Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a solid carbon composition forms a solid carbon product derived from a hydrocarbon mixture: including methane including carbon sourced from captured gas; and formed via methanation of a carbon dioxide mixture extracted from captured gas via a point source capture process. The solid carbon composition includes carbon sourced from captured gas and including: a first amount of carbon-13 isotopes; and a second amount of carbon-12 isotopes. The solid carbon composition exhibits an isotopic signature defining a ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes exceeding ?50.0 parts-per-thousand-versus-PDB-standard.

Abstract: One variation of a solid carbon composition forms a solid carbon product derived from a hydrocarbon mixture: including methane including carbon sourced from captured gas; and formed via methanation of a carbon dioxide mixture extracted from captured gas via a point source capture process. The solid carbon composition includes carbon sourced from captured gas and including: a first amount of carbon-13 isotopes; and a second amount of carbon-12 isotopes. The solid carbon composition exhibits an isotopic signature defining a ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes exceeding ?50.0 parts-per-thousand-versus-PDB-standard.

Abstract: One variation of a diamond composition includes carbon: including a first amount of carbon-13 isotopes and a second amount of carbon-12 isotopes; and sourced from a hydrocarbon mixture including hydrocarbons and formed via methanation of a carbon dioxide mixture. The carbon dioxide mixture: sourced from a sample of air including carbon dioxide and impurities; conveyed through a separation unit configured to remove impurities; including carbon dioxide and impurities; conveyed through a distillation column configured to regulate amounts of carbon-13 isotopes and carbon-12 isotopes; and exhibiting a target ratio of carbon-13 isotopes to carbon-12 isotopes at an outlet of the distillation column. The diamond composition: formed via chemical vapor deposition; and exhibiting an isotopic signature defining a final ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes within a first target range corresponding to the target ratio exhibited by the carbon dioxide mixture.

Abstract: One variation of a diamond composition includes carbon: including a first amount of carbon-13 isotopes and a second amount of carbon-12 isotopes; and sourced from a hydrocarbon mixture including hydrocarbons and formed via methanation of a carbon dioxide mixture. The carbon dioxide mixture: sourced from a sample of air including carbon dioxide and impurities; conveyed through a separation unit configured to remove impurities; including carbon dioxide and impurities; conveyed through a distillation column configured to regulate amounts of carbon-13 isotopes and carbon-12 isotopes; and exhibiting a target ratio of carbon-13 isotopes to carbon-12 isotopes at an outlet of the distillation column. The diamond composition: formed via chemical vapor deposition; and exhibiting an isotopic signature defining a final ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes within a first target range corresponding to the target ratio exhibited by the carbon dioxide mixture.

Abstract: One variation of a diamond composition includes carbon: including a first amount of carbon-13 isotopes and a second amount of carbon-12 isotopes; and sourced from a hydrocarbon mixture including hydrocarbons and formed via methanation of a carbon dioxide mixture. The carbon dioxide mixture: sourced from a sample of air including carbon dioxide and impurities; conveyed through a separation unit configured to remove impurities; including carbon dioxide and impurities; conveyed through a distillation column configured to regulate amounts of carbon-13 isotopes and carbon-12 isotopes; and exhibiting a target ratio of carbon-13 isotopes to carbon-12 isotopes at an outlet of the distillation column. The diamond composition: formed via chemical vapor deposition; and exhibiting an isotopic signature defining a final ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes within a first target range corresponding to the target ratio exhibited by the carbon dioxide mixture.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a diamond composition includes carbon: including a first amount of carbon-13 isotopes and a second amount of carbon-12 isotopes; and sourced from a hydrocarbon mixture including hydrocarbons and formed via methanation of a carbon dioxide mixture. The carbon dioxide mixture: sourced from a sample of air including carbon dioxide and impurities; conveyed through a separation unit configured to remove impurities; including carbon dioxide and impurities; conveyed through a distillation column configured to regulate amounts of carbon-13 isotopes and carbon-12 isotopes; and exhibiting a target ratio of carbon-13 isotopes to carbon-12 isotopes at an outlet of the distillation column. The diamond composition: formed via chemical vapor deposition; and exhibiting an isotopic signature defining a final ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes within a first target range corresponding to the target ratio exhibited by the carbon dioxide mixture.

Abstract: One variation of a diamond composition includes carbon: including a first amount of carbon-13 isotopes and a second amount of carbon-12 isotopes; and sourced from a hydrocarbon mixture including hydrocarbons and formed via methanation of a carbon dioxide mixture. The carbon dioxide mixture: sourced from a sample of air including carbon dioxide and impurities; conveyed through a separation unit configured to remove impurities; including carbon dioxide and impurities; conveyed through a distillation column configured to regulate amounts of carbon-13 isotopes and carbon-12 isotopes; and exhibiting a target ratio of carbon-13 isotopes to carbon-12 isotopes at an outlet of the distillation column. The diamond composition: formed via chemical vapor deposition; and exhibiting an isotopic signature defining a final ratio of the first amount of carbon-13 isotopes to the second amount of carbon-12 isotopes within a first target range corresponding to the target ratio exhibited by the carbon dioxide mixture.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.

Abstract: One variation of a method includes: ingesting an air sample captured during an air capture period at a target location for collection of a first mixture including carbon dioxide and a first concentration of impurities; conveying the first mixture through a liquefaction unit to generate a second mixture including carbon dioxide and a second concentration of impurities less than the first concentration of impurities; in a methanation reactor, mixing the second mixture with hydrogen to generate a first hydrocarbon mixture comprising a third concentration of impurities comprising nitrogen, carbon dioxide, and hydrogen; conveying the first hydrocarbon mixture through a separation unit configured to remove impurities from the first hydrocarbon mixture to generate a second hydrocarbon a fourth concentration of impurities less than the third concentration of impurities; and depositing the second hydrocarbon mixture in a diamond reactor containing a set of diamond seeds to generate a first set of diamonds.