PART V - Papers - A Correlation of Thermodynamic Variables for Iron-Rich Iron-Nickel-Carbon Alloys

A detailed analysis has been used to correlate the avalable thermodynami c da In on iron-ric11 Fe-Ni (41loys in the body-centered a, and the face-centered y phases. The inp ut injovrt~ation required by the a am lysis consists of tile heat of the a, to y transformation at 1123°K, the heat of mixing of y at 1123°K, tile specific heats of both a, and y (decomposed into Debye, electronic, and magnelic contributions), and the positional and magnetic entropies of both a, and y. PYLrrzary oirt.bul of the analysis is the free energy of each phase as a Junction of temperature and composition. FOr Fe-Ni alloys the adjustment of twenty-one parunletevs allows the accurate reproduction of enthalpy data for both phases, the heat of mixing- for y, the a/y equilibrinm compositions in the Fe-Ni phase diagram, and the usually accepted enthalpy and entropy of a and y iron. Also obtaitzed are fuirly accurate reproductions of electronic specific heat coefficients predicted from electron- to-atom ratio interpolations and To temperatuves eslimanted from transformation studies. Also considered in the calculation are the elastic constants, Curie temperatures, saturation magnlelizalion values, and indications of short- range order. The measnred activity coefficient of iron in anstetnite could not be accurately matched. The major source of uncertainty in the model is thought to be the magnetic contribution to the entropy of austenite. Calcrclations were extended to Fe-ni-C alloys using available carbon-acliuity data. The free energy of transformation from martensile to r at fixed composition was obtained as a function of nickel and carbon contetzt, and binary thetal-carbon phase diagrams Were estimaled as a function of nickel contenl. We needed thermodynamic information for Fe-Ni and Fe-Ni-C alloys at temperatures between 400" and 800°K in order to interpret the results of several phase-transformation studies. The most recent theoretical analysis of the thermodynamics of Fe-Nialloysl was based on a lumped-parameter, regular-solution model and used the Fe-Ni phase diagram available at that time.' Because significant difficulties were encountered in attempting to extend this analysis to Fe-Ni-C alloys, and because more experimental data has become available recently, we decided to attempt a new correlation. The analysis used here allows the extrapolation of measured and calculated thermodynamic values to lower temperatures and the extension of the thermodynamic analysis to Fe-Ni-C alloys. The structure of this correlation consists of expressions containing a total of twenty-one adjustable parameters. The forms of these expressions are discussed in the next section; however, a less formal summary is presented now to provide a physical overview of the model and to indicate its connections to prior work. Primary input information for this correlation is described below. The measured values of the specific heat of iron3 and its analysis475 and theoretical estimates of the specific heat of y* iron at low tempera- loys at 1123°K has been measured by solution calori-metry.7 The enthalpies of both a, and y have been measured most recently by Scheil and Saftig,B who used a dry-ice calorimeter. These data are used to formulate expressions for the heat of mixing of y and the heat of transformation of a, to y both at 1123°K. The a and y solubility limits in the Fe-Ni phase diagram have been redetermined recently9 by methods which assure a close approach to equilibrium. The a to y transformation can occur without change in nickel content or free energy at a temperature called TO; TO temperatures for various nickel contents have been estimated from transformation studies. The computed free-energy functions are adjusted by means of the parameters to fit both the phase diagram and the TO temperatures. Primary emphasis is placed on the phase diagram fit. Iron activities have been measured in Fe-Ni austenite10 between 973" and 1173°K. These activity data, which cannot be fitted accurately with our model, indicate that iron is substantially ideal in iron-rich austenite. Secondary, but helpful, information for the present correlation is provided by neutron diffraction and saturation magnetization measurements on both body-centered and face-centered Fe-Ni alloys."-'3 These results were interpreted11 in terms of composition-insensitive, localized magnetic moments on both iron