For the layered rhombohedral structure, if we define foct1 as the average atomic-scattering power at the lithium octahedral sites, foct2 as the average atomic-scattering power at transitionmetal octahedral sites, and fO as the atomic-scattering power of oxygen that builds up the skeleton, then the structural factors for the rhombohedral-(003)R and (104)R peaks can be calculated, respectively, as (3foct1– 3foct2– 1.1fO), and (3foct1 + 3foct2 + 5.8fO). The migration of transition metals from their own layer
to the lithium layer greatly increases foct1 due to the much larger atomic-scattering power of the transition metals. Since
the foct1 and foct2 have opposite signs for the (003)R peak, the increased foct1 will reduce significantly the amplitude square of
Fhkl. In contrast, foct1 and foct2 have the same signs in the structure factor of the (104)R peak, and therefore, the increase of foct1 will engender an increase in the amplitude square of Fhkl for the (104)R peak. This is the origin of using the intensity ratio of the (003) to (104) peaks to indicate the degree of cation mixing (transition metals in lithium-layer sites). During the initial stage of heating, the reducing intensity ratio of the (003)R to (104)R peaks in the TR-XRD patterns clearly denotes the migration of
transition metal cations into the lithium layers where vacancies had been created during the overcharge process
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