Determination of the structure factor of simple liquid metals from the pseudopotential theory and optimized random-phase approximation: Application to Al and Ga.

Abstract

We present the results of calculations of the static structure factor S(q) of liquid Al and Ga at the melting point. These calculations were motivated because many simple liquid metals exhibit structure anomalies taking the form of a shoulder on the main peak or even an asymmetry in the peak itself, while other liquid metals are correctly predicted by the standard models of liquid structure. Al and Ga have similar valence, electronic density, and size of their ionic radius; therefore, their pair potentials are somewhat similar. Despite this, their structure factors display most of the differences that can be observed among the variety of liquid metals. Starting from the Shaw optimized model potential [Phys. Rev. 174, 769 (1968)], a pair potential is constructed. A comparative examination of the electron-gas response function of Vashishta and Singwi [Phys. Rev. B 6, 875 (1972)] and of Ichimaru and Utsumi [Phys. Rev. B 24, 7385 (1981)] is carried out. Different depletion hole distributions are also used and full nonlocality is taken into account through effective masses. So S(q) is calculated by means of the optimized random-phase approximation. Particular attention is also devoted to the low-q region. By comparison with Monte Carlo computation, we show the limitation of various thermodynamic perturbation methods, such as the random-phase approximation or the soft-sphere model. The study of S(q) provides a stringent test of the model potential, where the electron-ion pseudopotential and the local-field correction are of prime importance, but where effective masses and depletion hole distribution may also have a role to play.