Abstract: The embodiments herein relate to methods, apparatus, and systems for forming and purifying solid carbon material from a molten carbonate salt electrolyte. Various embodiments also provide methods, apparatus, and systems for recycling certain materials including the carbonate salt electrolyte, carbon dioxide, water, etc. Advantageously, the system utilizes carbon dioxide in one or more processes, for example to purify the solid carbon and regenerate the carbonate salt electrolyte. These methods, apparatus, and systems provide an efficient technique to consume carbon dioxide in the production of solid carbon, with substantial advantages over systems that attempt to form solid carbon from a stream of carbon dioxide provided directly to an electrolysis reactor.