Is the mean value of the 3d-electron radius $$\langle r^{4} \rangle$$ in the equation of the crystal-field theory constant?

Abstract

In the equation of the crystal-field theory $$\Delta = \frac{{Q \cdot \langle r^{4} \rangle }}{{\overline{R}{^5} }}$$ , where Δ is the crystal-field splitting, $$\overline{R}$$ is the mean metal–ligand distance in the 3dN-ion-centered coordination polyhedron and Q is constant, $$\langle r^{4} \rangle$$ , the mean value of the fourth power of the 3d-electron radius, is assumed to be also constant (Burns 1993). Here, this assumption is proved by means of high-pressure optical absorption spectroscopy on octahedral Fe2+ in siderite FeCO3 in combination with the data of X-ray diffraction structural refinement by Lavina et al. (2010). It is shown that in the pressure range 1·10–4 to 44.5 GPa or $$\overline{R}$$ ranging from 2.15 to 1.97 A, the value of Q $$\cdot \langle r^{4} \rangle$$ does not deviate more than ~ 4% from its average value.