Certain dust particles in space are expected to appear as clusters of individual grains .
The morphology of these clusters could be fractal or compact .
In this paper we study the extinction by compact and fractal polycrystalline graphitic clusters consisting of touching identical spheres , based on the dielectric function of graphite from Draine & Lee ( [ 1984 ] ) .
We compare three general methods for computing the extinction of the clusters in the wavelength range 0.1 - 100 ~ { } \mu m , namely , a rigorous solution ( Gérardy & Ausloos [ 1982 ] ) and two different discrete-dipole approximation methods – MarCODES ( Markel [ 1998 ] ) and DDSCAT ( Draine & Flatau [ 1994 ] ) .
We consider clusters of N = 4 , 7 , 8 , 27 , 32 , 49 , 108 and 343 particles of radii either 10 nm or 50 nm , arranged in three different geometries : open fractal ( dimension D = 1.77 ) , simple cubic and face-centred cubic .
The rigorous solution shows that the extinction of the fractal clusters , with N \leq 50 and particle radii 10 nm , displays a peak within 2 % of the location of the observed interstellar extinction peak at \sim 4.6 \mu m ^ { -1 } ; the smaller the cluster , the closer its peak gets to this value .
By contrast , the peak in the extinction of the more compact clusters lie more than 4 % from 4.6 \mu m ^ { -1 } .
At short wavelengths ( 0.1 - 0.5 \mu m ) , all the methods show that fractal clusters have markedly different extinction from those of non-fractal clusters .
At wavelengths > 5 \mu m , the rigorous solution indicates that the extinction from fractal and compact clusters are of the same order of magnitude .
It was only possible to compute fully converged results of the rigorous solution for the smaller clusters , due to computational limitations , however , we find that both discrete-dipole approximation methods overestimate the computed extinction of the smaller fractal clusters .