Interactions between carbon species and β-spodumene by first principles calculation

Abstract

First principles calculations were carried out to study the interactions between carbon species and a β-spodumene matrix. Stabilities of low-index surfaces of β-spodumene with different terminations were firstly evaluated by surface energy calculations and results indicate that the Si–O–Li terminated (100) surface is the most stable surface with the lowest surface energy among the considered surfaces. The adsorption of carbon on the surface of β-spodumene and the formability of carbon-β-spodumene species are studied to clarify the interaction properties between them. The carbon species will be easily doped into or adsorbed on the surface of β-spodumene. The electronic structures reveal weak bonding interactions between the carbon layer and β-spodumene matrix, while these interactions can be strengthened by the adsorption of Li atoms on the carbon layer resulting in strong bonding interactions between them and therefore increasing the charge transfer between the carbon layer and β-spodumene matrix. Therefore the appearance of Li in the carbon species will improve the binding properties between the carbon species and β-spodumene matrix.

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1. Introduction

Glass-ceramics have been widely used in industry, such as aerospace, architecture, and daily necessities, due to their excellent performance and low cost. Lithium aluminosilicate (LAS), one of the most important glass-ceramics, has been extensively studied over the past few years. LAS owns an ultra-low coefficient of thermal expansion and fine electrical properties and has been applied as a structural material of precision components, such as the lens of a telescope.¹

The major components of LAS are β-quartz solid solution and β-spodumene (Li₂O–Al₂O₃–SiO₂). It was found that the firstly precipitated β-quartz solid solution will transform to β-spodumene in Li₂O–MgO–ZnO–Al₂O₃–SiO₂ glass when the content of Li₂O is higher than 2.5%.² In LAS, a lithium atom coordinates with four oxygen atoms, and Si and Al atoms randomly distribute in five tetrahedra formed by Si/Al and O atoms. These five circles produce interstitial space with a diameter about 3 Å.³ The interstitial spaces are often filled by Li⁺ to compensate for the charge defect caused by the substitution of A1³⁺ to Si⁴⁺.

The near zero coefficient of thermal expansion is one of the most attractive properties of LAS and it is well known that the coefficient of thermal expansion of LAS based glass-ceramics is very sensitive to the content of SiO₂. However, the low ductility of LAS glass-ceramics hinders their applications as a functional material. SiC and C fibers are usually used to reinforce LAS. The additions of SiC and C produce interface and interphases with the matrix of LAS, which play important roles on the physical properties of LAS.^4,5 The interface can prevent the propagation of microcrack caused by the stress to protect the brittle matrix. Continuous interface can be constructed by heat treatment in glass-ceramics.^6,7 The mixture of LAS with SiC fiber will produce carbon-rich interface at high temperatures.^8,9 This interface region enhances the connections between SiC fiber and LAS matrix, and therefore, improves the mechanical property of LAS.^10,11 Furthermore, owing to the strong bonding interactions with C, the C reinforced LAS glass-ceramics show good strength at high temperature.^12–15 Previously, we studied the mechanical and thermal properties of carbon fiber reinforced β-spodumene, and found that the diffusion of Li atom to the carbon fiber from β-spodumene drives the formation of the interfacial zone improving the thermal and mechanical properties of LAS.¹⁶

Recently, theoretical calculations on the flotation of spodumene were reported.^17,18 The O atoms in spodumene are found to be the most active for H⁺ bonding,¹⁷ and calcium hydroxide is the effective species to activate the flotation.¹⁸ The electronic and optical properties of alpha spodumene are also studied, but β-spodumene is rarely referred.^19,20 Previously, we found the formation of LiC₂₄ compound enhances the physical properties of carbon fiber reinforced spodumene composite.¹⁶ However, the formation mechanisms of Li–C compound and the interaction mechanisms between carbon layer and β-spodumene are still unclear. Therefore, in this work, the interaction mechanisms between carbon species and β-spodumene surface were further studied by theoretical calculations.

2. Computation method

The energy and electronic structure of β-spodumene and β-spodumene-C layer are calculated by Vienna Ab-initio Simulation Package (VASP) code.^21,22 The atomic configurations of the β-spodumene were obtained from experiment.³ The unit cell of bulk β-spodumene contains 8 Si, 4 Al, 24 O and 4 Li atoms. The stabilities of low-index surfaces of β-spodumene, i.e., (001), (010), (100), (110), and (111) surfaces, were examined. The bulk and surface of the β-spodumene with defects (C doping and vacancy) were also studied. The surfaces of β-spodumene were modeled by slabs of about 0.7 × 0.9 × 1.7 nm³ in size plus 1.5 nm vacuum in the c direction. The interface model between carbon layer and β-spodumene slabs with proper supercell approach was used to decrease the lattice misfit. Projector augmented wave (PAW) method with generalized gradient approximation function^23,24 was used for all calculations. The reference configurations for the valence electrons of considered elements are: Li: s¹p⁰, C: s²p², O: s²p⁴, Al: s²p¹, and Si: s²p². The energy cutoff of plane wave basis set was selected as 400 eV. Monkhorst–Pack²⁵ k-point grids for these systems were all carefully checked. The energy differences between 5 × 5 × 4, 6 × 6 × 5, and 7 × 7 × 5 are 1.0 meV around and a 6 × 6 × 5 grid was used for the bulk β-spodumene. The k-point grids for surface and interface systems are chosen corresponding to the bulk phase.

3. Results and discussions

3.1. Stability of β-spodumene surface

The calculated lattice parameters of bulk β-spodumene are a = 7.607 Å and c = 9.302 Å, which are well consistent with the experimental values (a = 7.541 Å and c = 9.156 Å). The total energy of high-temperature phase (β-spodumene) is about 0.26 eV higher than the low-temperature phase (α-spodumene). The β-spodumene is the principal crystalline phase in many low-expansion ceramic materials,¹⁶ and therefore, the β-spodumene is considered in this work. The stability of a surface can be evaluated via surface energy, E_s, defined as:where U_s and U_b are the total energies of surface model and the bulk phase with same number of atoms, respectively. Fig. 1 illustrates some low-index surfaces of the β-spodumene.

Fig. 1 Side view of supercells of selected low-index surfaces of β-spodumene. (a) (001) surface with Al–O–Si termination, (b) (010) surface with O–Al–Li termination, (c) (100) surface with Si–O–Li termination, (d) (110) surface with O–Al–Li termination, and (e) (111) surface. d₁ to d₃ indicate the separation between layers. The largest green, small blue, medium gray and smallest red balls denote the Li, Si, Al, and O atoms, respectively.

The distances between Li–Li, Al–Al, and Si–Si ions in neighboring planes are almost identical before relaxations. Significant distortions on positions of Li and Al ions in surface layer were observed in some models after relaxation. Generally, the Si ions are rarely distorted during the relaxation and they are therefore selected as tracers to indicate the distance between layers. The d₁, d₂, and d₃ are measurements of the distance between Si atoms in the adjacent layers as shown in Fig. 1.

Table 1 shows the surface energy and distance between layers. Among the considered surfaces, the most stable surface is the Si–O–Li terminated (100) surface with surface energy of 1.351 J m⁻² following with Si–O–Li terminated (111), O–Al–Li terminated (010), O–Al–Li terminated (110), and Al–O–Si terminated (001) surfaces with surface energies of 1.534, 1.538, 2.5, and 2.617 J m⁻², respectively. For the Al–O–Si terminated (001) surface, the outer layer distance (d₁) is about 0.02 and 0.01 Å larger than that of inner layer (d₂) and (d₃), respectively. The average distance between Si and O is about 0.028 Å smaller than that of bulk phase. Four types of (010) surface with different terminations were studied. The most stable configuration of the (010) surface is the O–Al–Li terminated one, in which the values of d₁ and d₂ are about 1.3 Å smaller than the d₃ meaning great shrinks of (010) surface occurred. In the Si–O–Li terminated (100) surface, the distance between its top two layers are expanded about 1.0 Å comparing to the inner layers. The average distance between Si and O atoms in the topmost layer of the most stable configuration is about 1.647 Å, which is 0.009 Å larger than that in the bulk phase (1.638 Å).

Table 1 The surface energy and separation between layers of β-spodumene surfaces with different terminations

Surface	Termination	Es (J m^−2)	d1 (Å)	d2 (Å)	d3 (Å)
(001)	Al–O–Si	2.617	2.255	2.234	2.342
	Si–O–Li	2.638	2.335	2.252	2.215
	Li–Al–Si	3.330	2.316	2.221	—
	O–Al–Li	3.352	2.542	2.212	2.201
(010)	Al–O–Si	2.016	2.879	3.147	4.492
	Si–O–Li	2.754	4.104	3.179	4.277
	Li–Al–Si	2.352	3.437	3.159	4.317
	O–Al–Li	1.538	3.151	3.177	4.493
(100)	Al–O–Si	2.585	4.701	3.147	4.267
	Si–O–Li	1.351	4.321	3.155	3.433
	Li–Al–Si	1.737	3.144	4.628	2.990
	O–Al–Li	2.040	4.181	4.258	3.172
(110)	Al–O–Si	4.999	2.497	2.577	2.568
	Si–O–Li	5.000	2.497	2.577	2.568
	Li–Al–Si	4.999	2.497	2.577	2.568
	O–Al–Li	2.500	2.497	2.577	2.568
(111)		1.534	1.994	1.984	—

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For the (110) surface, it was shown the difference of total energies between different terminations is less than 3 meV indicating the similar stability between them. However, it owns the largest surface energy than other low-index surfaces considered herein. The distance between topmost two layers (d₁) shrinks about 0.07 Å comparing with the d₃. The relaxation will cause the average distance between Si and O in topmost layer become 0.038 Å larger. Only one type of (111) surface was studied. Its d₁ shrinks about 0.15 Å comparing with the d₃ after relaxation. However, the average distance between Si and O in topmost layer is almost unchanged (only 0.001 Å elongation being within the error range).

From above studies, the Si–O–Li terminated (100) surface owns the lowest surface energy and it is therefore selected as the model of β-spodumene surface in following text. Generally, the relaxations will make a elongation of the Si–O distance, which may indicate the decreasing of bonding strength between them in the surfaces.

3.2. Stability of β-spodumene with defects

3.2.1. Bulk β-spodumene. Three kinds of defects, vacancy, substitution, and interstitial, are considered in β-spodumene systems. Vacancies studied herein are the single vacancy of Li, Al, O, and Si atoms. It is worth to note that great amounts of active forms of carbon are involved in the preparation of carbon fibers.²⁶ The deformations of the graphene layers and breaking of the C–C bonds will occur due to the diffusion of ions during the hot pressing. These stresses will cause the graphite exfoliation and detachment of graphite from the surface of carbon fiber. Furthermore, the CO and CO₂ gases are formed during the reaction between carbon fibers and glass matrix at high sintering temperature, which will cause irreversible damage and disintegration of the graphite lattice.¹⁶ Thus substitution of C atom for Li, Al, O, or Si atom was investigated. It is worth to note that the formation energies of C defects in both the bulk and surface of β-spodumene will be strongly affected by the chemical potential of reference phase or compound of carbon atoms. The chemical potential of C defect in β-spodumene should be much closer to that of C atom than that of graphite due to the disintegration of carbon fibers at high sintering temperature. In the interstitial occupation, the C atom is assumed to occupy C1 to C3 sites as shown in Fig. 2. Formation energy of defect in the β-spodumene is evaluated via the definition below:

E_f = E − E₀ − E₁ + E₂ (2)

where E_f, E, and E₀, are the formation energy, total energies of β-spodumene with and without defect, respectively. E₁ stands for the energy of atomic C for the substitution and equals to zero for the vacancy defect, and E₂ represents the energy per host atom (substituted by C or moved out) in their ground states. For the interstitial occupation, E₂ equals to zero. Ten different sites, three interstitial sites and seven substitutions, of C in bulk β-spodumene were modeled as shown in Fig. 2. Table 2 listed the formation energies of the defected systems. The really large vacancy formation energies of all elements Li, Al, Si, and O indicate that it is hard to generate any kind of vacancy in the β-spodumene. It is worth to note that the chemical potential of host atom moved out to form a vacancy, is equal to the total energy per atom of its ground state. Therefore, the formation energy of vacancy may be overestimated. The substitution of C for Si and the occupation at interstitial sites are preferable with negative formation energy. Therefore, there are strong bonding interactions between active C atoms and the matrix of β-spodumene.

Fig. 2 The doped β-spodumene bulk systems. The substitutions of C for O1 to O4, Al, Li, and Si atoms are performed individually and the C1 to C3 (the small brown balls) indicate the interstitial sites for C.

Table 2 Formation energies of vacancy and C defects in the bulk β-spodumene (eV)

Defect	Location	Ef
Vacancy	Li	9.035
	Al	12.596
	Si	9.029
	O	24.624
Substitution	Li	−0.299
	Al	0.060
	Si	−2.624
	O1	1.936
	O2	−0.145
	O3	1.402
	O4	1.297
Interstitial	C1	−1.968
	C2	−2.135
	C3	−2.804

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3.2.2. Surface. Simulations of defects in surface were performed for the Si–O–Li terminated (100) surface, the most stable surface among the considered surfaces. Firstly, we studied the doping of C atom in the Si–O–Li terminated (100) surface. The calculated formation energies are listed in Table 3. The formation energy of C doping in the surface is significantly reduced comparing to that in the bulk β-spodumene. Generally, surface doping owns the thermodynamic favorite with negative formation energy except the substitutions of O1, O2 and Li2. The C atom prefers to occupy the Si1 (substitution) and the Inter-5 sites (as shown in Fig. 3), which is similar with the occupation in the bulk β-spodumene.

Table 3 Formation energies of vacancy and C defects in the Si–O–Li terminated (100) surface of β-spodumene (eV)

C doping	Ef	Vacancy	Ef	Positions	Ech
Sub-Li1	−2.134	Li1	4.194	1 (on Al)	−4.025
Sub-Li2	1.011	Li2	4.261	2 (on Al)	−3.432
Sub-Li3	−2.500	Li3	3.994	3 (on Li)	−2.950
Sub-Al1	−2.752	Al1	9.942	4 (on Li)	−4.380
Sub-Al2	−2.167	Al2	9.421	5 (on O)	−4.179
Sub-Si1	−4.911	Si1	11.422	6 (on Si)	−3.080
Sub-Si2	−3.111	Si2	12.942	7 (on O)	−4.015
Sub-O1	0.255	O1	5.583	8 (on Si)	−4.728
Sub-O2	0.275	O2	5.963	9 (on Vac)	−2.786
Sub-O3	−0.285	O3	5.921	10 (on Vac)	−2.740
Sub-O4	0.369	O4	6.040
Inter-1	−3.070
Inter-2	−2.843
Inter-3	−3.508
Inter-4	−3.724
Inter-5	−4.135

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Fig. 3 Positions of defects in the Si–O–Li terminated (100) surface of β-spodumene. Labels on the atoms present these atoms were removed individually to form a vacancy. Small brown balls (1 to 5) are the interstitial sites of the C dopant, which are denoted as Inter-1 to Inter-5 in Table 3.

Second, the formation energy of vacancies in this surface was evaluated. Owing to different chemical environments, four O vacancies, three Li vacancies, and two for both Al and Si vacancies, as shown in Fig. 3, are considered. In term of the formation energy as shown in Table 3, the Al, Si and O vacancies are hard to be formed, especially the Al and Si vacancies. The formation energy of Li vacancies is around 4.0 eV, which is the lowest value among the considered vacancies. Thus the Li vacancy in the surface may be formed under high temperature. Experimentally it was found Li atoms homogeneously distribute around the carbon fiber in β-spodumene/carbon fiber composite, which may associate with the relatively lower formation energy of Li vacancy.¹⁶ Furthermore, the lithium was proved to be the only mobile particle in Li₂O–Al₂O₃–SiO₂,²⁷ and the mobile Li ions can incorporate in a crystal phase and minimize the residual glass phase during its crystallisation.²⁸

3.3. Adsorption of C species on surface

3.3.1. Carbon atom. The adsorption properties of C atom/layer on the surface of β-spodumene are studied to explore the formation mechanism of LiC₂₄ compound. Ten different positions are considered for C atom adsorption. The cohesion energy is calculated via definition below:

E_ch = E − E₀ − E_c (3)

where E_ch, E₀, and E_c are the cohesion energy, total energy of β-spodumene surface, and the total energy of C atom or layer, respectively. The adsorptions of C on all considered positions are exothermic as shown in Table 3. Therefore, the active carbon atoms will easily adsorb on the β-spodumene surface, especially on the Si position (Fig. 4).

Fig. 4 The top view of the adsorption positions of C and O atoms on the Si–O–Li terminated (100) surface of β-spodumene. The largest green, small blue, medium gray and smallest red balls denote the Li, Si, Al, and O atoms, respectively. Eight interstitial sites were considered, illustrating as the brown balls with 1 to 8 numbers.

3.3.2. Carbon layers. Above results reveal that the carbon atoms are easy to dope into the bulk and adsorb on the surface of β-spodumene. There are strong bond interactions between carbon and the matrix of β-spodumene, which will help to form the intermediate zone between carbon and β-spodumene as observed by our previous experiments.¹⁶ The interaction properties between carbon layers and β-spodumene surface are further studied. Mono- and double-carbon layers are considered. Two types of stacks, the AB (A) and BA (B) stacking, were applied to construct the interface model between the carbon layers and the Si–O–Li terminated (100) surface of the β-spodumene, as shown in Fig. 5. These two interfaces show close total energies. The initial separation between carbon layer and β-spodumene surface is chosen to be 1.25 to 3.0 Å varying with an interval of 0.25 Å. The interfacial ions are allowed to relax to find the stable configurations of interfacial zone between carbon and β-spodumene. This simulation approach will be beneficial for avoiding the interface getting into local optimality caused by the conjugate-gradient algorithm. Fig. 5 shows the relationship between total energy and separation of the interface, in which the interfacial configurations are varied via the separation. Therefore, there is an obvious fluctuation of the total energy with the separation. Generally, the total energy of interfaces decreases with the increasing of separation. The most stable interface appears when the relaxed separation between carbon and β-spodumene is 2.85 Å for AB type interface and 2.87 Å for BA type interface, respectively.

Fig. 5 Two type of interface systems between carbon layers and β-spodumene surface. (a) AB stacking, (b) BA stacking, and (c) the relationship between total energy and distance between C layer and spodumene surface.

Owing to a large number of C atoms are involved (24 and 48C atoms for single and double carbon layers), the evaluation of the cohesion energy of carbon layer on the β-spodumene surface could be sensitive to the choice of the reference state of carbon, i.e., the atomic carbon, graphite and the isolated layered carbon. The isolated carbon layer is selected as the reference state by considering the appearance of large amounts of carbon atoms in the interfacial zone. The cohesion energies of double carbon layers are 2.248 and 2.245 eV for AB and BA interfaces, respectively. Several intercalation models are employed to study the interactions between the mono-layer of carbon and spodumene as shown in Fig. 6. The large cohesion energy of intercalation indicates the carbon layer is hard to embed into the spodumene as shown in Table 4, while it is highly possible to adsorb on the surface of β-spodumene forming the interfacial zone.

Fig. 6 The simulated intercalation models of A type with different positions of carbon layer. The C layer of B type is a 180° rotation according to A type.

Table 4 Cohesion energy (eV) of C intercalation on β-spodumene surface with different positions of carbon layer showing in Fig. 6

Positions	A	B
a	1.182	1.203
b	13.015	12.666
c	10.411	11.227
d	5.403	10.126
e	8.416	5.446

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3.4. Interactions between Li and C on β-spodumene interface

As shown in Table 3 that the Li vacancy of β-spodumene is possible to form in the surface, the interactions between Li and dopant C are further studied to clarify the possible formation mechanisms of LiC₂₄. Fig. 7 shows the initial and relaxed configurations of interaction models containing the substitution of Li with C and adsorption of Li on carbon layer. The distance between the topmost atom of β-spodumene and carbon layer is 2.907 Å in the carbon layer adsorbed system (Fig. 7(a)), in which the distance between Li and C atoms is 3.027 Å. The positions of C atoms in carbon layer are rarely affected by the bottom surface of the β-spodumene, indicating the weak interactions between carbon layer and β-spodumene. For the Li substitution of C system (Fig. 7(b) and (c)), the Li initially locates at one C site but obviously moves downward to the β-spodumene surface after relaxation. Therefore, Li atoms prefers to bond with the topmost oxygen in β-spodumene surface with a distance of 1.972 Å between them. For the adsorption of Li on the carbon layer, the vertical distance between Li and carbon layer is 1.708 Å, and the Li–C bond length is 2.270 Å. Therefore, there may be strong interactions between Li and C atoms, which will enhance the binding strength between β-spodumene and carbon. However, the high temperature demands will be needed for the formation of Li–C compound¹⁶ by considering the energy difference of 3.212 eV between the Li adsorption model (Fig. 7(e)) and the initial model (Fig. 7(a)).

Fig. 7 Interactions between Li and C on β-spodumene surface. (a) Adsorption of C layer on the surface of β-spodumene, (b) the initial and (c) relaxed configurations of Li substitution of C systems, (d) the initial, and (e) relaxed configurations of Li adsorption system.

3.5. Electronic mechanisms

In order to study the bonding mechanisms and charge transfer between Li/carbon layer and β-spodumene surface, the density of states (DOS) and charge difference distributions (CDD) are studied and shown in Fig. 8 and 9, respectively. Fig. 8(a) shows the DOSs of C/β-spodumene interface. The main bonding peaks of Li, O, Al and Si atoms from β-spodumene surface are distributed in the energy region of (−6.4, −1.6) eV, while the bonding peaks of C atoms distribute in a broad energy region. There are two regions for the bonding interactions between carbon layer and β-spodumene surface, (−9.0, −4.0) eV and (−4.4, −3.0) eV. The carbon layer bonds with the Si, Al in low energy zone while with the Li atom in high energy zone. Fig. 8(b) shows the DOSs of Li adsorbed on C/β-spodumene interface system, the bonding peaks of β-spodumene matrix are moved about 1.0 eV toward the Fermi energy level comparing to the non-Li adsorbed system (Fig. 8(a)), but the distributions of bonding peaks of carbon layers are almost unchanged. The Li1 s and p orbitals overlap well with the C p in the energy region of (−7.5, 0) eV. There are strong bonding interactions between adsorbed Li and carbon layer, which will drive the formation of the Li–C compound as observed experimentally.¹⁶

Fig. 8 The density of states of C/β-spodumene interface systems. (a) C/β-spodumene interface, and (b) Li adsorbed on C/β-spodumene interface.

Fig. 9 The charge difference distributions of C/β-spodumene interface systems with different cleavage planes showing in Fig. 7(a) and (e). (a) I, (b) II, (c) III.

Fig. 9 shows the CDD of interface systems. The CDD was defined as the difference between the charge of C/spodumene interface (Fig. 9(a)) and of the carbon layer (Li adsorbed) and β-spodumene matrix (Fig. 9 (b) and (c)). The CDD can be obtained from the subtraction of charge density of interface systems with the charges of separated two parts by the cleavage plane. Three cleavage planes I, II, and III are chosen to study the charge transfer between slabs as shown in Fig. 7(a) and (e). The cleavage plane I separates the interactions between the C layer and the defect-free β-spodumene surface as shown in Fig. 7(a), while the cleavage planes II and III represent the separations of Li adsorbate and Li adsorbed C layer in Li adsorbing systems as shown in Fig. 7(e), respectively. Fig. 9(a) shows the charge transfer between carbon layer and β-spodumene slabs, the alterations of charge distributions are concentrated in the carbon layer, except the transfer of charge from the topmost Li atom (Li1) to the carbon layer. Therefore, the bonding interactions between carbon layer and spodumene surface are weak.

The charge distributions are greatly changed in Li adsorbed systems as shown in Fig. 9(b) and (c). Fig. 9(b) shows the charge transfer between Li and C/β-spodumene slabs, and Fig. 9(c) shows the charge transfer between Li adsorbed carbon layer and β-spodumene slabs. Fig. 9(b) shows the charge transfer from Li to the carbon layer causing strong bonding interactions between them. Fig. 9(b) and (c) both show the charge transfer from the carbon layer to the β-spodumene slabs, which will improve the binding properties between carbon layer and β-spodumene matrix.

4. Conclusions

The interactions between carbon species and the β-spodumene are studied by first principles calculations. The Si–O–Li terminated (100) surface owns the smallest surface energy of 1.351 J m⁻². The point defects in either the bulk or surface of β-spodumene are unstable, except the Li vacancy in the surface system. The carbon atom can easily dope into the bulk and adsorb on the surface of β-spodumene. Both the mono- and double- carbon layers can adsorb on the β-spodumene surface due to the small cohesion energies, but high temperature demands will be needed for the formation of Li–C compound. The electronic structures reveal that the Li improves the binding properties between carbon layer and β-spodumene matrix. Therefore, the formation of Li–C compound may be a good way to adjust the binding properties between carbon species and β-spodumene.

Acknowledgements

This work was supported by the Natural Science Foundation of Shandong, China, Grant No. ZR2014EMM013, No. ZR2014EMQ009, and the Fundamental Research Funds for the Central Universities Grant No. HIT. KITP. 2014030. JH Dai also acknowledges the innovation foundation from HIT. Simulations were performed using HPC resources in CAS Shenyang Super-computing Center.

References

1. L. Barbieri, C. Leonelli, T. Manfredini, C. Siligardi and A. B. Corradi, J. Am. Ceram. Soc., 1997, 80, 3077–3083.
2. G. H. Beall and L. R. Pinchney, J. Am. Ceram. Soc., 1999, 82, 5–16.
3. C. T. Li and D. R. Peacor, Z. Kristallogr., 1968, 126, 46–65.
4. J. D. Mathias, P. M. Geffroy and J. F. Silvain, Appl. Therm. Eng., 2009, 29, 2391–2395.
5. A. Luedtke, Adv. Eng. Mater., 2004, 6, 142–144.
6. R. J. Kerans, R. S. Hay, T. A. Parthasarathy and M. K. Cinibulk, J. Am. Ceram. Soc., 2002, 85, 2599–2632.
7. R. Naslain, O. Dugne, A. Guette, J. Sevely, C. R. Brosse and J. P. Rocher, J. Am. Ceram. Soc., 1991, 74, 2482–2488.
8. A. Jha and M. D. Moore, Glass Technol., 1992, 33, 30–37.
9. J.-Y. Hsu and P. F. Speyer, J. Mater. Sci., 1992, 27, 374–380.
10. T. I. Mah, M. G. Mendiratta, A. P. Katz and K. S. Mazdiyasni, Am. Ceram. Soc. Bull., 1987, 66, 304–307.
11. M. D. Thoulless, O. Sbaizzero, L. S. Sigl and A. G. Evens, J. Am. Ceram. Soc., 1989, 72, 525–532.
12. R. F. Cooper and K. Chyung, J. Mater. Sci., 1987, 22, 3148–3160.
13. A. L. Xue and I.-W. Chen, J. Am. Ceram. Soc., 1993, 76, 2785–2789.
14. A. Jha and M. D. Moore, Glass Technol., 1992, 33, 30–37.
15. X. B. Ren, H. J. Li, J. H. Lu, L. J. Guo, J. Wang and X. R. Song, Int. J. Inorg. Mater., 2011, 26, 847–851.
16. L. Xia, G. L. Zhao, X. X. Huang, G. W. Wen, J. Q. Dai and Z. H. Zhao, Acta Mater., 2013, 61, 3522–3532.
17. G.-C. He, H.-M. Xiang, W. Jiang, Q. Kang and J.-H. Chen, Rare Met., 2014, 33, 742–748.
18. F.-S. Yu, Y.-H. Wang, J.-M. Wang, Z.-F. Xie and L. Zhang, Rare Met., 2014, 33, 358–362.
19. A. F. de Lima, S. O. Souza and M. V. Lalic, Opt. Mater., 2008, 30, 1048–1051.
20. A. F. de Lima, S. O. Souza and M. V. Lalic, Opt. Mater., 2009, 31, 1478–1482.
21. G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 558–561.
22. G. Kresse and J. Furthmüler, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
23. P. E. Blöchl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953–17979.
24. G. Kresse and J. Furthmüler, Comput. Mater. Sci., 1996, 6, 15–50.
25. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Solid State, 1976, 13, 5188–5192.
26. S. Chand, J. Mater. Sci., 2000, 35, 1303–1313.
27. S. Ross, A. M. Welsch and H. Behrens, Phys. Chem. Chem. Phys., 2015, 17, 465–474.
28. S. Chakraborty and R. Pyare, Adv. Appl. Ceram., 2008, 107, 227–231.

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