The crystal structure of LiCoO is presented in Fig We
The crystal structure of LiCoO2 is presented in Fig. 1. We can notice that the Li and Co atoms occupy the centers of two different edge-sharing [CoO6]-octahedra, which results in formation of separate Li and Co layers. Hence, the layered structure of LiMO2 is able to intercalate lithium into transition metals compounds.
Because of high degree of chemical disorder occurring in the considered materials (Li or O vacancy defects and Co/Ni/Mn alloying), the electronic structure calculations of such precise oxygen nonstoichiometry measurement solid solutions become much more complicated than the corresponding computations of ordered LiMO2 compounds. The fully spin- and charge-self-consistent Green function Korringa-Kohn-Rostoker method (KKR) combined with the coherent potential approximation (CPA) was employed [21,22] to treat chemical disorder as random. It is worth noting that such approach allows to perform electronic structure calculations in the whole range of composition without changing the symmetry of the unit cell, which makes an important difference comparing with other computational methods based on supercell models of disordered systems. In the KKR-CPA computations, the crystal potential of the muffin-tin form was constructed within the local density approximation (LDA), applying the Perdew-Wang formula . The Fermi vasopressin receptor (E) was determined accurately using the generalized Lloyd formula  and employing an elliptic contour in the complex energy plane. Total, site- decomposed and l-decomposed DOS were computed employing k-space integration technique over a dense mesh of small tetrahedrons in the irreducible part of the Brillouin zone. Because of the presence of transition metals, which commonly exhibit an intense d-like DOS peaks in the vicinity of E, the KKR-CPA calculations were carried out considering both non-spin-polarised and spin-polarised cases, expecting the onset of magnetic moments on these atoms.
Results and discussion
Conclusions The results of KKR and KKR-CPA electronic structure calculations were presented for LiMO2 compounds and LiNiCoMn0.1O2 solid solutions, respectively. It was found that Mn impurity located in semiconducting LiCoO2 matrix might exhibit magnetic moment. The mixing energy of LiNiCoMn0.1O2, as resulted from the total energy KKR-CPA calculations, was found to be negative, indicating relative crystal stability in the whole range of composition. Depending on Li content as well as relative Co/Ni/Mn concentrations, electronic structure of Li(Co-Ni-Mn)O2 can exhibit semiconducting-like, half-metallic-like or even metallic-like properties. The appearance of magnetic moments on transition metal elements is strongly related to the presence of large peak of d −states and can be understood in term of Stoner mechanism. Interestingly, it was shown from the spin-polarised KKR-CPA computations of LiNi0.55Co0.35Mn0.1O2 and LiNi0.65Co0.25Mn0.1O2 that magnetic moments might appear when decreasing Li concentration. The largest value of magnetic moment, about 1.5μ, was calculated on Mn atoms, while smaller moments was found on Co and negligible on Ni atoms. Besides, in view of the spin-polarised KKR-CPA results one can expect that the onset of magnetic properties as well as the presence of the O vacancy defects in the studied Li(Ni-Co-Mn)O cathode materials may affect overall DOS shape near E. It can also influence the charge/discharge curve during delithiation process if assuming close correlation of its shape with DOS features and position of E [11,12].
Acknowledgments This work was partially supported by the AGH UST statutory tasks (No. 11.11.220.01/5) from the Polish Ministry of Science and Higher Education. The work was also partially funded by the National Science Centre Poland under the project OPUS-12 (UMO-2016/23/B/ST8/00199).
Introduction The Cubic-Plus-Association (CPA) equation of state (EoS) is a combination of the SRK EoS and the association term that is based in the work of Wertheim  and is used in SAFT . The model has been described extensively in the literature, including two review articles , , other reviews , a recent monograph  and other recent books . Readers are referred to the original articles and these other works for more details on CPA. No model equations are presented here. The reader must be familiar with the concepts of association sites/schemes and the combining rules used in CPA for following the discussion of this and the forthcoming article on the CPA application to biodiesel-related systems.