleum basins. These instabilities may be induced by either in-situ stresses that are high relative to the strength of the formations or physico-chemical interactions of the drilling fluid with the shales.This paper describes fundamental concepts of mud pressure penetration and flow of water between the wellbore and formation due to their chemical potential difference, and associated mud support changes as the drilling fluid interacts with shales. Due to the low permeability of shales, the penetration of the drilling fluid filtrate would result in an increase in pore pressure over a considerable distance from the wellbore. This instability mechanism strongly depends on properties of the drilling fluid filtrate and pore fluid, and the rock material composition.In addition to mud pressure penetration, water would be induced to either flow into or out of the formation depending on the relative chemical potential of the drilling fluid and the formation. A more stable wellbore condition could be achieved by optimising the chemical potential of drilling fluids.Drilling fluid and shale properties required for the models, which are determined using analytical and laboratory techniques, are presented herein. The effects of the time-dependent mechanisms on wellbore stability are demonstrated for a polyacrylamide, an ester-based and an oil-based mud. The results demonstrate that a more effective mud support can be obtained by optimising the adhesion and viscosity of the drilling fluid filtrate, and chemical potential of the drilling fluid.

Thermodynamic analysis of the In-Ga-Sb system

The phase diagram and thermodynamic data for the In-Ga-Sb system are fit with a model for the III-V liquid phases, in which the enthalpy and excess entropy of mixing are quartic functions of the atomic fraction and the enthalpy of mixing is a quadratic function of temperature. The Gibbs energy, enthalpy, and entropy of formation of the III-V compounds are obtained as functions of temperature from the heat capacities and the standard enthalpy and entropy of formation at 298 K. The fits are quantitatively satisfactory and better than any hitherto obtained, particularly for the III-V liquidus lines and the ternary liquid. The partial pressures of Sb2 and Sb4 are calculated along the three phase curves of In1-uGauJSb(s), and relations given to obtain the relative chemical potentials of In and/or Ga are from these. The enthalpy of mixing of the III-V liquids is calculated for a few hundred degrees above the compound melting points, where presently there are no data. Characteristics of an improved model are postulated.

Hydrophobic or Micellar Behavior of 2-butyl and 2-pentyl-2-(hydroxymethyl)-1,3-propaneDiol in Water. Volumes and Osmotic Coefficients

n-butyl-2 and n-pentyl-2-(hydroxymethyl)-1,3-propanediol, named OT and NT, respectively, have been examined in aqueous solutions at 30, 40, and 50°C for NT and at 40°C for OT, using density and vapor pressure osmometry techniques. OT does not form true micelles but rather hydrophobic aggregates at the critical hydrophobic interaction concentration (CHIC). CHIC = 0.68 mol kg -1 for this compound. NT gives micellar association and the CMC has been determined at these temperatures. The values obtained are 0.247 (30°C) and 0.239 (40 and 50°C) mol kg -1 using density measurements, and 0.260 (30°C), 0.273 (40°C), and 0.276 (50°C) mol kg -1 using vapor pressure osmometry data. The volume changes during micellization are 3.81 (30°C), 3.74 (40°C), and 3.75 (50°C) cm 3 mol -1. The concentration dependence of properties such as the osmotic coefficient, the molal activity coefficient, the nonideal Gibbs energy of the solute, and the relative chemical potential are also studied in the temperature range explored. The aggregation numbers of NT micelles n = 11.7 (30°C), 12.0 (40°C), and 15.8 (50°C), with an accuracy ± 0.2, have been calculated using the phase-separation model. Results are discussed and compared to those obtained from the 1,2,3-alkane triol series.

Thermodynamics of Hydrogen Dissolved in Pd‐Tb and Pd‐Dy Alloys

AbstractThe thermodynamic parameters for absorption of hydrogen by Pd‐Tb alloys with up to 8.0 at.% Tb and Pd‐Dy alloys with up to 6.0 at.%. Dy have been determined from measurements of the pressure‐composition isotherms at temperatures between 273 K and 473 K and hydrogen pressures up to 100 Torr. The results are compared with those of previously determined palladium‐rare earth (RE = Sc, Y, Ce, Gd, Yb) alloys. The relative partial molar enthalpy of solution of hydrogen, ≈︁, at infinite dilution, and the standard enthalpy change, ΔH, for β‐hydride formation for both Pd‐Tb and Pd‐Dy alloys become more exothermic with increasing Tb and Dy contents. The relative chemical potential, Δμ, of dissolved hydrogen at infinite dilution at a given temperature in Pd‐RE alloys decreases with a decrease of apparent H—H attractive interaction energy with several exceptions. With the exception of Pd‐Ce alloys and some high solute metal content alloys, the stabilities of dissolved hydrogen at infinite dilution and β‐hydride phase for a series of Pd‐RE‐hydrogen systems are mainly governed by the lattice expansion of palladium by the substituent RE atoms which reduces the elastic strain energies necessary for hydrogen occupation of the octahedral interstices.

Calculating the helical twisting power of dopants in a liquid crystal by computer simulation.

The helical twisting power determines the pitch of the helical structure produced by introducing a given concentration of chiral dopant molecules to a nematic liquid-crystal phase. By using alternative, twisted, periodic boundary conditions, and measuring the relative chemical potentials of right- and left-handed dopants in a twisted nematic phase, we have succeeded in measuring this property by computer simulation of a simple molecular model. The technique should be generally applicable.

Thermodynamics of Micellar Systems: Volumes, Osmotic Coefficients, and Aggregation Numbers of a Homologous Series of 1,2,3-Alkane Triols in Water

Aqueous solutions of a homologous series of alkanetriols, from 1,2,3-hexanetriol to 1,2,3-nonanetriol, have been examined with different techniques, including density determination, freezing point depression, and vapor pressure osmometry. Their hydrophobic or micellar parameters were determined at different temperatures (0, 20, 30, and 40°C): volumes of monomers or micelles, volume changes during micelle formation, osmotic coefficient, activity of the solute and solvent, nonideal free energy of the solute, and relative chemical potential. 1,2,3-Hexanetriol does not form micelles and tends to form hydrophobic aggregates at 2.09 (20°C) and 1.80 (30°C) mol · dm -3. 1,2,3-Heptanetriol is a key compound since it is difficult to speak about clusters or real micellization at 1.03 (30°C) and 0.98 (40°C) mol · dm -3. 1,2,3-Octanetriol and 1,2,3-nonanetriol self associate in a manner similar to that of conventional surfactants. The CMCs respectively obtained are 0.370 to 0.320 mol · dm -3 (temperature range of 0 to 40°C) and 0.098 mol · dm -3 (40°C). Calculations using the phase separation model led to the following values for the aggregation numbers: 2.3 ± 0.2 for 1,2,3-hexanetriol, 7.6 ± 0.1 for 1,2,3-heptanetriol and 31.9 ± 0.1 for 1,2,3-octanetriol. The values directly obtained by freezing point depression (31.5 ± 1.8 ) or vapor pressure osmometry measurements (27.1 ± 0.9) at 40°C for 1,2,3-octanetriol show that the phase separation model is thus satisfactorily applied for this compound. The calculated free energy of the micelle formation agrees with published data for similar nonionic surfactants.

Activities of copper in the Y–Ba–Cu–O system

The vapor pressures of Cu in equilibrium with YBa2Cu3O6.24 were measured as a function of temperature by the Knudsen effusion method using a quadrupole mass spectrometer as the detector. The data were fitted to ln [P(Cu)/bar]=(−66104±4485)(1/T)+(35.360±3.869). The activity of Cu [in YBa2Cu3O6.24(s) ] was calculated as the ratio of the above equilibrium pressure divided by the vapor pressure of pure Cu(s). From the activities, relative chemical potentials were calculated. The vapor pressure of Cu from the superconductor intersects the vapor pressure of Cu from pure Cu(s) at 1290±20 K, which indicates that the superconductor decomposes to metallic Cu at temperatures greater than 1290 K.

Partial Pressures and Thermodynamic Properties of PbTe ‐ SnTe Solid and Liquid Solutions with 50, 70, and 100 Mole Percent SnTe

The partial pressures of , , and have been determined for solid solutions and their melts with , extending earlier studies. The partial pressures were determined from measurements of the optical absorbance between 250 and 700 nm of the vapor phase coexisting with a condensed phase or phases of known composition and temperature. Partial pressures were obtained for the Te‐saturated solid solutions as well as for one composition for that was inside the solid solution homogeneity range. For , the partial pressure of reaches a broad maximum of near 755°C for Te‐saturation and is about at the 851°C solidus temperature. The atomic percent of Te on the Te‐rich solidus line is 50.193 at both 581 and 851°C with an undetermined maximum at an intermediate temperature. The liquidus temperature is 870°C. For , the partial pressure of shows a broad maximum at near 737°C and is at the 834°C solidus temperature. With one exception, the chemical potential of Te relative to Te(l) for SnTe melts between 48.81 and 55.0 atom percent (a/o) Te agree within 7% at 827°C with published values obtained from EMF measurements of the relative chemical potential of Sn. The value for 48.81 a/o Te at 827°C obtained here is higher by 23%. The Gibbs energies of mixing of the solid solutions and their melts is calculated from the partial pressures of and and is close to, but within experimental error, distinct from that for ideal solutions.

Partial and integral molar thermodynamic properties of Ni xTe 1− x(s, x = 0.595 to 0.630) alloys

The vapour pressure of tellurium over non-stoichiometric Ni x Te 1− x ( x = 0.595, p) and ( x = 0.610, p 1) have been measured between 981 to 1150 K using a Knudsen-effusion mass-loss technique and can be represented by the equations: log 10 ( p kPa )±0.062 = 8.050 − 11706( K T ) , and log 10 ( p 1 kPa )±0.017 = 7.569−11944( K T ) . Using the vapour pressures of tellurium over tellurium metal the relative chemical potentials of Te in the two alloys were calculated. The molar Gibbs free energy of formation of the nickel-rich alloy Ni 0.630Te 0.370 was obtained by measuring tellurium pressures p 2 over biphasic (Ni + nickel-rich alloy) in the temperature range 1071 to 1188 K. The vapour pressures are given by the equation: log 10 ( p 2 kPa )±0.057 = 7.399 − 12303( K T ) , from which the standard molar Gibbs free energy of formation of the nickel-rich alloy was calculated to be Δ f G m o ( Ni 0.63Te 0.37, s , T)/ ( kJ·mol −1 )±0.21 = −22.29±0.00198( T K ) .

Ab initio theory of polar semiconductor surfaces. I. Methodology and the (22) reconstructions of GaAs(111).

A methodology is developed for the theoretical study of the polar surfaces of compound semiconductors. It is based on the calculation of the total energy in the context of density-functional theory in the pseudopotential approximation. The method is used to investigate the (2\ifmmode\times\else\texttimes\fi{}2) reconstructions of GaAs(111). Emphasis is given to the relative chemical potential, which plays a crucial role in determining the lowest-energy geometry for surfaces with different stoichiometries. The total-energy versus chemical-potential curves indicate that there are at least two stable reconstructions. We predict one to be an As-triangle geometry and the other the Ga vacancy.

Ab initio theory of polar semiconductor surfaces. II. (22) reconstructions and related phase transitions of GaAs(1-bar1-bar1-bar).

The (2\ifmmode\times\else\texttimes\fi{}2) reconstructions of GaAs(1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{}) are studied with use of a theoretical approach based on the calculation of the total energy in the context of density-functional theory and the pseudopotential approximation. New models are proposed for the As-rich and Ga-rich reconstructions. The relative chemical potential plays a crucial role in determining the lowest-energy configuration. The total-energy versus chemical-potential curves indicate the possibility of phase transitions between different configurations. One such transition concerning the experimentally observed (\ensuremath{\surd}19 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}19 ) reconstruction can be explained as an intermediate phase between the proposed low-energy (2\ifmmode\times\else\texttimes\fi{}2) reconstructions.

Role of chemical potentials in surface reconstruction: A new model and phase transition of GaAs(111)2x2.

The role of chemical potentials in surface reconstructions is examined and shown to be crucial for binary semiconductor srufaces such as GaAs(111)2\ifmmode\times\else\texttimes\fi{}2. We predict that under As-rich conditions a new model, the As triangle, is the lowest-energy geometry, whereas the Ga-vacancy model is appropriate for Ga-rich conditions. A change in the relative chemical potential of Ga and As should produce a phase transition between the two structures.

E.m.f. and calorimetric investigations on lead germanates

Relative chemical potentials of PbO in the univariant fields between the compounds Pb 5GeO 7, Pb 11Ge 3O 17, Pb 3GeO 5, Pb 5Ge 3O 11, PbGeO 3, and PbGe 3O 10 were determined by measurements of e.m.f. at 673 and 873 K. Enthalpies of solution of these compounds and of the pure oxides in aqueous alkaline tartrate yielded the enthalpies of mixing. After completing these results by heat-capacity determinations, the calorimetric and e.m.f. values of the partial molar enthalpy of mixing at 873 K could be compared. It was concluded from the discrepancy for Pb 11Ge 3O 17, that this compound exhibits a range of homogeneous composition variation expressed by Pb 11Ge 3−δO 17−δ. The enthalpies of formation from the oxide components are given by Δ ox H m/(kJ · mol −1): −(8.5 ± 5.6), Pb 11Ge 3O 17; −(21.6 ± 1.6), Pb 3GeO 5; −(48.0 ± 3.2), Pb 5Ge 3O 11; −(10.7 ± 0.8), PbGeO 3. The e.m.f. of the cell Ni/NiO/ZrO 2/PbO/Pb as well as the enthalpy of transformation of GeO 2(quartz → glass) were redetermined.

Thermodynamic and viscometric studies on the thermotropic phase-stability of cholesteryl myristate, palmitate, stearate, and oleate.

By means of differential scanning calorimetry and polarizing microscopy, the transition paths, temperatures, enthalpies and isopiestic heat capacities were measured for four mesogenic esters, i.e. cholesteryl myristate (ChM), palmitate (ChP), stearate (ChS), and oleate (ChO). By using the above-mentioned thermodynamic quantities, relative chemical potential diagrams were constructed to clarify the thermodynamic phase stability of each ester. The viscosity behavior of each ester was measured at various temperatures under various conditions : continuous heating and cooling as well as isothermal. The effect of thermal history before the isothermal measurements was also examined. On the basis of chemical potential and viscometric diagrams, the phase stability of each ester with or without the influence of shear in the viscometer is discussed. Each ester in cholesteric phase was estimated to behave as a continuum without shear, but as a swarm under shear. The nature of the peak or hump in the transtion region between isotropic and cholesteric phases is also discussed.

Differential scanning calorimetry study of polymorphism in cholesteryl oleate.

The phase transitions among various phases, i.e. crystalline (k), isotropic liquid (i), cholesteric (c) and smectic (s) phases, of cholesteryl oleate (ChO) were studied by using differential scanning calorimetry (DSC) and polarizing microscopy. We used two commercial samples of ChO and a gift with a known history of synthesis and purification. The transition temperatures, Ttr, and enthalpies, ΔtrH, of these samples were all in good agreement with each other. The DSC thermograms of k/i transition showed the coexistence of two kinds of crystals with a higher melting temperature (k1) and a lower one (k2) in k. By analysis of the thermograms, we determined the enthalpic and molar fractions of k1 in k, f1 and x1, respectively, which depend on the method and conditions of crystallization. Three types of crystallizing procedures, i.e. solvent evaporation, cooling of ChO solution in ethanol, acetone or 1-pentanol, and in situ crystallization in the DSC pan, were examined at various temperatures. At higher temperature, a higher value of f1 or x1 was obtained. Using the values of Ttr and ΔtrH at various transitions, we could draw the curves of relative chemical potential, μrel, of the k1, k2, i, c and s phases of ChO vs. temperature, The stability of various ChO phases and the thermodynamic nature of the transition paths are discussed on the basis of the above μrel diagram.