Structure and bonding in metals. Most metals and alloys
crystallize in one of three very common structures: body-centered cubic
(bcc), hexagonal close packed (hcp), or cubic close packed (ccp, also
called face centered cubic, fcc). In all three structures the
coordination number of the metal atoms (i.e., the number of equidistant
nearest neighbors) is rather high: 8 for bcc, and 12 for hcp and ccp.
We can contrast this with the low coordination numbers (i.e., low
valences - like 2 for O, 3 for N, or 4 for C) found in nonmetals. In
the bcc structure, the nearest neighbors are at the corners of a cube
surrounding the metal atom in the center. In the hcp and ccp
structures, the atoms pack like stacked cannonballs or billiard balls,
in layers with a six-coordinate arrangement. Each atom also has six
more nearest neighbors from layers above and below.
Remember where we found the metallic elements in the periodic table - everywhere except the upper right corner. This means that as we go down a group in the p-block (let's say, group IVA, the carbon group, or group VA, the nitrogen group), the properties of the elements gradually change from nonmetals to metalloids to metals. The carbon group nicely illustrates the transition. Starting at the top, the element carbon has two stable allotropes - graphite and diamond. In each one, the valence of carbon atoms is exactly satisfied by making four electron pair bonds to neighboring atoms. In graphite, each carbon has three nearest neighbors, and so there are two single bonds and one double bond. In diamond, there are four nearest neighbors situated at the vertices of a tetrahedron, and so there is a single bond to each one:
The two elements right under carbon (silicon and germanium) in the periodic table also have the diamond structure (recall that these elements cannot make double bonds to themselves easily, so there is no graphite allotrope for Si or Ge). While diamond is a good insulator, both silicon and germanium are semiconductors (i.e., metalloids). Mechanically, they are hard like diamond. Like carbon, each atom of Si and Ge satisfies its valence of four by making single bonds to four nearest neighbors.
The next element under germanium is tin (Sn). Tin has two allotropes, one with the diamond structure, and one with a slightly distorted bcc structure. The latter has metallic properties (metallic luster, malleability), and conductivity about 109 times higher than Si. Finally, lead (Pb), the element under Sn, has the ccp structure, and also is metallic. Note the trends in coordination number and conducting properties:
The elements C, Si, and Ge obey the octet rule, and we can easily identify the electron pair bonds in their structures. Sn and Pb, on the other hand, adopt structures with high coordination numbers. They do not have enough valence electrons to make electron pair bonds to each neighbor (this is a common feature of metals). What happens in this case is that the valence electrons become "smeared out" or delocalized over all the atoms in the crystal. It is best to think of the bonding in metals as a crystalline arrangement of positively charged cores with a "sea" of shared valence electrons gluing the structure together. Because the electrons are not localized in any particular bond between atoms, they can move in an electric field, which is why metals conduct electricity well. Another way to describe the bonding in metals is nondirectional. That is, an atom's nearest neighbors surround it in every direction, rather than in a few particular directions (like at the corners of a tetrahedron, as we found for diamond). Nonmetals (insulators and semiconductors), on the other hand, have directional bonding. Because the bonding in metals is non-directional and coordination numbers are high, it is relatively easy to deform the coordination sphere (i.e., break or stretch bonds) than it is in the case of a nonmetal. This is why elements like lead are much more malleable than C, Si, or Ge.
Materials properties of metals and alloys. How much do the 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:
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 four years from now!
Defects in metallic crystals. 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. A "bubble raft" computer simulation was shown in class to illustrate (in two dimensions) how metals crystallize in a close-packed arrangement, how defects form in their structures, and how defects like dislocations and grain boundaries are relatively mobile.
Plastic deformation, work-hardening and annealing of metals. 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 on the next page, 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 demonstration was done in class showing work hardening of a piece of copper wire. When struck many times with a hammer, the copper wire became stiffer, and it was possible to hang a hammer 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. 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 becomes more 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).
Malleability of close-packed (hcp and ccp) vs. non-close-packed (bcc) structures. 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). 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 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.
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Remember where we found the metallic elements in the periodic table - everywhere except the upper right corner. This means that as we go down a group in the p-block (let's say, group IVA, the carbon group, or group VA, the nitrogen group), the properties of the elements gradually change from nonmetals to metalloids to metals. The carbon group nicely illustrates the transition. Starting at the top, the element carbon has two stable allotropes - graphite and diamond. In each one, the valence of carbon atoms is exactly satisfied by making four electron pair bonds to neighboring atoms. In graphite, each carbon has three nearest neighbors, and so there are two single bonds and one double bond. In diamond, there are four nearest neighbors situated at the vertices of a tetrahedron, and so there is a single bond to each one:
The two elements right under carbon (silicon and germanium) in the periodic table also have the diamond structure (recall that these elements cannot make double bonds to themselves easily, so there is no graphite allotrope for Si or Ge). While diamond is a good insulator, both silicon and germanium are semiconductors (i.e., metalloids). Mechanically, they are hard like diamond. Like carbon, each atom of Si and Ge satisfies its valence of four by making single bonds to four nearest neighbors.
The next element under germanium is tin (Sn). Tin has two allotropes, one with the diamond structure, and one with a slightly distorted bcc structure. The latter has metallic properties (metallic luster, malleability), and conductivity about 109 times higher than Si. Finally, lead (Pb), the element under Sn, has the ccp structure, and also is metallic. Note the trends in coordination number and conducting properties:
The elements C, Si, and Ge obey the octet rule, and we can easily identify the electron pair bonds in their structures. Sn and Pb, on the other hand, adopt structures with high coordination numbers. They do not have enough valence electrons to make electron pair bonds to each neighbor (this is a common feature of metals). What happens in this case is that the valence electrons become "smeared out" or delocalized over all the atoms in the crystal. It is best to think of the bonding in metals as a crystalline arrangement of positively charged cores with a "sea" of shared valence electrons gluing the structure together. Because the electrons are not localized in any particular bond between atoms, they can move in an electric field, which is why metals conduct electricity well. Another way to describe the bonding in metals is nondirectional. That is, an atom's nearest neighbors surround it in every direction, rather than in a few particular directions (like at the corners of a tetrahedron, as we found for diamond). Nonmetals (insulators and semiconductors), on the other hand, have directional bonding. Because the bonding in metals is non-directional and coordination numbers are high, it is relatively easy to deform the coordination sphere (i.e., break or stretch bonds) than it is in the case of a nonmetal. This is why elements like lead are much more malleable than C, Si, or Ge.
Materials properties of metals and alloys. How much do the 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 Yield Stress (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 four years from now!
Defects in metallic crystals. 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. A "bubble raft" computer simulation was shown in class to illustrate (in two dimensions) how metals crystallize in a close-packed arrangement, how defects form in their structures, and how defects like dislocations and grain boundaries are relatively mobile.
Plastic deformation, work-hardening and annealing of metals. 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 on the next page, 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 demonstration was done in class showing work hardening of a piece of copper wire. When struck many times with a hammer, the copper wire became stiffer, and it was possible to hang a hammer 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. 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 becomes more 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).
Malleability of close-packed (hcp and ccp) vs. non-close-packed (bcc) structures. 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). 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 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.
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