  Effects of size and charge asymmetry between oppositely charged ions or
particles on spatial inhomogeneities are studied for a large range of charge
and size ratios. We perform a stability analysis of the primitive model (PM) of
ionic systems with respect to periodic ordering using the collective variables
based theory. We extend previous studies [A. Ciach et al., Phys. Rev.E
\textbf{75}, 051505 (2007)] in several ways. First, we employ a non-local
approximation for the reference hard-sphere fluid which leads to the
Percus-Yevick pair direct correlation functions for the uniform case. Second,
we use the Weeks-Chandler-Anderson regularization scheme for the Coulomb
potential inside the hard core. We determine the relevant order parameter
connected with the periodic ordering and analyze the character of the dominant
fluctuations along the $\lambda$-lines. We show that the above-mentioned
modifications produce large quantitative and partly qualitative changes in the
phase diagrams obtained previously. We discuss possible scenarios of the
periodic ordering for the whole range of size- and charge ratios of the two
ionic species, covering electrolytes, ionic liquids, charged globular proteins
or nanoparticles in aqueous solutions and charge-stabilized colloids.
