John Chipman

Thermodynamics and phase diagram of the Fe-C system

A critical review of published data provides a fairly accurate knowledge of the thermodynamic properties of all of the phases of the system Fe-C that are stable or metastable at atmospheric pressure. Selected data are shown as tables and equations. A proposed phase diagram differs only slightly from others recently published but has the following features. Peritectic compositions and the α-γ equilibrium are shown to agree with measured values of the activity of iron in the solid and liquid solutions and the thermodynamic properties of pure iron. Of all the reported carbides of iron only two may be studied under equilibrium conditions. The solubilities of cementite and of χ-carbide in α-Fe are deduced from measured equilibria. Both are metastable at all temperatures with respect to graphite and its saturated solution in iron. The χ-carbide becomes more stable than cementite below about 230° Certain published data on ε-carbide permit an estimate of its free energy as a precipitate during the aging process.

Thermodynamics of the Fcc Fe−Ni−C and Ni−C alloys

The activity of carbon in the fcc solid solution of the Fe−Ni−C system has been measured at 800°, 1000°, and 1200°C by comparison with observed values in the Fe−C binary by equilibration with methane-hydrogen mixtures. Defining the lattice ratiozC≡nC/(nFe+nNi−nC), the activity coefficient ΨC≡aC/zC has been determined as a function of temperature and composition. At infinite dilution log ΨC goes through a maximum at about 70 pct Ni in agreement with Smith. The partial molar free energy of carbon in the dilute solution referred to graphite is not a linear function of the base alloy composition, but has a large deviation with maximum at about 60 pct Ni. Similar maxima occur in both ΔHC° and ΔSC°. Linear equations are derived for the activity coefficient of carbon in three composition ranges of Fe−Ni−C alloys; a simplified equation applicable to nickel steels is included. The solubility of graphite in nickel has been determined. The marked deviation from linearity is ascribed to the existence of iron atoms in two electronic states, γ1 and γ2 which differ in energy and are antiferromagnetic and ferromagnetic, respectively.

Activity of carbon and solubility of carbides in the FCC Fe-Mo-C, Fe-Cr-C, and Fe-V-C alloys

The activity of carbon in austenitic Fe-Mo-C, Fe-Cr-C, and Fe-V-C alloys has been studied by equilibration with controlled CH4-H2 atmospheres at temperatures in the range 850° to 1200°C. The observations included a number of compositions in the two-phase fields, γ + carbide. Equations are given for the activity coefficient of carbon as a function of temperature and composition in the austenite field and from these the other thermodynamic properties of the solution may be computed as desired. The phase boundaries γ/γ + carbide were determined by breaks in the isoactivity lines. This was supplemented in the case of Fe-Mo-C alloys by metallographic linear analysis of equilibrated samples. The results confirm certain published phase diagrams and discredit others.

Activity of silicon in liquid Fe-Si and Fe-C-Si alloys

Abstract Experimental data are presented which establish the solubility of graphite at temperatures of 1290–1690°C in Fe-Si-C solutions up to 20–24 weight per cent Si. The occurrence of βSiC as a stable equilibrium phase is established and its solubility in graphite-saturated iron is determined at temperatures of 1200–1690°C. The distribution of silicon between the immiscible liquids iron and silver has been studied in the composition range NS1(Fe) = 0.15−0.55 and in similar solutions containing substantial additions of carbon. The experimental data, together with a large amount of collateral information in the literature, are used to establish the following thermodynamic properties of the solution: the heat of mixing and partial molal enthalpies of the components in Fe-Si solutions; the activities of Si and Fe in the binary solutions at temperatures of 1420–1700°C; the molal heat, free energy and entropy of mixing at 1420°; the activities of Si and Fe in graphite-saturated solutions at silicon concentrations from zero to SiC saturation at temperatures of 1420–1700°C. The results are cross-checked by calculations based on free-energy and equilibrium data for SiC and SiO2 and are compared wherever possible with published information. Close agreement in these cases and with related data on Fe-C solutions promotes confidence in the tabulated results.

Thermodynamics of the carbides in the system Fe-Cr-C

Phase relations in the Fe-Cr-C system in the temperature range 900 to 1150°C have been studied using metallographic and X-ray methods and the electron microprobe. An isothermal section of the phase diagram at 1000°C is shown. Lattice dimensions of the three carbides were determined for several values of the ratio Cr:(Fe +Cr). The solubilities of the carbides at each temperature were determined by metallographic study of quenched specimens. The distribution of Cr between austenite (γ) and the several carbides was determined by use of the electron microprobe. Data of Wada et al on the activity of carbon were used to calculate activities at the y-phase boundary and the free energy of the several carbides as a function of their chromium content. The data are treated thermodynamically on the basis of assumed random mixing of Cr and Fe atoms in each carbide. While this randomness was not definitely proved, the assumption was shown to be reasonable and the results useful. Extrapolation to 0 and 100 pct Cr gives values for the standard free energy of Cr7C3 and the hypothetical carbides Cr36C, and Fe7C3.

Thermodynamics of austenitic Fe-C alloys

New data on the activity of carbon in austenite have been obtained by CO2/CO equilibration of Fe-C alloys in the temperature range 900° to 1400°C. Equations for the thermodynamic properties of carbon and iron in austenite are obtained from the data combined with selected data from the literature. A slightly modified phase diagram is presented. The stability of cementite is also determined from data published earlier and the results of the present study. Parameters of the various models of the behavior of carbon in austenite taken from the literature are also calculated from the data.

Thermodynamics of the fcc Fe-Mn-C and Fe-Si-C alloys

The activity of carbon in austenitic Fe-Mn-C and Fe-Si-C alloys has been studied by equilibration with controlled CH4-H2 atmospheres at temperatures in the range 848° to 1147°C and for composition up to about 60 pct Mn and 7 pct Si. The activity coefficient of carbon is diminished by manganese and is increased by silicon. Activity coefficients and derived values of the partial molar free energy, enthalpy, and entropy of solution of graphite in the alloy are expressed in mathematical form. The heat of solution of graphite, which is positive in the Fe-C binary alloys, decreases with increasing manganese and increases with increasing silicon concentrations. The partial molar entropy is independent of manganese, but is decreased by silicon.

Thermodynamics of liquid Fe-C solutions

The activity of carbon in liquid iron has been determined at low concentrations by means of the CO-CO2 equilibrium and at high concentrations by the solubility of graphite. At intermediate concentrations there is a broad region in which measurements have not been made because of thermal instability of gas mixtures high in CO. Because of this phenomenon it is suggested that the reported activity coefficients at low concentrations may be in error and are only useful in determining a limiting value at infinite dilution. At temperatures below the melting point of iron, activity coefficients at intermediate concentrations along the liquidus line are calculated from recent measurements of the activity in austenite and of the solidus and liquidus lines of the phase diagram. The results agree fairly well with the data of Richardson and Dennis at higher temperatures. Several interpolation formulae are investigated. Equations are presented which describe the thermodynamic properties of the binary liquid solution at all compositions between the eutectic and 1760°C.

Thermodynamics of the solid phases in the system Fe−Mn−C

Phase relationships in the Fe−Mn−C system in the temperature range 600 to 1100°C have been studied using metallographic and X-ray methods and the electron microprobe. Isothermal sections of the phase diagram of the system are reported based on the present results and those of earlier investigators. The fcc λ-phase (austenite) containing carbon is stable at all values ofyMn=xMn/(xMn+xFe) in the range 890 to 1100°C and in a more restricted composition range at lower temperatures. Its composition under conditions of equilibrium with the carbides (Fe, Mn)3C, (Fe, Mn)23C6, ε, and liquid are shown for several temperatures. The free energy of formation of the cementite phase, (Fe, Mn)3C, at 1000°C, from γ-Fe, γ-Mn (undercooled) and graphite is ΔG1273=−35,790yMn−2760yFe+3RT (yMn lnyMn+yFe lnyFe). The data show that the alloyed cementite is essentially and ideal mixture of Fe3C and Mn3C,i.e., the metal atoms are distributed at random on the metal sites in the lattice.

Thermodynamics of Binary and Ternary Solutions Containing One Interstitial Solute

The activity of a very dilute interstitial component is proportional to the ratio of filled to unfilled interstitial sites. In a liquid solution in which solvent and solute atoms are strongly bonded to form in effect molecules of a soluteABb, each solvent atom is regarded as providingb sites forB atoms. The activity of the solute and other properties of the solution are treated by the same equations as those describing the interstitial solution. Concentrations are stated in terms of the ratiosyi = ni/(n1 +n2) where components 1 and 2 are lattice atoms andi represents any component. The activity coefficient of the interstitial component is defined as Ϋ3 =a3/z3 where z3 = Y3J(1 —y3/b). Henry’s law for the solute at great dilution is Ϋ3 = constant. Examples are cited in which log Ϋ3 is a linear function ofy3 or in other cases ofz3. A simple form of the Gibbs-Duhem relation for ternary solutions is used to deduce the effects of an interstitial solute on the activities of the individual lattice components.