The iodate anion group has been widely used for design
and synthesis
of functional materials including nonlinear optical materials but
rarely for magnetic materials. Particularly, none of magnetic iodate
fluorides has been reported yet. In this work, first, two novel magnetic
iodate fluorides MIO3F (M = Co 1 and Ni 2) have been synthesized by a hydrothermal method and characterized
by magnetic susceptibility, magnetization, and heat capacity measurements
as well as thermogravimetry, Fourier transform infrared spectroscopy
(FT-IR), and ultraviolet–visible–near-infrared (UV–vis–NIR)
spectroscopy. Compounds 1 and 2 are isostructural
and crystallize in the monoclinic space group P21/n with alternating M2+–F2–M2+–O2–M2+ zigzag spin chains along the b axis, which are
further separated by triangular IO3 groups in the ab plane. Magnetic susceptibilities suggest that 1 exhibits an antiferromagnetic long-range order (LRO) at 16.5 K,
confirmed by heat capacity results with released entropy consistent
with the theoretical value for a pseudo-spin of 1/2 for Co2+ at low temperatures. Meanwhile, 2 displays a broad
maximum around 10.5 K for low dimensional magnetism followed by a
sharp peak at 5.7 K indicating the occurrence of an LRO transition,
in good agreement with the heat capacity measurement. Field-dependent
magnetizations show an obvious spin-flop transition around 4.5 T and
a magnetic hysteresis loop between 4.5 and 7 T for 1,
but only a slight slope change could be observed around 2.3 T for 2. Thermal stability, FT-IR, and UV–vis–NIR
spectroscopy of 1 and 2 are also reported.
The shorest path problem(SPP) is currently being greatly studied in fuzzy sets and systems area. Previously published algorithms and methods for the fuzzy shortest path problem based on discrete or continuous types fuzzy sets of fuzzy arc lengths.However,to present an arc real length in vague set is more reasonable than in fuzzy set.Moreover,carrying on various kinds of operation between the fuzzy numbers and sets,we find that some information will be lost.In this paper ,we present a novel approach to solve the shortest path problem in network base on vague sets. Firstly,we determine the vague shortest path length from source node to the destination node in the classical directed network. Secondly,by mean of vague similarity measure to evaluate similarity degree between vague path lengths. At last ,Comparing the result of similarity measure,the path with the hightest similarity degree is the shortest path.An illustrative example is given to demonstrate that the result of the approach with vague sets is closer to intuitive judgment.
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