Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...

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As stated previously hard-sphere collisions at the lower end of the energy range
dominate as the process for atomic displacements. This occurs since the kinetic
energy of the ion is not sufficient to penetrate the electron cloud of the stationary
atom. If the kinetic energy is sufficient to penetrate the electron cloud collisions of the
Rutherford type dominate. To approximate the transition from hard-sphere scattering
to Rutherford scattering a theory developed by Kinchin and Pease (1955) is
considered.
The theory assumes that the presence of the electron cloud cuts off the Coulomb
interaction between the nuclei of the moving and stationary atoms at a distance r0
given by,
r
0
a
(3.18)
3 3 1 2
( Z Z )
2
1
0
2
2
Thus if the kinetic energy of the ion is less than the Coulomb potential between the
moving and stationary nuclei it is assumed that the collisions are of the hard-sphere
type. If the kinetic energy is greater than the Coulomb potential then the collisions are
of the Rutherford type. A kinetic energy LA at which this transition occurs is defined
and given by,
L
2 3 2 3 1 2
2E
RZ
1 Z 2 ( Z1
Z 2 ) ( M 1 M 2 )
A (3.19)
M 1
where ER is the Rydberg energy and M1 the mass of the stationary atom. Seitz and
Koehler (1956) also showed that the assumption of Rutherford scattering is only valid
for scattering angles of the order b/a, where b is the distance of closest approach.
Thus at smaller angles the effect of screening electrons is still felt. Therefore
collisions only occur for impact parameters less than r0, at which the minimum energy
which can be transferred is,
E
*
2
2
2
2
3
2
3
4E
R Z1
Z 2 ( Z1
Z 2 ) M 2
( )
(3.20)
E
M
1