Where must the silicate and carbon dust particles observed in nebulae have formed?

Answer

Within the dense, outflowing atmospheres of evolved, cool supergiant stars.

The required density for condensation is extremely high ($10^9$ times greater than in typical nebulae), indicating that dust must form in the dense outflow before being expelled into the lower-density interstellar space.

Where must the silicate and carbon dust particles observed in nebulae have formed?
SpaceastronomycompositionnebulaElements