  We study the internal and external alignment of carbonaceous grains,
including graphite and hydrogenated amorphous carbon (HAC), in the interstellar
medium (ISM) within the RAdiative Torque (RAT) paradigm. For internal alignment
(IA), we find that HAC grains having nuclear paramagnetism due to hydrogen
protons can have efficient nuclear relaxation, whereas both HAC and graphite
grains can have efficient inelastic relaxation for grains aligned both at
low$-J$ and high$-J$ attractors. For external alignment, HAC and graphite
grains can align with the radiation direction ($k$-RAT) at low$-J$ attractors
but cannot have stable alignment at high$-J$ attractors due to the suppression
of radiative precession. HAC also has slow Larmor precession compared to the
randomization by gas collisions and cannot be aligned with the magnetic field
($B$-RAT). Small HAC grains of $a<0.05\mu$m drifting through the diffuse ISM
can be weakly aligned along the induced electric field ($E$-RAT) at high$-J$
attractors due to its fast precession. Paramagnetic relaxation by nuclear
magnetism is found inefficient for HAC grains due to the rapid suppression of
nuclear susceptibility when grains rotate at high$-J$ attractors. We then study
the alignment of carbon dust in the envelope of a typical C-rich Asymptotic
Giant Branch star, IRC+10216. We find that grains aligned at low$-J$ attractors
can occur via $k$-RAT with the wrong IA in the inner region but via $B$-RAT in
the outermost region. However, grains aligned at high$-J$ attractors have the
right IA alignment via $k$-RAT due to efficient inelastic relaxation. The
polarization pattern observed toward IRC+10216 by SOFIA/HAWC+ can reproduced
when only grains at low$-J$ attractors are present due to removal of grains at
high$-J$ attractors by the RAT disruption.
