The growth and ordering of a Pb layer deposited on Cu(001) at 150 K ha
s been studied using atom beam scattering. At low coverage, ordered Pb
islands with (sqaure-root 61 x square-root 61)R tan-1 (5/6) symmetry
are formed. This is a high-order commensurate phase with 30 atoms in t
he unit cell. From the measurement of the island diffraction peak prof
iles we find a power law for the mean island size versus coverage with
an exponent n = 0.54 +/- 0.03. A scaling behavior of growth is confir
med and a simple model describing island growth is presented. Due to t
he high degeneracy of the monolayer phase, different islands typically
diffract incoherently. Therefore, when islands merge they still diffr
act as separate islands and coalescence effects are thus suppressed. F
rom the result for n we conclude that the island density is approximat
ely a constant in the coverage range 0.1 < THETA < 0.5 where the order
ed islands are observed [THETA is defined as the ratio between the num
ber of Pb atoms and the number of Cu atoms in the underlying Cu(001) l
ayer]. We thus conclude that most islands nucleate at THETA < 0.1 and
then grow in an approximately self-similar fashion as THETA increases.