CHAPTER 4. Solidification and Crystalline Imperfections in Solids. 4-1. Objectives. Describe the process of the solidification of metals distinguishing between homogeneous and heterogeneous nucleation.
Crystals that will
Volume free energy Gv
Released by liquid to solid transformation.
ΔGv is change in free energy per unit volume between liquid and solid.
free energy change for a spherical nucleus of radius r is given by
Surface energy Gs
Required to form new solid surface
ΔGs is energy needed to create a surface.
γ is specific surface free energy.
ΔGs is retarding energy.
Since when r=r*, d(ΔGT)/dr = 0
r* = critical radius of nucleus
γ = Surface free energy
ΔHf = Latent heat of fusion
Δ T = Amount of undercooling.
available, the greater
the number of
Nuclei growing into grains
Forming grain boundaries
and steep temperature gradient.
the mold wall.
Of steel ingots
Casting unit for aluminum
Grain structure of
with (a) and
After “Metals Handbook” vol. 8, 8th ed., American Society of Metals, 1973, p.164)
Growth of single
crystal for turbine
(After Pratt and Whitney Co.)
can vary from fraction of a
percentage to 100%
of carbon can dissolve
interstitially in iron.
Iron atoms r00.129nm
Carbon atoms r=0.075nm
to plastic defor-
cooling or particle
Figure: Vacancies moving to form vacancy cluster
also considered as
For Mg Single Crystal predicts a yield stress of 17.2*0.5=8.6GPa
Measured yield stress is 0.7MPa
10,000 times less than expected!
At Saddle Point
After M. Eisenstadt, “Introduction to Mechanical Properties of Materials,” Macmillan, 1971, p.117
After A.G. Guy , “Essentials of Materials Science,” McGraw-Hill, 1976, p.153
After M. Eisenstadt, “Introduction to Mechanical Properties of Materials,” Macmillan, 1971, p.118
of both edge and screw
irregular atomic arrangement
will appear as dark lines
when observed in electron
Dislocation structure of iron deformed
14% at –1950C
(After John Wolff et al., “Structure and Properties of Materials,” vol 3: “Mechanical Properties,” Wiley, 1965, p.65.
(After “Metals Handbook” vol. 8, 8th ed., American Society of Metals, 1973, p.164)
Electron produced by heated tungsten filament.
Accelerated by high voltage (75 - 120 KV)
Electron beam passes through very thin specimen.
Difference in atomic arrangement change directions of electrons.
Beam is enlarged and focused on fluorescent screen.
of ligament as
seen in TEM
(After L.E. Murr, “ Electron and Ion Microscopy and Microanalysis, “ Marcel Decker, 1982, p.105)
Electron source generates electrons.
Electrons hit the surface and secondary electrons are produced.
The secondary electrons are collected to produce the signal.
is used to
TEM of fractured metal end
After V.A. Phillips, “Modern Photographic techniques and Their Applications,” Wiley, 1971, p.425
- iridium or carbon nanotubes
are used for tips.
Constant height and current modes
Surface of platinum with defects
can be scanned.
polymer coating technique.
3D view of
In 1018 steel
(After A.G. Guy, “ Essentials of materials Science,” McGraw-Hill, 1976.)
paper and abrasive solution.
at grain boundaries.
reflect light. Hence
observed by optical
After M. Eisenstadt, “Introduction to Mechanical Properties of Materials,” Macmillan, 1971, p.126
N = 2 n-1 N = Number of grains per
square inch of a polished
and etched specimen at 100 x.
n = ASTM grain size number.
N < 3 – Coarse grained
4 < n < 6 – Medium grained
7 < n < 9 – Fine grained
N > 10 – ultrafine grained
1018 cold rolled steel, n=10
1045 cold rolled steel, n=8
d = C/nLM
C=1.5, and M is
3 inches 5 grains.
Er = Energy of reactants
E* = Activation Energy Level
ΔE* = Activation Energy
Ep = Energy of Products
Due to reaction
K = Boltzman’s Constant = 1.38 x 10-23 J/(atom.K).
T = Temperature in Kelvin.
n = Number of molecules greater than energy E*
Ntotal = Total number of molecules
K = Boltzman’s Constant
C = Constant
T = Temperature in Kelvin.
nv = Number of vacancies per m3 of metal
Ev = Activation Energy to form a vacancy
T = Absolute Temperature.
K = Boltznam,s Constant.
C = Constant
Rate of reaction = Ce-Q/RT
Q = Activation energy J/mol
R = Molar gas constant J/mol.K
T = Temperature in Kelvin
C = Rate constant ( Independent of temperature)
ln (rate) = ln ( C) – Q/RT
Or Log10 (rate) = Log10 (C) – Q/2.303 RT
Which is similar to
Y = b + m X
Which is equation of a straight line
With Y intercept as ‘b’ and slope ‘m’.
(After J. Wulff et al., “Structure and Properties of Materials,” vol. II: “Thermodynamics of Structure,” Wiley, 1964, p.64.)