The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: metal hydrogen phosphate, molybdenum disulfide, or boron nitride.

The method as recited in claim 1, 4 atiher eemprisingw herein moving the at least six carbon atoms in between the first l ayer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: Ti(HP O 4)2 H20; Ti(HP O 4)2 2H20; Zr(HP O 4)2-H20; Zr(HP O 4)2-2H20; Hf(HP O 4)2-H20; Sn(HP O 4)2-2H20; Pb(HP O₄)2-H20; Ce(HP O₄)2r 1.33H20; 2 LixNizCObMncO 2, wherein z is in a first range from about 0.05 to about 0.80, b is in a second range from about 0.02 to about 0.60, c is in a third range from about 0.05 to about 0.60, and x is in a fourth range from about 0.98 and about 1.05; a Phyllosilicate; HTiNb O5; HSr₂Nb₃ O10; K₄Nb₆ 0 17; KNb₃ Os; Kl-xLax Ca₂ -x Nb₃ O₁O where x is in a fifth range from about 0 to about 1; or (PbS) 1.1s TiS2.

The method as recited in claim 1, ft4iher -wherein reactin g the at least six carbon atoms co mpri ses ee mpfisin g-reacting the at least six carbon atoms at a pressure selected from a range from about 10 -9 torr to about equal to one atmosphere and at a temperature in a range from about 725 degrees Celsius to about 1325 degrees Celsius.

The method as recited in claim 1, further comprising disposing an inert gas in the reaction chamber.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first layer and the second layer to form doped graphene.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form doped graphene, wherein the doping material includes at least one of A₂ H 6, A(CH₃)3, A(CF₃)3, or A(Si(CH₃)3)3, where A = B, Al, Ga, or In. withdrawn

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form 3 doped graphene, wherein the doping material includes at least one of XH3, X(CH₃)3, X(CF₃)3, or X(Si(CH₃)3)3, where X = N, P, As, or Sb. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene.

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene in [[a]] the reaction chamber usi ng an aromatic solvent.

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using at least one of benzene, toluene, xylene, mesitylene, biphenyl, hexafluorobenzene, chlorobenzene, or benzonitrile. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using a biphasic solvent. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using chlorine gas. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an organic liquid. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber, wherein the reaction chamber is effective to acidify the first and second layers. 4 withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using water. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an molten alkaline salt or nitride. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using an acoustic device. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat waves tuned to a frequency of the graphene. withdrawn

2 1. The method as recited in claim 1, ft4hef-eempiing wherein moving the at least six carbon atoms in between the first and second l aye f-layers of the host material --whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 16 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first and second layef layers of the host material --wher e co m prises moving the at least six carbon atoms in between la yers of t he host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 1.5 A to about 16 A.

The method as recited in claim 1, f utwher comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material-whe r e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 33 A.

The method as recited in claim 1, f tAhe-emprising wherein moving the at least six carbon atoms in between the first and second laye f -layers of the host material --wher e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the layer structure with a-the layer spacing in -a-r ange-of about 6.2A.

The method as recited in claim 1, ftt4her comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l--wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 16 A.

The method as recited in claim 1, f w4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l-- whe r e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the layer structure with a-the layer spacing in -a-ran ge of about 3.4A.

The method as recited in claim 1, f tn4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 33 A.

The method as recited in claim 1, f u4he--eempising wherein moving the at least six carbon atoms in between the first and second l aye -layersof the 6 host material,-whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 2 A to about 20 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material,- whe f e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 16 A to about 33 A.

3 0. The method as recited in claim 1, 4 atkef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --whei e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the lay er structure with a-the la y er s p acin g in a ran g e of about 6 A to about 7 A.

3 1. A structure formed in accordance with the method of claim 1, the structure comprising: a first and a second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and a layer of graphene disposed in between the first and the second layer of the host material. withdrawn

A system effective to form graphene in accordance with the method of claim 1, the system comprising: a source of carbon atoms; 7 a reaction chamber in communication with the source of carbon atoms, wherein the reaction chamber includes a first and second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and the reaction chamber is effective to move at least six carbon atoms from the source into the reaction chamber; move the at least six carbon atoms in between the first and the second layer; and react the carbon atoms under reaction conditions sufficient to form the graphene. withdrawn

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: metal hydrogen phosphate, molybdenum disulfide, or boron nitride.

The method as recited in claim 1, 4 atiher eemprisingw herein moving the at least six carbon atoms in between the first l ayer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: Ti(HP O 4)2 H20; Ti(HP O 4)2 2H20; Zr(HP O 4)2-H20; Zr(HP O 4)2-2H20; Hf(HP O 4)2-H20; Sn(HP O 4)2-2H20; Pb(HP O₄)2-H20; Ce(HP O₄)2r 1.33H20; 2 LixNizCObMncO 2, wherein z is in a first range from about 0.05 to about 0.80, b is in a second range from about 0.02 to about 0.60, c is in a third range from about 0.05 to about 0.60, and x is in a fourth range from about 0.98 and about 1.05; a Phyllosilicate; HTiNb O5; HSr₂Nb₃ O10; K₄Nb₆ 0 17; KNb₃ Os; Kl-xLax Ca₂ -x Nb₃ O₁O where x is in a fifth range from about 0 to about 1; or (PbS) 1.1s TiS2.

The method as recited in claim 1, ft4iher -wherein reactin g the at least six carbon atoms co mpri ses ee mpfisin g-reacting the at least six carbon atoms at a pressure selected from a range from about 10 -9 torr to about equal to one atmosphere and at a temperature in a range from about 725 degrees Celsius to about 1325 degrees Celsius.

The method as recited in claim 1, further comprising disposing an inert gas in the reaction chamber.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first layer and the second layer to form doped graphene.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form doped graphene, wherein the doping material includes at least one of A₂ H 6, A(CH₃)3, A(CF₃)3, or A(Si(CH₃)3)3, where A = B, Al, Ga, or In. withdrawn

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form 3 doped graphene, wherein the doping material includes at least one of XH3, X(CH₃)3, X(CF₃)3, or X(Si(CH₃)3)3, where X = N, P, As, or Sb. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene.

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene in [[a]] the reaction chamber usi ng an aromatic solvent.

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using at least one of benzene, toluene, xylene, mesitylene, biphenyl, hexafluorobenzene, chlorobenzene, or benzonitrile. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using a biphasic solvent. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using chlorine gas. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an organic liquid. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber, wherein the reaction chamber is effective to acidify the first and second layers. 4 withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using water. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an molten alkaline salt or nitride. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using an acoustic device. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat waves tuned to a frequency of the graphene. withdrawn

2 1. The method as recited in claim 1, ft4hef-eempiing wherein moving the at least six carbon atoms in between the first and second l aye f-layers of the host material --whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 16 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first and second layef layers of the host material --wher e co m prises moving the at least six carbon atoms in between la yers of t he host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 1.5 A to about 16 A.

The method as recited in claim 1, f utwher comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material-whe r e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 33 A.

The method as recited in claim 1, f tAhe-emprising wherein moving the at least six carbon atoms in between the first and second laye f -layers of the host material --wher e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the layer structure with a-the layer spacing in -a-r ange-of about 6.2A.

The method as recited in claim 1, ftt4her comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l--wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 16 A.

The method as recited in claim 1, f w4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l-- whe r e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the layer structure with a-the layer spacing in -a-ran ge of about 3.4A.

The method as recited in claim 1, f tn4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 33 A.

The method as recited in claim 1, f u4he--eempising wherein moving the at least six carbon atoms in between the first and second l aye -layersof the 6 host material,-whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 2 A to about 20 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material,- whe f e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 16 A to about 33 A.

3 0. The method as recited in claim 1, 4 atkef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --whei e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the lay er structure with a-the la y er s p acin g in a ran g e of about 6 A to about 7 A.

3 1. A structure formed in accordance with the method of claim 1, the structure comprising: a first and a second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and a layer of graphene disposed in between the first and the second layer of the host material. withdrawn

A system effective to form graphene in accordance with the method of claim 1, the system comprising: a source of carbon atoms; 7 a reaction chamber in communication with the source of carbon atoms, wherein the reaction chamber includes a first and second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and the reaction chamber is effective to move at least six carbon atoms from the source into the reaction chamber; move the at least six carbon atoms in between the first and the second layer; and react the carbon atoms under reaction conditions sufficient to form the graphene. withdrawn

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: metal hydrogen phosphate, molybdenum disulfide, or boron nitride.

The method as recited in claim 1, 4 atiher eemprisingw herein moving the at least six carbon atoms in between the first l ayer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: Ti(HP O 4)2 H20; Ti(HP O 4)2 2H20; Zr(HP O 4)2-H20; Zr(HP O 4)2-2H20; Hf(HP O 4)2-H20; Sn(HP O 4)2-2H20; Pb(HP O₄)2-H20; Ce(HP O₄)2r 1.33H20; 2 LixNizCObMncO 2, wherein z is in a first range from about 0.05 to about 0.80, b is in a second range from about 0.02 to about 0.60, c is in a third range from about 0.05 to about 0.60, and x is in a fourth range from about 0.98 and about 1.05; a Phyllosilicate; HTiNb O5; HSr₂Nb₃ O10; K₄Nb₆ 0 17; KNb₃ Os; Kl-xLax Ca₂ -x Nb₃ O₁O where x is in a fifth range from about 0 to about 1; or (PbS) 1.1s TiS2.

The method as recited in claim 1, ft4iher -wherein reactin g the at least six carbon atoms co mpri ses ee mpfisin g-reacting the at least six carbon atoms at a pressure selected from a range from about 10 -9 torr to about equal to one atmosphere and at a temperature in a range from about 725 degrees Celsius to about 1325 degrees Celsius.

The method as recited in claim 1, further comprising disposing an inert gas in the reaction chamber.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first layer and the second layer to form doped graphene.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form doped graphene, wherein the doping material includes at least one of A₂ H 6, A(CH₃)3, A(CF₃)3, or A(Si(CH₃)3)3, where A = B, Al, Ga, or In. withdrawn

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form 3 doped graphene, wherein the doping material includes at least one of XH3, X(CH₃)3, X(CF₃)3, or X(Si(CH₃)3)3, where X = N, P, As, or Sb. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene.

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene in [[a]] the reaction chamber usi ng an aromatic solvent.

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using at least one of benzene, toluene, xylene, mesitylene, biphenyl, hexafluorobenzene, chlorobenzene, or benzonitrile. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using a biphasic solvent. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using chlorine gas. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an organic liquid. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber, wherein the reaction chamber is effective to acidify the first and second layers. 4 withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using water. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an molten alkaline salt or nitride. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using an acoustic device. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat waves tuned to a frequency of the graphene. withdrawn

2 1. The method as recited in claim 1, ft4hef-eempiing wherein moving the at least six carbon atoms in between the first and second l aye f-layers of the host material --whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 16 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first and second layef layers of the host material --wher e co m prises moving the at least six carbon atoms in between la yers of t he host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 1.5 A to about 16 A.

The method as recited in claim 1, f utwher comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material-whe r e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 33 A.

The method as recited in claim 1, f tAhe-emprising wherein moving the at least six carbon atoms in between the first and second laye f -layers of the host material --wher e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the layer structure with a-the layer spacing in -a-r ange-of about 6.2A.

The method as recited in claim 1, ftt4her comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l--wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 16 A.

The method as recited in claim 1, f w4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l-- whe r e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the layer structure with a-the layer spacing in -a-ran ge of about 3.4A.

The method as recited in claim 1, f tn4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 33 A.

The method as recited in claim 1, f u4he--eempising wherein moving the at least six carbon atoms in between the first and second l aye -layersof the 6 host material,-whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 2 A to about 20 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material,- whe f e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 16 A to about 33 A.

3 0. The method as recited in claim 1, 4 atkef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --whei e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the lay er structure with a-the la y er s p acin g in a ran g e of about 6 A to about 7 A.

3 1. A structure formed in accordance with the method of claim 1, the structure comprising: a first and a second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and a layer of graphene disposed in between the first and the second layer of the host material. withdrawn

A system effective to form graphene in accordance with the method of claim 1, the system comprising: a source of carbon atoms; 7 a reaction chamber in communication with the source of carbon atoms, wherein the reaction chamber includes a first and second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and the reaction chamber is effective to move at least six carbon atoms from the source into the reaction chamber; move the at least six carbon atoms in between the first and the second layer; and react the carbon atoms under reaction conditions sufficient to form the graphene. withdrawn

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: metal hydrogen phosphate, molybdenum disulfide, or boron nitride.

The method as recited in claim 1, 4 atiher eemprisingw herein moving the at least six carbon atoms in between the first l ayer and the second layer co m prises moving the at least six carbon atoms in between layers of the host material that includes ef-at least one of: Ti(HP O 4)2 H20; Ti(HP O 4)2 2H20; Zr(HP O 4)2-H20; Zr(HP O 4)2-2H20; Hf(HP O 4)2-H20; Sn(HP O 4)2-2H20; Pb(HP O₄)2-H20; Ce(HP O₄)2r 1.33H20; 2 LixNizCObMncO 2, wherein z is in a first range from about 0.05 to about 0.80, b is in a second range from about 0.02 to about 0.60, c is in a third range from about 0.05 to about 0.60, and x is in a fourth range from about 0.98 and about 1.05; a Phyllosilicate; HTiNb O5; HSr₂Nb₃ O10; K₄Nb₆ 0 17; KNb₃ Os; Kl-xLax Ca₂ -x Nb₃ O₁O where x is in a fifth range from about 0 to about 1; or (PbS) 1.1s TiS2.

The method as recited in claim 1, ft4iher -wherein reactin g the at least six carbon atoms co mpri ses ee mpfisin g-reacting the at least six carbon atoms at a pressure selected from a range from about 10 -9 torr to about equal to one atmosphere and at a temperature in a range from about 725 degrees Celsius to about 1325 degrees Celsius.

The method as recited in claim 1, further comprising disposing an inert gas in the reaction chamber.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first layer and the second layer to form doped graphene.

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form doped graphene, wherein the doping material includes at least one of A₂ H 6, A(CH₃)3, A(CF₃)3, or A(Si(CH₃)3)3, where A = B, Al, Ga, or In. withdrawn

The method as recited in claim 1, further comprising moving a doping material into the reaction chamber in between the first and the second layer to form 3 doped graphene, wherein the doping material includes at least one of XH3, X(CH₃)3, X(CF₃)3, or X(Si(CH₃)3)3, where X = N, P, As, or Sb. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene.

The method as recited in claim 1, further comprising removing at least part of the first and second l aye r -la y ersof the host material from the graphene in [[a]] the reaction chamber usi ng an aromatic solvent.

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using at least one of benzene, toluene, xylene, mesitylene, biphenyl, hexafluorobenzene, chlorobenzene, or benzonitrile. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using a biphasic solvent. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using chlorine gas. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an organic liquid. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber, wherein the reaction chamber is effective to acidify the first and second layers. 4 withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using water. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene in a reaction chamber using an molten alkaline salt or nitride. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using an acoustic device. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat. withdrawn

The method as recited in claim 1, further comprising removing at least part of the first and second layer of the host material from the graphene using heat waves tuned to a frequency of the graphene. withdrawn

2 1. The method as recited in claim 1, ft4hef-eempiing wherein moving the at least six carbon atoms in between the first and second l aye f-layers of the host material --whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 16 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first and second layef layers of the host material --wher e co m prises moving the at least six carbon atoms in between la yers of t he host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 1.5 A to about 16 A.

The method as recited in claim 1, f utwher comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material-whe r e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 3 A to about 33 A.

The method as recited in claim 1, f tAhe-emprising wherein moving the at least six carbon atoms in between the first and second laye f -layers of the host material --wher e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the layer structure with a-the layer spacing in -a-r ange-of about 6.2A.

The method as recited in claim 1, ftt4her comprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l--wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 16 A.

The method as recited in claim 1, f w4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host materia l-- whe r e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the layer structure with a-the layer spacing in -a-ran ge of about 3.4A.

The method as recited in claim 1, f tn4her eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --wher e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 7.6 A to about 33 A.

The method as recited in claim 1, f u4he--eempising wherein moving the at least six carbon atoms in between the first and second l aye -layersof the 6 host material,-whei e co m prises moving the at least six carbon atoms in between layers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 2 A to about 20 A.

The method as recited in claim 1, f ttihef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material,- whe f e co m prises moving the at least six carbon atoms in between la yers o f the host material that includes a-the lay er structure with a-the lay er s p acin g in a ran g e of about 16 A to about 33 A.

3 0. The method as recited in claim 1, 4 atkef eemprisingw herein moving the at least six carbon atoms in between the first layer and second layer of the host material --whei e co m prises moving the at least six carbon atoms in between lay ers o f the host material that includes a-the lay er structure with a-the la y er s p acin g in a ran g e of about 6 A to about 7 A.

3 1. A structure formed in accordance with the method of claim 1, the structure comprising: a first and a second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and a layer of graphene disposed in between the first and the second layer of the host material. withdrawn

A system effective to form graphene in accordance with the method of claim 1, the system comprising: a source of carbon atoms; 7 a reaction chamber in communication with the source of carbon atoms, wherein the reaction chamber includes a first and second layer of a host material, wherein the host material includes a crystalline compound with a layer structure with a layer spacing in a range from about 1.5A to about 33A; and the reaction chamber is effective to move at least six carbon atoms from the source into the reaction chamber; move the at least six carbon atoms in between the first and the second layer; and react the carbon atoms under reaction conditions sufficient to form the graphene. withdrawn