Determination of thermodynamic interaction parameters in solid V-Ti-Cr alloys using the mass spectrometer

The Knudsen effusion method was combined with a mass spectrometer sensing technique in order to determine thermodynamic interaction parameters of solid solution bcc alloys of V-Ti-Cr. A regular solution model was used to relate the vaporization data to ion current ratios obtained from the mass spectrometer. The temperature range of the vaporization experiments was 1400° to 1700°C, with alloy compositions ranging from 10 to 66 at. pct of each of the three components in the ternary system. Modified interaction parameters were calculated by assuming only binary interactions (which is a good approximation at low third component concentrations). The results are: Ω _TiV = 1.8 ± 0.2 kcal/g-atom; 0 <N _Cr < 0.2 ({iT} _AV = 1800 K) Ω _TiCr = 1.9 ± 0.4 kcal/g-atom; 0.1 <N _V < 0.4 ({iT} _AV = 1750 K) Ω _VCr = 3.1 ± 0.7 kcal/g-atom; 0.1 <N _Ti < 0.4 ({iT} _AV = 1850 K) A temperature dependent form was an appropriate refinement of the results for the Ti-Cr system from 1500 to 1840 K. That expression is $$\Omega {\text{ = 28 (1 - }}\frac{T}{{1840 K}}{\text{ kcal/g - atom}}$$ Overall, experimental results show important, but not complete, agreement with estimates from phase diagrams and theoretically calculated values.     

Determination of hydrogen pęrmeation parameters in alpha titanium using the mass spectrometer

The kinetic parameters of hydrogen permeation through α-Ti were determined from mass spectrographic measurements between 400° and 800°C and 0.004 and 2.0 torr H₂. The specimens were hollow cylinders and the hydrogen source was gaseous hydrogen. Hydrogen entered the specimen wall at the inside surface and emerged from the specimen at the outside surface. The permeated hydrogen flux is given byP = 1.6 × 10⁻⁵ p exp (-14,900 ± 856/RT) mole torr/s cm² where the hydrogen pressure isp and the permeation activation energy is 14,900 cal mole⁻¹ The surface dependent nature of hydrogen permeation in α-Ti is established in these experiments by the observations that 1) permeation is not proportional to the square root of input hydrogen pressure, 2) the concentration gradient calculated from experimental permeation data is lower than it would be if equilibrium solubility had developed, and 3) the diffusional frequency factor as determined under nonsteady-state conditions is low by a factor of three compared with values determined by others.     

Representation of thermodynamic properties of multi-component systems using interaction parameters

Integral excess free energy of a multi-component – ternary system has been expressed in terms of the Maclaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction parameters. The partial thermodynamic property of component 1 derived by the use of logarithmic functions together with a geometric progression is presented. The equation is found to be capable of interpreting thermodynamic data over a wide compositional range of the ternary system and is independent of compositional paths. An alternative approach for the determination of generalised relations between interaction parameters to that of Lupis and Elliott has been developed.     

Representation of thermodynamic properties of quaternary systems using interaction parameters

Integral excess free energy of a quaternary system has been expressed in terms of the MacLaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction coefficients. The derivation of the partial functions involves extensive summation of various infinite series pertaining to the first order and quaternary parameters to remove any truncational error. The thermodynamic consistency of the derived partials has been established based on the Gibbs-Duhem relations. The equations are used to interpret the thermodynamic properties of the Fe-Cr-Ni-N system.     

A thermodynamic study of solid Pd-Pt alloys

The vapor pressure of palladium over nine Pd-Pt alloys was measured by the torsion-effusion method. Calorimetric heat-of-solution measurements were carried out on specimens from the same alloys to derive the enthalpy of formation. The activities and partial and integral free energies at 1600°K, computed from the vapor-pressure measurements, were combined with the integral enthalpies at 298°K to determine the integral entropies, assuming Neumann-Kopp behavior. The activities and the free energies of formation exhibit very small negative deviations from ideal behavior. The enthalpies of formation are moderately negative over the entire composition range. The entropies of formation are positive but smaller than the ideal entropies at 1600°K. The thermodynamic results provide additional evidence for the existence of short-range order in the Pd-Pt system.     

Representation of excess thermodynamic properties of ternary systems using interaction parameters

A ternary function has been developed based on the Maclaurin infinite series, which is expressed in the neighborhood of each of the pure components of the system. Each of the series is subjected to various boundary conditions. The ternary function is based on the summation of these series. In the process of converting the terms of these infinite series to the corresponding infinite dilution constants and interaction parameters, the ternary function also distinguishes between the binary and ternary interaction parameters of the system. The truncation of the infinite series pertaining to the binary and ternary interaction terms is adjusted by a suitable technique which is described in the text. The function is thermodynamically consistent and capable of interpreting properties of the ternary system.     

High temperature thermodynamic properties of solid ta-w alloys

The partial molar and integral molar thermodynamic properties of solid Ta-W alloys have been determined between 1050 and 1300 K using galvanic cells with a thoria-based electrolyte. The activities in this system exhibit negative deviations from ideality, but the magnitude of the negative deviation is less than that observed previously for the Ta-Mo alloys. The negative excess free energies of mixing are due mainly to the enthalpies of mixing. The observed small negative excess entropies of mixing can be attributed to vibrational contributions and/or short range ordering in these alloys. Graduate Student, School of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, Pa. 19104, School of Metallurgy and Materials Science, University of Pennsylvania.     

A thermodynamic model of solid solutions and its application in solid alloys

Based on the free volume theory,lattice model,the Scatchard-Hildebrand theory,novel expressions of configuration partition function and excessive Gibbs free ene...     

Integral treatment for the representation of thermodynamic properties in multicomponent systems using interaction parameters

The partial thermodynamic functions of the solvent component of a ternary system have been deduced in terms of the interaction parameters by integration of several series which emerge from the Maclaurin infinite series based on the integral property of the system and subjected to appropriate boundary conditions. The series integration shows that the resulting partial functions are suitable for interpreting the thermodynamic properties of the system and are independent of compositional paths. In the present analysis, the higher order terms of these series are found to make insignificant contributions. Formerly Visiting Professor, Technical University Berlin     

The thermodynamic properties of solid Al−Mg alloys

By measurements of the electromotive force of reversible galvanic cells of the form Mg (solid)/MgCl₂ in fused LiCl/KCl eutectic/Mg _x Al _y (solid) between 370° and 550°C, values have been determined for the free energies, entropies, and heats of formation of all the solid phases of the Al?Mg binary alloy system. The aluminum-rich solid solution appears to be essentially regular with a small positive heat of formation, while the magnesium-rich terminal solution shows negative heats and entropies of formation. The intermediate phases β, γ, and ε all exhibit moderate negative heats and large negative excess entropies of formation; in the case of β and γ these properties pass through pronounced minima, at compositions within their homogeneity ranges, indicative of highly ordered stoichiometric conditions. The results are discussed in relation to known phase structures.     

On the thermodynamic behavior of cadmium in Te-saturated HgTe-CdTe and CdSe-CdTe solid alloys

The activity of cadmium in Te-saturated HgTe-CdTe and CdSe-CdTe alloys in the temperature range of 720 to 840 K was measured by an electrochemical technique using LiCl-KCl + 5 wt pct CdCl₂ as the molten salt electrolyte. From the electromotive force (emf), values measured at different temperaturesi the partial and excess molar thermodynamic quantities,viz., Δ G _Cd ^M ,Δ G _Cd ^XS ,Δ H _Cd ^M ,Δ S _Cd ^M andΔ S _XS ^Cd , have been calculated. From the activity data, the equilibrium vapor pressure of cadmium over the alloys have been estimated. The thermodynamic data obtained in the present investigation are consistent with the view that the HgTe-CdTe system consists of a single-phase field throughout the entire range of composition and with the structural changes in the CdSe-CdTe system. The results have been discussed in the light of Darken’s stability and excess stability parameters of the systems and physical properties,viz., energy gap and magnetic susceptibility.     

Mass spectrometric study of the thermodynamic properties of solid Au−Pt alloys

The ratios of vapor pressures of gold in equilibrium with liquid gold and with each of eleven Au−Pt alloys have been measured over the approximate temperature range of 1340° to 1520°K by means of a dual-chamber effusion cell and a mass-spectrometric detection system. From these ratios, thermodynamic activities and related integral and partial molar thermodynamic quantities have been evaluated at 1423°K. When the thermodynamic quantities are referred to a hypothetical standard state of superheated gold at 1423°K, the results indicate both substantial positive deviations from ideal behavior and positive molar heats of mixing as is expected for miscibility-gap systems. The integral moalr quantities are adequately predicted by either the subregular or the Lumsden model. Observed integral entropies are discussed in terms of thermal, electronic, and configurational contributions, whereas the positive integral molar free energies are tentatively attributed to strain effects arising from ion-core repulsions. R. W. Jones formerly Graduate Student, Northwestern University, Evanston, Ill. This research was supported by the Advanced Research Projects Agency through the Northwestern University Materials Research Center. Partial support for the mass spectrometer facility was provided by the U. S. Atomic Energy Commission, Document Code COO-1147-30.     

A self-consistent model for predicting interaction parameters in multicomponent alloys

Several models have been proposed to predict interaction parameters in multicomponent alloys from the physical characteristics of constituent elements. But all these models are not self-consistent, i.e., they do not meet the basic requirement of the reciprocal relation, ε _i ^j =ε _j ⁱ , automatically. In this article, a new and self-consistent model is proposed by coupling Chou’s geometric solution model with Miedema’s model on the enthalpy of mixing for binary alloys. The new model is applied to the calculation of interaction parameters in a large number of iron-based alloys, and the agreement between calculation and experimental data is found to be reasonable.     

A thermodynamic study of copper-iron and copper-cobalt liquid alloys by mass spectrometry

The thermodynamic activities in the liquid Cu-Fe and Cu-Co binary systems were measured by a high temperature mass spectrometric technique. From the obtained data, the heats of mixing in the Cu-Co liquid binary were calculated. Both the Cu-Fe and Cu-Co systems are thermodynamically similar, with large positive deviations from ideality in the activities. The activity coefficients in the liquid Cu-Co system at 1823 K were found to be symmetrical and can be expressed by lnγ_Cu= 1.76X _Co ² The heat of mixing in the liquid Cu-Co system was found to be described by a cubic function δH_m = −17.9 _Co ³ − 7.6X _Co ² + 25.5_Co (kJ/mol) The activity coefficients in the liquid Cu-Fe system at 1873 K were found to satisfy two quadratic formalisms in the binary In γ_Cu = 2.10X _Fe ² − 0.13 0.65 ≤X _Fe ≤ 1 In γ_Fe = 1.79X _Cu ² + 0.04 0 ≤X _Fe ≤ 0.65     

On the gibbs energy interaction parameters of oxygen and nitrogen in liquid alloys

A number of theoretical models reported in the literature for predicting the values of the Gibbs energy interaction parameters of oxygen and nitrogen in liquid alloys is briefly reviewed. The validity of these models is tested using the large number of experimental data available in the literature. It is found that the Wagner model together with the correlations proposed by Chang and coworkers predict values in best agreement with the experimental values. Formerly Graduate Research Assistant, Materials Department, College of Engineering and Applied Science, University of Wisconsin-Milwaukee     

Rapid tryptic mapping using enzymatically active mass spectrometer probe tips

A method has been developed for rapid, sensitive, and accurate tryptic mapping of polypeptides using matrix-assisted laser desorption/ionization time-of-flight mass analysis. The technique utilizes mass spectrometer probe tips which have been activated through the covalent immobilization of trypsin. The enzymatically active probe tips were used for the tryptic mapping of chicken egg lysozyme and the results compared with those obtained using either free trypsin or agarose-immobilized trypsin. A significant increase in the overall sensitivity of the process was observed using the active probe tips, as well as the production of more characteristic proteolytic fragments and the elimination of background signals due to the autolysis of the trypsin. Further, probe tip digestions were found to be rapid and convenient.     

Thermodynamics of binary systems using interaction parameters

A four-parameter equation for determining the excess integral property of a binary system is deduced based on the Maclaurin infinite series. The series is expressed separately in the neighborhood of each of the pure components of the system. The components are subjected to appropriate boundary conditions at the various stages of the treatment. The present form of the function is found to be capable of interpreting thermodynamic properties of several relatively weakly interacting binary systems based on the present equation. The infinite dilution parameters compare favorably with the values reported in the literature.     

thermodynamic properties of liquid Ag-Si alloys

The thermodynamic properties of silicon in liquid Ag-Si alloys in the range of 1100 to 1325°C have been measured by an electrochemical cell employing silica-saturated lithium silicate as the electrolyte. The range of composition studied is 0.015 <x _Si < 0.29. For the change in standard state from pure liquid silicon to silicon at infinite dilution with the composition in atom fraction: Si(I) = Si (inf. dil.): △G° = 5,000 + 5.47T, (J/g-atom) The results of the study are in good agreement with the measurements on the phase diagram by Hager. Member of AIME; Visiting Scientist, Mass.(1969)     

Calculation of thermodynamic parameters of 75 gaseous PCDDs using the density functional theory

In this paper, the thermodynamic parameters are calculated for all gaseous Poly Chlorinat Dibenzo-p-dioxins （PCDDs） using the Density Functional Theory （DFF） method and both the enthalpy of formation （ΔfH^0） and Gibbs free energy of formation （Δf G^0） are derived, from which the order of stability of individual congeners is then predicted. All these properties, together with the calculated entropies （ S^0） and heat capacities （ Cp）, are presented as a function of the number of chlorine atoms in the various PCDD molecules. The accuracy of the method used here, is evaluated by comparing the thermodynamic parameters of gaseous chlorobenzenes with experimental values collected from literature.