216
C. Tang (唐晨宇) and Y. Wang (王延颋)
Fig. 5.1 A typical form of the Lennard-Jones potential
An interaction is short-range if the integral Eq. (3.38) converges, and long-range
otherwise. The LJ potential is obviously a short-range interaction, and we can regard
the LJ force as zero when the distance r > r c .
5.4.3 Force Fields for Metals
We usually have to describe metals by many-body force fields, since the valence
electrons can move globally in due systems. A general model that can describe both
pure metal and alloy is the Embedded Atom Model (EAM), the potential of which
is given as
V i = F α
⎛
⎝
i =j
ρ α
r ij
⎞
⎠ +
1
2
i =j
φ αβ
r ij
(5.3.39)
In Eq. (3.39), the distance r ij refers to the distance between atom i and atom j.
The term φ αβ refers to the two-body potential between two metal atoms of type α
and type β, respectively. The term ρ α represents the amount of electron density that
atom j of type α generates at the position where atom i locates, whereas function F α
refers to an embedded function that represents the energy needed to embed atom i
of type α into the electron cloud.
There are various other force fields for metals whose functional forms are usually
a many-body functional term of electron density plus a two-body term.
C. Tang (唐晨宇) and Y. Wang (王延颋)
Fig. 5.1 A typical form of the Lennard-Jones potential
An interaction is short-range if the integral Eq. (3.38) converges, and long-range
otherwise. The LJ potential is obviously a short-range interaction, and we can regard
the LJ force as zero when the distance r > r c .
5.4.3 Force Fields for Metals
We usually have to describe metals by many-body force fields, since the valence
electrons can move globally in due systems. A general model that can describe both
pure metal and alloy is the Embedded Atom Model (EAM), the potential of which
is given as
V i = F α
⎛
⎝
i =j
ρ α
r ij
⎞
⎠ +
1
2
i =j
φ αβ
r ij
(5.3.39)
In Eq. (3.39), the distance r ij refers to the distance between atom i and atom j.
The term φ αβ refers to the two-body potential between two metal atoms of type α
and type β, respectively. The term ρ α represents the amount of electron density that
atom j of type α generates at the position where atom i locates, whereas function F α
refers to an embedded function that represents the energy needed to embed atom i
of type α into the electron cloud.
There are various other force fields for metals whose functional forms are usually
a many-body functional term of electron density plus a two-body term.