Rainer Schmid

Bio: Rainer Schmid is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topics: Gibbs free energy & Liquidus. The author has an hindex of 5, co-authored 5 publications receiving 379 citations.

Thermodynamic analysis of the iron-copper system I: The stable and metastable phase equilibria

Abstract: Thermodynamic and phase diagram data in the Fe-Cu system are evaluated. For the liquid and fcc phases, the Margules-type of equations is used. For the bcc phase, the same type of equation is used to describe the non-magnetic contribution to the Gibbs energy. In addition, a magnetic term is included. Using the thermodynamic equations derived from equilibrium data, the stable and metastable equilibria of this system are calculated. Agreement between the calculated and experimental phase diagram is good except for temperatures higher than 1720 K. For these temperatures, the calculated liquidus tends to be higher. The possibility of supercooling which may account for some of the lower temperatures measured should not be excluded. The calculated metastable miscibility gap of the liquid phase also agrees with the experimental data.

A thermodynamic analysis of the Cu-O system with an associated solution model

Abstract: An extension of the associated solution model is developed and applied to the Cu-O liquid phase Associated species “Cu2O” in the liquid solution are assumed, which interact with the surrounding free Cu and O atoms All thermodynamic properties and the phase diagram calculated from this model are in good agreement with the experimental information The success of this mathematical description is, of course, no proof for the physical existence of associated species A consistent set of thermodynamic data of the various solid, liquid, and gaseous phases is given by this comprehensive evaluation In addition, linear approximations for the Gibbs energies of reaction of formation and the interaction coefficients are offered A metastable liquidus of the compound CuO at elevated pressure is predicted, the congruent melting point being 1228 °C at δC atP O 2 = 244 atm (247 MPa)

Magnetic contributions to the thermodynamic functions of alloys and the phase equilibria of Fe-Ni system below 1200 K

Abstract: A generalized approach is proposed to calculate the magnetic contribution to the thermodynamic functions of alloys. This approach is applied successfully to the Fe-Ni binary system. The predicted magnetic specific heat of the fcc phase at 75 at. Pct Ni is in agreement with the experimental data within the accuracies of the data and the predicted values. The magnetic contributions to the Gibbs energies of the fcc and bcc phases for the Fe-Ni alloys obtained from this approach are added to the nonmagnetic portion of the Gibbs energies. The nonmagnetic portion of the Gibbs energy of the fcc phase is obtained from extensive thermochemical data at high temperatures as discussed in the paper immediately following this one. The total Gibbs energies of the fcc, bcc, and the orderedγ′-(FeNi3) phases are then used to calculate/predict phase equilibria of the Fe-Ni binary at temperatures lower than 1200 K. The calculated equilibria are in agreement with available experimental data. In addition, a irascibility gap of the fcc phase at low temperatures is predicted, resulting in the formation of a monotectoid equilibrium at 662 K as given below: {fx1361-02} The existence of the miscibility gap is due to the magnetic Gibbs energy term of the fcc phase which is composition dependent. Experimental results reported in the literature support the predicted miscibility gap.

Magnetic contributions to the thermodynamic functions of pure Ni, Co, and Fe

Abstract: An empirical mathematical equation is proposed for the magnetic contribution to the specific heat of pure metals The corresponding functions for enthalpy, entropy, and Gibbs energy are of simple form Two parameters used for each element are the critical temperature,Tc, and the total magnetic entropy The parameters have been determined from a careful separation of magnetic and nonmagnetic contributions to the specific heat Debye temperatures for Ni, Co, and Fe have been determined considering data to much higher temperatures than other studies The magnetic specific heats extracted from experimental data agree very well with the proposed equation over the entire temperature range and for all three elements Comparisons with different mathematical functions found in the literature give agreement only for the case of iron The total magnetic entropy given by a classical relation is found to be high, and a quantitative correction is given Various magnetic standard states are discussed The lattice stabilities of bcc- and fcc-iron are calculated assuming that the difference of the nonmagnetic specific heats is linear from 500 K to 1810 K A simple equation is obtained in which the anomalous temperature dependence is explained by the independently determined magnetic contribution The calculated values agree very well with Orr and Chipman’s assessment The stability of bcc iron at low temperatures is quantitatively rationalized

A thermodynamic study on an associated solution model for liquid alloys

Abstract: Liquid alloys with a rapid increase of component activities over a narrow composition range may be modelled by an associated solution model. Associated species with a fixed stoichiometry in that composition range are postulated in equilibrium with elemental species. Palrwise interactions among all species are described by Margules-type equations. The success of this description is, of course, not a verification of the physical existence of associated species. The thermodynamic background of this model is investigated in this study. For binary liquid alloys, the key equations governing the calculation of activities in internal equilibrium are presented graphically. Formulae for the calculation of the Gibbs energy, enthalpy and entropy of mixing in the postulated species-system are developed and related to the corresponding effects in the binary liquid alloys. The formation of very asymmetric and twin miscibility gaps is discussed. The difference between the Gibbs energy of species and real alloys at stoichiometry is pointed out. Limiting cases of weak and strong association are discussed and formulae for terminal values of activity coefficient and partial enthalpy of solution are developed. Structural related properties of Sn-Te liquid alloys are calculated and compared to experimental data. A quantitative prediction of data in ternary and multicomponent alloys is one major motivation for the precise description of binary alloys and a suitable extension of the associated solution model is presented. The model is compared to other associate models and to sublattice models. Despite the different physical picture, close phenomenological and mathematical resemblance is discovered among the associated solution and the sublattice model.

Liquidus relations in Y–Ba–Cu oxides

Abstract: The liquidus relations in the system YO1.5–BaO–CuOx in air in the compositional region near the superconducting oxide YBa2Cu3Ox were studied by differential thermal analysis, x-ray diffraction, electron microprobe analysis, and visual observation. The temperatures of 11 invariant points and the corresponding reactions were determined. YBa2Cu3Ox was found to melt incogruently at 1015 °C to Y2BaCuO5, which in turn melts incongruently to Y2O3 at 1270 °C. These reactions mean that preparing the superconducting phase by melting and rapid cooling will result in the presence of these two phases as well. The peritectic reaction YBa2Cu3Ox + CuO⇉Y2BaCuO5 + liquid at 940 °C accounts for the observation of partial melting, improved synthesis purity, and grain growth at temperatures of 950 °C. The determination of these invariant temperatures and reactions provide insight into optimal processing conditions.

A revision of the Fe-Ni phase diagram at low temperatures (<400 °C)

Abstract: The low-temperature Fe-Ni phase diagram was assessed experimentally by investigating Fe-Ni regions of meteorites using high resolution analytical electron microscopy techniques. The present phase diagram differs from the available experimental phase diagram based on observations of meteorite structure, but it is consistent with the available theoretical diagram in that α/Ni3Fe equilibrium was found at low temperatures. The a phase containing 3.6 wt.% Ni is in local equilibrium with the γ′ (Ni3Fe) phase containing 65.5 wt.% Ni, while the γ′' (FeNi) phase is present as a metastable phase. The new phase diagram incorporates a monotectoid reaction (γ1 → α + γ2, where (γ1 is a paramagnetic fcc austenite, a is a bcc ferrite, and γ2 is a ferromagnetic fcc austenite) at about 400 °C, a eutectoid reaction (γ2 → α + γ′) at about 345 °C, and a miscibility gap associated with a spinodal region at low temperatures. The miscibility gap is located between 9.0 and 51.5 wt. % Ni at ∼200 °C. The new low-temperature Fe-Ni phase diagram is consistent with all the phases observed in the metallic regions of meteorites.

Thermodynamic and magnetic properties of metastable FexCu100−x solid solutions formed by mechanical alloying

Abstract: Metastable solid solutions of Fe and Cu, which are immiscible in equilibrium, have been formed using high-energy ball milling of elemental powder mixtures. Single-phase face-centered-cubic (fcc) solid solution was obtained for 0