Chemistry Reference
In-Depth Information
on the potential energy governing the acceptance of the trial displacements, the
functional form of the force, and the ''all-local'' approximation used in deter-
mining the change in potential energy accompanying the trial move of each
node are given in Refs. 108 and 109. Lastly, it must be noted that this meth-
odology also allows for a finite-temperature treatment of the system (see dis-
cussion below).
QC and FNL-QC Applications
The QCmethod has been applied to the study
of a wide variety of materials and mechanical problems. From a materials stand
point, it has been used to model both metals [especially face-centered cubic (fcc)]
and semiconductors (mostly Si
110-112
). As examples, some of the most recent
works that utilized QC methods to investigate the behavior of metals include
studies of copper,
106,113-118
nickel,
119,120
aluminum,
104,113,120-123
silver,
116
palladium,
116
gold,
103,120
and fcc metals in general.
124
With respect to
mechanical behavior, the phenomena most commonly investigated using QC
methods are grain boundary structures,
113,114,121
nanoindentation and
dislocation nucleation,
115,116,119-121,123
cracks,
118,122
interfaces,
117,118
the
formation and strength of dislocation junctions,
124
and cross slip and
mobility of dislocations.
106
References to several other application studies can
be found, for instance, in Ref. 71.
A more complete, and continously updated list of QC-related publications
can be found on the Web at http://www.qcmethod.com/qc\_publications. html.
Extensions of the QC Method
Because of its versatility, the QC method has
been widely applied and, naturally, extended as well. While its original
formulation was for zero-temperature static problems only, several groups
have modified it to allow for finite-temperature investigations of equilibrium
properties as well. A detailed discussion of some of these methodologies is
presented in the discussion of finite-temperature methods below. Also,
Dupoy et al. have extended it to include a finite-temperature alternative to
molecular dynamics (see below). Lastly, the quasi-continuum method has
also been coupled to a DFT description of the system in the OFDFT-QC
(orbital-free DFT-QC) methodology discussed below.
Coupled Atomistic and Discrete Dislocation Method
The coupled atomistic and discrete dislocation (CADD) method was
developed by Shilkrot, Miller, Dewalt, and Curtin
71,125-128
as a continuum/
atomistic hybrid methodology where defects (specifically dislocations) are
allowed to move, can exist in both the atomistic and the continuum region,
and, lastly, are permitted to cross the boundary between such domains. The
methodology has later been expanded to model finite temperature as well.
129
Similarly to the FEAt and CLS methods, CADD is based on a spatial
separation of the physical problem into regions, which are modeled by either
