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Physical Metallurgy 4th Lecture

Physical Metallurgy 4th Lecture. MS&E 410 D.Ast dast@ccmr.cornell.edu 255 4140. We went over these boys already, including why they have color ! Now Hg is really interesting metal, next HW. HW 4-1

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Physical Metallurgy 4th Lecture

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  1. Physical Metallurgy4th Lecture MS&E 410 D.Ast dast@ccmr.cornell.edu 255 4140

  2. We went over these boys already, including why they have color ! Now Hg is really interesting metal, next HW

  3. HW 4-1 This is dentist related (Dentists have developed many new materials, btw, including the first superalloys). When you get a “Silver Filling” the assistant prepares a liquid to pasty metal mixture, that hardens at room temperature (RT !) in your mouth to a hard and corrosion resistant alloy. Using the all powerful internet, and you being a material scientist/budding metallurgist, find out 1. What are the ingredients in the mixture 2. Why does it harden ? What goes on here ? Hint: Some dentist do not like to drill them out.

  4. If you are a really sharp guy you might come up with a theory why the melting point tends to go down with increasing Z ! HW 1. Find the melting point of Ga and In Find the lowest temperature at which InxGa1-x melts What is the composition of that alloy ?

  5. TIN “Metal on the Verge of a covalent Breakdown” White tin (metallic, T>13.2C ) and grey (sc, T<13.2) tin before. Fundamentally interesting is that grey tin has a coordination number of 4 (which predicts sc behavior if you know J.C. Phillips Theory in “Bands and Bonds in Semiconductors) but in the metallic state has a a higher coordination number (HW 1) Si has a coordination number of 4 but when converting to a liquid (Liquid Si T> 1420C) has the same coordination number like Sn. Solid Si being a SC, liquid Si being metal like, the S-L transition has the highest enthalpy of all elements in the periodic table

  6. HW 4-2 1. Determine the coordination number of Sn in the metallic phase. 2. Google the coordination number of liquid Si, report your finding. 3. Why is there a relation to Sn ? (Hint: Consider the ductile to brittle transition in Fe) 4. What is solid to liquid enthalpy in Kcal/mol of Si ? How does it compare to that of Fe ?

  7. These metals have s-p pairs (capable of making sp3 hybrids like in Si) and one or two “lone” p electrons in there outer shell.

  8. As Se can be monoclinic, trigonal, and amorphous Trigonal Se is made up of S8 molecular rings. The s-p hybrid forms the bond between atom. The more tightly bound lone p pair holds the stack together. Se is a semiconductor. Its photo conductivity was first discovered in it’s use a resistor in railway telegraphs (Se bars in a wooden box)

  9. Uranium To separate it into its isotopes, you need access to each atom. I.e. a gas UF6 Separation was the most difficult step in building the Atomic bomb. Handled by metallurgists and chemists Isotopes be sorted out by diffusion or centrifugation. Uranium has a density of 19 gr/cm3, 1.6 times higher than Pb. Used in depleted U ammunition.

  10. UF6 has the shape of an octahedron Note that the one 6d electron has a higher energy than the two electrons in 7s. The three electrons in the 5 f shell have similar energies to the 6 d’s. Total available is 6

  11. The free electron theory of metals I am going to this differently from Prof. Baker. The plan is to let you discover some of it by yourself, by doing HW problems. Let’s skip the particle in a box and start with the free electron model. We will see that it is amazingly powerful.

  12. For a free electron wave we have which can be written, using a form that shows better that k is a measurement of the (group) velocity

  13. The energy increases quadratically with k. For reasons to be seen later, we plot the every increasing k usually only up to /a. You can think about the periodicity of a cubic lattice.

  14. The diffraction of waves does not their energy. In the classical picture, the ball bounces off an infinite stiff wall. In QM, the equivalent of this bounce is adding a crystal momentum vector. In a 2-D picture this looks like this

  15. The reduced zone scheme is certainly easier on the eye ! And saves space as well. So far it looks self evident.

  16. We now add the 3rd zone, the one that in real space contains k vectors between 2 /a and 3 /a  This is interesting ! We now have, at the same energy level, 2 allowed k vectors !! The two waves have the same energy. One had one G vector added to it, the other 2.

  17. Out to the 6th zone, the “band picture” of a free electron metal looks like this How real is that ?

  18. Most crystals have different periodicities in different directions. For example, in the diamond cubic lattice there are reflections on the (111) and (220) reflections. Corresponding to these periodicities, you can walk in reciprocal space into from the origin  to L, center of the hexagonal face and from the origin to X the center of the square face L  X

  19. Pretty shocking: The free electron theory, for Ge, not even a metal, does nearly as well as LCAO ! Linear Combination of Atomic Orbital Theory vs Free Electrons for Ge

  20. What happens if “we add the lattice” to the free electrons ? 1. The lattice disturbs the free electron only in a minor way 2. Its “worst” effect is diffraction. It takes many lattice planes to reflect a wave. Each reflection is relatively weak. See point one above. 3. The closer the periodicity of the wave to the periodicity of the lattice, the more reflected the electron wave will be

  21. Strong forward wave; weak reflected wave The incident wave is much longer than the lattice Equal forward and backward wave. Standing wave The incident wave matches the lattice

  22. Electron cloud centered at the ions, the energy is lower THE TWO STANDING WAVE FIELDS Electron cloud centered between atoms, higher energy

  23. The periodic potential inserts a “splitting” at the “first Brillouin zone boundary”. Which is a fancy way that you have a Bragg reflection at the lattice, resulting in a standing wave. One centered at the atoms, the other in between. The “energy gap” is 1/2 of the first Fourier coefficient of the potential expanded in G vectors. The stronger that component, the bigger the “band gap”

  24. Modifying the free electron model “to eliminate all “crossovers” 1. Erase all cross over points 2. Larger erasing at densest packed planes. 3. Smoothly reconnect ? The free electron model, with corrections for “crossovers” gives a good description of the first two Brillouin zones. Higher bands get a bit trickier…..

  25. Homework 4-3 1. Look up the density of Mg, in units of atoms per cm3 2. Put the Magnesium atoms into a simple cubic lattice. Calculate the lattice constant. 3. Make an E vs k diagram, using eV vs A-1 using the free electron model, from E =0 to E where the electron wave is fully reflected at the (100) planes. 4. Now put the Mg atoms into the real hexagonal lattice. Make an E vs k diagram as follows. On the left of the origin let k increase until reflection on the basal planes occurs. On the right side of the origin, let k proceed until you get reflection on the prismatic planes. 5. Challenge for bright cookies liking physics (born physical metallurgists) Now assume that energy gaps develop at the reflection points. Assume that (with increasing periodic potential), these gaps increase twice as fast for reflection on the basal plane as for reflection planes. What would the basal plane energy gap to be for the Mg to turn into a semiconductor ?

  26. HW 4-4 Voluntary and for born metallurgists and future masters of Metallurgical Failure Analysis* To answer this questions, you must live in a house that has Al storm windows, or Al doors, such that one door (or window) faces the street, the other the back yard. 1. Inspect the corrosion pattern. Is it the same for both location ? 2. If not, which one is worse 3. If different, what do you think is the cause ? * A profitable business as expensive to litigate accidents, from boiler explosions to air plane crashes need metallurgical experts to answer the question: Who is liable and must pay ?

  27. Auxiliary materials

  28. Cast iron: White and grey Liquid cast Fe contains 4.2% by weight carbon. When you cool it fast, the carbon has no time to nucleate and make graphite flakes. Hence the carbon gets trapped as Fe3C (called cementite). Cementite is very hard. The hard cementite particles make for a very wear resistant surface. The castomg looks white (compared with below) and is white cast iron. Slower cooling produces Fe in which the carbon precipitated out as graphite flakes. Therefore, it looks grey. Iron cast into sand molds always cools slowly, hence is grey cast iron throughout. Iron cylinders cast into metal molding (cocilles) cool rapidly at the surface and slow in the interior. They have a hard surface but a tough and vibration damping interior which is ideal for rollers in precision machinery. That’ what we cast in the foundry I worked: Parts for precision machines, such as lathes, centerless round grinding machines, machines making paper etc

  29. Rust resistance of Cast Iron Drain Covers in Ithaca Cities streets

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