Phase Equilibria and Vapor Pressures of Pure Phosphorus and of the Indium/Phosphorus System and Their Implications Regarding Crystal Growth of InP
Klaus J. Bachmann, E. C. Buehler · Journal of The Electrochemical Society · 1974
The vapor pressure as a function of temperature of several commercial grades of red phosphorus and a specially prepared crystalline sample has been measured. For crystalline red P we obtain a heat of sublimation, δ H s = 31.9 ± 1 kcal / mole . The commercial grades yield vapor pressures, which above 450°C are described by the equation In p = − ( 10.8 ± 0.4 ) × 10 3 / T + ( 16.5 ± 0.6 ) . The sublimation equilibrium of red P can be utilized for controlling phosphorus pressures, p > 10 atm , with a reproducibility of 10% if commercial P of at least 5N purity is used. Measurements of the pVT relation of phosphorus vapor in the regimes 800 ° K ≤ T ≤ 1400 ° K and 3 atm ≤ p ≤ 35 atm reveal deviations up to 10% from ideal gas behavior. Excellent accuracy in describing the behavior of phosphorus vapor is obtained when van der Waals equation is used in conjunction with the critical data of Marckwald and Helmholz and a critical coefficient of 0.375 for calculation of both the co‐volume and the interaction parameter. Consideration of the pressure dependence of the equilibrium constant Kp for the reaction P 4 = 2 P 2 yielded approximate values for the fugacity constant at 1000° and 1100°C. The pTx relation at the liquidus in the vicinity of stoichiometric InP for indium‐rich and phosphorus‐rich compositions were established by simultaneous vapor pressure and DTA measurements. The melting point of stoichiometric InP is 1335 ° ± 1 ° K and the corresponding equilibrium phosphorus pressure is 27.5 ± 1 atm . T−x liquidus data calculated with the assumption of ideal behavior of the liquid are in good agreement with our experimental data. Interpretation of the liquidus pressure data yields values of the standard enthalpies and entropies at 298° K Δ H ° 298 = 22.1 kcal / mole , Δ S ° 298 = 15.78 e . u . for the reaction InP s ) = In s + 1 / 4 P 4 g and Δ H ° 298 = 36.0 kcal / mole , Δ S ° 298 = 25.28 e . u . for the reaction InP s ) = In s + 1 / 2 P 2 g These results are in excellent accord with the standard enthalpies reported by Panish and Arthur and agree within 3% with literature data on the standard entropies of the reactants. The growth of n‐ and p‐type InP crystals via the gradient freeze technique is discussed and the degree of control of the liquidus concentration is evaluated for various conditions of crystal growth.