  Central quantities in spectroscopy and magnetism of transition ions in
crystals are crystal field parameters (CFPs). Nature self-imposed limits on
orthorhombic and lower symmetry CFPs, and existence of intrinsically
incomparable CFP sets are elucidated. Comparisons of such CFP sets result in
controversial claims, incorrect structural conclusions or CFP systematics, and
misinterpretation of spectroscopic data. Considerable extent of such pitfalls
in literature indicates many researchers remain unaware of the intrinsic
features of low symmetry CFPs. This calls for coordinated remedial actions. To
avoid pitfalls, comparative methodology based on standardization of the
rhombicity ratio to express CFP sets in the same region of CF parameter space
is proposed. Wider utilization of alternative CFP sets in the multiple
correlated fitting technique to improve reliability (blessings) of final fitted
CFPs is advocated. This review may be of interest to physicists and chemists
working on various materials as well as to science historians and philosophers.
