Chapter 7: Metals and Alloys: Mechanical PropertiesEdit
How much do the mechanical properties of metals and alloys vary with processing? The answer is, a great deal. Consider the following hypothetical situation: Upon graduation, you go to work as an engineer for Boeing. Your job is to work with aluminum companies to help them produce high strength alloys. Why? A large jet airplane weighs a total of 500 tons. Of that total, 50 tons is cargo, 150 tons is the plane structure, and the remainder is fuel. If you can triple the strength of the materials in the structure (aluminum), you can reduce the mass of the structure to 50 tons and increase the cargo to 150 tons. Look at what has been done already:
|Material||Tensile strength yield (psi)|
|pure (99.45%) annealed Al||4 x 103|
|pure (99.45%) cold drawn Al||24 x 103|
|Al alloy - precipitated, hardened||50 x 103|
By chemical and physical manipulation we have already increased the yield strength 12 times over annealed Al. Yet the yield strength of a "perfect" single crystal of pure Al is ca. 106 psi. We still have 3 orders of magnitude to go. This just shows that there will still be plenty to do on this project between now and graduation!
7.1 Defects in metallic crystalsEdit
Non-directional bonding has an important impact on the mechanical properties of metals. Because there is no strong preference for one atomic position over another, the structure is not greatly impaired by the vacancy of a single atom or the dislocation of a group of atoms. These "mistakes" in packing of metal atoms within crystals are called defects. The deformability of metals is the direct result of defects in the crystal structure. Defects in materials like Al and Fe are responsible for the three orders of magnitude difference between the yield stress of annealed polycrystalline samples (i.e., normal articles of commerce) and perfect single crystals.
There are several different kinds of defects that can be found in metallic crystals. One kind is called a vacancy, i.e., a place where an atom is missing in the structure. A dislocation, on the other hand, is a line defect; it runs somewhat like a string through the crystal. A dislocation is the result of one atom or group of atoms being pulled slightly out of position with respect to perfect crystal packing. A third kind of defect is called a grain boundary; it is a two-dimensional interface between two different crystal grains in a solid sample. Since the two crystallites have in general different orientation, the structures do not match up exactly at the interface.
7.2 Work hardening, alloying, and annealingEdit
One of the questions we would like to ask is, why are the yield stresses of normal (polycrystalline) metal samples so much lower (by a factor of 1000) than they are in perfect single crystals? The answer has to do with the motion of dislocations. Consider the picture below, which shows planes of metal atoms near a dislocation (the individual atoms are numbered to help you see which bonds are broken and which are formed). The arrows indicate force applied under shear stress. Notice how the dislocation moves by breaking/making metal-metal bonds.
The key point here is that we can induce plastic deformation (shear) by breaking only one line of metal-metal bonds at a time along the dislocation line. This involves far less force than breaking an entire plane of bonds, as we would need to do to shear a perfect crystal. In a given polycrystalline sample, there are many dislocation lines that run perpendicular to all possible shear directions, so their motion can be used to "tear" the metal apart. Turbine rotors on large jets (like DC-10's) are made of very expensive single crystal titanium alloys, so that these shearing deformations can be avoided.
We can see that motion of dislocations is basically bad news if we want a metal to be strong and hard (e.g., if we want a structural material, or a knife that can hold a decent edge). There are several ways we can overcome (to some extent) this problem:
1. Use single crystals and anneal out all the dislocations (expensive - especially with large items like turbine blades, and impossible with very large items like airplane wings or bridges).
2. Work hardening of the metal - this moves all dislocations to grain boundaries (the dislocation essentially becomes part of the grain boundary). Since a grain boundary is a planar defect, it is much less responsive to stress than a line defect.
3. Introduce impurity atoms (that is alloying elements) or impurity phases that "pin" the motion of defects. An impurity atom stops the motion because it is a different size, or makes stronger bonds, than the other metal atoms; the line defect has a hard time moving away from rows of such atoms. An impurity phase (like Fe3C in iron) makes extra grain boundaries that can stop the motion of defects. This effect is analogous to the graphite fibers in fiber-reinforced cross-linked polymers (used, e.g., in tennis rackets) that stop the propagation of cracks.
A simple illustration of work hardening can be done with a piece of copper wire. When struck many times with a hammer, the copper wire became stiffer, and it is possible to hang a weight from it. Dislocations move to the crystal grain boundaries during work hardening, effectively halting their motion and at the same time making the individual crystal grains smaller. Because the crystal grains are now smaller, the amount of grain boundary area has increased, and with it the free energy of the material. Annealing reverses the process by lowering the free energy. When the wire is annealed in a flame (heated so that atoms can move and rearrange), the crystal grains grow, and the dislocations reappear. The copper again becomes ductile, and bends easily. Cold-working (work hardening) of metals is important for strengthening structural materials (e.g., iron beams) and for making brittle, hard edges (this is why blacksmiths hammer on knives and swords when they are making them. If you have ever watched them, they do the same thing to horseshoes, when they cool down, to make them stiff).
7.3 Malleability of metals and alloysEdit
Metals with close-packed structures (hcp and ccp) such as copper, gold, silver, zinc, magnesium, etc. are in general more malleable than those with the bcc structure (tungsten, vanadium, chromium, etc.). Why? In the close-packed structure, there is relatively little corrugation between sheets of metal atoms. This means that these planes can slip past each other relatively easily. In the bcc structure, there are no close-packed planes, and much greater corrugation between atoms at different levels. This makes it much harder for one row to slide past another.
This effect explains the hardness of alloys like brass (CuZn, which has a bcc structure), which are made by combining two soft metals (Cu and Zn, which are respectively ccp and hcp as pure metals, are both soft and ductile). Bronzes - originally made as alloys of copper and arsenic, but later as alloys of copper and tin - are harder than either of the constituent metals for the same reason. In the Bronze Age, possession of these harder alloys provided a tactical advantage in warfare (see image at right), that was later supplanted when the technology for smelting iron was developed.
7.4 Iron and steelEdit
One other place where the difference between the hardness of a bcc and a close-packed metal is important is in steelmaking. Between room temperature and 900oC, iron has the bcc structure, and is a tough, hard metal ("tough as nails"). Above 900oC, pure iron switches over to the ccp (austenite) structure, which is much more ductile. So hot iron can be bent and worked into a variety of shapes when it is very hot but still solid (it melts at 1535oC). Rapid quenching of hot iron - e.g., when the blacksmith plunges a red hot piece directly into cold water - cools it to room temperature, but doesn't allow time for the ccp --> bcc phase transition; therefore, such pieces are still relatively malleable and can be shaped.
Carbon is added (about 1% by weight) to iron to make "carbon steel", which is a very hard material. Carbon is rather soluble in the ccp phase of iron, but not in the bcc phase. Therefore, when the ductile ccp phase cools and turns into bcc ("tempering" the steel, which means cooling it slowly enough so the ccp to bcc transformation can occur), the iron can no longer dissolve the excess carbon. The carbon forms grains of an extra phase, Fe3C ("cementite" - a very hard material) which are dotted throughout the matrix of bcc iron grains. The effect of all these little grains of Fe3C is to stop the motion of dislocations, making for a very hard, brittle material. This is why knives and swords are quenched, cold worked into the appropriate shapes, heated up again and tempered (before they are sharpened) when they are made.
7.5 Amorphous alloysEdit
7.6 Discussion questionsEdit
- Discuss the thermodynamics of work hardening and annealing in terms of the microscopic picture of defects in metallic crystals.
1. Show in a drawing how a planar dislocation moves through a solid under stress.
2. Explain (on the basis of structure) why alloys such as bronze make better structural materials than the constituent metals (copper and tin). How did the discovery of these alloys change civilization?
3. A layer sequence for an FCC = CCP metal is shown below. A body diagonal passes through the centers of atoms numbered 4 and 11. A close-packed plane perpendicular to this diagonal contains the centers of atoms numbered 2, 6, 7, 10, 12, and 14.
(a) Other close-packed planes of atoms parallel to this one pass through the cell. Segregate the remaining eight numbered atoms (not contained by this plane) into groups by the parallel plane which contains the center of the atom.
(b) Identify the other body diagonals by the numbered atoms that the diagonals pass through, and also identify one representative face diagonal by numbered atoms.
4. Below are sections of the lithium oxide unit cell.
(a) Describe how to obtain (and do obtain) the empirical formula.
(b) What is the coordination number and geometry for each type of ion?
(c) Which atom is close-packed?
(d) What type and fraction of holes are filled by the other ion?
5. If half the cesium is removed from the CsCl structure, such that each Cl atom is then tetrahedrally coordinated, what structure type is generated?
6. The crystal structure of barium titanate is shown below.
(a) What is the empirical formula of the compound?
(b) Which atoms (if any) are close packed?
(c) How many oxygen atoms coordinate (i) Ti4+ and (ii) Ba2+?
(d) Why are the coordination numbers are different?