Effective charge on silicon atom in the metal silicides ${\mathrm{Mg}}_2\mathrm{Si}$ and CaSi

The effective charges of Si in both magnesium $\left({\mathrm{Mg}}_2\mathrm{Si}\right)$ and calcium silicides (CaSi and ${\mathrm{Ca}}_2\mathrm{Si}$) have been investigated by measuring high-resolution Si $K\alpha$ x-ray fluorescence spectra. CaSi showed small but positive chemical shifts $(+0.03\mathrm{eV})$, while the chemical shift of ${\mathrm{Mg}}_2\mathrm{Si}$ was negative $(-0.14\mathrm{eV})$, as expected from their electronegativity (Ca: 1.00; Mg: 1.31; Si: 1.90). The similarity of the chemical shift for the Fe silicides and the calculations for the free single Si atom suggested that the effective charge of Si for CaSi was positive. From the observations the effective charges on Si in CaSi and ${\mathrm{Mg}}_2\mathrm{Si}$ were estimated to be $+0.1$ and $-0.3$ electrons. The discrete variation Hatree-Fock-Slater calculations for ${\mathrm{Mg}}_2\mathrm{Si}$ and CaSi also showed opposite chemical shifts and effective charges: $-0.09\mathrm{eV}$ and $-0.35$ electrons for ${\mathrm{Mg}}_2\mathrm{Si}$ and $+0.09\mathrm{eV}$ and $+0.26$ electrons for CaSi, respectively. The composition of the nearest-neighbor atoms of Si, which are Si in CaSi and Mg in ${\mathrm{Mg}}_2\mathrm{Si}$, cause the opposite effective charges between the two silicides.

Figure 1

The Si $K\alpha$ x-ray fluorescence spectra of Mg and Ca silicides. Dot: the raw experimental data. Solid line: The Si $K\alpha$ x-ray spectrum after the Savitzky-Golay smoothing, the parameters of which are given in the text. The broken lines represent the curve-fitting spectra by using the smoothed Si $K\alpha$ spectrum of pure Si.

Figure 2

The correlation between the effective charges on Si and the chemical shifts in the Si $K\alpha$ lines. Open circle: DV$X\alpha$ calculations for the free single Si atom. The open triangle and square represent calculations for ${\mathrm{Mg}}_2\mathrm{Si}$ (${\mathrm{Mg}}_8\mathrm{Si}$ cluster) and CaSi (${\mathrm{Ca}}_8\mathrm{Si}$ cluster), respectively. The closed triangle and square indicate measured ones for ${\mathrm{Mg}}_2\mathrm{Si}$ and CaSi, respectively.