Many studies deal synthesis of carbon materials including all the disclosed states. This study describes the binding mechanism of different state carbon atoms. The binding energy as per gauge of certain state carbon atom is being invited under the application of force. In evolving different structures of carbon atoms their admissible electron-dynamics generate binding energy. Evolution of graphite structure is one-dimensional when certain amalgamated atom executes electron-dynamics to gain stable state to bind atom of attained stable state. Evolution of graphite structure is two-dimensional when amalgamated atoms under attained dynamics deal difference in surface format forces at the point of binding. Structural evolution is two-dimensional for nanotube and four-dimensional for fullerene (bucky balls). Structure evolution of graphite, nanotube and fullerene involve surface format forces mainly to invite binding energy of their atoms as per gauge of electron-dynamics. Structural evolutions of diamond and Lonsdaleite are under the joint application of surface format forces and grounded format forces to invite binding energy of atoms. Structural evolution of graphene involves both surface and space format forces to invite binding energy of atoms. Glassy carbon is related to layered wholly topological structure where layers of gas state carbon atoms, graphitic state and lonsdaleite state are being involved in successive manner to invite binding energy under space, surface and grounded format forces. Due to maintenance of electrons, carbon atoms do not bind when in the gas state. Diamond is south to ground tetra-dimensional, Lonsdaleite is south to ground bi-dimensional and graphene is ground to north tetra-dimensional topological structures. The Mohs hardness of carbon-based materials under different levitation gravitation behaviors attempting at electron level under contraction expansion of clamping energy knot is sketched. Carbon atoms when in fullerene structure is the best model to understand the influencing force at ground surface and the best model to explain binding mechanism in atoms of other elements.