Coordination and structural energetics of various phases of Ni

Nickel is one of the most versatile metals in the transition series of the periodic table. We have investigated the coordination and the cohesion of Ni corresponding to its various phases. The neighboring distances and the coordination numbers are estimated from the observed and simulated pair distribution functions (PDF) g(r) relevant to the various phases. Since the profiles of these functions are not symmetric, we have used the concept of minimum-to-minimum positions of the PDFs to estimate the successive coordination numbers for the solid amorphous and microcrystalline phases. The approximate values of the pseudo-lattice vectors estimated from the peak positions of the PDFs are employed to calculate the total energies for the amorphous and the microcrystalline phases of Ni in terms of the pseudopotential theory. The roles of the s- and d-electrons in the cohesion of Ni have been investigated by calculating the free energies for the relevant phases. The calculated energetics reveal the relative stability of the various phases in a qualitative manner. It is noted that the d-electrons play the dominant role in predicting the stability of the various phases; the s-electrons merely supplement the d-electron trend. Since the formalism corresponds to very low temperature, the lattice vibrations [Einstein model] do not seem to play any visible role in the prediction.