Free energies of formation of WC and W₂C, and the thermodynamic properties of carbon in solid tungsten

Abstract

The activity of carbon in the two-phase regions W + WC and W + W₂C has been obtained from the carbon content of iron rods equilibrated with mixtures of metal plus carbide powders. From this activity data the standard free energies of formation of WC and W₂C have been calculated to be ΔG _f ⁰(WC) = -10,100 + 1.19T ± 100 cal/mole (-42,300 + 4.98T ± 400 J/mole) (1150 to 1575 K) ΔG _f ⁰(W₂C) = - 7300 - 0.56T ± 100 cal/mole (- 30,500 - 2.34T ± 400 J/mole). (1575 to 1660 K) The temperature of the eutectoid reaction W₂C = W + WC was fixed at 1575 ± 5K. Using available data for the solubility of C in solid W, the relative partial molar free energy of C in the dilute solid solution was calculated to be

$$\Delta \bar G_C^\alpha {\text{ = 23,000 }} - {\text{ }}[{\text{0}}{\text{.68 }} - R\ln X_C^\alpha ]{\text{ }}T \pm 3000 cal/mole (96,200 - [2.85 - R\ln X_C^\alpha ]{\text{ }}T \pm 12,600 J$$

The heat solution of C in W obtained was$\Delta \bar H_C^\alpha {\text{ = 23,000 }} \pm {\text{ 5000 cal/mole (96,200 }} \pm {\text{ 20,000 J/mole)}}$ and the excess entropy for the interstitial solid solution, assuming that the carbon atoms are in the octahedral sites,$\Delta \bar S_C^\alpha {\text{ = (}}xs,i{\text{) }} = - {\text{1}}{\text{.5 }} \pm {\text{ 2 cal/deg - mole (}} - {\text{6}}{\text{.3 }} \pm {\text{ 8 J/deg - mole)}}$.