Radial distribution functions in solid cobalt

Abstract

Radial distribution functions have been calculated from X-ray diffraction data for Co-α(h.c.p.) and Co-β(f.c.c.) near the allotropie transformation temperature. These functions provide values of lattice parameters, mean square amplitudes of vibration, vibrational coupling factors, and the mean force potential function. The mean square amplitude of vibration, u ̄ s 2 , for α and β at 417° C are 0.0155 Å 2 and 0.0168 Å 2, which correspond to Debye temperatures of 332°K and 320°K, respectively. The Debye temperature and coupling factors obtained for β at 417° C were consistent with a second experimental distribution function determined at 678° C, indicating that those parameters are essentially invariant over that range of temperature. From the mean force potential functions the elastic modulii for nearest neighbor directions have been determined. In both α- and β-phase the measured value is approximately 2.0 × 10 12 dyn/ cm 2. The α-phase modulus may be estimated from other data and is found to be in excellent agreement. The difference between the nearest neighbor potential minima in the α- and β-phases at 417° C is 100 cal/g-atom. Since this energy difference is almost exactly the heat of transformation, it appears that pertinent thermodynamic values may be derived from the X-ray results.