  Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of
randomly oriented and placed deterministic fractal structures are studied
theoretically. In the standard analysis, a very few parameters can be
determined from SAS data: the fractal dimension, and the lower and upper limits
of the fractal range. The self-similarity of deterministic structures allows
one to obtain additional characteristics of their spatial structures. The paper
considers models which can describe accurately SAS from such structures. The
developed models of deterministic fractals offer many advantages in describing
fractal systems, including the possibility to extract additional structural
information, an analytic description of SAS intensity, and effective
computational algorithms. Generalized Cantor fractals and few of its variants
are used as basic examples to illustrate the above concepts and to model
physical samples with mass, surface, and multi-fractal structures. The
differences between the deterministic and random fractal structures in
analyzing SAS data are emphasized. Several limitations are identified in order
to motivate future investigations of deterministic fractal structures.
