(a) Illustration of the transition from an undistorted octahedron cage with a O h octahedral symmetry to a trigonally distorted cage with a D 3h octahedral symmetry and the associated further crystal field splitting of the d-states. (b) Dependence of the ratio k 64 on the anion parameter u characterizing the trigonal distortion for S-spinels. The black dots denote the results for the original spinel structures with the Mg ion in a tetrahedral site and the octahedral vacancy being empty, and the black line corresponds to the analytical expression Eq. 5. The blue diamonds are determined for the relaxed spinels with the octahedral site occupied by a Mg anion. The blue line is a linear regression of these results.

(a) Illustration of the transition from an undistorted octahedron cage with a O h octahedral symmetry to a trigonally distorted cage with a D 3h octahedral symmetry and the associated further crystal field splitting of the d-states. (b) Dependence of the ratio k 64 on the anion parameter u characterizing the trigonal distortion for S-spinels. The black dots denote the results for the original spinel structures with the Mg ion in a tetrahedral site and the octahedral vacancy being empty, and the black line corresponds to the analytical expression Eq. 5. The blue diamonds are determined for the relaxed spinels with the octahedral site occupied by a Mg anion. The blue line is a linear regression of these results.

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In the area of sustainable energy storage, batteries based on multivalent ions such as magnesium have been attracting considerable attention due to their potential for high energy densities. Furthermore, they are typically also more abundant than, e.g., lithium. However, as a challenge their low ion mobility in electrode materials remains. This stu...

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Context 1
... spinel structures often exhibit a trigonal distortion of the octahedra that corresponds to a displacement of the X-ions along the [111] direction and changes the O h octahedral symmetry to a D 3h octahedral symmetry but keeps the overall octahedral shape unchanged (see Fig. 2a). 44 The trigonal distortion can be characterized by a u anion parameter 45 that reflects the displacement of the X-ions along the [111] direction in units of the lattice constant a. Sickafus et al. 45 showed that this parameter can be expressed through Besides the additional cystal field splitting, the trigonal distortions also modify ...
Context 2
... and tend to be more conducting. The various transition metal ions with d 1 up to the d 10 configurations lead to magnetic structures that are caused by the strong Coulomb repulsion within the d-orbitals. 50 In addition, the d-orbital electron interaction decreases the atomic distances and adds more trigonal distortion to the system as shown in Fig. ...
Context 3
... on the properties of the spinels, we have plotted in Fig. 4 the density of states (DOS) of MgB 2 X 4 spinels with B =Sc and Y, and X = S and Se that can be realized experimentally. 51,52 Note that these spinel structures also exhibit trigonal distortions, but they are smaller than those for the spinels with later d-band metals, as shown in Fig. 2b. In Sc and Y, the d-orbitals are empty which leads to unoccupied t 2g (green) and e g (yellow) manifolds. In both compounds with Sc and Y cations, respectively, the valence bands are dominated by S-and Se-p bands, respectively, in the energy range from −4 eV to 0 eV. For both systems, the DOS of the t 2g and e g states is rather broad ...
Context 4
... order to see this, we focus on the ratio k 64 between the Mg-X bond length in the occupied tetrahedral and octahedral sites, as shown for some ternary spinels by the blue symbols in Fig. 2b. According to our calculations, for the MgAl 2 S 4 system characterized by a ratio of about k 64 = 1.08, the octahedral and the tetrahedral site become energetically degenerate with regard to the Mg occupation, as illustrated in Fig. 6a. This can be explained by a competition between bond length and coordination as a function of the ...

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Preprint
Full-text available
In the area of sustainable energy storage, batteries based on multivalent ions such as magnesium have been attracting considerable attention due to their potential for high energy densities. Furthermore, they are typically also more abundant than, e.g., lithium. However, as a challenge their low ion mobility in electrode materials remains. This stu...