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C: Physical Processes in Nanomaterials and Nanostructures

Mechanochemistry of Stable Diamane and Atomically Thin Diamond Films Synthesis From Bi- and Multilayer Graphene: A Computational Study Shiddartha Paul, and Kasra Momeni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02149 • Publication Date (Web): 14 May 2019 Downloaded from http://pubs.acs.org on May 14, 2019

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The Journal of Physical Chemistry

Mechanochemistry of Stable Diamane and Atomically Thin Diamond Films Synthesis From Biand Multilayer Graphene: A Computational Study Shiddartha Paul1, Kasra Momeni1,2,3,* 1 Department

of Mechanical Engineering, Louisiana Tech University, Ruston, LA 71270, United States.

2

Center for Two Dimensional and Layered Materials, Materials Research Institute, The Pennsylvania State University, University Park, PA, 16802, USA

3 Center

for Atomically Thin Multifunctional Coatings, Materials Research Institute, The Pennsylvania State University, University Park, PA, 16802, USA

Keywords: Graphene, Diamond, Phase-Transformation, Molecular Dynamics, Passivation.

ABSTRACT — Mono- and few-layer graphene exhibit unique mechanical, thermal, and electrical properties. However, their hardness and in-plane stiffness are still not comparable to the other allotrope of carbon, i.e. diamond. This makes layered graphene structures to be less suitable for

*

[email protected]; [email protected]

ACS Paragon Plus Environment

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application in harsh environments. Thus, there is an unmet need for the synthesis of atomically thin diamond films for such applications that are also stable under ambient conditions. Here, we demonstrate the possibility for the synthesis of such diamond films from multilayer graphene using molecular dynamics approach with reactive force fields. We study the kinetics and thermodynamics of the phase transformation as well as the stability of the formed diamond thin films as a function of the layer thickness at different pressures and temperatures for pristine and hydrogenated multilayer graphene. The results indicate that the transformation conditions depend on the number of graphene layers and surface chemistry. We revealed a reduction in the transformation strain by up to 50% while transformation stress has reduced by as much as five times upon passivation with hydrogen atoms. While the multilayer pristine graphene to diamond transformation is shown to be reversible, hydrogenated multilayer graphene structures had formed a metastable diamond film. Our simulations have further revealed temperatureindependence of transformation strain, while transformation stresses are strong functions of temperature.

Carbon can form different structures, such as graphite, Phagraphene1, diamond, graphene, and nanotubes, which have diverse mechanical2 and electrical properties. For example, Graphene is a semiconductor material without any band gap and a high mechanical strength. It can endure high elongations where the strain can shift its band gap and this can result in a good mechanical and electrical coupling for electromechanical devices. Graphene can also sustain a very high inplane tensile elastic strain, up to 25%3. Diamond has excellent mechanical hardness and thermal


2

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conductivity. Static compression applied on a few layers of pristine graphene at high temperatures, transforms it to the diamond 4. Pressure applied on a multilayer graphene with a certain radical group, e.g. hydogen (-H), hydroxyl (-OH), or flourine (-F), can transform the sp2 hybridization of carbon in the graphene structure into sp3 hybridization as in the, diamond structure 5. The sp2 to sp3 hybridization opens the band gap and also change the electrical, magnetic, and mechanical properties 6 . Density functional theory (DFT) 7 and ab initio 8 methods have been used widely to study the phase transformation of multilayer graphene to diamond at high compressive pressure

9,10,11,12.

Moreover, existence of atomically thin nanodiamond has

been reported in several computational studies 13,14,15,16, where the interlayer gap between the graphene layers reduced and formed a covalent bond. Effect of the pressurizing medium on the transformation conditions of multilayer graphene to diamond has also been investigated using DFT technique

17.

Different methods can be adopted to apply the pressure and induce the

graphene-diamond phase transformation. For example, multilayer graphene can be placed between two piston walls

18

or indentation process

19,20

can be adapted to pressurize the

structure in a certain direction. Conversion of multilayer graphene requires overcoming a certain energy barrier for the transformation of the sp2 bond to sp3. Hydrogen and fluorine atoms have been introduced 5,21,16 as chemical radicals to reduce the graphene to diamond transformation pressure. This helps to get sp3 hybridized carbon bonds in graphene to create covalent bonds between two adjacent graphene layers. Hydrogenation of graphene has a significant effect on the mechanical characteristics

22

and its transformation to diamond. The concentration of

hydrogen on in graphene layers can decrease failure strength of the graphene structure and facilitate the sp2 to sp3 hybridization. Recent experimental and computational investigations23


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have shown that shearing of multilayer graphene can reduce the compressive stress required for graphene to diamond phase transformation. Experimental studies are performed to prove formation of atomically thin diamond when two or more layers of graphene were pressurized with water6,5. The multilayer graphene structure has been pressurized at a high temperature in an aqua-ambient condition, which helped to transform the sp2 hybridization to sp3 by hydrogenation. This transformation initiates the formation of diamond structure. Diamond indenter has also been used to pressurize

20

the

multilayer graphene to form the diamond structure and existence of the newly formed diamond has been confirmed by AFM microhardness and Raman spectroscopy. In this study, we will use atomistic molecular dynamics technique with reactive force fields to study the kinetics of bi- and few-layer graphene to diamond phase transformation at different thermochemical conditions. This is a powerful technique which has been utilized to study phase transformation in various materials. 1,24–27 We will calculate the transformation stress and strain for the formation of diamond thin films at different thermochemical conditions. We then analyzed the energy barrier for the diamond formation and the stability of the formed diamond structures. Computational Model Graphene samples of infinite dimensions are considered by applying periodic boundary conditions in the plane of the graphene layers. A simulation cell of 56.54×26.41Å in the plane of graphene layers is considered. The dimension of simulation cell in the direction normal to the graphene plane varies by change in the number of graphene layers. The initial interlayer distance between graphene layers is assumed to be the length of -bond between graphene layers, i.e.


4

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3.4Å 28. We placed one graphene layer on top of the other layer while shifting it by 1.41Å, which is the C-C bond length in the y-direction. As a result, graphene layers form the ABAB stacking where carbon atoms in one layer are located in the middle of the hexagonal gap of its adjacent graphene layer, see Figure 1(b) and Figure 1(c).

Figure 1 | Structure and configuration of the modeled system. (a) Bond length and configuration of hydrogen and carbon for the hydrogenated graphene model; (b) Top view of ABA stacking, where C atom of bottom layer positioned at the center of hexagonal adjacent top graphene layers; (c) Different stackings of multilayer graphene structures, where the ABA stacking is considered for our studies; The structure of (d) Cubic Diamond (CD) and (e) Hexagonal diamond (HD). Hydrogenated graphene is modeled by adding hydrogen atoms to the outer side of top and bottom graphene layers. The C-H bond length is 1.10Å 10 and H atoms are situated perpendicular to each carbon atom of their neighboring graphene layer. The motion of atoms in the system is constrained in the plane of graphene layers, i.e. xy-plane 29. All the simulations are performed


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using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package28. Interatomic Interactions Model — There are several potentials for modeling the C-C and C-H bonds, e.g. ReaxFF or LCBOP. Here, we have chosen Adaptive Intermolecular Reactive Bond Order (AIREBO) due to its capability for reproducing experimentally measured mechanical properties of graphene30 which is the focus of this study. Orekhov et al.30 compared the MD simulation results for AIREBO and LCBOP potentials with experimental results and found that AIREBO has very good agreement with the experimental measurements in comparison with the LCBOP. The AIREBO potential is used to model the interactions between the C-C and C-H atoms, which could reproduce the thermophysical properties of the C-H system

31.

The integration of pairwise

interactions in AIREBO potential can be represented by following equation 1

+ 𝐸𝑙𝑗𝑖𝑗 + ∑𝑘 ≠ 𝑖,𝑗 ∑𝑙 ≠ 𝑖,𝑗,𝑘 𝐸𝑇𝑂𝑅𝑆𝐼𝑂𝑁 𝐸 = 2∑𝑖 ∑𝑗 ≠ 𝑖[𝐸𝑅𝐸𝐵𝑂 ]. 𝑖𝑗 𝑖𝑗

(1)

The AIREBO potential is the modification over the reactive empirical bond-order (REBO) potential, which also considers the torsional (𝐸𝑇𝑂𝑅𝑆𝐼𝑂𝑁 ) and Lennard-Jones (𝐸𝑙𝑗𝑖𝑗) interactions. The 𝑖𝑗 REBO potential (𝐸𝑅𝐸𝐵𝑂 ) is a combination of attractive (𝑉𝐴𝑖𝑗) and repulsive (𝑉𝑅𝑖𝑗) interactions in 𝑖𝑗 certain ratio (𝑏𝑖𝑗) as (2)

𝐸𝑅𝐸𝐵𝑂 = 𝑉𝑅𝑖𝑗 + 𝑏𝑖𝑗𝑉𝐴𝑖𝑗. 𝑖𝑗 The repulsive term is expressed by the Brenner equation 32,

[

𝑉𝑅𝑖𝑗 = 𝑤𝑖𝑗(𝑟𝑖𝑗) 1 +

𝑄𝑖𝑗 𝑟𝑖𝑗

]

(3)

𝐴𝑖𝑗𝑒 ―𝛼𝑖𝑗𝑟𝑖𝑗.

Here, the 𝑄𝑖𝑗, 𝑟𝑖𝑗 and 𝛼𝑖𝑗 parameters depend on i and j. The bond weighting parameter 𝑤𝑖𝑗(𝑟𝑖𝑗) depends on switching function S(t) as


6

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𝑤𝑖𝑗(𝑟𝑖𝑗) = 𝑆(𝑡𝑐(𝑟𝑖𝑗)),

(4)

𝑆(𝑡) = Θ( ―𝑡) + Θ(𝑡)Θ(1 ― 𝑡)0.5[1 + cos (𝜋𝑡)],

(5)

𝑡𝑐(𝑟𝑖𝑗) =

𝑟𝑖𝑗 ― 𝑟𝑚𝑖𝑛 𝑖𝑗 𝑟𝑚𝑎𝑥 ― 𝑟𝑚𝑖𝑛 𝑖𝑗 𝑖𝑗

(6) .

The attractive interaction is expressed as 3

𝑉𝐴𝑖𝑗

= ―𝑤𝑖𝑗(𝑟𝑖𝑗)

∑𝐵

(7)

(𝑛) 𝐵(𝑛) 𝑖𝑗 𝑟𝑖𝑗 . 𝑖𝑗 𝑒

𝑛=1

The attractive interaction (𝑉𝐴𝑖𝑗) is multiplied by the bond order interaction ratio between atoms i and j as 1

𝑟𝑐 𝑑ℎ 𝜎𝜋 𝑏𝑖𝑗 = 2[𝑝𝜎𝜋 𝑖𝑗 + 𝑝𝑗𝑖 ] + 𝜋𝑖𝑗 + 𝜋𝑖𝑗 ;

(8)

𝜎𝜋 where 𝑏𝑖𝑗 is a many body potential term. Here, 𝑝𝜎𝜋 𝑖𝑗 and 𝑝𝑗𝑖 are not necessarily equal as they

depend on the penalty function (𝑔𝑖) of bond angle 𝜃𝑗𝑖𝑘 between the vector 𝑟𝑖𝑗vector 𝑟𝑘𝑖, i.e.

𝑝𝜎𝜋 𝑖𝑗

[

= 1+

∑𝑤

𝑖𝑘(𝑟𝑖𝑘)𝑔𝑖(cos 𝜃𝑗𝑖𝑘)𝑒

𝑘 ≠ 𝑖,𝑗

𝜆𝑗𝑖𝑘

+ 𝑃𝑖𝑗

]

―1/2

.

(9)

The C-C bond length calculated by the AIREBO potential is 1.396Å which is in good agreement with the experimentally measured value of 1.415Å 33 The AIREBO potential allows the smooth formation and breaking of covalent bonds, as well as the associated change in hybridization. The torsional and Lennard-Jones (LJ) interactions included in the AIREBO potential allow modeling of hydrogenated graphene and its reactions during the phase transformations. Compressing Walls Model — The compressive pressure is applied by sandwiching the multilayer graphene structures between walls with a repulsive interaction force-field as


7


[ ( ) ( )]

2 𝜎 𝐸=𝜀 15 𝑟

9

𝜎 + 𝑟

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3

,

(10)

which is the integration over a 3D half-lattice of LJ 12-6 potential. The σ and ɛ parameters are the equilibrium distance and energy well of the LJ parameters, respectively. For the pristine graphene, the repulsive parameters of the force-field of the wall were estimated based on the C-C Lennard-Jones interaction parameters 34 where σC-C = 3.4Å and ɛC-C = 0.056 eV. In the case of hydrogenated graphene, the repulsive force-field wall was modeled using C-H Lennard-Jones interaction parameters 35 where σC-H = 2.82Å and ɛC-H = 0.00262216 eV. These piston walls are initially placed at the corresponding LJ equilibrium distance from the structure for both cases of pristine and hydrogenated graphene systems. During loading, the bottom wall is fixed while the top one has moved toward the structure to create the compressive stress. We investigated the formation of diamond from multilayer pristine and hydrogenated graphene structures with two to eight layers at 0K, 500K, 800K, 1000K, 1200K and 1500K temperatures. Statistical analysis is performed by assigning different initial seed velocities to the structures to investigate the sensitivity of the results. After each compression step, all the multilayer graphene structures had been relaxed using the NoseHoover thermostat 36 for 200ps to ensure that the structure reached equilibrium and C atoms have enough time to form diamond to avoid reporting of the kinetically stabled diamond structures. We applied compressive loading in the direction normal to the graphene planes at an initial strain rate of 1 ps-1, but when the strain gets close to the critical transformation point, the strain rate was changed to 0.1 ps-1. Unloading was performed at a strain rate 1 ps-1. These strain rates are calculated with respect to the position of the walls. We also relaxed the structure using


8

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the same ensemble during each step of unloading. We calculated the stress for individual atoms using the virial stress formulatoin 37,

𝜎𝑖𝑗 =

(

)

𝑛 1 1 𝛼 𝛼 𝛼 ∑ 𝑚 𝑣 𝑣 𝑟𝑗𝛼𝛽𝑓𝑖𝛼𝛽 , + 𝑖 𝑗 𝛼 2 𝛺 𝛽 = 1,𝑛

(11)

where i and j denote indices in the Cartesian coordinate system; α and β are the atomic indices; mα and νβ denote the mass and velocity of atom α; rαβ is the distance between atoms α and β; and 𝛺 is the atomic volume of atom α. For virial stress calculations we have used the cell volume of the simulation. Result and Discussion In the following two subsections, we will elaborate our results for the transformation of pristine and hydrogenated multilayer graphene structures to diamond. For each case, the simulations are performed at various temperatures for different number of graphene layers. The phase transformation stress is calculated by summing all the stress components normal to the graphene plane, zz. The transformation strain is also calculated as the change in the thickness of the multilayer graphene film with respect to its thickness at the end of the relaxation step, i.e. zz. We used the engineering strain38, 𝜀 = 𝐿 𝐿0 ―1, in our calculations where L is the distance between the top and bottom graphene layers (thickness) at each time and 𝐿0 is the initial value of L. Statistical analysis has been performed by assigning different seed velocity values for each temperature. The reported experimental values are based on the earliest detection of diamond. Thus, there is a variation in the reported experimental transformation stresses that depends not only on the process but also on the sensitivity of the measurement devices. Generally, the experimental measurements4,39 detect nucleation of diamond phase from a bulk graphite when


9


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at least 10% volume fraction of graphite has transformed to diamond and reported transformation stresses between 1GPa to 15GPa. Thus, in this study we have calculated the transformation stress as the stress that is needed to transform 10% of graphene layers to diamond. We have also calculated the transformation stress for the formation of 50% diamond (see Supporting Information). Our calculations indicate transformation stresses in the range of 120GPa at different temperatures which is in agreement with the experimental studies. 4,39 Pristine Graphene — Our results for transformation of pristine graphene to diamond for different number of graphene layers and temperatures are presented in this section. The general mechanism can be depicted as under compressive loads the distance between atoms of adjacent graphene layers reduces which results in the formation of new bonds. For phase transformation, the carbon atoms in the graphite need to overcome the activation energy barrier. From the basic definition of enthalpy, equation

(12), we have the relation between enthalpy, internal

energy, pressure and volume as 40 𝐻 = 𝐸 + PV,

(12)

where E is the internal energy, P is pressure, and V is volume. We know that the enthalpy increases with pressure for compressible solids. Hence, at high pressures, the C atoms of graphene structure can overcome the activation enthalpy for phase transformation and initialize the diamond nucleation. Our results indicate that for the pristine graphene, maximum volume fraction of formed diamond increases by increasing temperature. Figure 2 shows the formation of diamond under compressive loading in the three-layer (3L) and 8L pristine graphene. We also investigated the reversibility of this phase transformation and stability of the formed diamond thin films by


10

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removing the applied compressive stress. We found that the formed diamond structure vanishes after unloading even at 0K, see Figure 2 bottom row. Thus, the formed pristine diamond thin film is not stable and transforms back to the multi-layer graphene through a barrier-less phase transformation as the external load has removed.

Figure 2 | Three-layer and eight-layer pristine graphene phase transformation. The maximum percentage of the diamond structure formed after compression (top row) and its reverse transformation to graphene upon unloading (bottom row) are shown for three-layer graphene at (a) 0K and (b) 1500K. The corresponding results for the eight-layer graphene for (c) 0K and (d) 1500K are shown. The energy pathway for 8L pristine graphene at 0K has been shown in Figure 3. At point ‘A’, a small portion of graphene transforms to diamond which results in a drop in the energy curve. Beyond point ‘A’ the diamond fraction decreases up to point ‘B’ where there will be no diamond remained. After that the energy increases rapidly as a function of strain and volume fraction of diamond structure will also increase. At point ‘C’, the volume fraction of diamond maximizes and reaches 91.9%, which will decrease upon further compression. We stopped applying any further compression beyond point D, where the diamond fraction has reduced to 51.6%. Upon unloading


11


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the volume fraction of diamond structure decreases along with the total energy of the system. Diamond structure completely vanishes at point ‘E’. The structure after unloading will have a nonzero residual stress and its energy is lower than the initial energy of the structure due to partial inter-layer bonding between adjacent graphene layers.

Figure 3 | Energy pathway during loading and unloading of 8L pristine graphene at 0K temperature. The key transition points and associated structures are shown. Normalized energy of the system is shown for loading (solid black line) and unloading (dashed red lines). A small portion of graphene transforms to the diamond at  = -18% (point A) during loading which will disappear later at  = -46% (point B). Upon further loading the energy and volume fraction of diamond increase again and reaches a maximum at point ‘C’. At this point, increasing compression although increase the energy of the system but results in the reduction of diamond volume fraction. Unloading starts at point ‘D’ and at point ‘E’ all diamond will transform back to graphene. The color map of the inset atomistic structures is the same as in Fig. 2.


12

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Transformation strain and stress are calculated for multilayer pristine graphene at different temperatures (Figure 4). Our results indicate that the transformation strain is independent of temperature and number of graphene layers (Figure 4a) when the numerical error (~2%) is considered. Almost all the graphene layers will transform to diamond at ~46% compressive strain normal to graphene plane, zz. This is consistent with previous claims on temperature independence of the transformation strain 41. Lagrangian formulation for strain components can explain this temperature independence of graphite to diamond transformation strain as formulated by Wentz-Covitch et al. 42, 𝐿=

∑12𝑚 𝐪 𝑑𝐪 ― 𝑬({𝐪 }, 𝜺) + 12𝑊 Tr(𝜺 𝜺) ― 𝑃 𝑇 𝑖 𝑖

𝑖

𝑖

𝑇

𝑒𝑥𝑡Ω𝑐𝑒𝑙𝑙.

(13)

𝑖

Here 𝑚𝑖 is the mass of the i th atom, 𝐪𝑖 is the rescaled atomic coordinates, 𝜺 is the strain tensor, 𝑊 represent the fictious mass which is adjusted with the other dynamical variables, 𝑃𝑒𝑥𝑡 is the external pressure, Ω𝑐𝑒𝑙𝑙 is cell volume, superscript T represents transpose operation, and Tr() is the trace of a tensor. The relation between the coordinate of an atom, ri, and the rescaled coordinate, 𝐪𝑖, is 𝑟 ( 𝜺,𝐪𝑖) = (1 + 𝜺) 𝐪𝑖. From equation (13) we can derive the following expression form 𝒒𝑖 and 𝜺: 𝒒𝑖 = ―

𝜺=

1 (1 + 𝜺) ―1𝒇𝑖 ― 𝑑 ―1𝑑𝐪𝑖, 𝑚𝑖

(14)

Ω𝑐𝑒𝑙𝑙 𝑊

(Π ― 𝑃𝑒𝑥𝑡𝐈)(1 + 𝜺𝑇) ―1. 𝑡

𝑁𝑚𝑖𝐯𝑖 𝐯𝒊 Ω𝑐𝑒𝑙𝑙

Here Π = ∑𝑖

(15)

+ 𝝈 , 𝐯𝑖 = (1 + 𝜺)𝐫𝑖, and I is the identity tensor. Equation (15) indicates that

the strain is temperature-independent but depends on the Ω𝑐𝑒𝑙𝑙 and 𝑊.


13


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Figure 4 | Transformation strain and stress for the pristine graphene to the diamond transformation. Transformation strain (a) and stress (b) are calculated as a function of temperature for a different number of graphene layers. It is shown that considering the 2% error of the calculations, the transformation strain is independent of the temperature and number of graphene layers. In contrast, the transformation stress increases with temperature. The graphene to diamond transformation stress increases as temperature increases that is consistent with previous reports

11,

Figure 4(b). The transformation stress for 3L graphene is

slightly higher than its corresponding value for the 4L graphene which can be due to domination of surface tension for 3L graphene. For 3L graphene at 0K suddenly transforms to diamond (first order transformation), where almost the entire structure transforms to diamond. That explains the sudden increase in the measured transformation strain. If we consider formation of 50% graphene to diamond as the transformation criteria, then transformation stress increases to 80 GPa and remains constant as the number of layers increase (Figure S1 in the Supporting Information). This can be interpreted by the lower contribution of thermal energy compared to mechanical energy at higher volume fractions of diamond (higher stresses).


14

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1 2 3 Heterogenous structures form, where graphene partially transforms to diamond, during the 4 5 graphene to diamond phase transformation where the energy of carbon atoms in the graphene 6 7 8 phase increases and thus the activation barrier for graphene to diamond transformation will 9 10 reduce. By increasing the pressure, the height of this energy barrier reduces which facilitates 11 12 13 formation of the diamond phase. Thus, volume fraction of diamond increases as we increase the 14 15 pressure and all the graphene will transform to diamond when the energy barrier for graphene 16 17 18 to diamond transformation reduces to zero. This is the point where graphene becomes unstable 19 20 rather than being metastable. We found that the height of this energy barrier is a function of the 21 22 number of graphene layers. 23 24 25 Atoms at diamond phase can transform back to graphite. At high temperatures, the rate of 26 27 direct and reverse diamond to graphite transformation increases. This thermally activated 28 29 30 transformation can be modeled using the Arrhenius relation 43, 31 32 ∆𝐺 33 Г𝐺𝑡ℎ― 𝐷 ― (16) 𝑘𝐵T 34 , = 𝑒 35 Г𝐷𝑡ℎ― 𝐺 36 37 Here, Г𝐺𝑡ℎ― 𝐷 is the rate of jumping from graphite to diamond interface and Г𝐷𝑡ℎ― 𝐺 is vice versa; 38 39 40 ∆𝐺 is the difference of Gibbs free energy between graphite and diamond phase; kB is Boltzmann 41 42 constant, and T is the temperature. Defining 𝑝𝐷 ― 𝐺 and 𝑝𝐺 ― 𝐷are the direct and reverse diamond 43 44 45 to graphene and phase transformation probabilities, respectively, we have 46 47 𝐺48 (17) Г𝑡ℎ― 𝐷 = 𝑝𝐷 ― 𝐺𝑣𝑡ℎ, 49 50 Г𝐷𝑡ℎ― 𝐺 = 𝑝𝐺 ― 𝐷𝑣𝑡ℎ. (18) 51 52 53 Here 𝑣𝑡ℎ is the total rate of thermally activated jumps. For these phase transformation 54 55 probabilities, we have 56 57 58 59 ACS Paragon Plus Environment 60

15


―

𝑝𝐷 ― 𝐺 =

1 ―

1+𝑒

,

∆𝐺 𝑘𝐵T

𝑒

𝑝𝐺 ― 𝐷 =

Page 16 of 39

∆𝐺 𝑘𝐵T ―

1+𝑒

(19)

.

∆𝐺 𝑘𝐵T

Table 1: Percentage of Cubic Diamond (CD) and Hexagonal Diamond (HD) for different multilayer pristine graphene structures (3L to 8L) at the different temperatures. Temperature #Layers

0K

500K

800K

1000K

1200K

1500K

CD

HD

CD

HD

CD

HD

CD

HD

CD

HD

CD

HD

3L

27.8*

0.0

0.1

0.0

0.1

0.0

0.0

0.1

0.0

0.1

0.1

0.0

4L

0.2

0.0

0.1

0.2

1.4

0.2

0.1

0.0

0.0

0.1

0.0

0.2

5L

0.3

0.0

1.0

0.0

1.1

0.0

0.1

0.0

0.1

0.0

0.1

0.0

6L

1.4

0.2

0.5

0.0

0.6

0.3

0.2

0.0

0.1

0.0

0.1

0.0

7L

5.3

0.0

0.3

0.0

0.1

0.0

0.1

0.0

0.1

0.0

0.1

0.0

8L

8.9

0.2

7.2

0.1

5.5

0.1

2.3

0.0

4.2

0.1

1.9

0.3

Note: Data is taken at 10% nondiamond volume fraction. The volume fractions of the 1st and 2nd nearest neighbors are not shown here. Thus, the sum of CD an HD volume fractions is smaller than 10%. *

For 3L graphene at 0K the graphene to diamond transformation is of first order, where

almost the entire structure transforms to diamond. That is why the volume fraction of CD is greater than 10% here.

From equation (19), we can see that the probability of thermally activated jumps from the diamond to graphene phase is dominant at a higher temperature when ∆𝐺 is a weak function of temperature. Thus, at high temperatures, a large deriving force is required to transform graphene to diamond, which results in a larger transformation stress as temperature increases.


16

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During the diamond nucleation process, the compressive stress and thermal vibrations create inter-layer distortions and stacking sequences which promote the formation of sp3 bonds. The compressive transformation stress, 𝜎𝑐𝑡, for multilayers of graphene as a function of temperature are shown in Figure 4(b). Static compression of the hexagonal graphite (HG) results in the formation of cubic diamond (CD) and hexagonal diamond (HD)

12,

see Figure 1. The HG→HD

transformation requires higher pressure compared to HG→CD due to its higher energy barrier and the different stacking sequence of carbon atoms in the CD phase 12. Thus, the transformation stress will be determined by the volume fraction mixture of the CD and HD phases, and is more sensitive to the volume fraction of the HD phase. This is in agreement with the results presented in Table 1 when the calculation errors are taken into account. For example, at 800K the 5L and 6L graphene systems have almost the same transformation. While 1.1% volume fraction of the 5L is diamond (1.1% CD and 0.0% HD), the 6L graphene system has an overall 0.9% volume fraction of diamond (0.6% CD and 0.3% HD). This indicates that the weighting factor of the HD is larger than the CD in the transformation stress. The volume fraction of CD in the 8L structures is much higher than all other structures at all temperatures. Thus, the transformation stress of 8L graphene structure is higher than its value for all other structures as shown in Figure 4(b). This phenomenon become clearer when we see the transformation stress for 50% diamond (see Supporting Information). Hydrogenated graphene — We investigated the effect of surface passivation with hydrogen on the formation of diamond from multilayer graphene. We followed the same procedure for loading and unloading of the hydrogenated graphene structures as we explained in previous section for the pristine graphene. Figure 5 shows that the hexagonal diamond fraction is


17


Page 18 of 39

predominant. The percentage of the converted diamond is lower than that for the pristine graphene. However, the formed hydrogenated diamond films are metastable and remain even after removing the external pressure. This is in contrast to pristine diamond films, where the formed diamond structure becomes unstable after unloading and transforms back to multilayer graphene. Figure 5 also shows that after unloading, the volume fraction of transformed diamond increases, which is due to the absence of repulsive interactions of the wall after the unloading stage. This implies that the transformation of hydrogenated graphene structures to diamond is an irreversible process. Moreover, Figure 5 shows that the percentage of the diamond is higher for hydrogenated graphene structures with smaller number of graphene layers. In Figure 6, the energy pathway during the phase transformation has been represented for 8L hydrogenated graphene at 0K. Transformation of the hydrogenated graphene starts at point ‘A’ that is detected by the slight drop of energy. The energy and diamond fraction both increase upon further compression up to point ‘B’ where the diamond fraction decreases and the energy drops. At point ‘C’ the diamond structure totally vanishes followed by a sudden drop in the energy indicating formation of a new structure. During unloading (red dotted line in Figure 6) at point ‘D’ diamond structure reappears. At point ‘E’ the diamond percentage reaches the maximum and remains even after bringing the walls back to their original location. This indicates stability of the formed diamond thin films.


18

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Figure 5 | Two-layer and eight-layer hydrogenated graphene phase transformation. The maximum percentage of the diamond structure formed after compression (above) and its reverse transformation to graphene upon decompression (bottom) are shown for two-layers graphene at (a) 0K and (b) 1500K. The corresponding results for the eight-layer graphene for (c) 0K and (d) 1500K are also shown. Figure 7 shows the variation of transformation strain and stress for hydrogenated multilayer graphene structures as a function of temperature using the same statistical approach adopted for pristine graphene structure earlier. The results indicate temperature independence of the transformation strain, Figure 7(a), as in the case of multilayer pristine graphene structures. While the transformation strain monotonously increases by increasing the number of layers, the hydrogenated graphene system with odd number of layers have a lower transformation strain compared to the corresponding system of relatively same size but even number of graphene layers. Although the transformation strain for both systems with odd and even number of graphene layers increases with increasing the number of layers. It should be mentioned that the systems with two and three graphene layers have a different behavior compared to the rest of the system which is due to domination of surface atoms. Furthermore, the transformation stress for hydrogenated graphene systems is a weak function of temperature that is in contrast to


19


Page 20 of 39

multilayer pristine graphene, i.e. G in Eq. (19) is a linear function of temperature. Transformation stress for the 2L and 3L systems is distinctly larger than the other systems which is due to the domination of surface stresses. The transformation stress will also reduce by increasing the system size although the rate of change is different for the systems with odd and even number of layers.

Figure 6 | Energy pathway during compression of 8L hydrogenated graphene at 0K temperature. A small portion of graphene transforms to the diamond at =-6.5% (point A) during loading and the diamond structure retained up to =-51.1% (point B); beyond that point, the diamond structure starts vanishing where at =-55.1% (point C ) diamond completely vanishes. The diamond structure starts to form again at =-47.5% (point D) during unloading and gets to the maximum volume fraction at =-37.14% (point E). Upon unloading, the hydrogenated multilayer graphene won’t come back to its original shape and the formed diamond thin film remains. The color map of the inset atomistic structures is the same as in Fig. 5.


20

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The 2L and 3L hydrogenated graphene have the largest transformation stress among all other multilayer graphene systems, Figure 7 (b). This can be explained by the dominant surface tension effect in the 2L and 3L graphene system. The surface stress, 𝜎𝑠𝑟 𝑖𝑗 , in solid interfaces can be calculated using the Shuttleworth equation 25, i.e. 𝜎𝑠𝑟 𝑖𝑗 = 𝛾𝛿𝑖𝑗 +

∂𝛾 , ∂𝜀𝑖𝑗

(20)

where 𝛾 is the surface energy and 𝛿𝑖𝑗 is the Kronecker delta function. The first term generates a hydrostatic pressure and the second term is the structural part of the stress tensor indicating the work for stretching of the surface. The surface tension basically hinders the formation of the outof-plane sp3 bonds. Thus, higher pressure is needed to overcome this barrier.

Figure 7 | Transformation strain and stress of the hydrogenated graphene as a function of the number of layers at different temperatures. Transformation strain (a) and stress (b) are calculated as a function of temperature for a different number of hydrogenated graphene layers. It is shown that considering the calculation error, the transformation strain is independent of the temperature.


21


Page 22 of 39

Comparing the compressive transformation stresses, σct, in Figure 7(b) and volume fraction of CD and HD in Table 2, indicates that σct is a strong function of the phase compositions in the transformed diamond thin films. This is consistent with our results for the pristine multilayer graphene. For example, 3L has a temperature-independent transformation stress which is consistent with the temperature-independent composition reported in Table 2. It should be noted that the volume fraction of different diamond structures in Table 2 are evaluated by considering the hydrogen atoms in addition to the carbon atoms when coordination numbers are calculated. This is key for correct determination of the crystal structure and volume fraction of each diamond phase. Therefore, although comparing the composition of different diamond phases in a specific system could give us an idea about the variation of the transformation stress across different temperatures, same conclusions are not possible by comparing variation of compositions for different systems. This is because some of the hydrogen atoms are located in CD or HD coordination in a system, which increases the volume fraction of these phases. Although, this artificial increase in the volume fraction of CD and HD remains consistent for a system of specified graphene layers across different temperatures, this will not be the case for systems with different number of layers. Excluding the hydrogen atoms when we are calculating the volume fraction of CD and HD did not change this conclusion. This is because atoms beyond the first nearest neighbors must be considered to determine whether a carbon atom belongs to CD or HD crystal structure. Table 2. Percentage of Cubic Diamond (CD) and Hexagonal Diamond (HD) for different multilayer hydrogenated graphene structures (2L to 8L) at the different temperatures. #Layers

0K

500K

Temperature 800K 1000K

1200K

1500K


22

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CD 2L

HD

16.6* 0.0

CD

HD

CD

HD

CD

HD

CD

HD

CD

HD

16.8

14.8

11.6

8.5

8.7

4.4

6.1

3.8

5.5

2.7

3L

0.1

0.0

0.6

0.0

0.7

0.0

1.4

0.3

1.0

0.2

0.9

0.1

4L

5.7

5.6

2.3

2.2

0.9

0.8

0.7

0.3

0.9

0.4

0.9

0.3

5L

1.7

1.9

0.6

0.5

1.5

1.2

0.5

0.5

0.3

0.6

0.3

0.8

6L

2.9

2.4

5.5

0.9

5.1

0.1

5.7

0.2

5.8

0.1

3.6

0.0

7L

5.2

3.5

1.3

0.1

1.3

1.9

1.9

1.9

1.4

0.8

1.4

0.7

8L

5.0

2.9

2.4

0.6

2.2

0.0

2.7

0.0

2.2

0.0

2.9

0.0

Note: Data is taken at 10% nondiamond volume fraction. The volume fractions of the 1st and 2nd nearest neighbors are not shown here. Thus, the sum of CD an HD volume fractions is smaller than 10%. *

For 2L graphene at 0K the graphene to diamond transformation is of first order, where almost

the entire structure transforms to diamond. That is why the volume fraction of CD is greater than 10% here.

The transformation strain for hydrogenated graphene structures is also drastically reduced compared to the pristine multilayer graphene, Figure 7(a). For example, 𝜀𝑡 for the 3L graphene has reduced by a factor of five for the hydrogenated graphene and by a factor of three for the thicker 8L graphene. However, the transformation stress for the hydrogenated 3L graphene has increased compared to the pristine graphene. This can be due to distortion of the graphitic structure44,16 and the change in surface stresses upon hydrogenation. The 3L system requires more stress to straighten up the graphene structure, but less strain to nucleates the diamond formation. For the case which formation of 50% is considered as the transformation criteria, the transformation stress reduces by 20% for the 3L graphene and cut by a half for the 8L graphene


23


Page 24 of 39

structure (see Figure S2 in Supporting Information). The sp3 hybridization due to hydrogen absorption facilitates the formation of interlayer bonds and transformation to diamond. These results emphasis the key role of surface effects and passivation on the phase transformation characteristics. Conclusions We have presented an atomistic study of phase transformation of multilayer graphene to diamond using the molecular dynamics approach with reactive force fields. We investigated the effect of surface passivation with hydrogen atoms on transformation stress and strains at different temperatures as a function of thickness of graphene layers. We further explored the thermodynamics and kinetics of this phase transformation and analyzed the composition of the formed diamonds. Compressive stress required for the synthesis of diamond from multilayer graphene was calculated and its dependence of temperature was investigated. The mechanism of this phase transformation was explained and the relation between thermodynamic conditions and morphology of the converted diamond structure was reported. Simulations were performed for both hydrogenated and pristine multilayer graphene. The phase transformation mechanism and conditions significantly vary due to the dominance of surface effects. For the pristine graphene no chemical radical like -H (hydrogen) or -OH (Hydroxyl group) has been used to facilitate the sp3 hybridization process. The required transformation stress is higher for pristine multilayer graphene compared to the corresponding structures which are passivated with hydrogen atoms. We revealed a drop in the transformation stress of up to five times and a drop in the transformation strain of up to 50%. The transformation strain found to be independent of temperature for both pristine and hydrogenated graphene structures.


24

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However, the transformation strain for the hydrogenated graphene shows a strong dependence on the number of layers in contrast to the pristine graphene structures that show thickness independence. Furthermore, the transformation stress was shown to have a strong dependence on the composition of the final diamond structure. Thus, we can conclude that transformation of multilayer graphene structures to diamond is a strain-controlled process. We further revealed that the diamond film with passivated surfaces is metastable and remains even after unloading the structure, while the clean surface diamond structures formed from pristine graphene transform back to graphene upon unloading. The effect of surface tension has shown to play a significant role in ultrathin three-layer graphene structures which results in significant increase in the transformation stress. In summary, the results presented in this study enlighten the kinetic and thermodynamic conditions necessary for the formation of ultra-thin films of diamond. They can guide the synthesis of diamond films with tailored characteristics for application in various industries such as optoelectronics, defense, and coating industries. Supporting Information: The Supporting Information is available free of charge on the ACS Publications website. The results for using transformation of 50% volume fraction from graphene to diamond has been presented in the supplemental information. Transformation strain and stress for the to the diamond transformation at different temperature for pristine and hydrogenated graphene. Percentage of Cubic Diamond (CD) and Hexagonal Diamond (HD) for different multilayer pristine graphene structures (3L to 8L) and hydrogenated graphene structure (2L to 8L) at the different temperatures.


25


Page 26 of 39

Author Information: Corresponding Author: [email protected]; [email protected] Funding Sources This project is supported by Louisiana Tech University, and the National Science Foundation 2D Crystal Consortium – Material Innovation Platform (2DCC-MIP) under NSF cooperative agreement DMR-1539916. This project is also partly supported by Louisiana EPSCoR-OIA1541079 (NSF(2018)-CIMMSeed-18 and NSF(2018)-CIMMSeed-19) and LEQSF(2015-18)LaSPACE. Calculations are performed using Louisiana Optical Network Initiative (LONI). References: (1)

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Table of Contents Image


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Figure 1 | Structure and configuration of the modeled system. (a) Bond length and configuration of hydrogen and carbon for the hydrogenated graphene model; (b) Top view of ABA stacking, where C atom of bottom layer positioned at the center of hexagonal adjacent top graphene layers; (c) Different stackings of multilayer graphene structures, where the ABA stacking is considered for our studies; The structure of (d) Cubic Diamond (CD) and (e) Hexagonal diamond (HD). 265x88mm (150 x 150 DPI)



Figure 2 | Three-layer and eight-layer pristine graphene phase transformation. The maximum percentage of the diamond structure formed after compression (top row) and its reverse transformation to graphene upon unloading (bottom row) are shown for three-layer graphene at (a) 0K and (b) 1500K. The corresponding results for the eight-layer graphene for (c) 0K and (d) 1500K are shown. 338x116mm (96 x 96 DPI)


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Figure 3| Energy pathway during loading and unloading of 8L pristine graphene at 0K temperature. The key transition points and associated structures are shown. Normalized energy of the system is shown for loading (solid black line) and unloading (dashed red lines). A small portion of graphene transforms to the diamond at e = -18% (point A) during loading which will disappear later at e = -46% (point B). Upon further loading the energy and volume fraction of diamond increase again and reaches a maximum at point ‘C’. At this point, increasing compression although increase the energy of the system but results in the reduction of diamond volume fraction. Unloading starts at point ‘D’ and at point ‘E’ all diamond will transform back to graphene. The color map of the inset atomistic structures is the same as in Fig. 2. 295x183mm (96 x 96 DPI)



Figure 4 | Transformation strain and stress for the pristine graphene to the diamond transformation. Transformation strain (a) and stress (b) are calculated as a function of temperature for a different number of graphene layers. It is shown that considering the 2% error of the calculations, the transformation strain is independent of the temperature and number of graphene layers. In contrast, the transformation stress increases with temperature. 338x122mm (96 x 96 DPI)


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Figure 5 | Two-layer and eight-layer hydrogenated graphene phase transformation. The maximum percentage of the diamond structure formed after compression (above) and its reverse transformation to graphene upon decompression (bottom) are shown for two-layers graphene at (a) 0K and (b) 1500K. The corresponding results for the eight-layer graphene for (c) 0K and (d) 1500K are also shown. 338x115mm (96 x 96 DPI)



Figure 6 | Energy pathway during compression of 8L hydrogenated graphene at 0K temperature. A small portion of graphene transforms to the diamond at =-6.5% (point A) during loading and the diamond structure retained up to = 51.1% (point B); beyond that point, the diamond structure starts vanishing where at = 55.1% (point C ) diamond completely vanishes. The diamond structure starts to form again at =-47.5% (point D) during unloading and gets to the maximum volume fraction at =-37.14% (point E). Upon unloading, the hydrogenated multilayer graphene won’t come back to its original shape and the formed diamond thin film remains. The color map of the inset atomistic structures is the same as in Fig. 5. 298x188mm (96 x 96 DPI)


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Figure 7 | Transformation strain and stress of the hydrogenated graphene as a function of the number of layers at different temperatures. Transformation strain (a) and stress (b) are calculated as a function of temperature for a different number of hydrogenated graphene layers. It is shown that considering the calculation error, the transformation strain is independent of the temperature. 338x121mm (96 x 96 DPI)


and Multilayer Graphene - ACS Publications

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