IN view of the interest attaching to the vaporisation and diffusion of solids, the following observations may be worthy of record.

The Diffusion of Solids

https://geosci.uchicago.edu/~grossman/EG2000GCA.pdf

Condensation in dust-enriched systems

https://link.springer.com/content/pdf/10.1007%2FBF02667204.pdf

The Fe-Ni (iron-nickel) system

Phase diagram calculation: past, present and future

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.

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

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.

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

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 alloys and the phase equilibria of Fe-Ni system below 1200 K

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

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

A quasi-subregular solution model is used to describe the thermodynamic properties of the liquid phase; values of the solution parameters are obtained from extensive and consistent thermochemical data reported in the literature. For the fcc and bcc phases, the same model is used to account for the nonmagnetic part of the Gibbs energy and the magnetic contribution is taken from the previous paper. Again, the values for the quasi-subregular solution parameters for the fcc phase are obtained from extensive and consistent thermochemical data reported in the literature at high temperatures. The values of the solution parameters for the bcc phase are obtained from the thermodynamic values of the liquid and fcc phases and the known phase boundary data. The calculated phase equilibria are in good agreement with the available data. Based on the thermodynamic data, the metastablel + γ andl + δ phase boundaries as well as theT
 0
 (γ + l) andT
 0(δ +l) curves are calculated.

A thermodynamic analysis of the phase equilibria of the Fe-Ni system above 1200 K

The high-temperature thermodynamic data and phase equilibria of the FeCr binary reported in the literature are assessed. A set of thermodynamic values for the liquid, bcc and fcc phases are obtained. These values are internally consistent and the calculated phase equilibria are in agreement with the measured phase boundary data. Metastable equilibria for the liquid and fcc phases are also calculated.

Ying-Yu Chuang

Papers

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

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

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

A thermodynamic analysis of the phase equilibria of the Fe-Ni system above 1200 K

A Thermodynamic description and phase relationships of the FeCr system: Part II the liquid phase and the fcc phase