As a second example of the application of the functional derivatives, we show that the pair distribution function can be obtained as a functional derivative of the configurational partition function. For a system of N spherical particles, with pairwise additive potential, we write [Pg.303]

The correlation functions provide an alternate route to the equilibrium properties of classical fluids. In particular, the two-particle correlation function of a system with a pairwise additive potential determines all of its thermodynamic properties. It also determines the compressibility of systems with even more complex three-body and higher-order interactions. The pair correlation functions are easier to approximate than the PFs to which they are related they can also be obtained, in principle, from x-ray or neutron diffraction experiments. This provides a useful perspective of fluid stmcture, and enables Hamiltonian models and approximations for the equilibrium stmcture of fluids and solutions to be tested by direct comparison with the experimentally determined correlation functions. We discuss the basic relations for the correlation functions in the canonical and grand canonical ensembles before considering applications to model systems. [Pg.465]

The first example of the application of atomistic simulation to a materi-als-related area is probably the work of Vineyard and co-workers. They used classical trajectories to model damage induced in a solid by bombardment with ions having hyperthermal kinetic energies. These calculations, which were done at about the same time as Rahman s initial studies on liquids, provided important data related to damage depth as well as new insights into many-body collisions in solids. The potentials used were continuous pair-additive interactions similar to those employed in Rahman s simulations. [Pg.210]

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