Electron states, one-electron density matrix and Fourier-transformed Compton profile of ordered and disordered one-dimensional potential arrays

The properties of the one-electron density matrix of one-dimensional potential arrays have been studied using the transfer-matrix formalism. The potential arrays are constructed from square-well potentials with only the lowest even and odd states bound in order to facilitate an extension of the results to three-dimensional $s{p}^n$ bonded systems. Infinite ordered arrays with filled bands (semiconductors, insulators) and with partially filled bands (metals), finite arrays and disordered arrays with structural, compositional and localized disorder are considered. It is shown that the one-electron density matrix, its spatial average (autocorrelation function or Fourier-transformed Compton profile), and the density of states converge rapidly with the cluster size irrespective of the boundary conditions or surface potentials used. The influence of disorder on the density matrix is investigated in detail for the discussion of real amorphous materials. It is concluded that localized disorder (point defects such as vacancies and iterstitials) has a more pronounced effect on the density matrix than extended disorder (structural or compositional). In addition, the relation between the autocorrelation function and the microstructure of the system is discussed and correlated with experimental findings. Finally, several new aspects for the interpretation of experimental autocorrelation functions are considered.