Discrimination of different crystalline structures in manyparticle- systems using scaling indices

Kurzfassung

Bond order parameters and scaling indices are local measures which are used to determine local structures in a point distribution. Local invariants, which measure the angular relation between the point and its next neighbors, are calculated for each point in the distribution for determining the bond order parameters [1]. Scaling indices measure how the number of neighbors in a vicinity of radius r scales with r for each point in the distribution. Anisotropy can then be implemented weighting the dimensions differently in the calculation of the distance measure [2]. We calculated the local invariants q4, q6 and a set of anisotropic scaling indices for each point of three artificially created point distributions of perfect bcc-, fcc- or hcp-like shape with additive Gaussian noise, and determined the quality of discrimination. It is found that the limit noise level (Gaussian noise std.dev.) for a sufficient discrimination is about 10% of the average point distance for scaling indices, and only about 8% for bond order parameters. The results from these data sets are then transferred to experimentally obtained data, e.g. for discriscriminating local crystalline structures of bcc, fcc and hcp type in 3d data of plasma crystals in a PK-3- Plus experiment [3]. [1] P. J. Steinhardt, D. R. Nelson, M. Ronchetti, Phys. Rev. B, 28 784 (1983) [2] C. Räth, R. Monetti, J. Bauer, I. Sidorenko, D. Müller, M. Matsuura, E.-M. Lochmüller, P. Zysset, F. Eckstein, New J. Phys. 10, 125010 (2008) [3] H. M. Thomas, G. E. Morfill, V. E. Fortov, A. V. Ivlev, V. I. Molotkov, A. M. Lipaev, T. Hagl, H. Rothermel, S. A. Khrapak, R. K. Suetterlin, M. Rubin-Zuzic, O. F. Petrov, V. I. Tokarev and S. K. Krikalev, New J. Phys. 10, 033036 (2008)