Coarse-grained Quantities in Aperiodic System. II

As an application of the general properties of coarse-grained quantities of aperiodic sys tems which were studied in the preceding paper, the method of ensemble average of periodic systems (MEAPS) is discussed for obtaining frequency spectra of aperiodic systems. Histo grams of frequency spectra of isotopically disordered diatomic linear chains for various sets of long range and short range order parameters were calculated by the MEAPS, and were compared with the result calculated by the negative-factor-counting method (NFC). It was numerically shown that the suitable choice of the width of histograms is very important for the result of the MEAPS to be a good approximation; the choice can be done referring lo the stability of the histogram with change of the ensembles. The comparison then indicates that the MEAPS using periodic chains with not more than 8 atoms in a unit cell gives better approximation than the moment method using 20 moments. Although for the spectra of one-dimensional systems the NFC is a better method than the MEAPS, the latter has a wider range of applicability so that the result of this study may lend support for the investigation of more complicated quantities of systems by this method of approach.