Part VI – June 1968 - Papers - A Study of the Thermodynamics of Carbon in Austenite by an Electrochemical Method

A galvanic cell, using as electrolyte a fused salt solution of calcium carbide and as electrodes carbon and a Fe-C alloy of known composition, has been set up to study the thermodynamics of Fe-C alloys in the temperature rmzge 800" to 1000°C. Time independence and reproducibility of the cell electromotive force were taken as evidence of the reversible behavior of the cell. Carbon was believed to be present in the electrolyte as the so-called acetylide ion, C;-. The plots of the cell electromotive force us temperature for a specific alloy composition were straight lines within the limits of experimental error. The average Partial molar enthalpy of carbon in iron relative to pure carbon was found to be +10,610 i 93 cal per g-atom C. Thermodynamic analysis of the data has led to the following equation for the carbon activity, ac, based upon pure carbon as the standard state: In ac = In Zc + 10,560/RT + (10.02 + 77O/T)ZC - 2.350 where ZC is the lattice ratio [nC/(nF, - nc )] and T is the absolute temperature. This equalion gives carbon activity values generally slightly lower than those from gas equilibration studies reported in the literature. METAL LOGRAPHIC examination of a polished cross section of the steel anode used in the electrolysis studies of fused salt solutions of calcium carbide by Morris and Harry revealed extensive carburization of the steel by the electrodeposited carbon. This carburization was reflected in the variability, with time, of the applied potential to the electrolysis cell, necessary to maintain a constant current density at the electrodes. This observation suggested the setting up of a galvanic cell of the "alloy concentration" type to study the thermodynamics of some metal-carbon alloys. Cells of this general type have been widely used for the study of alloy systems.2 In view of the availability of published data in respect of the austenite phase of the Fe-C system, it was decided to carry out measurements upon these alloys before proceeding to studies of less well documented systems. The galvanic cell may be written: where [C] is carbon dissolved in iron. The electrolyte was a fused salt solution of calcium carbide, containing some 5 to 10 mol pct of carbide. The cell reaction is believed to be: C(s)-[CI [I1 Carbon forms an interstitial solid solution in iron, with the atoms located in the octahedral interstices. In the fcc crystal structure of austenite there is one octahedral interstice per iron atom. Thus, the lattice ratio, ZC, shown by Gurney3 to be the fundamental concentration parameter in the context of interstitial solutions, is given by: where nc and nFe are the number of carbon and iron atoms, respectively. chipman4 has recently shown empirically the advantages of using this concentration parameter instead of the more usual atom ratio or atom fraction. The cell electromotive force, E, assuming reversible behavior, is related to the carbon potential or the partial molar free energy of carbon in the solid solution relative to pure carbon at the same temperature and pressure, GP at the composition ZC, by the equation: where z is the carbide ion valency and F is the Faraday constant. An activity of carbon, ac, in the solution relative to the value of unity assigned to pure carbon, and an activity coefficient, qC , are defined such that: where R is the gas constant and T the absolute temperature. GF is further related to the relative partial molar enthalpy Hm, and the temperature coefficient of the cell electromotive force, (aE/aT)Zc, by the equations: Measurement of the cell electromotive force thus enables calculation of the relative partial molar thermodynamic properties of carbon in iron, if z is known. At E = 0, the solid solution is in equilibrium with pure carbon. More convenient for many purposes is the standard state based upon the infinitely dilute solution, Henry's law. The relationship between the activity coefficient of carbon based upon this standard state, and that based upon the pure carbon standard state, qC , may be obtained by considering the free energy of transfer of carbon from the latter standard state to the former. The relationship is: where +:H is the activity coefficient of carbon in the hypothetical standard state based on a reference of