We show that for particle sizes ranging from a few hundred angstroms up to several tens of microns in diameter the force exerted by radiation pressure in some red giant and AGB stars exceeds the force of gravity and thus offers the potential for graphite, SiC, corundum, and spinel grains to grow to the size range observed in primitive meteorites (e.g., up to ~25 μm). In the highest mass AGB stars radiation pressure on growing grains greatly exceeds the force of gravity and thus ejects a grain from the star before it can grow larger than a few tens of nanometers. Only in very low mass AGB stars (less than 3 M) does the radiative force balance the gravitational force to such a fine degree that the net acceleration on individual particles ranging from a few nanometers up to about 25 μm produces particle velocities that are comparable to atmospheric turbulence. Our analysis shows that the large graphite, SiC, corundum, and spinel crystals found in primitive meteorites can only have formed in the atmospheres of the lowest mass red giant and AGB stars, where particle growth is able to occur on timescales of a hundred thousand years under near-equilibrium conditions. We note that this suggestion is contrary to the standard assumption that grains can only form in stellar winds and implies that there may be a class of grains that can form in chemical equilibrium deep within the stellar atmosphere, just above the photosphere.