## 2 Methods and Materials  
### Chemical State Information by SXES  
Electron-beam-induced X-ray emission was used for elemental analysis by using an X-ray energy dispersive spectroscopy (EDS) instrument, and elemental and partial chemical analyses were performed using an EPMA. Among those X-rays, X-rays due to transitions from valence bands (bonding state) to inner-shell levels, usually lower than 1 keV, have information about the chemical bonding states of elements. Recent soft X-ray emission spectrometry using gratings, which was first developed for TEM [22; 23; 24] and then transferred to SEM and EPMA [5; 6; 7], has an energy resolution better than 1 eV, which is about two orders better than that of EDS and allowed us to obtain chemical bonding information by using X-ray emission. Another spectrometer system for soft X-rays is under examination [25].  
Figure 1 shows the electronic transitions in a material caused by electron beam irradiation. Firstly, incident electrons excite electrons, a and b. This automatically causes energy losses of the incident electrons, which is the physical quantity to be measured in electron-energy-loss spectroscopy in TEM. The excited material quickly returns to the ground state. In the de-excitation process, downward electronic transitions of c and d to inner-shell core-hole states, which were created by the excitation process b, occur by accompanying X-ray emissions under a dipole-selection rule condition. Both emissions of c and d in Figure 1 are used in elemental analysis. However, only the X-ray emissions caused by the transition c includes information about the energy distribution of bonding electrons, the density of states of valence bands (VB). Thus, X-rays due to transitions c are a sensitive tool for chemical state analysis. As the energy spread of VB is smaller than 10 eV, an energy resolution better than 1 eV is necessary for obtaining information of chemical bonding states by SXES.  
Figure 2a shows a schematic figure of the SXES mapping system used. The SXES system (JEOL SS-94000 SXES), which is composed of varied-line-spacing gratings (aberration-corrected gratings) and a CCD detector, was attached to an EPMA (JEOL JXA-8230). The distance from the specimen to the detector was about 50 cm. The combination of the two VLS gratings of JS50 XL and JS200N covers 50-210 eV for the 1 st-order diffraction lines, and 100-420 eV for the 2 nd-order diffraction lines [7]. The energy resolution of about 0.2 eV was realized for the 1 st-order AI L-emission at about 73 eV. Figure 2b shows the 1 st-order B K-emission (corresponds to transition c in Figure 1) spectra of pure boron (\(\beta\)-rhombohedral boron, \(\beta\)-r-B), CaB\({}_{6}\), AlB\({}_{2}\), and hexagonal-BN (h-BN). N-K(2) in the h-BN spectrum is the 2 nd-order line of N K-emission, which shows a larger intensity than B K-emission because the bonding orbital is dominated by an N-orbital component, owing to its lower energy than that of B. The peak energy positions (vertical arrows) and the shoulder structures (vertical lines) of the B K of these materials are different from each other, reflecting different chemical bonding states owing to different crystal structures. By using a high energy resolution, elemental and chemical state analyses and those mappings are possible [5; 6; 7; 26; 27; 28; 29; 30]. The emission due to the process d is also affected by the chemical state of the materials [31; 32].