It is possible that in the course of motion, some facets will become of zero length. It is also possible that for reasons of stability new facets ought to be created either in the initial surface and/or in the course of motion. These issues are addressed in this section.
Facets with 
are qualitatively different from facets with
. If a facet with approaches zero
length, its chemical potential becomes infinite; this happens only
when an entire particle is shrinking to a point, and thus never happens
when volume is conserved for each particle (as is always true for SD
and sometimes taken to be true for SALK). On the other hand,
if a facet of weighted mean curvature zero is reduced to zero length,
then its potential converges to 0 and the facet can simply be
removed; its adjacent facets
become collinear and are simply merged to one
segment. This entire process of replace three segments by one is
called merging.
Adding new facets is the reverse of this process. Facets of
nonzero 
can be introduced only where the potential is already
infinite (as, for example, in an initial surface with corners that are
too sharp, omitting directions that are directions in 
). But a facet of
zero length and zero weighted mean curvature can be inserted in a
pre-existing facet at a place where the potential is zero,
dividing that pre-existing facet into two facets. There are two
senses in which such a facet could be inserted; the conditions under
which one should make such insertions and which sense to use is
discussed under the appropriate rule (SD or SALK) below.
The production of new facets by inserting facets
has been called shattering by
Roosen[2] and refers to the production of many
facets during motion of crystalline interfaces in a diffusion field.
Here, since the production of many facets turns out not to happen, we
use the word stepping to refer to the process of replacing one
facet by two collinear facets (the sum of whose lengths is that of the
original facet) connected by a zero-length
facet of zero weighted mean curvature.