Civil Engineering Reference
In-Depth Information
As the electrical field is applied, the electrons accelerate and scatter off the
above-listed defects and the vibrating ion cores themselves. The localized scatter-
ing on the defects causes the electrons to lose kinetic energy and to change their
direction. Yet, the electrons still have a net movement (i.e., current) in the opposite
direction of the applied field. This net movement can be described by the electron
drift velocity, which is the average electron velocity in the direction of the applied
force. The electron drift velocity is given as
I
N
|
E
|
A
V
D
=
(3.2)
where
I
is the current magnitude,
n
is the number of valence electrons per unit
volume,
e
is the charge of an electron, and
A
is the cross-sectional area that the
current passes through [
1
]. The drift velocity is on the order of a few mm/s for the
electrical current magnitudes during EAF.
The concept of electrons scattering off the material defects and the ion cores is
known as Joule or resistive heating. As the electrons are accelerated by the electric
field, they accelerate and only reach a velocity that is usually below the Fermi veloc-
ity (~1,800,000 m/s) and well below the speed of light (300 million m/s), as a result
of collisions with the material lattice. The Fermi velocity is the fastest possible veloc-
ity of an electron in a metal that is cooled to near zero Kelvin. Thus, at zero Kelvin,
the Fermi velocity of an electron is derived from the kinetic energy equal to the Fermi
energy. During the collisions, the electrons transfer kinetic energy to the ion cores,
which increases the ion cores vibrational energy. This increase in vibrational energy
causes the material to increase in temperature. Thus, when considering a larger mass
of the material, ion cores around the material defects will have greater vibrational
energy (i.e., greater temperature) due to lattice distortions and a greater frequency of
electron/ion core interaction. There is a greater frequency of electron/ion core interac-
tion due to the misalignment of the ion cores. In comparison, the defect-free lattice
regions will have a smaller vibrational energy increase due to the same applied elec-
tron flux through the lattice. Although the flux is the same, the defect region will not
incur as many electron/ion core interactions due to the aligned lattice structure. As a
result, the energy increases will be less. In addition, the vibrational energy gained in
each of the regions (i.e., defect and defect free) will provide or gain energy from its
neighboring ion cores. This creates vibrational energy gradients or thermal gradients
at the ion core level. From a lattice perspective, this translates to an average vibra-
tion energy of the individual ion cores within a grain (i.e., mean grain temperature).
Overall, the collection of mean grain temperatures and heating at grain boundaries
relates to the macro-observed temperature. This macro- or bulk temperature is what is
typically measured during experimental testing; however, there are higher peak tem-
peratures (i.e., vibrational energy) around defects within the material lattice.
When comparing Joule heating to raising the temperature of a material by con-
vection (e.g., in an oven), the average vibrational energy of the ion cores in the
lattice would increase. However, the vibrational energy would not have areas with
greater amounts of energy around the defect sites as there is not a direct inter-
action as with the electrical flow. Thus, heating by convection will provide a
