## IMD |
## Covalent Many-Body PotentialsIMD supports different types of many-body potentials for covalent materials, notably Tersoff potentials, Stillinger-Weber potentials, and Keating potentials. All these potentials are defined through analytic formulae, whose parameters are read from the parameter file. Stillinger-Weber type potentials can also be defined via tabulated parameter functions.
The three-body interactions of all covalent potentials are computed
using neighbour tables. The initial length of a neighbour table can
be specified with the parameter ## Tersoff Potential The Tersoff potential (J. Tersoff, Phys. Rev. B
where
For the computation, the repulsive two-body part contained
in this expression is computed from the parameters and filled
into the corresponding potential table. Alternatively, it is
possible to set the coupling constants The cutoff function is also given analytically, by the following expression:
The Tersoff potential with a slightly different parameter structure is
enabled using the compilation option g have the following form:
The indices of the parameters refer to atom types involved. The following IMD parameters correspond to the Tersoff potential parameters:
The values of the single-index parameters have to be given for all
atom types in a row. The values of the two-index parameters except
A
_{00} A_{01} ... A_{0(n-1)} A_{11}
A_{12} ... A_{(n-1)(n-1)}where n is the number of atom types. In the case of the
variables ters_chi and ters_om, the diagonal
values of the matrix are equal to 1 and the non-diagonal
values are read using the following format:
The parameters
## Modified Tersoff PotentialThe modified angular-dependent term
The following IMD parameters are relevant for the modified Tersoff potential:
## Stillinger-Weber Potential (analytic)
The Stillinger-Weber potential (F. H. Stillinger and T. A. Weber,
Phys. Rev. B The Stillinger-Weber potential is given by
where V and _{2}V are given by
_{3}
The angle V are zero
for _{3}r larger or equal to _{ij}a
and ^{1}_{ij}a, respectively. The following IMD
parameters correspond to the potential parameters:^{2}_{ij}
The values of the two-index parameters have to be given for all atom types in the following format:
A ,
_{00} A_{01} ... A_{0(n-1)} A_{11}
A_{12} ... A_{(n-1)(n-1)}where n is the number of atom types. In the case of
stiweb_la, the first index runs from 0 to n-1,
whereas the last two indices are expected like for the two-index
parameters.
## Zhou-Wadley Potential (analytic)
The Zhou-Wadley potential (X. W. Zhou and H. N. G. Wadley,
monatomic in Comp. Mat. Sci. The parameters are the same as those for the Stillinger-Weber potential (analytic). ## Stillinger-Weber Potential (tabulated)
Using the compilation option
The two-body part is then treated as any other short range
pair potential, and can be specified
independently of the three-body term. It is usually read from
from the potential file specified by the parameter The three-body term takes the following general form: Z is the force constant and f is a
cutoff function. The parameter _{c} (r)h indicates the
hybridization sp of the atoms. In the case
^{h}h=3 the coordination is fourfold, whereas in the case
h=2 the coordination is threefold.
The cutoff function ttbp_potfile. The
parameter ttbp_constant specifies the force constant
Z, and the parameter ttbp_sp the hybridization
constant h. ## Zhou-Wadley Potential (tabulated)
Using the compilation options The parameters are the same as those for the Stillinger-Weber potential (tabulated). ## Keating Potential
The Keating potential (P. N. Keating, Phys. Rev. The Keating potential, whose parameters have to be specified in the parameter file, takes the following form:
where the sums are over atoms i and nearest neighbour atoms
j,k with distance vectors
and r_{ij}. The parameters r_{ik}d
are the equilibrium distances between the atoms. They have to be
specified in the IMD parameter _{ij}keating_d. The values of these
parameters have to be given for all pairs of atom types in the following
format:
d
_{00} d_{01} ... d_{0(n-1)} d_{11}
d_{12} ... d_{(n-1)(n-1)}Here, n is the number of atom types.
The IMD parameters
The IMD parameter |