First Principles Calculation of the Entropy of Liquid Aluminum

Abstract

The information required to specify a liquid structure equals, in suitable units, its thermodynamic entropy. Hence, an expansion of the entropy in terms of multi-particle correlation functions can be interpreted as a hierarchy of information measures. Utilizing first principles molecular dynamics simulations, we simulate the structure of liquid aluminum to obtain its density, pair and triplet correlation functions, allowing us to approximate the experimentally measured entropy and relate the excess entropy to the information content of the correlation functions. We discuss the accuracy and convergence of the method.

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

“…One approach employed for the treatment of fluids, referred to as “direct evaluation of the entropy” [ 13 , 14 , 15 , 16 ], is based on expansions of the probability density to increasing orders in the correlation functions and powers of the density, in which a limited set of terms is retained. Stopping at the pair level, the pair correlation functions (see typical pair correlation functions in Figure 1 , Figure 2 and Figure 3 ) from simulations give an easily evaluated first approximation of the fluid entropy; if greater accuracy is sought, triplet correlations can be calculated and the triplet terms that contribute to the entropy can be evaluated [ 16 , 17 ]. Similarly, in the study of substitutional alloys, a cluster expansion of the configurational entropy is often evaluated by the cluster variation method (CVM) [ 18 ] in a process that includes increasingly higher levels of correlation to achieve the desired accuracy.…”

“…Alternative approaches should be explored. One approach employed for the treatment of fluids, referred to as "direct evaluation of the entropy" [13][14][15][16], is based on expansions of the probability density to increasing orders in the correlation functions and powers of the density, in which a limited set of terms is retained. Stopping at the pair level, the pair correlation functions (see typical pair correlation functions in Figures 1,2, and 3) from simulations give an easily evaluated first approximation of the fluid entropy; if greater accuracy is sought, triplet correlations can be calculated and the triplet terms that contribute to the entropy can be evaluated [16,17].…”

Ab-initio free energies of liquid metal alloys: application to the phase diagrams of Li-Na and K-Na

“…For binary alloys,we supplement AIMD with additional Monte Carlo chemical species swapping steps 26 in order to accelerate the sampling of diverse configurations. Enthalpies are taken directly from the ab-initio total energies, while entropies are obtained from integrals of correlation functions 21,22 . We carry out our simulations in canonical ensembles although our entropy model is expressed in the grand canonical ensemble, relying on locality of the correlations to achieve ensemble independence 27 .…”

“…We calculate absolute entropies directly from MCMD simulations performed at the temperatures, densities and compositions of interest by evaluating the leading terms in an expansion of the entropy in a series of progressively higher-order correlation functions 27,[32][33][34] . This method has been previously validated for elemental liquid Al and Cu, and applied to the AlCu binary liquid alloy 21,22 .…”

“…We recently developed an approximate method to calculate absolute entropy of liquid metals from AIMD simulations of their densities and pair correlation functions 21,22 . Since entropies cannot be derived directly from simulations, our method provides a feasible approach to calculate the absolute entropy, and hence the absolute free energy, with high accuracy and reduced computational effort.…”