  Periodic multilayers are nowadays widely used to perform x-ray analysis in
the soft x-ray range (photon energy lower than 1 keV). However, they do not
permit to obtain high-resolution spectra like natural or synthetic crystals.
Thus, multilayers cannot resolve interferences between close x-ray lines. It
has been shown and demonstrated experimentally that patterning a grating
profile within a multilayer structure leads to a diffractive optics with
improved resolving power. We illustrate the use of a Mo/B4C multilayer grating
in the Fe L and C K spectral ranges, around 700 eV and 280 eV respectively.
First, in the Fe L range, the improved spectral resolution enables us to
distinguish the Fe L\alpha and L\beta emissions (separated by 13 eV). In
addition, using a sample made of a mix of LiF and an iron ore, we show that it
is possible to easily resolve the F K and Fe L emissions. These examples
demonstrate that an improved x-ray analysis can be obtained with multilayer
gratings when there is the need to study samples having elements giving rise to
close emission lines. Second, in the C K range, by comparing C K\alpha spectra
from B4C and cellulose, we show that the shape of the emission band is
sensitive to the chemical state of the carbon atom.
