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Ionic Graphitization of Ultrathin Films of Ionic Compounds Alexander G. Kvashnin, Egor Yu. Pashkin, Boris I. Yakobson, and Pavel B. Sorokin J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b01214 • Publication Date (Web): 23 Jun 2016 Downloaded from http://pubs.acs.org on June 23, 2016

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The Journal of Physical Chemistry Letters

Fig. 1. a) Ball-and-stick models of two considered bulk phases of the investigated AB compounds, where A is Li, Na, K and Rb, while B is F, Cl, Br and I. The strain energy is presented as a function of unit volume for b) NaF and c) LiF B1 and B2 phases; the black dashed line in (b) is a common tangential line to the strain energies for both phases. 131x259mm (150 x 150 DPI)

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Fig. 2. Dark solid bars represent the relative energy difference between cubic (B1) and graphitic-like (G) bulk phases of the studied ionic compounds. The blue region with white dots shows the inverse of the critical number of layers for graphitization referred to the right ordinate axis depending on the compound type. 751x317mm (150 x 150 DPI)


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Fig. 3. The dependence of the critical number of layers on the electronegativity difference |χH-χM| for all considered compounds with electronegativity difference and critical number of layers of fluorides shifted to zero. The inset shows a tilt angle given from eq. (4) as a function of electronegativity and ion radius of metal atoms. 365x246mm (150 x 150 DPI)



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Ionic Graphitization of Ultrathin Films of Ionic Compounds A.G. Kvashnin,1,2 E.Y. Pashkin,2,3 B.I. Yakobson,4 P.B. Sorokin,3,5* 1

Skolkovo Institute of Science and Technology (Skoltech), Skolkovo Innovation Center 143026, 3 Nobel Street, Moscow, Russian Federation 2

Moscow Institute of Physics and Technology, 9 Institutsky lane, Dolgoprudny, 141700, Russian Federation

3

Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya Street, Troitsk, Moscow, 142190, Russian Federation

4

Department of Materials Science and NanoEngineering and the Smalley Institute for Nanoscale Science and Technology, Rice University, Houston, Texas 77005, USA 5

National University of Science and Technology MISiS, 4 Leninskiy prospekt, Moscow, 119049, Russian Federation

Corresponding Author *P.B. Sorokin, E-mail: [email protected].

ABSTRACT. Basing on ab initio density functional calculations, we performed a comprehensive investigation of the general graphitization tendency in rocksalt-type structures. In this paper, we determine the critical slab thickness for a range of ionic cubic crystal systems, below which a spontaneous conversion from a cubic to a layered graphitic-like structure occurs.

This

conversion is driven by surface energy reduction. Using only fundamental parameters of the

1


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compounds such as the Allen electronegativity and ionic radius of the metal atom, we also develop an analytical relation to estimate the critical number of layers.

In materials with a high ionic contribution to the atomic bonding, a large variety of different phases is rare. As a result, phase diagrams of these materials generally contain only a handful of phases, all of which contain high degrees of symmetry. During the transfer of electrons from cations to anions, the electron shells of the atoms become quasi-closed, and a noble gas-type crystal structure with high coordination numbers is formed. This limits the number of possible structures. For example, sodium chloride (NaCl) at ambient conditions displays a rocksalt or halite structure (the B1 phase, coordination number is 6), whereas at ~30 GPa it transforms into a CsCl-type structure (the B2 phase, coordination number is 8). 1 However, in spite of the electron transfer, lower symmetry phases of ionic materials have been found. A novel wurtzite-type phase of alkali metal halide materials was theoretically predicted by Čančarević et al. in Ref. 2. Despite having low energy and low density, this phase was not synthesized experimentally due to a negative phase transition pressure from B1 phase. Reducing the third dimension of the material and passing from bulk to atomic thickness may allow for the synthesis of novel phases without the issue of negative phase transition pressure. 2



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Recently, a theoretical analysis made by Freeman et al. 3 reported that polar materials with favorable zinc blende structures (with dominant covalent-ionic bonding) tend to split into layered structures for the case of the atomic-thick films. This prediction was confirmed in experimental works 4–7 where graphitic thin ZnO, AlN and SiC films were fabricated through different experimental techniques. Materials favoring a rocksalt structure with dominant ionic bonding can spontaneously transform into films of a new graphitic phase to reduce the stress from a polar surface. This was shown in Refs. 8–10 for NaCl. However, there is still no general theory for how this graphitization scenario of non-carbon ionic materials occurs. A general theory could make the synthesis of new ultrathin layered materials for nanoelectronics applications possible. The creation of such a theory would require the investigation of a wide family of chemical compositions to establish dependencies of the graphitization effect on the composition type. In this paper, we focused on a detailed investigation of this dependency. At first, we examined bulk cubic B1 and B2 phases of different ionic binary compounds of alkali metal and halogen atoms. We calculated the phase transition pressure for transformation from B1 to B2 phases and the corresponding bulk moduli for a wide range of halogen and metal atoms in the ionic compounds compared to reference data. Also the relative stability of bulk cubic (B1) and new graphitic (G) phases of all considered compounds were studied. We then proceeded to the quasitwo-dimensional phases and compared the energy of ultrathin cubic and graphitic films. The critical number of layers below which the cubic films become unstable was estimated. These values were used to establish a general relation between the critical number of layers and the basic parameters of the compounds.

3


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Our calculations were performed using density functional theory (DFT) 11,12 in the generalized gradient approximation with the Perdew–Burke–Ernzerhof (PBE) exchange correlation functional 13, as implemented in the VASP package 14. The plane-wave energy cutoff was equal to 500 eV, while the Brillouin zone was sampled using a 16×16×1 Monkhorst–Pack 15 grid for ultrathin films and a 16×16×6 grid for the bulk B1 and B2 phases. Atomic structure optimization was carried out until the maximum interatomic force became less than 0.01 eV/Å. To determine the bulk modulus of the cubic bulk phases of the studied compounds, each structure was hydrostatically compressed and dilated, the geometry optimization was carried out at every step. The data obtained of the energy dependence on volumetric change were used to determine the bulk modulus (B) using the Murnaghan equation of state: 16,17 9B V E (V ) = E0 + 0 0 16

2 2/3   V 2 / 3  3  V0  2 / 3     0  V0       − 1 B0′ +   − 1 6 − 4    ,  V     V    V     

(1)

where E0, B0, B'0, and V0 are ground state energy, bulk modulus at zero pressure, derivative of the bulk modulus at zero pressure, and equilibrium volume, respectively. The phase transition pressure was defined through the Gibbs free energies of two phases

G = Etot + pV − TS ,

(2)

which equals the slope of the common tangential line between the dependences of total energies on the volume for both of the considered phases. 18 We restrict our investigation to highly ionic compounds AB with Li, Na, K and Rb as element A, and F, Cl, Br, I as element B. Our study began with considering the stability of the films’ bulk counterparts. One of the most important characteristics determining the relative stability of one phase compared to others is the phase transition pressure. Therefore, initially we considered the two most common cubic bulk phases of ionic material: the B1 and B2 phases. These structures 4



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are shown in Fig. 1a. The phase transition pressures Pt of B1B2 transitions were calculated at 0 K, along with the bulk modulus of cubic B1 phase (see Table S1 in Supplementary materials). Pt depends on the energy difference between the two phases, and plays a crucial role in the stability of a new graphitic phase at nanoscale. All calculated data on the phase transition from B1 to B2 bulk phases and on the bulk modulus were compared with reference experimental and theoretical data summarized in Table S1 (see Supplementary materials).

Fig. 1. a) Ball-and-stick models of two considered bulk phases of the investigated AB compounds, where A is Li, Na, K and Rb, while B is F, Cl, Br and I. The strain energy is presented as a function of unit volume for b) NaF and c) LiF B1 and B2 phases; the black dashed line in (b) is a common tangential line to the strain energies for both phases. The phase transition pressure was determined by plotting the common tangential line between the functions of total energies per unit volume for both the B1 and B2 phases (see Fig. 1b). The strain energy was calculated as a function of unit volume in a wide range of relative 5


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compression/dilatation from -50% to 20%. This can be seen from the changing unit volume in Fig. 1b. Such large compressions were considered due to a large number of ionic materials undergoing a phase transition from B1 to B2 phase at very high pressures.19 We achieve a good agreement between our calculated data and the reference data, validating the accuracy of the chosen parameters and methods. It should be noted that there are no experimental data on the phase transitions for the lithium and a couple of sodium (NaBr and NaI) compounds. This is because both the B1 and B2 phases are equally stable and display almost equal energies and unit volumes in these cases. This can be also understood from the dependence of strain energy on the unit volume shown in Fig. 1c for NaF and LiF. If one plotted the total energy as a function of unit volume for B1 and B2 phases of these compounds, it would be found that the B2 curve lies strictly above the B1 curve. Therefore, the curves don’t intersect and no phase transition could be expected. This behavior makes it impossible to determine the values of phase transition pressure, and means that there are no ways to obtain such phase transition experimentally. Let us now consider the bulk cubic (B1) and graphitic (G) phases of the examined ionic compounds. As it was predicted earlier 9, the graphitic phase of sodium chloride (G-NaCl) is more unstable as a bulk phase than the nanoscale films. Energies of both cubic, EB1, and graphitic, EG, bulk phases were calculated, and the relative energy difference with respect to the corresponding bulk phase was evaluated as Erel = (EB1-EG)/EB1 (see Fig. 2, dark solid bars). The energy of the unstable bulk graphitic phase was calculated using constrained relaxation to prevent the connection of the layers with each other and the formation of a wurtzite structure. As seen below, four groups of ionic compounds display different energy tendencies that rise from lithium to rubidium compounds. The data in Fig. 2 allows us to see the general behavior of the 6



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Erel functions depending on the halogen type. Lithium compounds display negative slope of the relative energy as the atomic number of the halogen increases, while the behavior of sodium compounds seems independent from the halogen type. The trend becomes positive for potassium to rubidium compounds. The energy difference between the bulk cubic and graphitic phases indicates which compound in a case of atom-thick films will split with a smaller number of layers compared to others.

Fig. 2. Dark solid bars represent the relative energy difference between cubic (B1) and graphiticlike (G) bulk phases of the studied ionic compounds. The blue region with white dots shows the inverse of the critical number of layers for graphitization referred to the right ordinate axis depending on the compound type. The effect of splitting nanometer-thickness ionic films or ionic graphitization can be directly obtained from the comparison of films of different phases. We calculated the energies of thin quasi-two-dimensional cubic B1 films with (111) surface orientation of all the considered ionic compounds along with the energies of nanometer-thick slabs of new graphitic-like phase depending on their thickness (see Fig. S1 in Supplementary materials for details). The dependence of energy on the number of layers (thickness) tends to the energy of the bulk phase as the thickness increases. However, the dependence of energy on the number of layers for 7


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graphitic-like films has a gentler slope compared to the cubic films, which is primarily due to the weak interaction between the graphitic-like layers of the films. The interlayer binding energy between ionic materials has an order of magnitude comparable to the van der Waals interaction in graphite. 9 Due to the different slopes of energy curves between the cubic and graphitic-like slabs, the energy curves will intersect each other. This intersection shows the critical number of layers (thickness) above which thin cubic films become more stable than graphitic ones, and are no longer susceptible to ionic graphitization. The obtained data clearly shows a relationship between the critical number of layers for graphitization and the type of the compound. We can associate the obtained data with the fundamental characteristics of each constituent element. Due to the ionic nature of the bonding in such compounds, it is natural to use the difference between the electronegativities of atoms A and B of the AB compound as the main parameter. We choose Allen electronegativity as the main characteristic to describe the considered materials because it was derived using the average energies of the valence electrons in a free atom 20 which is closely related to the properties of the studied compounds. Moreover, the scale of Allen electronegativity distinguishes potassium atoms from rubidium atoms, while other considered scales show equal electronegativity values for these elements. The results of numerical calculations were summarized in the Error! Reference source not found., showing the electronegativity and the critical number of layers for each compound. One can note from Table 1Error! Reference source not found. that fluorine has the largest value for electronegativity, while other halogens have approximately the same values and differ from each other by no more than 0.5. This fact is highlighted in the obtained critical number of layers, as

8



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the compounds with fluorine have significantly different values for the critical number of layers compared to other materials. Table 1. Allen electronegativity of each constituent element in the ionic compound, and the critical number of layers of ionic graphitization of the cubic films. Li

Na

K

Rb

χ

0.912

0.869

0.734

0.706

F

4.193

19.86

10.98

12.18

12.92

Cl

2.869

25.39

11.19

11.12

11.00

Br

2.685

25.57

11.07

10.32

10.61

I

2.359

27.16

11.18

10.37

10.26

The obtained numerical data of the critical number of layers for all the studied films is shown in Fig. 2 by the blue semitransparent regions. It can be seen that the critical number of layers for graphitization of the nanometer-thick ionic slabs is well correlated with the relative energy of the bulk phases (see dark solid bars in Fig. 2). This fact shows that the properties of bulk phases for the studied ionic compounds are directly related with the stability of ultrathin films. A larger difference in energies between the bulk cubic and graphitic-like phases leads to a greater number of layers for graphitization, and vice versa. All dependencies are well fitted with a linear relationship, making it easier to analytically describe the dependence. Our simulation results can be well captured by fitting the theoretical predictions through parameters a and b as:

Ncritical = a ⋅ ∆χ + b ,

(3)

where ∆χ = χ A − χ B is the difference between Allen electronegativities of the metal atom χLi and the halogen atom χB in the considered compounds. It is can be clearly seen from the equation (3) that the films which have a greater electronegativity difference will have a higher critical number of layers for graphitization. Let us 9


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then consider the obtained dependence of the critical number of layers on the electronegativity difference for all the considered compounds shown in Fig. 3. Here we shifted the electronegativity difference and critical number of layers of fluorides to zero i.e. b = 0). One can note from the figure that slopes of the functions of the critical number of layers depending on electronegativity change from negative to positive moving down the periodic table from lithium to rubidium. This fact allows one to describe the graphitization ability of the ionic materials in terms of the slopes of the considered linear functions. The tilt angles of the considered functions were determined as a function of the ratio of ionic radius (RA) to the electronegativity of the metal atoms (χA) as shown in the inset of Fig. 3 by black dots. The obtained dependence can be well fitted with the hyperbolic law having the following form:

θ =α ⋅

χA RA

+ β = 243.3 ⋅

χA RA

− 162.3 ,

(4)

where α has dimension of Å, and β is a dimensionless constant. Combining equations (3) and (4) obtains the following relation for the critical number of layers:

 χ  N critical = tan α ⋅ A + β  ⋅ ∆χ .  RA 

(5)

10



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Fig. 3. The dependence of the critical number of layers on the electronegativity difference |χ χH-χ χM| for all considered compounds with electronegativity difference and critical number of layers of fluorides shifted to zero. The inset shows a tilt angle given from eq. (4) as a function of electronegativity and ion radius of metal atoms. The obtained equation (5) describes the graphitization effect in ultrathin slabs of ionic compounds with a rocksalt crystal structure and determines the critical number of layers for splitting. However, the obtained number should be rounded up to the nearest integer, as a fractional number of layers has no physical meaning. To determine the critical thickness for graphitization, one should use the following relation: hcritical = N critical ⋅

(

)

3d cub , where dcub is the

lattice parameter in angstroms of the considered ionic compound. In the presented work we explored the splitting tendency (ionic graphitization) in the ultrathin slabs of ionic compounds with a rocksalt crystal structure. The comparison of energies of atomthick films of cubic and new graphitic phases yields the critical number of layers below which the graphitic-like slabs become more stable than the cubic counterparts. Based on the obtained

11


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numerical data, the general function which describes the graphitization behavior in ionic films of nanometer thickness was derived.

Acknowledgements P.B.S. gratefully acknowledges the financial support of the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST «MISiS» (No K2-2015-033) and the Grant of President of Russian Federation for government support of young PhD scientists (MK-6218.2015.2). Calculations were made on 'Chebyshev' and 'Lomonosov' supercomputers of the Moscow State University for the possibility of using a cluster computer for our simulations and on the supercomputer cluster "Cherry" provided by the Materials Modeling and Development Laboratory at NUST "MISIS" (supported via the Grant from the Ministry of Education and Science of the Russian Federation No. 14.Y26.31.0005). Supporting Information Available: Supporting figures and tables.

References (1) (2) (3) (4) (5) (6) (7)

(8)

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(9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)

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