# Structure and Thermodynamics of Liquid Metals

• Jürgen Hafner
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 70)

## Abstract

For a crystal, the atomic structure is completely desribed by a diffraction experiment. The positions of the Bragg reflections specify the reciprocal lattice (and hence the symmetry of the unit cell) and the positions of the atoms within the unit cell may be calculated from the intensities of the Bragg peaks. For a disordered material such as a liquid or a glass, the diffraction pattern consists of diffuse rings with intensity I(q)given by
$$I(q) = f{(q)^2}\left\langle {\sum\limits_{l,m} {\exp \left[ {iq({R_l} - {R_m})} \right]} } \right\rangle ,$$
where q is the momentum transfer and the average is over all pairs (l, m)of atoms; f (q)is the scattering form factor of an individual atom. Normalizing the intensity I(q)by the number of atoms and by the square of the scattering form factor defines the static structure factor S(q); S(q) is the Fourier transform of the pair correlation function g(R). The latter represents the probability of finding a second atom at a distance R from a given atom:
$$S(q) = {N^{ - 1}}\left\langle {\sum\limits_{l \ne m} {\exp \left[ {iq} \right]({R_l} - {R_m})} } \right\rangle - N{\delta _{q,o}} = 1 + 4\pi n\int {\left[ {g(R) - 1} \right]} \exp (iqR){d^3}R,$$
where n = V/N is the number density of atoms. Thus for a liquid or a glass, a diffraction experiment yields only a one-dimensional projection of the three-dimensional structure, but this is usually all the structural information that can be obtained.

### Keywords

Entropy Compressibility Renin Germanium Verse