physical metallurgy 3rd lecture ms&e 410 d.ast [email protected] 255 4140
TRANSCRIPT
Ionization Energy
Can you explain why it decreasing with increasing Z ?
The low ionization energy is useful in electronic devices in which light or heat needs to “boil of electrons from a cathode” . Examples : Image intensifier tubes, radio valves.
Barium, an alkali earth metal has also a low function (2.7 eV) and is a less reactive alternative. But Cs is easier to work with
Atomic size to ionic size ratio decreases with increasing Z : Why?
Origin of the hcp structureBrillouin zone of the bcc lattice. It can contain 2 electrons.
We have 1 electron ! The Fermi Surface does, by a hair, not touch the zone boundary (ZB). That is, it is spherical. The lattice information resides in the ZB “which it never knows !”
Below -80C , Li does a martensitic transformation to hcp. As at room temperature when pressure is applied (why ?)
10 kbar = 1 GPa
Note that the alkali metal are quite compressive ! At relative moderate pressures their volume is 1/2 !
Cs, at 22 Kbar: bcc => fcc a denser packed lattice
The density of states, of alkali metals, here for Na (by J. Cornwell) nearly perfectly fits the free electron parabola !
The alkali earth metals have 2 electrons in their outer shell.
That means that the s band is filled. They would be insulators would it not for band overlap with lower bands.
A higher density of valence electrons and smaller ion cores favors close packing. Thus Be is hcp. The larger Ba is not.
Be is a very attractive metal but, being hcp*, does not have the 5 slip systems required to deform a poly-crystalline material. This has frustrated the Nuclear Industry for a long time as Be hardly absorbs Neutrons and is an excellent Neutron reflector
It only slips on the basal glide system. Question: How many do we have ?
Homework I
You can buy (but they are not cheap) tools that are made out of a Cu-Be alloy. Known as Beryllium Bronze. Picture below
1) Why are such tools produced ?
2) If you are a born metallurgist, what is the hardness (I will accept . anything from Brinell to Rockwell) of the best tools ?
3) If you are a born engineer, what is the lower left item ?
Hint: If you would work in the gas fields of Western Siberia, now supplying 70% of Europe’s gas, you would surely use them !
Homework 2.
How many second nearest neighbors are there in a) fcc b) hcp ?
What is the distance to the second nearest neighbor in a) fcc b) hcp if the distance between nearest neighbor is one unit length ?
The crystal structure of Mg and Tin (Latin Stanum)
In tin, you can look the material between the A planes as fcc containing a twin boundary.
Could you ponder if
a twin boundary is
an obstacle strong ? Weak ?
to dislocation glide we seek ?
The zone picture for Rare Earth metals
In hcp, atom density on the plane between the two basal planes is just as high as on the basal plane. Thus reflections from the basal plane cancel
Thus, there is no energy discontinuity across the bottom and top of the first Brillioun zone. That zone (band) is full with 2 electrons, but they can spill over without encountering a gap into the next higher band.
Homework 3
1. What would be the sign of the Hall effect for a free electron metal ?
2. Using the Internet (Google Scholar, INSPEC) make a list of the sign Hall effect for the first 5 group 2 metals (Be to Ba).
3. Being a born physical metallurgist what do you conclude ?
On to the transition metals and d electrons
The d electrons first appear with Sc (n=3) and go on till Hg where (n=5). Remember that the d electrons can have lower energies than the s electrons in the next shell
Nomenclature
“Real” metals start at group 4 and go on to group 12.
Why 12 ? Cause there are max 10 d electrons and 2 s !
The d electrons are colorful
Adding color to life. If you are good you can tell charge state by color.
For example Fe2+ in SiO2 (glass) is green and Fe3+ is brown.
Pigments based on transition metals are extremely stable.
These 650 year old transition metal pigments still as good as on day one
Organic colors fade. That’s the trouble with photos and inkjets.
d electrons => different chemical properties L=>R
1. The d shells are rigid, almost in contact, and having a high charge density, do not like to penetrate each other. Hence transition metals tend to be hard
2. Hunds rule “rules”
3. Tight binding rules (I.e. quantum based on atomic wave functions not Bloch waves)
The last point is beyond a 400 level course but essential for the understanding of transition metals, so I put in some figures from Suttons book.
Do not panic ! The next seven slides are to show you what can be done, if you know quantum mechanics. They are
NOT, that is NOT, part of this course.
The properties of transition metals are controlled by the partially filled, narrow, d band. The free-electron like s-p states don’t count for much.
Remember that the d-band is filled as long as possible with unpaired spins (bottom 5) and is full at 10 (5 pairs of paired spins)
In Pd, Ag, the 4 d shell is full and there is 0s (Pd) and 1s (Ag). Hence Pd is less reactive than silver. Cd has 2 s electrons
Pt has 9 d electrons in the 4th shell and 1 s in the 5. Au has a full d shell (10 electrons) and 1 s electron shielded also by d electrons
Friedel
modeled the d(E) band as a simple rectangle. The result is pretty close to experiment.
Conclusion:
the d electrons rule the physical properties, down to the elastic modulus !
Homework 4
1. Find the lattice constant of Au at RT and calculate the interatomic distance between Au atoms.
2. Look up the ionic radius of Au.
3. What is the clearance, in A, between the Au atoms ?
4. Repeat above calculation for Na.
5. Why is the clearance so different (limit 2 sentences)
IF you are a born metallurgist, you could guess on how much you might be able, to compress both metals at 20 Gpa of pressure.
Magnetism I
In the 3-d series, Fe has 6 s electrons, Co 7 and Ni 8. Given Hund’s rule, Fe has 4 uncompensated spins, Co 3, and Ni 2*. These uncompensated spins, if aligned between atoms, lead to ferromagnetism. If they do, Fe has a higher saturation magnetization than Co, and Co higher than Ni. Why they might align:
Hunds rule says that inside a partially filled d shell, parallel spin alignment is preferred. Why is that so ?
Physics:
Electrons with the same spin can not be in the same space at the same time. This effect lowers the electrostatic repulsion between electrons that fly around the core.
* Hunds rule is only approximate here.. Fe has 2.2 uncompensated electrons, Co 1.7 and Ni 0.6
Magnetism II
Same applies to a free electron gas. It forms because the electrons delocalize and convert the energy they have in an atom into kinetic energy. But the cost is that each energy state can be occupied only by one electron ! The next electron has to be in a higher energetic state (larger k vector, )
If a band is wide, the kinetic energy penalty is low.
If a band is narrow, the kinetic energy penalty is high.
Thus, magnetism is found only in transition metals that have a partially filled narrow d band.
mkE 2/2
Crystal structure.
The crystal structure, too, is dominated by the d electrons.
There are three possible overlaps of the d electron clouds between neighboring atoms (known as first nearest neighbor hopping integrals).
The values of these integrals dominates the selection of the crystal structure.
The color of Cu, Ag and Au
A free electron metal, should have no color as the electrons vibrate equally at all frequencies. To have color, there must be selective absorption.
The absorption comes from transitions between the filled states on top of the filled 3d band and the unfilled portions of the 4s band. The energy corresponds to blue-green. Hence, Cu, in reflection looks reddish. Au’s absorption peak is at 3800 A. In Ag the maximum absorption is around 2600A. Astronomers interested in the UV spectrum, therefore prefer Al “silvered” mirrors even so the reflectivity, in the visible, is lower.
Homework 5
This homework is preparation for the future. We have not touched on it, but thanks to the Internet, you can do it !!!
1. Look up what “white cast iron” is
2. Look up what “grey cast iron” is
3. Do they differ in carbon content ?
4. So, why is one white and the other grey ?
If you are a born metallurgist, you might a) guess what the structure of a rotating cylinder (for a paper making machine) is when cast into a cast iron mold b) what engineers like about the mechanical properties of such a casting.
PS: I once cast such cylinders working in a foundry
Homework 6This one is voluntary teaser. Now knowing what you know about Beryllium does this patent make any sense ?
Back up Slides
The smallest atomic volume occurs slightly above a 1/2 filled d shell.
Why ?
Consider overlap of d orbitals.
Consider number of nearest neighbor
