physical metallurgy 13 th lecture ms&e 410 d.ast [email protected] 255 4140
TRANSCRIPT
Recrystallization
Hardness
Electrical Resistivity
And energy released
Material Cu
Many physical properties change !
Notes
Do not confuse recovery with recrystallization
• Recovery - annealing inside the grain Well studied in reactor materials (radiation damage) Stages I - V (past this course)
• Recrystallization - changes in grain shapePrimary recyrstallization is driven by defect annealing (overwhelmingly dislocations). Example polygonization.Secondary recrystallization is driven by minimizing grain boundary area. Example “wild grain growth”
Time at which 50% of original grains are wiped out is t50. t50 is thermally activated. The activation energy involves both nucleation and growth.
Notes
• The temperature at which recrystallization sets in is that at which vacancy diffusion becomes substantial
•Vacancy diffusion permits dislocations to climb, required to untangle the dislocation structure.
• Vacancies become mobile around 0.6 times of Tm.
• Recrystallization not only changes grain shape but also texture. “Recrystallization texture” has a largeeffects on mechanical properties
• The activation energy for recrystallization is NOT that of vacancy diffusion… there is more to it ! You need to know the Johnson Mehl Avrami equation from kinetics and phase transformations.
Example
Texture changes in cold rolled AA 5283 at 260 (top) and 288 C (bottom)
[Liu et al, Scripta Met. 2003.
The effective activation energy is ~ 3 eV
Texture has large influence on Mechanical Properties
Studied extensively in aircraft alloys
Rules of thumb
• Vacancies become mobile around 0.6 times of Tm.
• Qself Diffusion = 0.00142 x Tm[OK] (Van Liempt relation)
Rule of thumb vs. measured in Al
• Recovery 286 C … about right
• 1.38 eV…. Measured is 1.48 eV· (142 kJ·mol- 1)
For later:
The activation energy in the Johnson Mehl Avrami equation is not the activation energy for self diffusion but the sum of the activation energy for nucleation plus three times the activation energy for growth. For Al that works out to be 388 ± 43, 312 ±39, 255 ± 32, 319 ± 18, and 364 ±63 kJ/mol depending what component of the texture is measured
Notes
• Typically the energy stored in dislocations is roughly 10% of the mechanical work put into the specimen.
• Recrystallization of Fe
Grain size vs deformation for very pure Fe (electrolytic iron).
Why is the grain size largest at small strains ? ASK ME !
Heterogeneous nucleation at sites of high disorder
Final g.s. insensitive to starting g.s. , temperature of recrystallization.
Concept of critical strain.
Growth function of T, impurities, g.b. orientation,
Concept of impurity locking.
HW 13-1
Assume cubic grains of 1 micron size. The atomic density is 9E22 per cm3. Assume the g.b. will “lock up” if one out of 5 atoms is an impurity. Assume that all impurities segregate to grain boundaries.
What is the lowest concentration, in atom% of the impurity you can tolerate ?
Many textbooks refer to this as secondary recrystallization. Driven by g.b. energy of order ~103 ergs/cm2
In thin films, the upper size of the grains that can be obtained by this phenomena is about 3 times the film thickness.
Notes
• The pressure term for a sphere isp = 2r
. and for a cylinderp = /r
• The only g.b. structure that is stable against this grain growth are 6 fold grains, having boundaries of 120o with each other
If you don’t believe it, do a line tension analysis !
3-D more complicated…. But many problems are thin films !
But what is the grain size distribution in real material ???
Grain size distribution in Al
Al is popular because it can be recrystallized at easy to handle temperatures into a large grain solid.
The grains are then separated by G.B. embrittlement using liquid In-Ga.
Measuring and counting of 1000 of grains is an other good Ph.D. topic !
NOTE wide distribution in size
Measured grain size distributions in a wide variety of metals. Normalized to average grain size
The black data are measured in recrystallized Al.
The other curves are various treatments to derive 3-D grain size distributions from 1-D metallographic data.
S is a model based on spherical grains.
The grain size distribution is generally log normal, which is to a cynic is to say that it is smooth enough to be fitted by two parameters. The same size distribution is found in nano crystalline materials… and easier to measure !
The lognormal distribution is characteristic for “statistical phenomena” and observed, e.g. in the failure time of IC circuits due to electromigration failure.
A deviation into IC metallurgy !
Which employs quite a few metallurgists.
But it will not be on the exam…. So relax !
Comments
• The formula holds only if the grain boundary movement is rate limited by processes at the grain surface and not by diffusion (in the latter case t1/3)
• A all linear model holds. I.e.
Boundary velocity is linearly dependent on the driving force, that is γκ, (γ is GB energy, κ is curvature)
Very much oversimplified.. Different boundaries move with different velocities.
Measured grain boundary velocity (top) and activation energy for motion for twist boundaries in Pb as function of rotation about [100].
This is way to primitive… we are neglecting the physics of the movement!
What limits it?
Yes … and we will soon see, a different effect on different grain boundaries !
Grain boundary velocity in Pb as a function of Sn addition for
a) a special boundary S
b) random high angle grain boundaries
D = ktn
is an empirical fit to grain growth data. However, modern theory, see Ann.Rev.Mat. Science can explain why the adjustable parameter n falls from 1/2 to 1/3.
Activation energy for motion of grain boundaries in Pb as a function of the addition of Sn.
Note
• Large increase at very small weight% in the case of general GBs
• No (!!!) increase in the case of special boundaries
The effect that very small, tiny, additions of elements can have dramatic influence on GB velocity is used in Superalloys
Excursion into practical metallurgy
27 ppm of yttrium oxide!
For once, that means that the ingredients that go into a superalloy must be pure, down to the ppm level, to achieve reproducible high temperature performance
Excursion, continued
European Patent EP1394278 … reduced Ta superalloy.. the alloy has a composition consisting essentially of, in weight percent, from about 4 to about 12 percent cobalt, from about 3.5 to about 7 percent tungsten, from about 2 to about 9 percent chromium, from about 0.5 to about 4.5 percent tantalum, from about 5.5 to about 7.5 percent aluminum, from 0 to about 3.5 percent rhenium, from about 0.1 to about 1.2 percent titanium, from 0 to about 3 percent molybdenum, from 0 to about 3 percent ruthenium, from about 0.5 to about 2 percent columbium, about 0.01 percent maximum boron, about 0.07 percent maximum carbon, from about 0.3 to about 1 percent hafnium, about 0.01 percent maximum zirconium, about 0.03 percent maximum yttrium, from 0 to about 0.5 percent vanadium, about 0.01 percent maximum cerium, and about 0.01 percent maximum lanthanum, balance nickel and impurity elements. (All compositional percentages herein are stated in weight percent, unless indicated to the contrary.)
The 0.01% level stuff is there to control GBs and surface oxide (internal and external surfaces)
We discussed this before. Cu is added to Al to slow down the grain boundary transport.
Oxygen is notorious for segregating to grain boundaries in Si.
A great pity, because otherwise we could grow large grain, very good solar silicon by recrystallizing small grain poly like Fe!
Impurity drag
D/kT = mobility
Einstein Relation
v = mobility . force
Grain boundary movement is a dissipate (friction like) process in which the velocity is proportional to the driving force.
What if the impurities cluster out as precipitates ?
Pinning boundaries by precipitating - e.g. M23C - precipitates
* Far from being trivial
In addition to surface energy, the precipitate will disrupt the movement of the grain boundary by “Bollmann type geometry” conflicts.
Surface grooves.
Surfaces contain many obstacles that can pin the thermal grain boundary groove required by force
equilibration with the G.B. energy
In thin films, when a grain growth, an ever increasing fraction of its surface is not a grain boundary but borders free space.
The surface energy against air, generally is 3 to 5 times that of a grain boundary. Thus there comes a point where grain growth will stop. Generally around 2 to 3 times the film thickness
The End