Multiwalled carbon nanotubes were grown vertically aligned on the iron, cobalt, and nickel catalytic nanoparticles deposited on alumina substrates by thermal chemical vapor deposition of acetylene in the temperature range 900-1000 degreesC. The growth rate of carbon nanotubes on the iron catalyst is about 2 tithes higher than those on the cobalt and nickel catalysts over the temperature range. The growth rate enhances approximately by a factor of 2 for the temperature increase from 900 to 1000 degreesC, irrespective of the catalysts. The degree of crystalline perfection of the graphitic sheets also depends on the catalysts, which has a good correlation with the growth rates. The results suggest that the bulk diffusion of carbons would play a major role in determining the growth rate as well as the crystallinity of carbon nanotubes.