1.5 Major Parameters of Surface Thermodynamics
13
are obtained [3]. Since the mole fractions of all components in the bulk α and β
phases are fixed, Γ i,1,2 is independent of the location of the dividing surface.
1.6 Surface Tension and Surface Stress
The reversible work d W p required for creating new surface by dA under plastic
deformation is defined by
d W p = γ dA.
(1.56)
On the other hand, the reversible work d W e for changing surface area by dA under
elastic deformation is defined by
d W e = gdA,
(1.57)
where g is named “surface stress.” In Eq. (1.57), g as well as γ is a scalar quantity,
which is valid only for an isotropic substance or for a crystal face with threefold, or
greater, axis of symmetry. In the case of an anisotropic substance, surface stress is a
tensor quantity g ij as explained later.
Couchman et al. [6] derived the relationship between γ and g for the isotropic
surface of one component system as follows. Provided that the total surface area A
consists of the number N of surface atoms, the surface area a per surface atom is
given by
a =
A
N
.
(1.58)
Since the location of the dividing surface can be chosen at Γ 1 = 0 in one component
system, γ is equal to the Helmholtz free energy per unit surface area f
σ or the Gibbs
free energy per unit surface area
G
σ
A
(see Eq. (1.32) or Eq. (1.36)). If the excess free
energy per surface atom is denoted by ϕ, γ is represented by
γ =
ϕN
A
=
ϕ
a
.
(1.59)
When the initial surface with A and N is changed by A + dA and N + dN at constant
temperature, the net change of surface area dA consists of the change of number of
surface atoms dN due to partly plastic deformation and of the change of area per
surface atom da due to partly elastic deformation. The corresponding work δW is
given by
δW = g
dA = δ(ϕN ),
(1.60)
13
are obtained [3]. Since the mole fractions of all components in the bulk α and β
phases are fixed, Γ i,1,2 is independent of the location of the dividing surface.
1.6 Surface Tension and Surface Stress
The reversible work d W p required for creating new surface by dA under plastic
deformation is defined by
d W p = γ dA.
(1.56)
On the other hand, the reversible work d W e for changing surface area by dA under
elastic deformation is defined by
d W e = gdA,
(1.57)
where g is named “surface stress.” In Eq. (1.57), g as well as γ is a scalar quantity,
which is valid only for an isotropic substance or for a crystal face with threefold, or
greater, axis of symmetry. In the case of an anisotropic substance, surface stress is a
tensor quantity g ij as explained later.
Couchman et al. [6] derived the relationship between γ and g for the isotropic
surface of one component system as follows. Provided that the total surface area A
consists of the number N of surface atoms, the surface area a per surface atom is
given by
a =
A
N
.
(1.58)
Since the location of the dividing surface can be chosen at Γ 1 = 0 in one component
system, γ is equal to the Helmholtz free energy per unit surface area f
σ or the Gibbs
free energy per unit surface area
G
σ
A
(see Eq. (1.32) or Eq. (1.36)). If the excess free
energy per surface atom is denoted by ϕ, γ is represented by
γ =
ϕN
A
=
ϕ
a
.
(1.59)
When the initial surface with A and N is changed by A + dA and N + dN at constant
temperature, the net change of surface area dA consists of the change of number of
surface atoms dN due to partly plastic deformation and of the change of area per
surface atom da due to partly elastic deformation. The corresponding work δW is
given by
δW = g
dA = δ(ϕN ),
(1.60)