The Ga– GaP System
The phase diagram for the system Ga– GaP is shown in Figure 13.13. Calculate the partial pressure of phosphorus vapor, p_{p2}, exerted by the GaP liquidus melt at 1273 K. The standard Gibbs free energy change for the reaction
\mathrm{Ga}_{(l)}+\frac{1}{2}\mathrm{P}_{2(g)}=\mathrm{GaP}_{(s)}
is
\Delta G^{\circ}=-178,800+96.2T+3.1T\ln T-3.61\times10^{-3}T^{2}-\frac{1.035\times10^{5}}{T}
At 1273 K,
\Delta G_{1273\,\,{K}}^{\circ}=-3.968\times10^{4}{\bf J}=-8.3144\times1273\ln{ K}_{1273\,\,{K}}
which gives
K_{1273\mathrm{\bf~K}}=24.97=\frac{a_{\mathrm{GaP}}}{a_{\mathrm{Ga}}P_{\mathrm{p}_{2}}^{1/2}}
In the preceding expression, a_{Ga} is the activity of Ga in the liquidus melt with respect to liquid Ga as the standard state, and, since the liquidus melt is in equilibrium with pure solid GaP, the activity of GaP, a_{GaP}, is unity. The variation of the liquidus composition with temperature in the range 1173– 1373 K can be expressed as
\ln X_{\mathrm{P}}=-{\frac{16,550}{T}}+9.902
which gives the liquidus composition at 1273 K as X_{P} = 0.045. In view of the low solubility of the solute P, it can be assumed that the solvent Ga obeys Raoult’ s law, in which case the activity of Ga in the liquidus melt is 0.955, and hence the partial pressure of P_{2} exerted by the liquidus melt is
p_{\mathrm{P_{2}}} =\left(\frac{1}{24.97\times0.955}\right)^{2} = 1.76\times10^{-3}\ {\mathrm{atm}}