Structural Diversity in Lithium Carbides

Structural Diversity in Lithium Carbides Yangzheng Lin1, Timothy A. Strobel1,∗ and R. E. Cohen1,2† 1Extreme Materials Initiative, Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road, NW, Washington, DC 20015, USA and 2University College London, UK The lithium-carbon binary system possesses a broad range of chemical compounds, which exhibit fascinating chemical bonding characteristics that give rise diverse and technologically important properties. While lithium carbides with various compositions have been studied or suggested previously, the crystal structures of these compounds are far from well understood. In this work we present the first comprehensive survey of all ground state (GS) structures of lithium carbides over a broad range of thermodynamic conditions, using ab initio density functional theory (DFT) crystal structure searching methods. Thorough searches were performed for 29 stoichiometries ranging from Li12C to LiC12 at 0 GPa as well as 40 GPa. Based on formation enthalpies from optimized van der Waals density functional calculations, three thermodynamically stable phases (Li4C3, Li2C2 and LiC12) were identified at 0 GPa, and seven thermodynamically stable phases (Li8C, Li6C, Li4C, Li8C3, Li2C, Li3C4, and Li2C3) were predicted at 40 GPa. A rich diversity of carbon bonding, including monomers, dimers, trimers, nanoribbons, sheets and frameworks, was found within these structures, and the dimensionality of carbon connectivity existing within each phase was observed to increase with increasing carbon concentration. Of particular interest, we find that the well- known composition LiC6 is actually a metastable one. We also find a unique coexistence of carbon monomers and dimers within the predicted thermodynamically stable phase Li8C3, and different widths of carbon nanoribbons coexist in a metastable phase of Li2C2 (Imm2). Interesting mixed 2 3 sp -sp carbon frameworks are predicted in metastable phases with composition LiC6. I. INTRODUCTION Li-C compounds over a broad compositional range to understand which kinds of precursors might exist un- Numerous novel carbon allotropes [1–16] have been der ambient and high-pressure conditions, and to gain predicted theoretically over the past decades. Some insights into the forms of carbon existing within them. of these proposed structures have excellent mechanical, A series of lithium carbon binary compounds (in- optical and/or electronic properties, which are impor- cluding Li6C[25–27], Li5C[25, 26], Li4C[25, 26, 28–33], tant for a wide range of potential applications. For Li3C[28, 32–36], Li8C3[33], Li2C[31, 33–36], Li4C3[29, example, three-dimensional (3D) metallic carbon al- 31, 33–35, 37–40], Li2C2[29, 31, 33, 36, 41–43], Li4C5[33, lotropes [1, 4, 13–16] are potentially important con- 44], LiC2[45], LiC3[45], LiC6[43, 46, 47], LiC10[48], ductors with excellent chemical inertness under ambient and LiC12[43, 46, 47], etc.) have been reported the- conditions, and carbon allotropes with high elastic con- oretically or experimentally since half a century ago. stants but low densities like clathrates [3, 5, 6, 17] would Most of those previous studies focused on the molec- be especially useful for light-weight structural materi- ular structure and the stability of molecular clusters. als. However, it is particularly challenging to synthe- Of these reported compounds, only Li2C2[33, 41, 49– size these materials from pure carbon, due to their rela- 55] and some graphite intercalation compounds (LiC6 tively higher enthalpies than graphite or diamond, and and LiC12, etc.)[47, 53, 56–60] have been investigated only limited experimental evidence for these phases cur- experimentally in their crystal structures. rently exists [18, 19]. Another way to synthesize pure Ab initio density functional theory calculations have carbon allotropes is to start from carbide precursors. many successful examples of predicting the relative sta- This approach has been successful in the production bilities for solid crystal phases of single elements and of so-called carbide-derived carbon [20]. Novel silicon multicomponent compounds under ambient and high- arXiv:1607.03170v1 [cond-mat.mtrl-sci] 11 Jul 2016 and germanium allotropes may be produced through pressure conditions. Some methods including random the leaching of metal atoms from metal silicide or ger- sampling [61, 62], minima hopping [63, 64] and those manide precursors [21–24], which suggests the possibil- implemented in Uspex [65, 66], Calypso [67, 68] or ity of making pure carbon allotropes from metal car- XtalOpt [69, 70] were developed in the past decade bides in a similar way. Considering that carbon atoms and have made the prediction of ground state crystal have a smaller radius than silicon atoms, we focus on the structures much easier and more efficient [71]. In the possibility of carbon framework-based lithium carbides. system of lithium carbon compounds, some searches In order to establish potential thermodynamic stabil- were performed previously for the stoichiometry Li C ity for these types of structures, we have investigated 2 2 [50–52] and some polymeric forms of carbon were predicted at high pressure [50, 52]. In this work, we predict two more stable high-pressure phases of Li2C2. We ∗ [email protected] provide the static convex hulls (i.e., formation enthalpy † [email protected] vs concentration diagrams) at 0 and 40 GPa, and thus 2 predict a broad range of novel, thermodynamically sta- modynamically stable and some metastable structures. ble, lithium carbide phases. Various forms of carbon For all the thermodynamically stable and metastable are found to exist within these stable crystal structures, structures, we calculated the phonon frequencies using and suggest energetically viable pathways to novel car- density-functional perturbation theory (DFPT) to de- bon /textcolorredmaterials. termine their dynamic stabilities. Twenty-nine stoichiometries of LimCn (m : n in 12:1, 10:1, 8:1, 6:1, 5:1, 4:1, 3:1, 8:3, 5:2, 2:1, 5:3, 3:2, 4:3, 5:4, II. COMPUTATIONAL METHODS 2:2, 4:5, 3:4, 2:3, 3:5, 1:2, 2:5, 3:8, 1:3, 1:4, 1:5, 1:6, 1:8, 1:10 and 1:12), which include all the possible ground We predict the GS crystal structures of lithium car- state lithium carbides between Li12C and LiC12 sug- bides through evolutionary algorithm-based searching gested by previous studies (see the introduction), have methods, as implemented in the opensource package been investigated in order to determine the GS struc- XtalOpt [69, 72]. The evolutionary algorithms in tures. While we consider our searching to be compre- XtalOpt were designed to generate new structures hensive over a broad range of composition, we acknowl- that have lower enthalpies than structures in previous edge the finite nature of these searches given limitations generations. All searches were initialized by 30–60 ran- of computational resources, and realize the possibility of domized or specified structures, and they were not ter- thermodynamically stable phases for unconsidered sto- minated until the lowest enthalpy structure survived af- ichiometries or number of primitive cell atoms. For a ter 300–600 generated structures. Each search used a given pressure, the thermodynamically stable structures fixed number of formula units of LimCn (m and n are are those whose formation enthalpies per atom lie on the irreducible integers except in Li2C2, where the reducible convex hull of formation enthalpy a function of compo- notation is preserved following standard convention). sition [81, 82]. For a compound LimCn, the formation The structure with the lowest enthalpy is regarded as enthalpy of a structure under pressure P is defined as the ground state for a given stoichiometry. At a given pressure and stoichiometry, several searches with differ- H m n (P ) − mH (P ) − nH (P ) ∆H(P )= Li C Li C (1) ent numbers (1–6) of formula units were performed to m + n avoid missing the true ground state structure. For computational efficiency, the largest number of primitive cell where HLimCn is the enthalpy per formula unit of LimCn atoms was limited to 20 in all searches. The symmetries for a given structure. HLi and HC are enthalpies per of low-enthalpy structures were refined using FindSym atom of lithium and carbon in their ground-state crystal [73, 74]. structures, respectively. The atomic concentration of The enthalpy of each structure within the evolution- carbon in the compound LimCn is defined as, ary algorithm searching was calculated from DFT re- n x = (2) laxation using the projector-augmented wave (PAW) C m + n method [75, 76] within the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) [77, 78]. The DFT structural relaxations were performed III. RESULTS AND DISCUSSIONS using pwscf in the package of Quantum-Espresso [79, 80]. In our DFT calculations, the electronic con- A. Thermodynamically Stable Lithium Carbides figurations for Li and C were 1s22s1 and [He]2s22p2, respectively. The plane-wave kinetic-energy cutoff was The van der Waals (vdW) interaction has proved to 80 Ry (1088 eV). During the searching process, the be important for predictions of both structural and en- × × Monkhorst-Pack (MP) k-point meshes k1 k2 k3 were ergetic information for graphite and graphite interca- × given according to ki = bi/(2π 0.06) (i = 1, 2, 3) lated lithium compounds [60, 83, 84]. Here we show in where b1, b2 and b3 are the lattice lengths (in unit of Table I that the vdW interaction is also crucial in pre- −1 A˚ ) in reciprocal space. The relative enthalpies of diction of the formation energies of Li2C2. Except in the lithium carbides converged up to 6 meV/atom within DFT-local density approximation (DFT-LDA) calcula- these settings. For each stoichiometry, several low- tions where the LDA PAW pseudopotentials (PAWs) enthalpy structures were selected carefully from all the were used, we used the PBE PAWs in all other DFT and crystal structures obtained by searchings.

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