Direct Correlation Function of a Crystalline Solid
Direct correlation functions (DCFs) play a central role in the statistical mechanics description of matter. Within the seminal concept of classical density functional theory they are closely related to the second functional derivative of the free energy functional. DCFs provide relevant information about the structure and the thermodynamics of a system and are - in the case of solids - closely related to local defects and mechanical properties. The explicit evaluation of DCFs for an ordered solid has been considered to be computationally too demanding, so far; therefore these functions are traditionally approximated by their liquid counterparts.
In this contribution we present for the first time explicit results for the DCF ccr of an ordered solid, namely of an fcc hard sphere crystal. With our detailed analysis we provide explicit evidence that the DCF of a solid differs substantially from its liquid counterpart, both in shape as well as in magnitude. It is intimately related to the small vacancy concentration of an (almost) ideal crystal. Our approach furthermore opens a new route for calculations of solid state properties which overcomes the limitations of zero-temperature considerations. Thus we pave with our contribution a new way to future statistical mechanics based investigations of solid state properties.