The thermal radiation effect of substrate on nano-microsized particles levitating in low-pressure reactive plasmas

•We theoretically showed that radiation from the heated substrate heats up the nano-microsized particle levitating in the sheath of reactive plasma just above the substrate to bring it into a higher temperature state.•An analytic expression for calculating the temperature of the particle heated up by radiation from the substrate was given in the case of sufficiently low pressure plasma.•It was inferred that microsized carbon particles observed in methane plasmas were viscoelastic at about 2000K in the sheath near the substrate heated up to 1100K.•A phase diagram of carbon onion aggregate (COA) was proposed by introducing three phases, COA-solid, COA-viscoelastic and COA-liquid in the temperature region lower than the melting point of graphite.