Chemical capacitance measurements reveal the impact of oxygen vacancies on the charge curve of LiNi0.5Mn1.5O4−δ thin films

The level of oxygen deficiency δ in high-voltage spinels of the composition LiNi0.5Mn1.5O4−δ (LNMO) significantly influences the thermodynamic and kinetic properties of the material, ultimately affecting the cell performance of the corresponding lithium-ion batteries. This study presents a comprehensive defect chemical analysis of LNMO thin films with oxygen vacancy concentrations of 2.4% and 0.53%, focusing particularly on the oxygen vacancy regime around 4 V versus Li+/Li. A set of electrochemical properties is extracted from impedance measurements as a function of state-of-charge for the full tetrahedral-site regime (3.8 to 4.9 V versus Li+/Li). A defect chemical model (Brouwer diagram) is derived from the data, providing a coherent explanation for all important trends of the electrochemical properties and charge curve. Highly resolved chemical capacitance measurements allow a refining of the defect model for the oxygen vacancy regime, showing that a high level of oxygen deficiency not only impacts the amount of redox active Mn3+/4+, but also promotes the trapping of electrons in proximity to an oxygen vacancy. The resulting stabilisation of Mn3+ thereby mitigates the voltage reduction in the oxygen vacancy regime. These findings offer valuable insights into the complex influence of oxygen deficiency on the performance of lithium-ion batteries based on LNMO.


S4.1. Stoichiometric LNMO
Here we derive the general form of the Li chemical potential, and hence the chemical capacitance, for the case of multiple Li sites with different vacancy formation energies (e.g., octahedral and tetrahedral Li sites in a spinel structure) and multiple redox couples with different redox potentials (e.g., Mn and Ni in ).We start by considering the general insertion equilibrium of Li into an arbitrary  1 -  0.5  1.5  4 - material according to where corresponds to formally neutral lithium in the external phase (i.e., a Li ion from the electrolyte  together with an electron from the current collector according to ) that defines the Li useful to reference the concentration of species to the total concentration of formula units with being the site occupancy of species and the corresponding number of sites per formula unit.

𝑥 𝑗 𝑗 𝑦 𝑗
For example, for the tetrahedral (T) and octahedral (O) Li sites in a typical spinel material.In the case of LNMO, two different transition metals (Mn and Ni) act as active redox couples in the insertion reaction with corresponding capacities of and .The goal is now to obtain (i) an expression for the total Li chemical potential and (ii) the concentration of all electronic and ionic species as a function of , i.e., a Brouwer diagram.Although the latter could be obtained by solving the corresponding system of mass action laws combined with the appropriate charge neutrality equations, it is not straightforward to obtain an expression for , and hence the chemical capacitance, via this approach.As in our previous study on on LiMn 2 O 4 , 1 we therefore approach the defect chemical calculation via the separate chemical potentials of ionic and electronic charge carriers, as shown in the following.
For the insertion equilibrium in eqn (S1) we can formulate the corresponding balance of chemical potentials as with being the total Li chemical potential.We note that equilibrium conditions require that all Li sites The total vacancy and electron site fractions can then be expressed as and An additional correction term was introduced in eqn (S9( to describe a possible shift of with respect , and , the total site fractions and should vary from 0 to 2 and 2 to 0, respectively, as the material is oxidized from to .This requires a value of to  2  2 + 0.5  3 + 1.0  4 + 0.5  4  4 + 0.5  4 + 1.5  4  = 0.5 account for the fact that in the fully reduced state of the material, i.e., at full occupancy of the octahedral sites, 0.5 formula units of remain.The correction term can also be conveniently used to describe the effect of dopants, as described in the next section. Finally, the total chemical potentials and of Li vacancies and electrons, respectively, can / = 0.70   that the chemical capacitance peaks (i.e., charge curve plateaus) occur around the same electrode potentials as observed experimentally.

S4.2. Oxygen-deficient LNMO
The defect chemical calculation of stoichiometric LNMO can easily be adapted for the presence of an electronically compensated donor dopant, such as oxygen vacancies, by subtracting the donor site fraction from the correction term according to    = 0.5 - •  = 0.5 - where is the charge number of the corresponding donor species.For oxygen vacancies , .The adapted Brouwer diagram for oxygen-deficient LNMO is shown in Figure 7b of the main manuscript for , with all other parameters remaining the same. = 0.1

Fig. S3
Fig. S3 Total effective electrode resistance as a function of electrode potential (a) and Li content (b).The Li   =   /3 +   content x was derived by normalization to the total electrode capacity obtained from the integration of via eqn (7) of the   ℎ