Chemical effects on the $K{\beta }^{″}$ and $K{\beta }_{2,5}$ x-ray lines of titanium and its compounds

High-resolution $K\beta$ x-ray spectra induced by 2 MeV protons in thick Ti, TiO, ${\text{Ti}}_2{\text{O}}_3$, ${\text{TiO}}_2$, ${\text{MgTiO}}_3$, ${\text{FeTiO}}_3$, TiC, TiN, and ${\text{TiB}}_2$ targets were measured using a wavelength dispersive spectrometer combined with a position-sensitive detector. The intensities and energies of the $K{\beta }_{2,5}$ and $K{\beta }^{″}$ lines relative to the $K{\beta }_{1,3}$ line were extracted. The influence of self-absorption in thick targets was investigated using related x-ray-absorption near-edge-structure spectra that are available in the literature to extract mass absorption coefficients close to the $K$ absorption edge. The correlation of the relative position of the $K{\beta }_{2,5}$ line with a titanium formal oxidation state in oxide compounds confirmed that the oxidation state of Ti in ${\text{FeTiO}}_3$ is probably a mixture of Ti III and Ti IV states, which has been recently reported by other authors using different methods. The strengths of the $K{\beta }_{2,5}$ and $K{\beta }^{″}$ transition probabilities per titanium-ligand pair were found to decrease exponentially as the average titanium-ligand bond distance increased, which is similar to results obtained for various compounds with vanadium or manganese as the central $3d$ metal atoms.

Figure 1

The measured and fitted spectra of all the samples. The spectra are aligned relative to the position of the $K{\beta }_{1,3}$ peak centroid.

Figure 2

The mass absorption coefficients for measured materials that were estimated from the corresponding XANES spectra [46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57] and tabulated data [58] before and after the absorption edge. At the bottom, the typical ranges of affected emission lines are indicated by horizontal bars.

Figure 3

The normalized thick-to-thin target relative yield function in the $K$-edge region for a thick Ti foil target bombarded with 2 MeV protons in our measurement geometry (dotted line) and associated convolution obtained using the spectral response function of our spectrometer (full line). The positions of the $K{\beta }_{2,5}$ and $K\beta L^1$ emission lines are emphasized.

Figure 4

The normalized thick-to-thin relative yield function for a) a thick Ti foil target bombarded with 1, 1.5, 2, 2.5, and 3 MeV protons and for b) thick Ti metal, ${\text{TiO}}_2$ (rutile), and ${\text{FeTiO}}_3$ targets bombarded with 2 MeV protons.

Figure 5

The fit of the $K$-edge region of the measured $K\beta$ spectrum for a metallic titanium sample. The zero value of the relative energy corresponds to the $K{\beta }_{1,3}$ centroid (4931.8 eV).

Figure 6

The fit of the $K$-edge region of the measured $K\beta$ spectrum for a metallic vanadium sample. The zero value of the relative energy corresponds to the $K{\beta }_{1,3}$ centroid (5427.3 eV).

Figure 7

The dependence of the measured energy difference between $K{\beta }_{2,5}$ and $K{\beta }_{1,3}$ on the formal oxidation state of measured oxides. The results are supported by data found in the literature [49, 67].

Figure 8

The relative intensities of the $K{\beta }^{″}$ x-ray line normalized to the intensity of $K{\beta }_{1,3}+K{\beta }_{res}+K{\beta }^{\prime }$ and divided by the number of ligands per the central titanium ion (i.e., the number of titanium-ligand pairs) as a function of the average titanium-ligand distance.

Figure 9

The relative intensities of the $K{\beta }_{2,5}$ x-ray line normalized to the intensity of $K{\beta }_{1,3}+K{\beta }_{res}+K{\beta }^{\prime }$ and divided by the number of ligands per the central titanium ion (i.e., the number of titanium-ligand pairs) as a function of the average titanium-ligand distance.

Figure 10

The relative intensities of $K{\beta }^{″}+K{\beta }_{2,5}$ x-ray lines normalized to the intensity of $K{\beta }_{1,3}+K{\beta }_{res}+K{\beta }^{\prime }$ and divided by the number of ligands per the central titanium ion (i.e., the number of titanium-ligand pairs) as a function of the average titanium-ligand distance.