Physical Metallurgy 2nd Lecture MS&E 410 D.Ast

Review: Ionic Bonding => electron transfer => ion => Coulomb Covalent => shared electron => localized => directional => exchange interaction Metallic => Electron gas => delocalized => ions in sea of e - Hydrogen bonds => non -relevant in metallurgy except in Pt, Pd => hydrogen storage

Characteristics of Metallic Bonds ( pure metals…not totally applies to interatomic compounds such as Ni 3 Al) Does not occur in molecules [ but very small (<2 nm) clusters are already fully metallic ] Metallic bond are similar to ionic in that the cohesive energy is electrostatic. Thus similar high melting points Similar to Covalent in that electrons are “shared” but now over entire crystal

Continued Alkali metals are nearly perfectly metallic => ions in an electron sea. Spherical s electrons, density per atom low (one), screening is weak, limiting packing density. Thus bcc with f.f. of 68%. Close packed f.f. 74% Zn is small, close packed (hcp) but has c/a = (ideal value 1.63) indicating a covalent bonding component. As does Cd Non-closest packed metals with small ions (bcc) must have a covalent component (Fe, W, Mo, V). This directional component comes from the d electrons.

Atomic size shrinks with charge state

Bond type may change with pressure (hcp silicon) or temperature. Most famous example of the latter is Sn (Tin) Below 13.2 C - diamond cubic Above 13.2 C - beta tin, metallic Tin Pest is the allotropic transformation of white (beta, metallic) tin to grey (alpha, non-metallic) tin. Tin which is undergoing this transformation becomes covered with grey powdery warts. Corroded tin-alloy objects often have a similar appearance and are sometimes said to have "Tin Pest", but this is quite a different phenomenon. The transformation was investigated in a series of papers by Cohen, starting about 100 years ago; he showed that although the transition temperature (below which grey tin is the stable allotrope) is 13.2 degrees C, in practice the transformation does not occur at an appreciable rate above about -15 degrees, reaching a maximum at about -30 degrees and becoming very small below -50 degrees. The transformation is catalysed by the presence of grey tin nuclei, but is strongly inhibited by the presence of 0.1% of lead, bismuth or antimony. Alpha tin (semiconductor) Beta tin (metallic) “Tin pest” is an apocryphal story, akin to medieval glass being thicker at the bottom!

Column 4 A White tin => grey tin As the core charge increases, outer electrons become easier ionized leading to increasing metallic character See left: 1. Carbon is perfectly covalent. 2. Si has “almost metallic” luster 3. Germanium yet “more metallic” than Si 4. Tin is located at the border between metallic and non-metallic. It’s green here, cause at RT it’s a metal. 3. Lead is a good metal

“Typical” Metal Properties 1. High specific density, close packing => non directional 3. Ductile - non directional bonds 4. High melting point => electrostatic energy 5. Shiny - reflective - mobile electrons 6. Electric conductors => mobile electrons 7. Thermal conductors => mobile electrons 8. High sound velocity (high E)

Crystal Structures Crystal = Lattice + base Lattice : A period point 3-D lattice formed by mathematical points. Has no physical reality without base ! Base : An atom, or group of atoms, or molecule, placed on a mathematical lattice point Bravais was a French Physicist who figured out that there are only 14 different ways to assemble atomic points in 3-D !

14 Bravais Lattices, arranged in 7 Crystal Systems To make it real the Bravais lattice needs atoms, or group of atoms The reciprocal lattice of “real space” fcc lattice is bcc, and visa versa

The diamond cubic lattice is made as follows 1. Take an fcc lattice of mathematical points 2. Put at each lattice point a barbell of two Si atoms, length 1/4 of the body diagonal, direction body diagonal 3. The result looks nothing like fcc but has fcc symmetry 4. The unit cell is picked, to reflect this symmetry, and to contain the fewest atoms to do so. In this case, the unit cell contains 4 atoms. 5. We could have picked an other unit cell, such as the primitive unit cell containing only one atom 6. The penalty for picking a unit cell with 4 atoms is that you have “forbidden” reflections diffraction.

The Si lattice is composed of two interlocking fcc lattice. An interesting consequence is that we have an interesting stacking of the densest packed planes {111} This brings up the question: If the crystal slips, does it slip between widely spaced or narrow spaced {111} planes ? Stay tuned….. Arrow points to base put on 0,0,0 of unit cell SiC, made up with a Si-C dumbbell base. Also shown is a first order coherent twin defect.

Pearson Notation x X# Crystal family (say cubic) Bravais lattice type (say Face Centered) Number of atoms per unit cell Example Fcc => cF4 Advantage: It tells you something about symmetry and forbidden reflections

Point groups There are 32 ways of applying symmetry operations to the Bravais lattice. The symmetry elements are: rotation, rotation + inversion, reflection across mirror planes, and center of symmetry. As symmetry drastically decreases the number of possible solutions in crystal physics problems, the group of these operations is important Space Groups If we allow translation, then we get 230 possibilities. Practically speaking, we can “screw up” the symmetry of the Bravais lattice by putting something with less than spherical symmetry on a lattice point. E.g. a 3 pointed Mercedes Star… NH 3..

Sphere packing Very important in metal physics !!!! First layer The second layer on top can either rest in the purple dimples or in the blue ones, but not in both !!!!

This has two very important consequences: 1. We “can roll a ball” from the pink dimples to the blue ones. The “rolling distance” is not a translation vector in the densest packed plane ! It is a/6{112} That translation vector is a/2{110} Obviously, it is easier to roll only partially. Expect “partial dislocations” later in the course.

2. The fact that there are twice as many dimples as we need, makes a big difference when we add the 3rd layer ! It’s atoms can either land on top of the atoms in the first layer, or on top of dimples in the first layer The first is hcp, the second is fcc

Two successive “partial roles” add up to the translation vector of the lattice. If we roll in two steps “we form a stacking fault band” => more perhaps later.

The difference between fcc and hcp As far as first nearest neighbors are concerned, there is no difference between the two lattices ! If you are an ant, and sit on an atom and can only inspect the next nearest neighbors it looks the same. As far as the second nearest neighbors are concerned, there is a difference. It is small but real ! The corresponding difference in Carbon chemistry is know as staggered and eclipsed bonds. Both fcc and hcp are the result of densest packing of spheres, filling 74% of the volume

“Mixtures” of fcc and bcc Various forms of SiC. C is cubic (fcc) ABCABCABC stacking H2 is hexagonal ABABABA H4 is hexagonal ABCBABCBA stacking. You may look upon it as a mixture of fcc and bcc, or fcc with stacking faults, or bcc with stacking faults !

In electronic this is important, but for metallurgist Cobalt is more interesting ! Cobalt is hcp but has such as small stacking fault energy that it is prone to make stacking mistakes. The stacking fault energy can be lowered by adding Ni (fcc) to the point where Cobalt becomes totally confused ! Role of Stacking Fault Energy on the Galling and Wear Behavior of a Cobalt-Base Alloy BHANSALI, K J; MILLER, A E Wear of Materials, 1981; San Francisco; Calif ; 30 Mar.-1 Apr pp Cobalt-base alloys have been traditionally known for their superior resistance to galling. Pin-on-block galling tests were used to study the influence of Ni substitution for Co on the galling behavior of a commercial Co-base alloy. Nickel additions resulted in lower self-mated threshold galling stresses. The tendency to galling is believed to be related to stacking fault energy. Alloys with low stacking fault energy have superior galling resistance to those with high stacking fault energy. The behavior is confirmed by experimental alloys, which are variations of Haynes Stellite 6, with varying Ni to Co ratio. A metallurgical model is proposed.24 refs.--AA

The hcp phase of Co can be switched into fcc by deformation and strain engineering. Co is an important material for magnetic disks

Random packing of spheres (Bernal) Bernal studied the random packing of spheres as models of amorphous solids by putting mixtures of ball bearing and black paint into leather bags. His graduate students than took it all apart and noted the position of each “atom”. Density : 64% (ideal stacking 74%) The “Bernal Limit” until recently, could not be proved. Exhausting computer simulation now confirm it. Bernal did many other things including writing books on social responsibly of science and laying the foundations of molecular biology.

Polymorphizm Change of crystal structure under pressure (important for geologists) and temperature Classical example, Fe (See lecture 1)\ Historical classification: First order- Ehrenfest definition Discontinuous change in slope of Gibb’s free energy No symmetry relations between two x-stal structures Second order - Ehrenfest definition Discontinuous change in second derivative of Gibb’s free.. Energy. A symmetry operation usually gets carried over.

We will leave this fine points to the physicist !!

Some important phase transitions in metallurgy A eutectic transformation, in which a two component single phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a eutectoid transformation. A peritectic transformation, in which a two component single phase solid is heated and transforms into a solid phase and a liquid phase. A spinodal decomposition, in which a single phase is cooled and separates into two different between the compositions of that same phase. The transition ferromagnetic and paramagnetic phases of magnetic materials at the Curie point. The martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Changes in the crystallographic structure such as between ferrite and austenite of iron. Order-disorder transitions such as in alpha-titanium aluminides.