Stable and Metastable Structures in Compressed LiC6: Dimensional

Article pubs.acs.org/JPCC

Stable and Metastable Structures in Compressed LiC6: Dimensional Diversity Chao Zhang,† Jie Lan,‡ Hong Jiang,† and Yan-Ling Li*,‡ †

Department of Physics, Yantai University, Yantai, 264005, China Laboratory for Quantum Design of Functional Materials, School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China

‡

S Supporting Information *

ABSTRACT: Unbiased structural searching, together with ab initio calculations, was performed to investigate the crystalline structures of lithium-intercalated graphite compound (LiC6) under pressure. Four low-enthalpy phases are found as the thermodynamic ground states of LiC6 up to 240 GPa, including an experimentally observed P6/mmm phase and three predicted orthorhombic phases (Pmmn, Immm, and Cmmm). For carbon atoms, the 2D graphite layered structure is predicted to transform first to a 3D nanofoam structure, then into a 2D diamond-like strips structure, and ultalimately to a 3D network structure. The covalent bonding among carbon atoms exhibits sp2 and sp3 hybridization in the orthorhombic phases, and sp3 hybridization tends to increase with increasing pressure. Phonon calculations verify that the competitive phases are thermodynamically stable. These findings elucidate the phase transitions of LiC6 under high pressure, offering major implications as regards the high-pressure behaviors of graphite intercalation compounds.

1. INTRODUCTION Metal carbides have been extensively investigated for their remarkable physical and chemical properties.1−5 Graphite intercalation compounds (GICs) are particularly attractive because of their unique anisotropic structural, electronic, and transport properties.6−9 GICs consist of stacks of graphite layers alternated with layers of intercalated atoms or molecules. A wide variety of intercalacants, such as alkaline earth or rare earth metals, can be incorporated in GICs because of the weak van der Waals interactions between the graphite layers. Intercalation provides a way to control the physical properties of the graphite host. Interest in GICs has been reignited by the discovery of relatively high superconducting transition temperatures (Tc) in YbC6 (6.5 K) and CaC6 (11.5 K).10 A large linear increase in Tc was observed in CaC6 from 11.5 K at ambient pressure to 15.1 K at 7.5 GPa, which was then followed by a sudden drop to 5 K at about 8 GPa.11 No superconducting transition was observed in CaC6 at above 2 K for pressure between 18 and 32 GPa, thereby signaling the formation of a new phase. The re-emergence of the superconductivity of CaC6 was predicted in a high-pressure phase (phase III, space group Pmmn) from 39 to 126 GPa. In phase III of CaC6, Tc initially increased and then decreased as pressure increased, reaching up to 14.7 K at 78 GPa.12 The re-entrance of superconductivity in heavily compressed CaC6 provides another instance wherein the peculiar physical behaviors of materials under extreme conditions can be analyzed. The novel electronic properties of metal carbides stem from the wide structural range of carbon forms, including onedimensional (1D) chains and strands, 2D slabs and layers, and 3D frameworks. Under the application of pressure, 2D carbon © XXXX American Chemical Society

layers in the R-3m phase of CaC6 transform into a 3D framework, in which calcium atoms from the 3D network are turned into a 2D buckled plane.12 A carbon open framework structure with a mixed sp2/sp3 bonding character is formed in the 3D framework of CaC6. The ratio of sp3 in the sp2/sp3 bonding character increases with the increasing of pressure, resulting in the polymerization of carbon atoms into diamondlike strips. Moreover, the sp3 hybridization of carbon atoms reduces the metallicity of CaC6. Carbon polymerization also occurs in metal dicarbides, such as Li2C2 and CaC2. Under ambient conditions, carbon atoms exist as strong covalent C2 dumbbells in CaC2. The dumbbell carbon polymerizes first into a 1D chain and then into a ribbon and ultimately into a 2D graphite layer under high pressure.13 The predicted Tc of the metallic high-pressure phases of CaC2 is comparable to those observed in CaC6. In the completed pressure−composition phase diagram of a Ca−C system, isolated atoms and zigzag tetramers were found in Ca2C and CaC, respectively. Carbon ribbons are present in carbon-rich compounds. As pressure increases, the C−C bond order decreases from triple to double to single bonds. Most interestingly, a low-pressure phase of Ca2C exhibits a quasi-2D metallic behavior and contains negatively charged calcium atoms.14 In addition, carbon dumbbells, zigzag chains, and ribbons are similarly found in SrC2 under high pressure.15 These findings confirm to the trend of that the polymerization of carbon atoms increases with Received: February 3, 2016 Revised: April 28, 2016

A

DOI: 10.1021/acs.jpcc.6b01206 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

stopped when the forces generally acting on the atoms were found to be smaller than 0.001 eV/Å. With this criterion, the change in the total energy between successive steps was less than 0.01 meV/cell. Phonon calculations were performed using supercell approach.33 Real-space force constants of supercells were calculated within VASP, and phonon frequencies and the corresponding phonon density of states were calculated from the force constants using the PHONOPY code.34,35 Under quasi-harmonic approximation (QHA), the phonon contribution to the Helmholtz free energy Fph(T, V) is given by

increasing pressure and expands the knowledge on carbon chemistry. LiC6 exhibits promising properties that are beneficial to the battery industry and for electronic applications.16−19 Although many studies have investigated the structural and electronic properties of LiC6, few attempts have been made to study its behavior under high pressure, particularly its pressure-induced phase transitions. Kganyago et al. studied the first phase (P6/ mmm) of LiC6 up to 25 GPa and presented a volume−pressure relationship. No new phases were predicted in their work.20 In our previous work of CaC6,12 we conducted a tentative exploration of LiC6 under pressure and first proposed two open framework structures (Pmmn and P63/mcm) of LiC6, as shown in Figure S7 of the Supporting Information of ref 12. Later, Lin et al. investigated Li−C system in a broad range of chemical compounds.21 They reproduced the two phases of LiC6, namely, Pmmn and P63/mcm phases, up to 70 GPa. Here, we have conducted a thorough theoretical investigation of the high-pressure behavior of LiC6 up to 240 GPa. The P63/mcm phase was found to be thermodynamically unstable. Apart from the Pmmn phase, two newly thermodynamically stable phases (Immm and Cmmm) was proposed. Under high pressure, LiC6 predictably undergoes P6/mmm → Pmmn → Immm → Cmmm phase transitions, and the calculated pressures of the phase transitions are 23.7, 48, and 178.4 GPa. Under compression, the graphite layered structure of carbon atoms in the P6/mmm phase is first transformed into a nanofoam structure in the Pmmn phase, then to a diamond-like strip structure in the Immm phase, and then to a 3D networks in the Cmmm phase.

Fph(T , V ) = kBT

∫0

∞

⎡ ⎛ ℏω ⎞⎤ g (ω) ln⎢2sinh⎜ ⎟⎥d ω ⎢⎣ ⎝ 2kBT ⎠⎥⎦

where ω represents the phonon frequencies, g(ω) is the phonon density of states, and T is the temperature. ℏ and kB are the reduced Planck constant and Boltzmann constant, respectively. The Gibbs free energy G(T, p) could be written as G(T , p) = U (V ) + Fph(T , V ) + pV

where V and p are volume and pressure, respectively, and U(V) is the total energy of electronic structure. This method had been successfully used to investigate the phonon vibrational contribution to phase transition of uranium dioxide.36

3. RESULTS AND DISCUSSION Knowing the chemical compositions only, we correctly reproduced the experimental P6/mmm phase at ambient pressure with GGA and LDA methods. This accomplishment validates the effectiveness of the USPEX methodology used in structural searches of LiC6. In addition to the known P6/mmm structure, five competitive structures with different symmetries are selected from a large set of structures. It is worth noticing that both GGA and LDA methods give the same competitive structures. The phase transition sequence of the competitive structures remains unaltered using GGA and LDA methods, and only the phase transition pressures of these structures change. The phase transition pressures of the competitive structures with LDA method are slightly smaller than that with GGA method (see Figure S1 in the Supporting Information). In addition, no significant changes were found GGA and LDA methods to calculate the electronic structure and phonon spectrum of the competitive structures. The van der Waals (vdW) interaction has been proved to be important for graphite and lithium intercalated graphite compounds at ambient conditions.37−39 Upon compression, bonding patterns, including vdW interaction, established at ambient conditions change dramatically in these compounds. In previous works, Lin et al.21 performed structure searches with GGA method and recalculated the competitive structures with optB88-vdW method. Their calculated phase transition pressures using optB88-vdW method are in excellent agreement with our results with GGA method. In fact, our previous calculations showed that the vdW interaction only influences formation enthalpy of GICs at ambient pressure and its effects on phase transition under high pressure are negligible.13,14 It is attributed to the sp2 hybridized carbon in graphite at ambient pressure and the sp3 hybridized carbon in diamond above 8 GPa. Therefore, it is appropriate to investigate the high-pressure behaviors of LiC6 using GGA method, and we presented the electronic structure and phonon results with GGA method in the following parts.

2. COMPUTATIONAL METHODS The ground state of a material under pressure usually corresponds to the global minimum of the Gibbs free energy surface, and finding this state is essentially a minimization problem and may be solved by searching for structures with the lowest Gibbs free energies. The search for low-enthalpy crystalline structures of LiC6 were performed via evolutionary algorithm (EA) technique as implemented in the USPEX code, which is specially designed for the global structural minimization unbiased by any known structural information.22−24 This method had been successfully predicted structures of various systems ranging from elemental solids24,25 to binary13,26 and ternary compounds.27 In the EA simulations, the underlying ab initio structural relaxations were carried out within the framework of density functional theory as implemented in the Vienna Ab-initio Simulation Package (VASP).28,29 In these calculations, the exchange and correlation energy was assessed by the generalized gradient approximation (GGA) in the scheme of Perdew−Burke−Ernzerhof (PBE)30 and the local density approximation (LDA) using Ceperley-Alder parametrization.31 The electron−ion interaction was described by means of projector augmented wave (PAW)32 with 1s22s1 and 2s22p2 as valence electrons for Li and C atoms, respectively. For the C atom, the hard pseudopotential was selected to carry out the calculations because hard pseudopotential was thought to be more suitable for high pressure research. For the crystalline structure searches, a plane-wave basis set cutoff of 700 eV and a coarse k-point grid were used to perform the Brillouin zone integrations. Candidate structures were selected and then recalculated using a higher Brillouin zone sampling of 2π × 0.018 Å−1 and a plane-wave basis set cutoff of 1000 eV. Iterative relaxation of cell volume, cell shape, and atomic positions was B


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The Journal of Physical Chemistry C The calculated enthalpy difference of the most energetically competitive structures of LiC6 relative to the Immm structure in the pressure range of 0−240 GPa are shown in Figure 1. The

Table 1. Lattice Parameters and Atomic Positions of LiC6 under Difference Pressures space group P6/mmm

pressure (GPa) 0

lattice parameters (Å, deg)

atomic positions (fractional)

a = b = 4.326, c = 3.783

Li 1a (0.0000 0.0000 0.0000) C 6k (0.3333 0.0000 0.2500) Li 2a (0.0000 0.0000 0.7466) C1 2a (0.0000 0.0000 0.1789) C2 4f (0.2087 0.0000 0.0380) C3 2b (0.0000 0.5000 0.3234) C4 4f (0.2959 0.0000 0.5318) Li 4c (0.6667 0.3333 0.2500) C1 12k (0.7884 0.0000 0.9349) C2 12k (0.5900 0.0000 0.0827) Li1 2a (0.0000 0.0000 0.0000) Li2 2c (0.0000 0.0000 0.5000) C1 8m (0.4077 0.0000 0.1763) C2 8m (0.1331 0.0000 0.1864) C3 8m (0.2275 0.0000 0.3140) Li 1b (0.0000 0.0000 0.0000) C1 2d (0.3333 0.6667 0.0328) C2 2d (0.3333 0.6667 0.2572) C3 2d (0.3333 0.6667 0.6848) Li 2a (0.0000 0.0000 0.0000) C1 4g (0.2131 0.0000 0.0000) C2 4h (0.4367 0.0000 0.5000) C3 4h (0.1358 0.0000 0.5000)

α = β = 90, γ = 120 Pmmn

23.7

a = 5.891, b = 2.480, c = 6.076 α = β = γ = 90

P63/mcm

45

a = b = 6.694, c = 4.160 α = β = 90, γ = 120

Figure 1. Enthalpy difference versus pressure for competitive structures of LiC6, referenced to the Immm phase.

calculated lattice parameters and atomic positions of the competitive structures at selected pressures are summarized in Table 1. Under ambient conditions, LiC6 adopts a simple hexagonal structure with P6/mmm symmetry. There is only one LiC6 unit in the conventional cell with Li atom at the Wyckoff 1a position and C atoms at the Wyckoff 6k position, as listed in Table 1. Under ambient pressure, the calculated lattice parameters of the P6/mmm phase are a = 4.326 Å and c = 3.783 Å, resulting in c/a = 0.875, which is in excellent agreement with the experimental data40 of c/a = 0.871. For GICs, intercalated metal atoms can be located in one of the three prismatic hexagonal sites denoted α, β, and γ. Hypothetically, if all the graphite layers A are stacked in an eclipsed form, three different simple stacks can be built: AαAα, AαAβ, and AαAβAγ. The first and second stacks demonstrate hexagonal symmetry, whereas the third one presents rhombohedral symmetry. Under ambient pressure, LiC6 adopts the first stack, and the representatives of the second and third stacks are YbC6 and CaC6, respectively.10 At approximately 23.7 GPa, the P6/mmm phase is predicted to give away to an orthorhombic structure with Pmmn symmetry. A conventional cell has four in-equivalent carbon atoms (labeled C1, C2, C3, and C4), forming a remarkable open framework structure. Along the y-axis direction, carbon atoms form a distorted hexagonal open framework structure with two short and four long borders, as shown in Figure 1. C1 and C3 atoms jointly construct zigzag chains that form the short border, whereas each type of C2 and C4 atoms forms individual zigzag chains that lie within the relatively long border. The C1 and C3 joint zigzag chain is shared by four open framework structures, and each C2 or C4 zigzag chain is shared by two open framework structures. Consequently, a rich hybridization occurs among the carbon atoms in the Pmmn phase of LiC6, that is, sp3 hybridization of C1 and C3 atoms and sp2 hybridization of C2 and C4 atoms. Li atoms sit at the center of the open framework structure, forming a 1D atomic chain along the y-axis direction. Under the phase transition pressure (23.7 GPa), the C−C bonding lengths in C2 and C4 zigzag chains are 1.409 and 1.407 Å, respectively, which are slightly

Immm

48

a = 15.267, b = 2.443, c = 4.063 α = β = γ = 90

P-3m1

120

a = b = 2.366, c = 6.907 α = β = 90, γ = 120

Cmmm

178.4

a = 10.854, b = 2.351, c = 2.361 α = β = γ = 90

smaller than that (1.520 Å) in C1 and C3 joint zigzag chains. The nearest neighbor distance between C and Li atoms is approximately 2.177 Å, which is smaller than the value of 2.480 Å of the Li−Li bonding length along the open framework extended direction (y-axis direction). Thus, a strong interaction exists between sp2 hybridized C and Li atoms because of the charge accumulation in the bonding region. As expected, LiC6 adopts a Pmmn structure, because CaC6, which a famous kind of GICs, adopts this structure as phase III under high pressure.12 Interestingly, the Pmmn structure enters the phase diagram of LiC6 at such a low pressure (23.7 GPa) compared with that in the phase diagram of CaC6 (39 GPa). The Pmmn structure of LiC6 provides another candidate material for achieving carbon foam, which has potential applications in purification, separation, adsorption, and catalysis.41 In view of the different guest sublattices, the size of the open framework structures in the two compounds exhibits slight differences under the same pressure. Under C


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atoms. The Li−Li bonding length along the z-axis direction in the P63/mcm phase is approximately 15% smaller than that in the Pmmn phase at 45 GPa, demonstrating a relatively strong Li−Li interaction in the P63/mcm phase. The Immm phase takes over for a relatively wide pressure range of 48−178.4 GPa. In this phase, carbon atoms integrate closely into diamond-like strip because of the external pressure and chemical precompression from the Li sublattice. The carbon strip consists of a slightly distorted (3, 0) carbon nanotube along the z-axis direciton, which is also a building block in the P63/mcm phase. The Immm phase can be viewed as an AαBβ periodically layered structure along the x-axis direction, where A and B represent the diamond-like strip layers and α and β denote the metal layers. The A and B diamond-like strip layers are mirror symmetrical with respect to the α or β metal layers. In the diamond-like strips, internal C atoms show obvious sp3 hybridization, whereas surface C atoms mostly form sp2 hybridization. At 48 GPa, the calculated C−C bonding length is approximately 1.500 Å, and the nearest neighbor distance between Li and C atoms is approximately 2.000 Å, indicating an enhanced interaction. In addition, the Li−Li bonding length is further compressed and reduced to 2.031 Å at 48 GPa in the Immm phase of LiC6. It is noteworthy that the Immm phase is very similar to phase IV of CaC6 with Cmcm symmetry. The only difference is that the metal atoms in the Cmcm phase of CaC6 are arranged in a puckered manner, whereas the metal atoms in the Immm phase of LiC6 are along a straight line along the z-axis direction. At above 178.4 GPa, a C-centered orthorhombic phase with Cmmm symmetry becomes energetically favorable up to 240 GPa, which is the highest pressure studied here. There are two LiC6 units in the conventional cell with a = 10.854 Å, b = 2.351 Å, and c = 2.361 Å at 178.4 GPa. The Li atoms occupy the Wyckoff 2a position, and the three in-equivalent C1, C2, and C3 atoms occupy the Wyckoff 4g, 4h, and 4h positions, respectively, as listed in Table 1. Similar to the Immm phase, the C1 and C3 atoms form diamond-like strips, showing sp3 hybridization between the C atoms. However, because of the external pressure, part of the C atoms residing in diamond-like strips in the Immm phase are squeezed into the interlayer space. The interlayered C atoms (C2) connect two adjacent diamondlike strips and exhibit sp2 hybridization. The nearest neighbor carbon atoms of Li are the interlayered C atoms, between which the distance is reduced to approximately 1.802 Å, indicating an enhanced interaction between Li and C atoms. In addition, the volume of carbon tetrahedrons in the diamondlike strips is significantly decreased under pressure. At 178.4 GPa, the average volume of tetrahedrons in the Cmmm phase is approximately 1.517 Å3, which is 14% smaller than that in the Immm phase at 48 GPa. Another metastable phase with P-3m1 symmetry is predicted. At 120 GPa, the optimized lattice parameters for the P-3m1 phase (Z = 1) are a = 2.366 Å and c = 6.907 Å, with the atomic positions of Li atoms being at the Wyckoff 1b site and C atoms at three in-equivalent Wyckoff 2b sites, as presented in Table 1. Similar to the Immm phase, layers of Li atoms are intercalated between the carbon strips. However, careful examination of the carbon strips reveals that they are puckered graphene layers that stacked along the z-axis direction, thus, showing a huge discrepancy in the diamond-like strips in the Immm phase. At 120 GPa, the puckering height of the graphene layers is 0.401 Å, and the nearest distance between adjacent graphene layer is 2.953 Å. Li atoms connects two in-equivalent C atoms with

ambient pressure, the size of the open framework structure in LiC6 is approximately 0.60 nm, which is similar to that in CaC6 (0.61 nm). With the application of pressure, the shape of the open framework structure is squeezed as a result of the enhanced interaction between the carbon host sublattice and the metal guest sublattice. The Pmmn phase only exists within a narrow pressure range of 23.7−48 GPa. Two other structures with hexagonal P63/ mcm and orthorhombic Immm symmetries dramatically compete for the low-enthalpy phase. In fact, the maximum enthalpy difference among the Pmmn, P63/mcm, and Immm structures is 0.1 eV/fu in the pressure range of 44−52 GPa. Interestingly, the P63/mcm phase is composed of neartriangular open framework structures and (3, 0) zigzag carbon nanotubes, which are both along the z-axis direction, as shown in Figure 2. Similar to the Pmmn phase, the Li atoms sit at the

Figure 2. Crystal structures of LiC6 for (a) P6/mmm, (b) Pmmn, (c) Immm, (d) Cmmm, (e) P63/mcm, and (f) P-3m1 phases. The green (large) and brown (small) spheres represent Li and C atoms, respectively.

center of the open framework structure. At 45 GPa, the optimized structural parameters for the P63/mcm phase (Z = 4) are a = 6.694 Å and c = 4.160 Å. The Li atoms take the Wyckoff 4c (0.6667 0.3333 0.2500), whereas C1 and C2 atoms occupy the Wyckoff 12k (0.7884 0.0000 0.9349) and the Wyckoff 12k (0.5900 0.0000 0.0827), respectively. The C1 atoms consist (3, 0) carbon nanotubes that connect six carbon open framework structure, and the exhibit sp3 hybridization. The C2 atoms form armchair chains shared by two open framework structures, and they display sp2 hybridization between carbon atoms. The average C−C bonding lengths between C1 atoms in (3, 0) carbon nanotubes is slightly smaller than that between C2 D


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Figure 3. Gibbs free energy difference as a function of pressure for various temperature for (a) P6/mmm phase referenced to Pmmn phase, (b) Pmmn phase referenced to Immm phase, and (c) Immm phase to Cmmm phase. The green dash lines are (a) P6/mmm phase, (b) Pmmn phase, and (c) Immm phase without considering temperature effects.

transition pressure between the Pmmn and Immm phases increases from 48 GPa without considering temperature effects to 49.2 GPa at 0 K and 54.2 GPa at 1000 K. Interestingly, the phase transition pressure of the Immm → Cmmm phase is reduced from 178.4 GPa without considering temperature effects to 176.9 GPa at 0 K and then increases to 177.8 GPa at 1000 K, as shown in Figure 3c. It originates from the special phonon dispersion relationships of the Immm phase. Therefore, the inclusion of phonon vibrational contribution to the Gibbs free energy does not change the phase transition sequence but only alters the phase transition pressures. The phonon band structures along the high-symmetry directions in the Brillouin zone (BZ) and the phonon projected density of states (PDOS) for the Pmmn phase at 30 GPa, the Immm phase at 65 GPa, and the Cmmm phase at 185 GPa are shown in Figure 4. The absence of imaginary frequency modes throughout the BZ indicates that these phases are thermodynamically stable at the selected pressures. Additional phonon calculations are performed to inspect the stability of these phases in their favored pressure ranges. For the Pmmn phase at 30 GPa, the relatively low-frequency modes (below 20 THz) originate mainly from the Li, C2, and C4 atoms. The C atoms dominate the remaining frequency range (above 20 THz) . The peaks centered at 40 THz contributed by C1 and C3 atoms correspond to the flat bands in the phonon band structure, particularly along the Z → T → Y directions. The very highfrequency modes from 40 to 50 THz originate mainly from the C2 and C4 atoms, and the C1 and C3 atoms contribute slightly to this region, as shown in Figure 4a. With increasing pressure, the Li-related vibration modes increase as well. The Li-related vibration modes disperse up to 30 THz in the Immm phase at 65 GPa. Interestingly, the vibration modes of Li atoms split in the Immm phase, as shown Figure 4b. The Li1 atoms mainly contribute to the frequency range below 15 THz, whereas the Li2 atoms mainly contribute to the frequency range of 15−30 THz. Similar to the Pmmn phase, the C-related vibration modes dominate the high-frequency range above 30 THz. For the Cmmm phase at 185 GPa, the maximum frequency shifts upward, reaching approximately 55 THz. Remarkably, the Lirelated vibration modes mainly contribute to the medium-

1.869 and 2.613 Å. On the other hand, the P-3m1 phase can be interpreted as an AαAα periodically layered structure along the z-axis direction, where A represents the carbon strip layers and α denotes the metal layers. The AαAα stacking of the P-3m1 phase is similar to the that of the P6/mmm phase. With regard to energy, the enthalpy of the P-3m1 structure is close to that of the P6/mmm structure. Thus, it is not unexpected that the metastable P-3m1 phase share the structural characteristics of the P6/mmm phase. To investigate the temperature effects on phase stability, we estimated the phonon vibrational contribution to the Gibbs free energy under selected pressures within QHA. In the temperature range of 0−1000 K, the phonon vibrational energy difference is below 150 meV/fu between the competitive phases at a given pressure. Especially, the phonon vibrational energy difference of the P6/mmm and Pmmn phases is only at the magnitude of 10 meV/fu between 15 and 30 GPa. Except for the P6/mmm, Pmmn, Immm, Cmmm, and P63/mcm phases, the enthalpies of other interesting phases are 300 meV/fu larger than the low-enthalpy phases around phase transition pressures. In addition, the P63/mcm is not thermodynamically stable. Thus, we focused on the P6/mmm, Pmmn, Immm, and Cmmm phases and showed the temperature effects on phase transition in Figure 3. Under low pressure, the phonon vibrational energy is substantially smaller than the absolute value of enthalpy and thus only slightly contributions to the Gibbs free energy. At 15 GPa, the calculated phonon vibrational contribution to the Gibbs free energy of the P6/mmm phase is 2.1% at 0 K and 0.3% at 1000 K, respectively. Due to the zero-point effect, the phase transition pressure of the P6/mmm → Pmmn phase increases from 23.7 to 24.1 GPa. Increasing temperature to 1000 K, the phase transition pressure is slightly raised to 24.3 GPa, as shown in Figure 3a. The phonon vibrational energy slowly increases with pressure, whereas the enthalpy prominently increases under pressure due to the pV term. At 50 GPa, the calculated phonon vibrational contribution to the Gibbs free energy of the Pmmn phase is 2.7% at 0 K and 0.8% at 1000 K, respectively. The temperature effects on the Pmmn and Immm phases around 48 GPa are show in Figure 3b. The phase E


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Figure 4. Phonon band structures and phonon PDOS of LiC6 for (a) Pmmn phase at 30 GPa, (b) Immm phase at 65 GPa, and (c) Cmmm phase at 185 GPa. The unit of phonon PDOS is states/THz/atom.

Figure 5. Electronic band structures and electronic PDOS of LiC6 for (a) Pmmn phase at 23.7 GPa, (b) Immm phase at 48 GPa, and (c) Cmmm phase at 178.4 GPa. The unit of electronic PDOS is states/eV/ atom.

frequency range of 20−35 THz, which is entirely different compared to the Pmmn and Immm phases. The C3 vibration modes mainly contribute to the low-frequency range (below 20 THz). The high-frequency range (above 35 THz) are coming from the C1, C2, and C3 atoms. The calculated electronic band structures along the highsymmetry directions in the BZ and the corresponding PDOS of LiC6 are shown in Figure 5. The electronic band structures of the Pmmn, Immm, and Cmmm phases under their favorable pressures reveal the metallic characteristic of LiC6 from 23.7 to 240 GPa. For the Pmmn phase at 23.7 GPa, the electronic density of states (DOS) near the Fermi level is dominated by the C 2p states with small contributions from the Li 2p states. The total electronic DOS at the Fermi level is approximately 0.445 states/eV/fu. Two steep bands cross the Fermi level along the Y → S direction in the BZ, which leads to a nearly constant DOS in the energy range of −1 to 1 eV, as shown in Figure 5a. These results indicate the good metallic feature of the Pmmn phase of LiC6. Under the application of pressure, the metallicity of LiC6 is weakened accompanied by the Pmmn to Immm structural transition. A valence band crossing the Fermi level at the X point and a conduction band crossing the Fermi level along the W → R direction overlap in the Immm phase at

48 GPa. It is noteworthy that a flat part of the conduction band along the W → R direction results in a peak of the electronic DOS at the Fermi level, as shown in Figure 5b. The total electronic DOS at the Fermi level of the Immm phase at 48 GPa is only half of that of the Pmmn phase at 23.7 GPa. With further compression, the total electronic DOS at the Fermi level exhibits a pronounced enhancement and reaches 0.330 states/eV/fu. Interestingly, a flat is also found band along the T → Y direction, yielding a small peak at the Fermi level, as displayed in Figure 5c. Thus, the metallic characteristics of LiC6 is once again strengthened under pressure. Given the small contributions of Li atoms, the electronic PDOS of the in-equivalent C atoms of LiC6 under pressure are displayed in Figure 6. In the vicinity of the Fermi level in LiC6 under pressure, the electronic DOS of C atoms mainly come from the C atoms that have the shortest distance with Li atoms. For the Pmmn LiC6 at 23.7 GPa, the electronic DOS of C atoms at the Fermi level is dominated by the C2 and C4 2p states with the same contribution. The C2 and C4 atoms in the form of zigzag chains have the nearest distance with Li atoms; as such, they display a strong interaction with Li atoms. The electronic DOS of C atoms at the Fermi level mainly comes F


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Figure 6. Electronic PDOS of C atoms in LiC6 for (a) Pmmn phase at 23.7 GPa, (b) Immm phase at 48 GPa, and (c) Cmmm phase at 178.4 GPa.

from C1 2p states and C2 2p states for the Immm and Cmmm phases of LiC6, respectively. The C1 atoms in the Immm phase located on the surface of the diamond-like strip layers and C2 atoms in the Cmmm phase at the interlayer are the nearestneighbor atoms of Li atoms. Furthermore, the C atoms that significantly contribute to the electronic DOS at the Fermi level exhibit sp2 hybridization and thus could receive the electron transferred from Li atoms. The electron localization function (ELF) was investigated to gain further insight into the bonding nature of the concerned phases of LiC6 under pressure. The ELF is considered an informative tool utilized for exploring different bonding interactions in solids.42,43 The calculated ELF of (010) planes of the Pmmn, Immm, and Cmmm phases are shown in Figure 7. The isosurface plots at an ELF value of 0.75, which is a typical number for characterizing covalent bonding, clearly illustrate the covalent bonding nature of C atoms in the three structures, as shown in Figure 7a,c,e. The sp3 hybridized covalent bond changes slightly with pressure, and electrons are aggregated at the center of the bond, as shown in the ELF isosurface plots. However, the sp2 hybridized covalent bond is weakened under pressure. The electrons involved in this type of bond are not only localized at the center of the bond, but are also dispersed to the side of the bond. Furthermore, the dispersion of the sp2 hybridized covalent bond becomes apparent under pressure, such as the C2−C2 covalent bond in the Cmmm phase at 178 GPa, as shown in Figure 7e,f. Far away from the covalent bond region, the ELF value around C atoms becomes small and reaches approximately 0.5, indicating delocalized characters. The ELF sections show that the ELF value between Li and C atoms approaches 0, which suggests nonbonding characteristics, as shown in Figure 7b,d,f. For the Li atoms in the three structures, the electrons are almost entirely depleted from their valence, which will be discussed later. To describe the charge transfer and chemical bonds clearly and quantitatively, a topological analysis of the static electron density was performed according to Bader’s quantum theory of atoms-in-molecules.44−46 Bader analysis was successfully applied to determine the bonding interactions in solids, in which the charge (QB) enclosed within the Bader volume is a good approximation of the total electronic charge of an atom. The calculated Bader analysis results of the P6/mmm, Pmmn,

Figure 7. ELF isosurface of LiC6 for (a) Pmmn phase at 23.7 GPa, (c) Immm phase at 48 GPa, and (e) Cmmm phase at 178.4 GPa with the ELF value of 0.75. The (010) plane of ELF for (b) Pmmn phase at 23.7 GPa, (d) Immm phase at 48 GPa, and (f) Cmmm phase at 178.4 GPa. The green (large) and brown (small) spheres represent Li and C atoms, respectively.

Immm, and Cmmm phases for LiC6 are summarized in Table 2. For the P6/mmm LiC6 under ambient pressure, each C atom gains approximately 0.147 electrons, whereas the Li atom loses roughly 0.882 electrons. These results demonstrate the significant charge transfer between Li atoms and C six-ring units. For the Pmmn phase at 23.7 GPa, the electrons lost by Li atoms are transferred to C atoms, specifically C2 and C4 atoms. This finding is consistent with the electronic DOS results. When further compressed, the Li atoms lose fewer electrons: 0.825 electrons for the Immm phase at 48 GPa and 0.668 electrons for the Cmmm phase at 178.4 GPa. Correspondingly, the C atoms gains fewer electrons. In other words, under external pressure, some electrons residing at the C atoms are transferred back to the Li atoms. It is noted that the C atoms that are not the nearest neighbor of Li atoms seem neutral, namely, the C1 and C3 atoms in the Pmmn phase, the C2 and C3 atoms in the Immm phase, and the C1 and C3 atoms in the Cmmm phase. The calculated effective Bader charge of these C G


Article

The Journal of Physical Chemistry C Table 2. Calculated Effective Atomic Charge According to Bader Partitioning of LiC6 phase

QB(Li) (e)

pressure (GPa)

P6/mmm

0

Pmmn

23.7

Immm

48

Cmmm

178.4

Li 0.882 Li 0.845 Li1 0.825 Li 0.668

QB(C) (|e|) C −0.147 C1 0.041 C1 −0.390 C1 0.005

Li2 0.775

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C4 −0.235

REFERENCES

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4. CONCLUSIONS The pressure-induced phase transitions of LiC6 have been systematically investigated by utilizing ab initio calculations. Upon compression, the simple hexagonal phase (P6/mmm) of LiC6 is predicted to transform to three orthorhombic structures, namely, Pmmn, Immm, and Cmmm phases. These phase transitions successively take place at 23.7, 48, and 178.4 GPa. Correspondingly, the 2D graphite layered structure of carbon atoms transform first into a 3D nanofoam structure, then into a 2D diamond-like strips structure, and ultimately into a 3D network structure. The electronic band structures show that these competitive phases are metallic. The C atoms that have relatively short distance with Li atoms mainly contribute to the total electronic DOS at the Fermi level. Phonon calculations show that the competitive phases are thermodynamically stable because of the absence of any imaginary frequencies in their favored pressure ranges. For the low-pressure phases (Pmmn and Immm), the C atoms dominate the high-frequency modes (above 30 THz). With increased pressure, the Li-related modes shift upward and mainly contribute to the medium-frequency range of 20−35 THz in the Cmmm phase. These results are expected to expand the understanding of the structural and electronic properties of GICs under high pressure and further enrich the carbon chemistry. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01206. Enthalpy difference versus of pressure for competitive structures of LiC6 with LDA (PDF).

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C3 0.042 C3 0.001 C3 −0.014

Program Development of Jiangsu Higher Education Institutions (PAPD).

atoms are either approximately zero or showing positive value, such as that for the C1 and C3 atoms in the Pmmn phase. This finding indicates that these C atoms only construct the host sublattice but hardly participate the charge transfer with Li atoms.

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C2 −0.229 C2 −0.011 C2 −0.325

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +(86)516-83500484. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants Nos. 11304269, 11347007, and 11304268) and the Qing Lan Project and the Priority Academic H


Article

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Stable and Metastable Structures in Compressed LiC6: Dimensional

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