Partial Quantities Research Articles

Thermodynamic Behavior of Impurity Atoms in α‐Range Alloys of the Noble Metals and Nickel

AbstractThermodynamic data for dilute α‐range alloys are necessary to understand atomic migration. Such data, however, are very scarce in the literature and contradict each other in many cases. A comparison is presented between the results of different experimental techniques particularly designed to measure partial thermodynamic quantities at low impurity concentrations. The results for I‐B‐noble metals alloys are surprisingly uniform and indicate an electronic origin of the dependence of the excess potentials on concentration, if the impurity atom has the same ion core as the host metal. If the impurity atom exhibits a much different ion core, a minimum in the excess chemical potential becomes observable at low concentrations. The reason could be either a size misfit or a dependence of the excess functions on the atomic mass. The viewpoint of the mass dependence is corroborated by results in the Ag–As‐system, which is characterized by almost no size misfit but a different atomic mass, and some recent measurements in Nickel‐alloys.

Thermodynamic properties of nonstoichiometric urania-gadolinia solid solutions in the temperature range 700–1100° C

Partial molar thermodynamic quantities for urania-gadolinia solid solutions of compositions U 1−yGd yO 2+x , with y values of 0.04 to 0.27, have been obtained using a solid electrolyte galvanic cell technique. The measurements were made for O/M ratios ranging from near stoichiometry to 2.20, and for temperatures ranging from 700 to 1100°C. The results for pure UO 2+ x are in accordance with data reported earlier. The oxygen potentials for U 1−yGd yO 2+x are higher than for pure UO 2+x and increase positively with increasing Gd content or excess oxygen. They can be represented as a function of the mean U valence, except at the stoichiometric composition. Both the partial molar entropy and enthalpy increase negatively with increasing Gd content or excess oxygen.

Energy Evaluation Method of Grain Drier (II) Minimum energy required for grain drying and partial quantities of grain moisture

Energy Evaluation Method of Grain Drier (II) Minimum energy required for grain drying and partial quantities of grain moisture

Prediction of excess gibbs energy and excess enthalpy on the basis of non-analytical solution-of-groups concept

New possibilities on how to employ the Solution-of-Groups concept predicting excess Gibbs energy and excess enthalpy have been presented here. On the basis of the Solution-of-Groups concept a procedure has been proposed by means of which excess functions can be directly recalculated from one system to another. To apply this procedure the energy parameters of group interactions do not have to be adjusted nor is any particular equation or model needed to describe group contributions. The two prediction methods suggested, i.e. the method of combination of excess functions and that of corresponding partial quantities, utilize experimental information from a related system and some geometrical characteristics of the components in question. Using a given simple criterion, cases are defined in which these methods can be used. The relations derived generally have been successfully applied to a large number of binary systems containing n-alkane and/or n-alkylhomolog. Predictions of ternary systems have been tested too, but the applicability of the methods presented is somewhat limited in this direction.

A thermochemical study of the phase reaction [formula omitted

The heat of reaction and equilibrium pressure for the oxidation reaction TbO 1.5+x + ( 3 28 − x 2 ) O 2 → ( 1 7 ) Tb 7 O 12 have been measured by means of a Tian—Calvet-type calorimeter and a thermal balance. The results of the weight measurement show a reproducible hysteresis loop. The heat of reaction has been measured along the oxidation branch of the hysteresis loop. The partial molar enthalpy indicates four distinct compositional regions. First, the TbO 1.5+ x region which can be described in terms of a point defect model and strong interaction between neighboring excess oxygen atoms. Second, the region between TbO 1.54 and TbO 1.61 is interpreted as the intrinsic hysteresis region and discussed in terms of the regular solution model. Third, the region between TbO 1.61 and TbO 1.70 is recognized as a pseudophase region. Fourth, a region of ι phase exists in which the partial thermodynamic quantities can be compared with those of CeO 1.714, PrO 1.714, and TbO 1.714. The partial molar enthalpy was also measured for a scanning loop which is also interpreted in terms of the four regimes.

Volume effects in the thermodynamics of ternary austenites

Elastic measurements have been made as a function of temperature and composition on a series of Fe-based substitutional solid solutions containing Mn, Ni and Cr. These data have been used to calculate the degree of error involved in applying statistical models to ternary carbon or nitrogen austenites when such models ignore the dilation of the substitutional lattice as a function of its composition. The results show that the error in the partial thermodynamic quantities and in the isothermal variation of the activity of the interstitial species with composition is of the order of scatter found in experimental thermodynamic data measured at constant pressure.

Macroscopic Equations for a Multicomponent Plasma

AbstractFrom the balance equations for partial quantities we derive equations for lumped quantities, e.g. a generalized Ohm's law. They are especially useful for a three‐component system (electrons, one species of ions and neutral particles). Certain conditions are derived and investigated to describe a plasma with more than three components by the lumped quantities.

Reaction of hydrogen with the high temperature (C14) form of TiCr 2

At −78 °C the high temperature (C14) form of the intermetallic compound TiCr 2 will react directly and reversibly with hydrogen to form two non-stoichiometric hydride phases having the nominal compositions of TiCr 1.9H 2.5 and TiCr 1.9H 3.5. The lower hydride phase is more stable than the higher. Standard free energies of formation of these phases at −78 °C are − 1.29 ± 0.04 and + 2.76 ± 0.02 kJ (g atom H 2 2) −1 with corresponding plateau pressures of approximately 0.2 and 30 atm. Relative partial molal thermodynamic quantities are also given for several other hydrogen compositions. At room temperature pressure-composition isotherms and X-ray diffraction data indicate the absence of any hydride phases: the starting (C14) intermetallic simply undergoes a lattice expansion with increasing hydrogen content without phase or structural changes. The critical temperature for the first miscibility gap region is approximately +15−20 ° C. Hysteresis is also absent in this intermetallic-hydrogen system.

Calorimetry within Hysteresis Loops of Metal/H Systems: Application to Pd/H

AbstractIt was suggested many years ago by Carl Wagner that if H2 is added to Pd/H whilst the system is on a desorption pressure plateau within the two solid phase coexistence region, H2 dissolves in both solid phases without formation of additional β‐phase. Similar considerations apply for the removal of H2 whilst on the absorption pressure plateau. This model, which has not been previously verified, has been confirmed in this research by calorimetric measurements of the enthalpies of scans between branches of the hysteresis loop for well‐annealed Pd samples. The experimental enthalpies lie between the values which correspond to the solution of H2 in each of the two pure coexisting solid phases. Besides confirming Wagner's suggestion, the calorimetric measurements described here provide a means to obtain partial thermodynamic quantities for the coexisting pure phases which may be difficult to obtain directly. — Values of the change of chemical potential of dissolved hydrogen with total hydrogen content, nt = H to metal, atom ratio, have been measured for scans from one branch of the hysteresis loop to the other. These values are consistent with the model and the experimentally determined enthalpies of solution. They demonstrate that relatively more H2 enters (or leaves) the β‐phase than the α‐phase during hysteresis scans.

Solid-state electrochemical studies of the mixed conductor Cu xMo 6S 8−y. II: Equilibrium partial thermodynamic properties

The equilibrium emf of the cell Pt/Cu/copper electrolyte/CuxMo6S7.59/Pt has been measured as a function of x and temperature. The resulting values of copper chemical potential, partial enthalpy, and partial entropy are compared with values calculated on the basis of a simple model which takes into account the distribution of copper between two types of site as well as the electronic configuration. There is a broad correspondence between experiment and theory, indicating that the configurational terms are the most important in determining the changes in partial quantities with composition, but more sophisticated treatments would be required to explain the detailed behavior.

Effect of complex-forming crown ethers on the micelle formation of sodium decanoate at 25°C

The effect of complex-forming macrocyclic polyethers, crown ethers, on micelle formation of sodium decanoate was investigated at 25°C. The effect of 12-Crown-4, 15-Crown-5, and 18-Crown-6 on the CMC for NaC 10 was determined by ultrasound measurements, and it was found that these crown ethers decrease the CMC. From EMF measurements the fraction of associated counterions to the micelles, β, has been determined. The results obtained for β have been interpreted in terms of partial association of Na +-crown ether complexes to the micelles. Partial molal volumes and compressibilities for NaC 10 in solutions containing crown ethers were determined by density measurements and ultrasound measurements, respectively. It was found that 12-Crown-4, which does not form complexes with Na + ions, has only a small effect on these quantities. The other crown ethers increase the partial molal quantities both below and above the CMC. These results have been interpreted in terms of complex formation below the CMC and association of Na +-crown ether complexes to the micelles above the CMC.

The effect of alcohols on the change in partial molal volumes and compressibilities at micelle formation of sodium decanoate at 25°C

The effect of methanol, ethanol, 1-propanol, and 2-propanol on the change in partial molal volume, ΔV m , and compressibility, Δκ s m , during micelle formation of sodium decanoate has been determined at 25°C. Partial molal volumes were determined from density measurements, and partial molal compressibilities were determined from ultrasound measurements. It was found that both ΔV m and Δκ s m had a maximum in the concentration range 1–3 m alcohol, and then decreased rapidly on further addition of alcohol. These results have been interpreted from changes in the separate values of the partial molal quantities of the surfactant in the singly dispersed state and in the micellar state, respectively. The effect of the alcohols on the CMC at 25°C has been determined by conductivity measurements. It was found that the CMC decreases with increasing concentration and chain length of the alcohol. The fraction of associated counterions, β, has been determined by EMF measurements, and it was found that ,β decreases upon alcohol addition. This result has been interpreted from the reduced surface charge of the micelles caused by the alcohols.

Partial molal volumes and compressibilities of sodium-alkylcarboxylates, disodium-alkyldicarboxylates, and N-diols in micellar solutions of sodium-alkylcarboxylates at 25°C

Partial molal volumes and compressibilities of sodium-alkylcarboxylates, disodium-alkyldicarboxylates, and n-diols in micellar solutions of sodium-alkylcarboxylates have been determined at 25°C. The partial molal volumes were determined from density measurements, and the partial molal compressibilities were determined from ultrasound measurements. The obtained partial molal quantities for n-diols are similar to those in liquid hydrocarbon. The corresponding quantities for the alkylcarboxylates and alkyldicarboxylates are higher than those in water, but smaller than expected if these molecules were completely solubilized in the micelles. The degree of solubilization for these molecules has been discussed. From the obtained partial molal volumes and compressibilities additivity relations for group partial molal quantities in the micellar phase have been established.

Theory and practice of a powerful technique for electrochemical investigation of solid solution electrode materials

The theory and practice of a solid-state electrochemical technique which allows measurement of the chemical diffusion coefficient and partial conductivities of the mobile species in a mixed ionic-electronic conductor, as well as the equilibrium partial thermodynamic quantities, are described. The theory incorporates nonideal thermodynamic behavior of the carriers as well as cross terms in the flux equations. Once the cell is assembled, all parameters can be measured as a function of composition without any further physical manipulation, so that the experiments are well suited to automatic control.

Partial molal volumes and compressibilities of n-alcohols in micellar solutions of sodium alkylcarboxylates

The partial molal volumes of n-alcohols (C 3C 10) in micellar solutions of sodium dodecanoate, sodium decanoate, and sodium octanoate have been determined at 25°C by density measurements. From ultrasound measurements the partial molal compressibilities of the alcohols in the micellar solutions have been determined. The partial molal volumes and compressibilities of the alcohols in micellar solutions are higher than those in water and are similar to the partial molal quantities for the liquid alcohol. The partial molal volumes and compressibilities decrease with increasing chain length of the surfactant and with increasing surfactant concentration. The same trend has been found for the corresponding quantities for liquid alcohols, and the results have been interpreted by comparing the interior of the micelles to liquid alcohols.

Thermodynamic properties of the mercury-uranium system

The mercury vapor pressure and e.m.f. data obtained in this investigation were combined with literature data to arrive at a consistent set of thermodynamic quantities for the mercury-uranium system. At 725 °C (998 K) the compound UHg x ( x ≈ 1.0) decomposes to UHg 2 and β-uranium. DTA data were employed to estimate the heat of reaction and to derive the free energy of formation of this compound. The free energy of formation (in joules) for the compounds in this system is given by the equations: ΔG°(UHg) = −27 585+ 19.94 T T<942 K ΔG°(UHg 2) = −52 720 + 37.59 T (548 – 853 K) ΔG°(UHg 3) = −63 555 + 46.76 T (433 – 684 K) ΔG°(UHg 2) = −78 010 + 66.42 T (388 – 683 K) Relations for the relative partial molal quantities for mercury and uranium in the various two-phase regions are derived. These data are reasonably consistent with the revised phase diagram.

Partial molal volumes and compressibilities of n-alkanes in aqueous solution of sodium-octanoate and sodium-decanoate

Partial molal volumes and compressibilities have been determined for n-alkanes (C 7C 10) in aqueous solution of sodium-octanoate and sodium-decanoate at 25°C. These quantities have also been determined for the pure liquid alkanes. The partial molal volumes and compressibilities were determined by density measurements and ultrasound measurements, respectively. The partial molal volumes and compressibilities of the alkanes in the surfactant solutions are higher than those in water, especially the compressibilities, and resemble the partial molal quantities of the liquid alkanes. The partial molal volumes are almost independent of the chain length and the concentration of the surfactant. The partial molal compressibilities decrease slightly with decreasing chain length of the surfactant and with increasing micellar concentrations. These results have been interpreted from differences in the hydration and the structure of the micelles.

Volumes and heat capacities of benzene derivatives in water at 25°C: Group additivity of the standard partial molal quantities

Differences in densities and heat capacities per unit volume were measured in water with a flow densimeter and a flow microcalorimeter for a series of substituted benzene compounds in water at 25°C. Apparent molal volumes and heat capacities were calculated from the data, and, by extrapolation to infinite dilution, the standard partial molal quantities were dervied. An additivity scheme is proposed to obtain the group contribution to these systems. The standard partial molal volumes and heat capacities of rather complex aromatic molecules in water can be predicted inside about 1 cm3 mol−1 and 10 J K−1 mol−1. The values of the volumes and heat capacities of groups adjacent to an aromatic ring are not the same as those on an aliphatic molecule but a simple relation exists between both sets.

Reaction of hydrogen with the low-temperature form (C15) of titanium-chromium (TiCr2)

At -78/sup 0/C the low-temperature form (C15) of the intermetallic compound TiCr/sub 2/ will react directly and reversibly with hydrogen to form two nonstoichiometric hydrides having the nominal compositions of TiCr/sub 1/ /sub 8/H/sub 2/ /sub 6/ and TiCr/sub 1/ /sub 8/H/sub 3/ /sub 6/. Both hydride phases are very unstable having, at -78/sup 0/C, dissociation pressures of approx. 2 and approx. 50 atm, respectively. Relative partial molal quantities for the formation of both hydrides are given. At room temperature, x-ray diffraction data indicate the existence of only one, highly nonstoichiometric hydride, TiCr/sub 1/ /sub 8/H/sub x/, where 2.1 < x < 3.6. This phase is orthorhombic with the lattice parameters varying slightly with hydrogen content. For a composition corresponding to TiCr/sub 1/ /sub 8/H/sub 3/ /sub 42/, a = 7.30, b = 5.18, and c = 4.94 A.

Apparent molal volumes and adiabatic compressibilities of ethylene glycol derivatives in water at 5, 25, and 45�C

Density and ultrasonic velocity measurements were made on a series of dilute equeous solutions of H(OCH2CH2)nOH, CH3(OCH2CH2)nOCH3, H(CH2)nOCH2CH2OH (n=1−4), and poly(ethylene glycol) at 5, 25, and 45°C. The additivity of the limiting partial molal volumes (\(\bar V{}^o\)) and adiabatic compressibilities (\(\bar K{}^o\)) for CH2 and CH2CH2O groups was tested by using the observed\(\bar V{}^o\) and\(\bar K{}^o\) values of the solutes. The\(\bar V{}^o\) and\(\bar K{}^o\) values of the CH3, CH2, CH2CH2O, and CH2OH groups were estimated and discussed in relation to hydration effects. The\(\bar V{}^o\) and\(\bar K{}^o\) values of alkoxyethanols calculated on the basis of the additivity of the group partial molal quantities were in good agreement with the observed values. The behavior of the limiting partial molal isothermal compressibility of alkoxyethanols was similar to that of the adiabatic compressibility.