Molecular dynamics thesis

4 Results
4.1 Verification and accuracy tests
A number of tests have been performed to verify the reproduction of the input
parameters for the Mo-Mo potential, to check the stability of the bcc structure against the fcc
structure, and to check the accuracy of the model and the program. The Voigt average shear
modulus and anisotropy ratio have not been checked, because this was not practical with the
Camelion MD code.
The results of simulations to test the reproduction of input parameters are given in
table III.
Table III. Reproduction of input parameters. The original input parameters, lattice parameter a, atomic
volume 
, bulk modulus B, Voigt average shear modulus G, anisotropy ratio A, cohesive energy E
C
, and
unrelaxed monovacancy formation energy 
E
1V
UF
at 0 K and the values (if determined) returned by
simulations.
quantity
input value
returned value
a (Å)
3.1472
3.1472
Ω
B (eV)
25.68
25.88
Ω
G (eV)
12.28
-
A
0.78
-
E
C
(eV)
6.81
6.81
E
1V
UF
(eV)
3.10
3.19
From table III it can be concluded that the input parameters reproduce well, except for the
unrelaxed vacancy formation energy. There is no explanation why this parameter has such a
high relative inaccuracy compared to the others.
The difference in cohesion energy between fcc and bcc molybdenum has been
determined to check bcc stability. Fcc molybdenum has a cohesion energy of -6.74 eV,
compared to -6.81 eV for bcc molybdenum, which shows that the bcc structure is stable
against fcc transformation.
To test numerical accuracy, two two-particle tests were performed. The first consists
of two atoms starting outside each others sphere of influence, having 1 eV kinetic energy
each. The velocities are directed toward each other, so the atoms perform a central collision.
The deviation of the velocity ratio v
before
/v
after
from unity is a measure of inaccuracy. During
the collision the atoms are inside each others cut-off range for exactly 100 steps and the
velocity ratio turned out to be 0.999983. The second test was an oscillator test. Two atoms
without kinetic energy are placed inside each others cut-off range. Their total energy after a
little under 300 oscillations (some 10000 steps) is 0.93 times their starting potential energy.
Compared to some of the approximations and assumptions made (applying Newtonian
mechanics to solid state physics, neglecting angular dependence in the electron density, and
using a numerical algorithm in an unstable system), the inaccuracy is acceptable, although
certainly not small.