Table 1 Description of three polymorphs of composition Li₆Mn₄O₁₀.

DFT structure information				Cation environment around metal, i.e. number of nearest neighbor Li⁺, Mn³⁺, Mn⁴⁺
Polymorph	Mn³⁺ moments	Mn⁴⁺ moments	Energy above hull (meV/atom)	Mn³⁺	Mn³⁺	Mn⁴⁺	Mn⁴⁺
A	3.501, 3.504	2.732, 3.005	21.7	8 Li⁺ 2 Mn³⁺ 2 Mn⁴⁺	8 Li⁺ 2 Mn³⁺ 2 Mn⁴⁺	8 Li⁺ 2 Mn³⁺ 2 Mn⁴⁺	8 Li⁺ 2 Mn³⁺ 2 Mn⁴⁺
B	3.232, 3.232	3.169, 3.169	45.9	8 Li⁺ 1 Mn³⁺ 3 Mn⁴⁺	8 Li⁺ 1 Mn³⁺ 3 Mn⁴⁺	7 Li⁺ 3 Mn³⁺ 2 Mn⁴⁺	7 Li⁺ 3 Mn³⁺ 2 Mn⁴⁺
C	3.442, 3.629	2.724, 3.027	113.5	8 Li⁺ 1 Mn³⁺ 3 Mn⁴⁺	8 Li⁺ 1 Mn³⁺ 3 Mn⁴⁺	8 Li⁺ 2 Mn³⁺ 2 Mn⁴⁺	6 Li⁺ 4 Mn³⁺ 2 Mn⁴⁺

The DFT structure information for the three polymorphs is Mn d-orbital magnetic moments and energy above hull per atom and the valence is classified by the Bayesian optimization model. The 12 edge-sharing nearest neighbor cations, identified using the Bayesian optimization assignments, are also described for each polymorph.

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