Lattice Energy Calculation for Li Inserted Graphite at Relaxation Process

Abstract

Introduction Relaxation analysis makes transition of electrode material from kinetic state to equilibrium state clear [1]. We have applied the Relaxation analysis to various kind of cathode and anode materials, such as γ-Fe2O3[2,3], LiMn2O4[4], LiFePO4[5], LiCoO2[6], LiMnPO4[7] and so on. In the previous work, we conducted relaxation analysis to graphite, the widespread anode material for lithium ion rechargeable batteries[8]. We analyzed the variation of stage structure of lithium-graphite intercalation compounds (Li-GICs) based on the one-dimensional Rietveld method[9]. It was indicated that defective stage 1 was formed at the lithium insertion process, and it separated into stage 1 without defect and stage 2 during the relaxation. Stage 2 had two kinds of interlayer distance. The wider interlayer distance increased, and narrower one decreased with the relaxation time. Generally, the structure of stage 2 is presented as the stack of Li-inserted graphene layer and Li-not-inserted graphene layer. However, from the point of symmetry, stack of graphene layers with two different Li concentration at the interlayer makes stage 2 structure. It was considered that, at Li insertion process, Li-rich interlayer and Li-lean interlayer stacked to construct stage 2, and that, at the relaxation time, structure of stage2 changed to stack of Li–fully-inserted graphene layer and Li-not-inserted graphene layer. This means that the stack of Li-fully-inserted graphene and Li-not-inserted graphene has the minimum lattice energy. In the present study, we compared the lattice energy of various stage 2 stacking graphene layers with different Li concentrations by the first principle calculations. Calculation We used Advance/PHASE software developed by Advancesoft corporation. The Advance/PHASE is based on first principle calculation with using the DFT (Density-Functional Theory) adopting the LDA (Local Density Approximation) and GGA (Generalized Gradient Approximation). Advance/PHASE solve the Kohn-Sham equation in SCF (self-consistent field). First, we constructed a stage 2 model having two graphene layer with 24 C atoms each. Second, we set 4 Li atoms in the model with 4 kinds of distribution as Fig.1. Number 1: 4 Li atoms are located in one interlayer with LiC6 type structure (ideal stage 2). Number 2,3,4 : Three kinds of Li configuration at the Li-lean layer. Results and Discussion The calculated lattice energies increased with the order as Number 1 < Number 2 < Number 3 < Number 4. This means that Number 1 configurations, the stack of Li-fully-inserted graphene and Li-not-inserted graphene (ideal stage 2), is the minimum, most stable. It is consistent the previous result that the wider interlayer distance increased, and narrower one decreased with the relaxation time for stage 2 at relaxation process.