Environmental Engineering Reference
In-Depth Information
is raised this planar 'solid' is expected to melt, but the nature of the transition is a
matter of debate 6.4 adsorbed monolayers 205 Fast multipole method:
(1) Divide the system into sets of successively smaller Sub- Simulation Cells.
(2) Shift the origin of the multipole expansion and calculate the multipole
moments at all subcell levels starting from the lowest level.
(3) Shift the origin of the local expansion and calculate the local expansion
coefficients starting from the highest level.
(4) Evaluate the potential and fields for each particle using local expansion
coefficients for the smallest subcell containing the particle.
(5) Add the contributions from other charges in the same cell and near neigh-
bor cells by direct summation.
1.3.2.1.7
PERIODIC SUBSTRATE POTENTIALS
Extensive experimental data now exist for adsorbed monolayers on various
crystalline substrates and there have been a number of different attempts made
to carry out simulations, which would describe the experimental observations.
These fall into two general categories: lattice gas models, and off lattice models
with continuous, position dependent potentials. For certain general features of
the phase diagrams lattice gas models offer a simple and exceedingly efficient
simulations capability. This approach can describe the general features of order or
disorder transitions involving commensurate phases. An extension of the lattice
gas description for the ordering of hydrogen on palladium in the C(2 2) struc-
ture has recently been proposed by giving the ad atoms translational degrees of
freedom within a lattice cell (Presber et al., 1998).The situation is complicated
if one wishes to consider orientational transitions involving adsorbed molecules
since continuous degrees of freedom must be used to describe the angular vari-
ables. Both quadrupolar and octu polar systems have been simulated. For a more
complete description of the properties of adsorbed monolayers it is necessary to
allow continuous movement of particles in a periodic potential produced by the
underlying substrate. One simplification, which is often used is to constrain the
system to lie in a two-dimensional plane so that the height of the ad atoms above
the substrate is fixed. The problem is still difficult computationally since there
may be strong competition between ordering due to the adatom or adatom interac-
tion and the substrate potential and incommensurate phases may result. Molecular
dynamics has been used extensively for this class of problems but there have been
Monte Carlo studies as well. One of the 'classic' adsorbed monolayer systems
is Kr on graphite. The substrate has hexagonal symmetry with a lattice constant
of 2.46A whereas the lattice constant of a compressed two-dimensional krypton
solid is 1.9A. The C(1 1) structure is thus highly unfavorable and instead we find
occupation of next-nearest neighbor graphite hexagons leading to a commensu-
rate structure with lattice constant 4.26 A. This means, however, that the krypton
Search WWH ::
Custom Search