The following figure shows patterns corresponding to the five representative
states for average concentration equal to 0.5. These figures are for . When
the surface stress is isotropic, i.e. state a,
we obtain interwoven structure. Due to the high symmetry of the surface stress (isotropic within the
epilayer), the pattern also exhibits a structure of high symmetry (no
direction preference). Our
simulation has shown that the interwoven structure still exists at . Hence
the ordering is such a slow process that it may be impractical to observe
ordered stripes in some isotropic systems, although the ordered stripe
configuration has lower energy.
(b) and (c) shows how the
anisotropy of surface stress (more accurately, its slope) can facilitate the
formation of stripes. In (b) and
(c), in the
vertical direction is smaller than in the
horizontal direction. This
anisotropy provides a direction preference and the phases very quickly line
up into periodic strips. Comparing (b) and (c) with (a), we can observe the width of the
stripes are roughly the same.
When the surface stress
in the direction is negative, we obtain the striking herringbone
structure in (d), or tweed structure in (e). From (d), we can observe two stripe variants that are
symmetric about both and axis. These
two kinds of variants are energy equivalent, reflecting the symmetry of the
surface stress. The stripes have
same width, but different length. The system does not provide any length scale for the length of stripes
and it will continue to change during later evolution. In (d), the direction of herringbone
structure is closer to the direction. Increase the magnitude of , i.e. approaches –1, the direction of herringbone turns away from
the direction. When , we obtain the tweed strictures as shown in
(e). The tweed structures align
along the 45 degree, in which the surface stress is pure shear. Herringbone reconstruction is typical
on Au (111) surface, however, the physical details are a little different
from our model. The tweed
structures have been found in several bulk systems. Unlike the surface tweed structures predicted by our
model, which have stable width, the tweed structures in bulk are not stable
and will continue to coarsen.
. When
the surface stress is isotropic, i.e. state 
. Hence
the ordering is such a slow process that it may be impractical to observe
ordered stripes in some isotropic systems, although the ordered stripe
configuration has lower energy. 
in the
vertical direction is smaller than 
in the
horizontal direction. This
anisotropy provides a direction preference and the phases very quickly line
up into periodic strips. Comparing (b) and (c) with (a), we can observe the width of the
stripes are roughly the same.
direction is negative, we obtain the striking herringbone
structure in (d), or tweed structure in (e). From (d), we can observe two stripe variants that are
symmetric about both 
and 
axis. These
two kinds of variants are energy equivalent, reflecting the symmetry of the
surface stress. The stripes have
same width, but different length. The system does not provide any length scale for the length of stripes
and it will continue to change during later evolution. In (d), the direction of herringbone
structure is closer to the 
direction. Increase the magnitude of 
, i.e. 
approaches –1, the direction of herringbone turns away from
the 
direction. When 
, we obtain the tweed strictures as shown in
(e). The tweed structures align
along the 45 degree, in which the surface stress is pure shear. Herringbone reconstruction is typical
on Au (111) surface, however, the physical details are a little different
from our model. The tweed
structures have been found in several bulk systems. Unlike the surface tweed structures predicted by our
model, which have stable width, the tweed structures in bulk are not stable
and will continue to coarsen.
