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Atomic Structure and Binding of Carbon Atoms

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21 August 2023

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22 August 2023

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Abstract
A carbon element exhibits complex behavior due to having several allotropic forms. Processing its precursors and compounds by different techniques and methods results in various carbon-based materials, which show a lot of uncertainties in their characterizations and analyses. Depending on the processing conditions of a carbon precursor, a carbon atom changes its state behavior. The conversion of the carbon atom from one state to another is due to the electron transfer mechanism. Bits of energy having shape-like dash transfer electrons to nearby unfilled states in conversion. The involved dash-shaped energy bit keeps partially conserved behavior. The forces exerted on the transferring electrons also keep partially conserved behavior. Under only attained dynamics of the carbon atoms, a two-dimensional or amorphous graphite structure forms. In the execution of electron dynamics, graphite, nanotube, and fullerene state atoms form one-dimensional, two-dimensional, and four-dimensional structures, respectively. In the depositing diamond atom, each outer ring electron undertakes the clamp of each energy knot belonging to the outer ring of the deposited diamond atom. As a result, binding in diamond state atoms is from east-west to south. So, growth in the diamond structure is from south to east-west. Lonsdaleite state atoms bind from the east-west to a bit south. In glassy carbon, the layers of gaseous, graphite, and lonsdaleite state atoms bind simultaneously. The order of the layers repeats in the growth of glassy carbon. Atoms in diamond, lonsdaleite, graphene and glassy carbon structures involve golf-stick-shaped energy bits. Processed carbon materials differently also study hardness under a new insight. This study discusses the fundamental and applied science of carbon atoms and their structures.
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Subject: Chemistry and Materials Science  -   Materials Science and Technology

1. Introduction

New strategies need to process and synthesize carbon materials. Characterizations and analyses of carbon materials can also help to explore a new science at both primary and applied levels. A force exerted at the electron level should also explain the role of energy at the electron level, which is discussed in preliminary detail [1,2,3].
In the structural formation of those carbon atoms where partially conserved energy involves at the electron level, a partially conserved force should also engage at the electron level. It can be the case in the structural formation of graphite, nanotube, and fullerene state atoms.
In the structural formation of those carbon atoms where non-conserved energy involves at the electron level, a non-conserved force should also engage at the electron level. It can be the case in the structural formation of diamond, lonsdaleite, and graphene state atoms.
Force and energy can also contribute together at the atomic level when a suitable state of carbon atoms amalgamates under attained dynamics. It can be the case in graphite atoms when forming a two-dimensional or amorphous structure.
The involvement of the energy at the electron level directs the force to engage at the electron level. As a result, atoms bind to form nano or micro-sized grains. The outer ring electrons of carbon atoms in any state do not study a conserved force. Those electrons keep a very close distance to the center. Overall, the nature of the involved energy should depend on the specific state or allotrope of a carbon atom. In the literature, several studies discussed the allotropic forms of carbon.
When the conservative forces exert on the electron in a silicon atom, an uninterrupted execution of its dynamics generates a photon of unending length [2]. It indicates that the built-in interstate gap of electron dynamics in the carbon atom differs from silicon. Both carbon and silicon atoms possess equal numbers of filled and unfilled states in the outer ring. But the outer ring electrons of a carbon atom and a silicon atom keep different distances from their atomic center.
Gaseous and solid atoms deal with the transitions while undertaking the liquid states, where the electrons remain within the occupied energy knots [3]. Those element atoms which execute confined interstate electron dynamics evolve structure instead to develop it [4]. Atoms belonging to all elements do not ionize [5]. A carbon film deposited in tiny-sized grains is due to the synthetic protocol [6]. Different morphological-featured carbon films got deposited at varying process conditions [7].
At different chamber pressures, the deposition of the carbon films shows different morphology and structure [8]. At different inter-wire distances, a carbon film was deposited in diamond and graphitic phases [9]. It means the electron transfer mechanism involves changing the chemical nature of an atom regardless of whether it belongs to the same element.
The force entering from the north pole and leaving the ground surface for the south pole behaves differently than the force exerted at the ground surface [10]. A recent study shows the transformation of graphene film into a diamond-like carbon film, where the elastic deformations and chemical natures were changed [11]. Wu et al. [12] reviewed the developments in Raman spectroscopy of graphene materials.
In a vapor deposition method, carbon nanofibers grow without a catalyst [13]. Different applications related to graphene hybrids were reviewed [14]. Nitrogen-incorporated carbon dots merged to modify a glassy carbon electrode [15]. A novel energy dissipation system was investigated by gathering the features of both carbon nanotubes and fullerenes [16]. Different carbon allotropes, in comparison, were studied for dehydrogenation of temperature [17]. Precise positioning of the vacancies in a diamond crystal was also studied [18]. Liu et al. [19] presented an efficient strategy to fabricate the graphite-graphene Janus architecture. Some parameters under optimized conditions of the process chosen to deposit the diamond [20].
Cheng and Zong [21] observed a structural evolution of damaged carbon atoms for a deeper surface layer. Maruyama and Okada [22] investigated the electronic and magnetic structures of a two-dimensional network of carbon atoms. Narjabadifam et al. [23] studied carbon nanocones through molecular dynamics simulation. Levitated nanodiamonds burn in the air because of the amorphous carbon [24]. Uncertainty in the temperature measurement of levitated nanodiamonds was removed [25].
Heat treatment improves the mechanical properties of carbon films deposited by magnetron sputtering [26]. A deposited carbon nanotube film shows enhanced electrode stability [27]. Carbon films deposit in a pulse-based CVD system to improve tribological properties [28]. The electronic states of carbon-based materials control the covalent bonds [29]. The relation of different parameters in depositing carbon films has been discussed separately [30]. High negative bias voltages reduce the hydrogen content in depositing carbon film [31].
The carbon films deposited with an enhanced thickness are not beneficial for all purposes [32]. A study discusses the structure of carbon films deposited by the sputtering method [33]. A graphitic phase of deposited carbon films reduces the friction coefficient in the vacuum medium [34]. Carbon films have lowered hydrogen content deposited by tuning the ratio of the graphitic and diamond phases [35].
The hardness of a single-walled carbon nanotube has been discussed separately [36]. Carbon nanotube deposited by the floating catalyst CVD technique offers potential application [37]. Carbon nanotube films show high thermal conductivity [38]. A recent study suggests the photochemical conversion of the graphitic phase into the diamond phase [39]. In the deposition of diamond-like carbon, the sp2 carbon or graphitic phase increases by introducing titanium [40]. In deposited carbon films by hot-filament CVD, a structural and electrical relation establish between amorphous carbon and graphene [41]. A recent study investigates porous carbon films for efficient electromagnetic applications [42]. Electrochemical sensor application has been studied in vertical mesoporous carbon films [43]. Ultrathin amorphous carbon films investigated thermal stability and diffusion characteristics [44].
These studies and the ones not cited raise some fundamental questions. How do the different allotropes of carbon form? How do the same-state carbon atoms bind in the formation of structure? What types of carbon atoms contribute to the structural formation of glassy carbon? Then how does the hardness of the different carbon structures vary? This study attempts to address these questions along with others.

2. Experimental details

Many published studies on carbon films and other carbon-based materials describe the experimental details. To deposit carbon films is extensively discussed in the literature. There are several techniques in the literature showing the deposition.
The purpose of the study is to explore the underlying science of different carbon states rather than the experimental detail. A binding mechanism in identical-state carbon atoms is also a subject of this study. The discussed science here is the central subject of every study considering the depositions of carbon materials in any form and by any technique.
Nevertheless, the experimental detail can consider in those studies processing different carbon-based precursors and compounds. This study explores fundamental and applied science about carbon atoms.
If one looks at the published studies of carbon, it is possible to draw models in different named allotropes of carbon. The study also identifies the kind of energy involved and the nature of forces engaged in the binding of same-state atoms. The current study also charts the Mohs hardness of different carbon materials under a new insight.

3. Atomic Structure Models and Discussion

3.1. Carbon lattice and structure of carbon allotropes or states

Different states of carbon atoms recognize by their names in the literature. However, they do not show a sketch of the electronic configuration in each state. The formation mechanism in the carbon lattice is also yet awaited. Different-state carbon atoms rely on the same number of electrons. A carbon atom has a fixed number of filled and unfilled states for any state. Changing the position of the electrons gives birth to the new chemistry of that atom. However, a separate study discussed the atomic structure of different elements and their transitional behaviors [3].
When overt photons intercrossed to form the twelve energy knots, they shape the carbon lattice. In intercrossing, overt photons keep the centers of their lengths at a common point. Figure 1a shows the lattice of a carbon atom. Two energy knots from each side of the center remained compressed from the neighboring states.
The lengths of the overt photons are so that their schedule crossing shapes the filled and unfilled states required to form the energy-knot-net of a carbon atom. Two pairs of overt photons, which have characteristics of photonic current, intercross along the east and west sides. Two pairs of photons, which have characteristics of photonic current, intercross along the north and south lines. All the intercrossed overt photons keep the positions of their mid-lengths at the same point. The lattice of a carbon atom is also referred to as the energy-knot-net, as shown in Figure 1a. The overt photons preserve their force by wrapping the energy [2].
The outer ring of the carbon atom has four filled and four unfilled states. This order of the states provides the option to form six different states of the carbon atom in addition to the gaseous state. Glassy carbon is a layered structure, which will discuss in a separate section.
In a carbon atom, four electrons form the zeroth ring. Figure 1 shows the different states of a carbon atom where all carbon states or allotropes contain four electrons in their central ring. The zeroth ring is related to the helium atom [3]. Figure 1 symbolically shows the electrons and energy knots for different carbon atoms.

3.2. Electron Transfer Mechanism

To convert the carbon atom from one state to another, the etching of carbon precursors, carbon atoms, or methyl radicals remained previously the topic of the studies. In a new investigation, it is not the case. Photon energy converts into binding energy under the application of atomic hydrogen discussed elsewhere [8].
When the gaseous carbon atom converts into the graphite state, the engaged forces are mainly related to the surface and space formats. Here, a one-bit energy shape like a dash involves along the left side, and a one-bit energy shape is like a dash along the right side.
The transferring electrons of the atom in the graphite state convert it into the lonsdaleite atom. A bit of dash-shaped energy along the west to south involved, whereas a bit of dash-shaped energy along the east to the south involved. The exerted forces on the transferring electrons remain partially conserved. The exerted forces are related to the surface and grounded formats.
Two electrons are transferred to the nearby positioned unfilled states to convert into the diamond atom. As a result, the ground point in the diamond atom goes further below the ground surface than the ground point in the lonsdaleite atom. A carbon atom fully expands under its diamond state.
In the conversion of a carbon atom from one state to any other state, two dash-shaped energy bits involve one along the left side and one along the right side. Figure 1 (i) shows an electron of a filled state transferring to the nearby unfilled state. Dash-shaped energy is like a pipe through which force can pass. Dash-shaped energy from one end connects to the tip of transferring electron and from the other end connects to the nearby unfilled state.
Figure 1 (i) shows the downward arrow increasing the potential of the electron and the upward arrow decreasing the potential of the electron in terms of gravity. Forces only exert on the two poles of an electron as its two sides remain hidden during the transfer. An energy bit covers the transferring electron from both sides. Energy bit does not permit force to exert on an electron from those sides.
Therefore, during the transfer, only the forces of two poles exert on the left or right-sided electron of the carbon atom. An electron keeps the required potential to transfer in a lower or higher state. If not, it will not pass through the hole of a connected dash-shaped energy bit. On transfer to the nearby state, the electron is fastened by the energy knot controlling from the center of its atom.
The expansion and contraction of a carbon atom under different states depend on the electrons’ potential energy and orientation.

4. Structural Formation in Identical-State Carbon Atoms

Graphite material is famous for being a layered structure or two-dimensional structure. As studied widely in the literature, carbon atoms form a sp2 hybridized state. It is an amorphous structure when the arrangement of graphite atoms is not in order. A nanotube structure is famous for being a one-dimensional structure. In fullerene, a buckyball or cage-like structure forms.
A diamond is famous for its tetrahedron structure of atoms, and it forms a sp3 hybridized state. Lonsdaleite keeps a hexagonal structure. In graphene, a honeycomb-like structure. A glassy carbon structure named turbostratic type structure. In the published literature and due to having different opinions, there can be more information on the structures of carbon allotropes.
As discussed in the below sections, the carbon atoms having the same state bind by studying the detail of force and energy at the electron level except in two-dimensional and amorphous graphite structures. Further, the structural formations under electron dynamics in different carbon allotropes do not explore yet.
The earlier studies refer to only two-dimensional and amorphous structures of graphite, and the detail of force and energy at the atomic level is not available. A structural formation in graphite is also not studied yet when under the execution of electron dynamics of the atoms.

4.1. Formation of graphite structure

4.1.1. Formation of graphite structure under the electron dynamics of atoms

A graphite structure can form in three different ways. This section includes the graphite structural formation by the electron dynamics of the atoms. Figure 2a shows the binding of the carbon atoms when in the graphite state. A carbon atom first converts into a graphite state before binding. Atom A binds to atom B by involving the dash-shaped energy of two bits.
A gaseous carbon atom converts into a graphite state by involving the energy of two bits, as each atom shows in Figure 2a. In Figure 2a, Atom C binds to Atom A from the opposite end by involving the dash-shaped energy of two bits. The exerted forces on the transferring electrons remain in the partial conservative mode. Figure 2a only shows the nucleation stage of the graphite. Further binding will start the growth process of a graphite structure.
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Figure 2. (a) Formation of graphite structure under interstate electron dynamics (1) unfilled state of a transferred electron and (2) involved dash-shaped energy bit, (b) formation of graphite structure when weak energy contributed under uniformly attained dynamics of graphite atoms, and (c) amorphous graphite structure when weak energy contributed under non-uniformly attained dynamics of graphite atoms.
Figure 2. (a) Formation of graphite structure under interstate electron dynamics (1) unfilled state of a transferred electron and (2) involved dash-shaped energy bit, (b) formation of graphite structure when weak energy contributed under uniformly attained dynamics of graphite atoms, and (c) amorphous graphite structure when weak energy contributed under non-uniformly attained dynamics of graphite atoms.
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Under electron dynamics, a graphite structure should grow in one dimension. The binding graphite atoms can be from both X-axes. However, electrons of the bound atoms get their orientation along the same axis, which is an adjacent orientation. The exerted forces on the electrons straight along the north-south poles almost diminish. However, there is a need for more work. In tiny-grain carbon film, atoms of arrays elongate and convert into the structures of smooth elements [6].
A nucleated structure of graphite grows by further binding the graphite state atoms. The graphite structure nucleated along the same axis. Figure 2a also shows the layer of the graphite structure from the rear side. The dash-shaped energy bits get involved in binding graphite atoms. These dash-shaped energy bits involve getting a graphite state by transferring electrons.
To transfer electrons from the left and right sides of the gaseous carbon atom in attaining the graphitic state, the potentials of the transferring electrons from upper states to lower states increase. Thus, that atom maintains the equilibrium in the conversion. To convert from a graphitic state to a gaseous state, transferred electrons change the potentials in an equalized manner [45].

4.1.2. Formation of graphite structure under the attained dynamics of atoms

Graphite state atoms first amalgamate under uniformly attained dynamics to form a two-dimensional structure. It means carbon atoms do not execute the electron dynamics in amalgamation. So, energy bits shaped like dash do not involve binding the graphite state atoms. The slight difference of forces remains along the east and west poles of just amalgamated graphite state atoms.
A slight difference in the forces between graphite state atoms enables keeping them bound as they were amalgamated only under the attained dynamics, which is shown in the arrays as labeled by (1), (2), and (3) in Figure 2b. Therefore, weak energy remains and keeps binding to the graphite state atoms.
Graphite state atoms naturally come into the order of two dimensions. The found force and energy among graphite state atoms bind them from east-west or west-east sides. However, there is a need to do further research.
Force and energy at the atomic level introduce the weak application to preserve the graphite structure. Due to the same dynamics of the graphite atoms, they bind under uniform force and energy. When force energy together contributes, a structure forms in two dimensions. It is in graphite state atoms not executing electron dynamics before binding.

4.1.3. Formation of amorphous graphite structure

An amorphous graphite structure is when the amalgamation of graphite state atoms is under the non-uniformly attained dynamics. Atoms do not position exactly from the east-west sides or west-east sides. Figure 2c shows the graphite state atoms bind under the non-uniformly attained dynamics where weak energy and force contribute. However, their contribution is in a non-uniform manner.
A structure of graphite state atoms can also be the amorphous carbon structure when the ground surface is not flat. Due to the amalgamation of graphite state atoms non-uniformly, force, and energy, a chemical in nature, contribute in non-uniform manners. Due to non-uniformly attained dynamics in amorphous graphite structure, amalgamated graphite state atoms also bind under the non-uniform force and energy. However, more work is required to understand the complete picture.
The amalgamation of graphite state atoms is under non-uniformly attained dynamics. However, weak force and weak energy contribute together in a non-uniform manner. Atomic arrangement in amorphous carbon is a continuous random network discussed elsewhere [46].

4.2. Formation of nanotube and fullerene structures

A structure of the carbon nanotube forms when atoms having a nanotube state bind. A nanotube atom can convert from the fullerene state atom before binding. Transferring electrons to the unfilled states is under the involved dash-shaped energy in conversion. A partial conservative force is engaged in the transfer of electrons.
Atoms of the nanotube state bind into a structure by involving partially conserved energy and engaging partially conserved force. On one quadrant electron, forces exert in the space and surface formats. The forces exerted on the electron of the opposite quadrant remain in the surface and grounded formats. In this manner, the binding carbon atom keeps equilibrium. So, carbon atoms having a nanotube state can bind to the targeted or central atom having a nanotube state.
Figure 3a shows atoms of the nanotube state bind to the targeted nanotube atom from both sides. It is a nucleation stage of the nanotube structure. The nucleation of the nanotube structure can be under two options, as shown in Figure 3a. A carbon nanotube initially referred to a finite carbon structure having the shape needle-like tube [47].
The binding of nanotube atoms is not along the same axis. However, the binding is along the same axis in the graphite atoms. The formation of structure in graphite atoms under electron dynamics is considered one-dimensional. However, the nanotube structure forms two-dimensional. Here, forces of the north-south poles also contribute. Though, the energy force remains partially conserved to form the nanotube structure.
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Figure 3. (a) nanotube structure in two different options and (b) fullerene or buckyballs structure in two different options.
Figure 3. (a) nanotube structure in two different options and (b) fullerene or buckyballs structure in two different options.
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A carbon atom converts into a fullerene state atom on electron transfer for each dedicated position. Electrons of the outer ring involve energy shaped like a dash. Overall, the electron of each quadrant engages the partial conservative force in transfer.
For the transfer, each electron of the outer ring considers the exertion of two forces. Involved dash-shaped energy (at the electron level) binds fullerene state atoms for each quadrant of the centered fullerene state atom, as shown in Figure 3b. Figure 3b shows the nucleation of the fullerene structure in two options.
In nucleating the structure, the fullerene state atoms bind to all four quadrants of the centered fullerene state atom. The structural formation in fullerene state atoms is four-dimensional. The exerting forces along the relevant poles of transferring electrons remain partially conserved. The dash-shaped energy bits also keep partially conserved behavior.
Both energy and force, a chemical in nature, behave partially conserved in forming a fullerene structure. However, more work is required. In pioneering work, a fullerene structure was discussed in a football-like shape [48].

4.3. Formation of a diamond structure

Figure 4a shows lonsdaleite and diamond state atoms. Lonsdaleite state atom keeps the ground point just below the ground surface. A lonsdaleite state atom is converted into a diamond state atom when electrons from the left and right sides transfer to the downward unfilled states. The lattice of the converted diamond atom also undertakes the same stretch level as the lattice of the deposited diamond atom.
Figure 4a shows the expected point of binding diamond atoms. A diamond atom deals with the solid maximally. So, the ground point of the diamond state atom remains below the ground point of the lonsdaleite state atom. A diamond state atom first gets deposited on a suitably treated substrate. Thus, the electrons of a deposited diamond state atom do not further gravitate. Again, due to the maximally-achieved potential energy of the electrons, there is no more stretching of their occupied energy knots. So, the electrons of a depositing atom are also in the exertion of forces exerted in the surface and grounded formats.
Each outer ring electron of the depositing diamond atom is clamped by each outer ring energy knot of the deposited diamond atom, as shown in Figure 4b. By involving the golf-stick-shaped energy bit, an outer ring electron of the depositing diamond atom also undertakes the clamp of the outer ring energy knot of the deposited diamond atom. In the structural formation of a diamond, exerting force on each electron also remains non-conserved. Orientation of the zeroth ring electrons adjusted accordingly.
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Figure 4. (a) Lonsdaleite atom conversion into a diamond atom (1) east-west poles, (2) ground point of lonsdaleite atom, (3) expected binding point of two diamond atoms, and (4) ground point of a deposited diamond atom, (b) binding of depositing diamond atom with the deposited diamond atom (1) zeroth ring of a deposited diamond atom, (2) outer ring of a deposited diamond atom, (3) substrate, (4) positioned outer ring energy knots of a deposited diamond atom, (5) involved golf-stick-shaped energy for each outer ring electron of a depositing diamond atom, and (6) orientated outer ring electrons of depositing diamond atom, and (c) diamond growth (1) diamond growth south to east-west and (2) embedded electrons of a deposited diamond atom.
Figure 4. (a) Lonsdaleite atom conversion into a diamond atom (1) east-west poles, (2) ground point of lonsdaleite atom, (3) expected binding point of two diamond atoms, and (4) ground point of a deposited diamond atom, (b) binding of depositing diamond atom with the deposited diamond atom (1) zeroth ring of a deposited diamond atom, (2) outer ring of a deposited diamond atom, (3) substrate, (4) positioned outer ring energy knots of a deposited diamond atom, (5) involved golf-stick-shaped energy for each outer ring electron of a depositing diamond atom, and (6) orientated outer ring electrons of depositing diamond atom, and (c) diamond growth (1) diamond growth south to east-west and (2) embedded electrons of a deposited diamond atom.
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Figure 4c shows the growth trend of diamonds. In the growth of the diamond structure, the expansion and contraction of the depositing and deposited atoms mutually adjust. Figure 4c also shows the electrons embedded in the substrate surface for the first deposited diamond atom. By keeping the maximum stretching of the occupied energy knots, electrons orientated from east-west to south in each depositing diamond atom. Thus, two diamond state atoms bind from east-west to south. It is the nucleation stage of a diamond. A diamond structure can grow with several faces. Different circles in Figure 4c designate the filled and unfilled states.
In Figure 4c, the overlapping of the circles designates the additional clamping of the electrons. On binding two diamond state atoms, the third diamond state atom comes into position to bind. Therefore, the growth of diamonds is from south to east-west. But the binding of diamond atoms is from east-west to south. The binding of diamond atoms remains between the surface and grounded formats. Thus, the structural formation in diamonds is related to the topological structure. Earlier studies discussed diamond structure with the atomic level understanding, which is not the case in this study. The current discussion is with the electron level understanding, which is more practical and authentic.
Under suitable parameters studied elsewhere [49], diamond nucleation was achieved at very low-pressure, which might be due to the presence of discussed golf-stick-shaped energy bits here. By choosing a suitable dopant, the band gap of the diamond can switch from indirect to direct [50]. However, a band gap is a photonic band gap under a new insight [5].

4.4. Formation of lonsdaleite and graphene structures

The ground point of the carbon atom having a lonsdaleite state is a bit below the ground surface as it exists below the ground point of the graphite state atom. Electrons of the lonsdaleite state atom keep lower potential energy than electrons of the diamond state atom. Hence, the energy knots are in the lesser stretch. The lonsdaleite state atom is less expanded than the diamond state atom. A lonsdaleite state atom is mainly a bit solid. Some historical facts of lonsdaleite structure and its study under conventional insight are given elsewhere [51].
Lonsdaleite state atom also experiences the non-conservative force for two electrons under the involvement of non-conserved energy. Lonsdaleite state atoms bind from east-west to a bit south, but the growth is from (a bit) south to east-west. However, further studies are required to get a better insight.
The single sheets of graphite are graphene, for which a detailed study is given elsewhere [52]. Under a new insight, the ground point of the graphene state atom exists just above the ground surface. However, the levitational force is in a non-conserved manner. The binding of graphene state atoms experiences forces mainly in the surface and space formats at the electron level. So, the growth of the graphene structure is in a reverse manner to the diamond structure.
The growth of graphene is from east-west to north. Principally, graphene state atoms should grow with a topological structure. Due to the limitation of forces exerted on the electrons in the surface and space formats, adherence to only a few layers in the graphene structure is possible. However, more work is required.

4.5. Formation of glassy carbon structure

Under conventional insights, a detailed study on glassy carbon reviewing its various aspects is given elsewhere [53]. In the nucleation of the glassy carbon structure under the new insight, three layers of different states of carbon atoms bind successively. By binding simultaneously, layers of gaseous carbon atoms, graphite state atoms, and lonsdaleite state atoms nucleate the glassy carbon structure.
To grow the structure of glassy carbon, layers of gaseous, graphite, and lonsdaleite state atoms repeat in the same order. The energy bits having the golf stick shape or the shape of a half-parabola get involved at the electron levels in binding the different state atoms arranged in the layers.
Layers of gaseous and graphitic carbon atoms bind under the exerted forces in the grounded and surface formats. The pair of orientated outer ring electrons in each gaseous state atom undertake clamping of the positioned energy knots of the outer ring of each graphite state atom, which is from the rear side in Figure 5. By increasing the potential energy of electrons, gaseous carbon atoms attempt for gravitational force.
Layers of lonsdaleite and graphite state atoms bind under the joint application of exerting forces in space and surface formats. The pair of orientated outer ring electrons in each lonsdaleite state atom undertake clamping of the positioned energy knots of the outer ring of each graphite state atom, which is from the front side, as shown in Figure 5. By decreasing the potential energy of electrons, lonsdaleite atoms attempt for levitational force.
Under a new insight, binding gaseous carbon atoms of each layer to the graphite state atoms of each layer involves oppositely J-shaped energy (or golf-stick-shaped energy) at the electron level. The clamping of each pair of unfilled energy knots to the half-length of each pair of electrons is from the rear side. The label (1) in Figure 5 shows the binding between the gaseous carbon atoms and graphite state atoms.
Under a new insight, binding lonsdaleite state atoms of each layer to the graphite state atoms of each layer involves J-shaped energy (or golf-stick-shaped energy) at the electron level. The clamping of each pair of unfilled energy knots to the half-length of each pair of electrons is from the front side. Label (2) in Figure 5 shows the binding between the lonsdaleite state and graphite state atoms. In Figure 5, label (3) indicates the compensation space between the layered structure in terms of atomic expansion and contraction.

5. Estimated hardness of carbon-based materials at Mohs scale

Figure 6 shows the hardness at the Mohs scale in different carbon-based materials, which is in estimation. Gaseous carbon has zero hardness at the Mohs scale. The plotted hardness in Figure 6 relies on the extracted data from the published studies. However, the research activities discussing hardness property should also consider the details of energy and force behaviors. As the graphite, nanotube, and fullerene structures keep partially-conserved energy and force, they can exhibit average hardness. On the other hand, lonsdaleite, graphene, and glassy carbon structures keep non-conserved energy and force. So, these structures can exhibit high hardness.
The high hardness of lonsdaleite, graphene, and diamond structures is due to the involvement of golf-stick-shaped energy bits. In these materials, orientated outer ring electrons undertaking additional clamping of positioned energy knots engage non-conservative forces. The same is the case in the structural formation of glassy carbon.
In Figure 6, the hardness model develops a sense of understanding and new insights into all sorts of carbon materials. The hardness of carbon films depends on the nature of the force and the kind of energy. Pieces of evidence from the published literature and presented details also support the model.
The published data on the hardness does not consider the energy force detail discussed here. There is an actual need to re-investigate the hardness of different carbon-based materials. A recent study evaluates the hardness of diamond films by nanoindentation [54]. Nevertheless, the hardness of nanostructures and nanomaterials also details the chemical aspect. There is a need to investigate carbon films from the beginning. Different carbon-based materials consider their structures depending on the details of the force and energy. Thus, all sorts of depositions and syntheses need to be re-visited.

6. Conclusion

A carbon atom converts from one state to another, where two dash-shaped energy bits involve. Electrons transfer from filled to nearby unfilled states in conversion. The carbon atom keeps an equilibrium state during the electron transfer mechanism. The structural formation is one-dimensional when graphite atoms execute electron dynamics. A structure is two-dimensional when graphite atoms bind under uniformly attained dynamics. Here, energy and force contribute uniformly at the atomic level.
Atoms of graphite state bind into a two-dimensional structure under weak force and energy. In the amorphous graphite structure, the energy force at the atomic level contributes non-uniformly. The structural formation in nanotubes is two-dimensional when atoms bind by the dynamics of suitable electrons. In a nanotube, electrons of opposite quadrants perform dynamics. In fullerene atoms, the structure is four-dimensional.
In fullerene, all four outer ring electrons of the atoms execute dynamics. In the structural formation of graphite (when in one dimension), nanotube, and fullerene, bits of partially conserved dash-shaped energy involve at the electron level by engaging the partially conserved force, too. Each outer ring electron of the depositing diamond atom undertakes a clamp of each outer ring energy knot of the deposited diamond atom. A bit of energy shape like a golf stick involves transferring the electron up to half-length to another energy knot. The half-length electron above the clamped energy knot remains under the exertion of non-conservative forces.
The binding in diamond state atoms is from the east-west to the south, so the growth is from south to east-west. It is a tetra-electron topological structure. The binding in lonsdaleite state atoms is from the east-west to a bit south, so the growth is from a bit south to the east-west. It is a bi-electron topological structure.
Layers of gaseous, graphite, and lonsdaleite state atoms repeat under the same order, and a glassy carbon structure grows. In glassy carbon, the orientated outer ring electrons of the gaseous and lonsdaleite atoms undertake another clamping of the positioned energy knots of the outer rings of the graphite atoms. In diamond, lonsdaleite, graphene, and glassy carbon structures, bits of non-conserved energy involve at the electron level by engaging the non-conserved force.
The hardness of carbon materials relates to the energy and force details at the electronic level. The study of carbon atoms and their structures opens new areas of investigation.

Data Availability Statement

All data generated or analyzed in this study is a part of this article.

Acknowledgments

The author acknowledges the financial support of all the offices and countries. He also thanks whomever he learned from at any stage of his life.

Conflicts of Interest

The author declares no conflict of interest.

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Figure 1. (a) Lattice of a carbon atom, atomic structure of carbon atom when in the (b) gaseous state, (c) graphite state, (d) nanotube state, (e) fullerene state, (f) diamond state, (g) lonsdaleite state, (h) graphene state, and (i) transferring electron (red circles indicate filled states and white circles indicate unfilled states).
Figure 1. (a) Lattice of a carbon atom, atomic structure of carbon atom when in the (b) gaseous state, (c) graphite state, (d) nanotube state, (e) fullerene state, (f) diamond state, (g) lonsdaleite state, (h) graphene state, and (i) transferring electron (red circles indicate filled states and white circles indicate unfilled states).
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Figure 5. Formation of glassy carbon structure where layers of gaseous carbon atoms, graphite state atoms, and lonsdaleite state atoms bind successively.
Figure 5. Formation of glassy carbon structure where layers of gaseous carbon atoms, graphite state atoms, and lonsdaleite state atoms bind successively.
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Figure 6. Plot between Mohs hardness and different carbon structures; (1) levitational force at the electron level, (2) graphene, (3) increasing levitational force, (4) gaseous carbon, (5) graphite, (6) increasing gravitational force, (7) diamond, (8) lonsdaleite, (9) fullerene, (10) maximum gravitational force, (11) nanotube, (12) maximum levitational force.
Figure 6. Plot between Mohs hardness and different carbon structures; (1) levitational force at the electron level, (2) graphene, (3) increasing levitational force, (4) gaseous carbon, (5) graphite, (6) increasing gravitational force, (7) diamond, (8) lonsdaleite, (9) fullerene, (10) maximum gravitational force, (11) nanotube, (12) maximum levitational force.
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Bibliographic detail

Preprints 82934 i001 In 1996, Mubarak Ali earned a B.Sc. degree in Physics and Mathematics. The University of the Punjab awarded him the degree. The M.Sc. degree in Materials Science got in 1998. Bahauddin Zakariya University Multan awarded him the degree of master with distinction. He completed his M.Sc. thesis at Quaid-i-Azam University Islamabad. He gained a PhD in Mechanical Engineering from the Universiti Teknologi Malaysia under the award of the Malaysian Technical Cooperation Programme (MTCP;2004-07) and a postdoc in advanced surface technologies at Istanbul Technical University under the foreign fellowship of The Scientific and Technological Research Council of Turkey (TÜBİTAK, 2010). Dr Mubarak completed another postdoc in nanotechnology at the Tamkang University Taipei, 2013-2014, sponsored by the National Science Council, now the Ministry of Science and Technology, Taiwan. He remained working as an Assistant Professor on the tenure track at COMSATS University Islamabad from May 2008 to June 2018, previously known as COMSATS Institute of Information Technology. His new position is in process. Before that, he remained a working assistant and deputy director at M/o Science & Technology, Pakistan Council of Renewable Energy Technologies, Islamabad, from January 2000 to May 2008. The Institute for Materials Research at Tohoku University Japan invited Dr Mubarak to deliver a scientific talk. His scientific research remained a part of many conferences organized by renowned universities in many countries. His core area of research includes materials science, physics & nanotechnology. He also won a merit scholarship for PhD study from the Higher Education Commission, Government of Pakistan. However, he did not avail the opportunity. He earned a diploma (in English) and a certificate (in the Japanese language) in 2000 and 2001, respectively, part-time from the National University of Modern Languages, Islamabad. He is the author of several articles available at the following links; https://www.researchgate.net/profile/Mubarak_Ali5 & https://scholar.google.com.pk/citations?hl=en&user=UYjvhDwAAAAJ
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Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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