§1. Welding as an interdisciplinary, ubiquitous, failure-prone field [00:06]
Studying welding and joining is integrative. It uses lots of interdisciplinary fields. It's not just a materials field — it's physics, chemistry, structures, civil engineering, mechanical engineering, electrical engineering, chemical engineering. It's a whole bunch of things. Welding is about 150 years old in terms of electric arc welding. It goes back thousands of years to people using forges and soldering and things like that.
It's ubiquitous. Very few manufactured products don't contain a joint. In fact, any product that uses two dissimilar materials has to have a joint between them. To have no joint, you have to have a monolithic material that's a standalone product useful in its own right rather than just a paperweight, and it's usually something fairly large. For years I got pieces like needles and things brought in. One student came up with a cast iron frying pan. Professor McClintock came up with an anvil. Has anyone come up with anything any larger? It turns out Professor Pelloux heard this once and he came up with an anvil — but it was the anvil of a forging press, about a thousand tons. So he may win the prize for the largest standalone object. It was a huge casting.
There are many failures, and this is kind of where we stopped last time. When I heard about the Space Shuttle Challenger in 1986 — my students told me about it that morning — I said, "I bet it failed at a weld." I was wrong, but it did fail at an O-ring joint. It was at a joint. Things typically fail at joints because they're the highest-stress locations in the structure. It's just sort of natural. They also may not be 100% efficient depending on the material.
§2. The Alexander Kielland: a non-critical weld brings down a platform [02:30]
There are some huge failures that cost a billion dollars or take lots of lives. There's an offshore oil platform called the Alexander Kielland, about 1980 in the North Sea. This was supposed to be a production platform for oil in the North Sea, and they changed it to a hotel. A great big storm comes by — these things should have been safe in a storm — but the whole thing capsized, and over 200 people died.
When they did the analysis, they found that the French shipyard that had built this offshore oil platform — someone had taken about a 16-inch diameter piece of steel and welded it to one of these legs. One of these legs on an offshore oil platform is a big piece of round steel about the diameter of this room. They had welded this 16-inch-diameter, basketball-sized piece on because they were going to put a sonar instrument there.
No one thought this was a critical part of the structure. The management of the shipyard had one group of people who worried about welding steel that went into the main structure — the great big 24-foot-diameter legs. They let the maintenance people worry about welding hanger-on pieces like this sonar bracket. The maintenance people went to the shop and got a pipe. It turns out it was a high-carbon steel pipe, and if you weld high-carbon steel, it's very easy to get cracking. They had a little crack about the size of your thumbnail. No one found it, because it wasn't a critical part of the structure — all the inspection was for the critical parts, like the welds in those 24-foot-diameter legs. The waves came along, and over time a fatigue crack grew to where it was 20-some feet long. When the storm came by, this 20-foot-long crack just snapped it. That's what caused the accident.
There are a lot of other things people said caused the accident. If you look up the Alexander Kielland, you'll find all kinds of stories — a lot of people said the cause was that they didn't have enough lifeboats. Well, you didn't need lifeboats if the structure hadn't failed. So it's a question of where you start your accounting.
§3. Steel dominates; welding is applied as an art [05:18]
I handed out a paper on the future of metals and pointed out that iron and steel constitute 95 pounds out of every 100 pounds of metal made in the world. Aluminum is less than 2%. Iron and steel is about a billion tons a year, so aluminum at 2% is about 20 million tons a year. That's a lot of aluminum, but it's nothing compared to the amount of steel. In fusion welding we'll talk a lot more about iron and steel because it's the dominant material, and in material selection you'll hear about why.
Welding is often applied as an art. As soon as someone gets a new heat source, they often try to use it to weld. People discovered over the ages how to do soldering and brazing on art objects. They even learned to do diffusion bonding. When we get to diffusion bonding, I'll tell you the story about how the Etruscans used to use tin to bond gold beads to copper objects. They just put them in a furnace and ended up getting a type of diffusion bond. I always say Pratt & Whitney patented this process in 1972 only because the Etruscans, who used it in 600 BC, didn't file an infringement against them. Some people think that King Tut's dagger had the same type of gold beads attached to it by this type of diffusion bonding. No one knows because no one's willing to cut up the dagger to find out.
Welding was initially used as an art to make all kinds of vessels. If you go to Kyoto, Japan, Sumitomo has a museum of Chinese castings — Sumitomo is a metals company in Japan, and 5,000 years ago the Chinese were making bronze castings. They had to weld on legs and things, and they did it by pouring molten metal between the leg and the other casting to make a more complex product. In the Middle Ages a lot of what was driving joining technology was military needs. Then people started discovering new types of science. Humphry Davy discovered the arc, gave the name to the electric arc in 1805 or 1806, and he tried to weld with it within the next year.
The earliest commercial use of a laser was in the mid-50s. Lasers were only invented in the mid-50s, but it's my understanding that General Electric used to use them this way: back in the mid-50s, people used vacuum tubes in their electronics. We didn't have silicon yet — silicon had been invented as a semiconductor in 1947, but it really hadn't been commercialized. So most power electronics had vacuum tubes, and some of these tubes would cost a couple hundred or $1,000. Back in 1950, that's a lot of money. So they would make these things, seal them in vacuum, and then find out that one of the joints inside had failed. Supposedly General Electric took a research laser — you'd have two tungsten or molybdenum wires inside the clear glass vacuum tube — and they would first hit it with a soft electron laser beam that would just soften the wire so it would make contact with the other wire, then come in with power and weld it back together to make the electrical connection and save the vacuum tube. So lasers were used early on. Electron beams were used early on, within the first five or ten years of their having been developed into high-power devices.
In my own experience, particle beams have been used for welding. In the mid-70s, they were making high-power lasers for military applications, but over here in Everett, Massachusetts — it's now the Mellon Bank building — AVCO Everett Research Laboratories had 25-kilowatt lasers developed for commercial applications under government contracts, and they tried to laser-weld heavy pieces of steel and other materials. One of my students went to work for them, and he said his main job was making sure the laser worked when one of the customers would come in to look at it, because 90% of the time it didn't even work.
§4. Particle beams, the Sheffield, and titanium submarines [10:57]
In the early 90s, the military had spent a quarter billion dollars developing particle-beam weapons — proton beams the Navy was supposedly going to shoot through the air to shoot down a missile coming toward the ship. In the Falkland Islands War in the 80s, a French Exocet missile fired by the Argentinians hit the British cruiser Sheffield, and an aluminum fire started. There's debate on whether it was an aluminum fire, but it probably was, and it wiped out the entire ship. One small missile that you could buy from arms dealers anywhere in the world could wipe out a capital ship of one of the world's major navies. So the US Navy was trying to develop these particle-beam weapons from the mid-80s through the early 90s, and then peace broke out with the former Soviet Union. They weren't quite as concerned anymore, but they had spent a quarter billion dollars and they wanted to find some application. They had a three-day workshop, invited me to it, and said, "Can we use these to weld nuclear submarines?" I went down and said, "Well, maybe you can melt a nuclear submarine, but with 5 megawatts of power, you don't need that to weld. You only need a few tens of kilowatts."
Anyway, I got a research project in the mid-90s to see if we could use particle-beam weapons to do welding and heat treatment. As soon as a new heat source technology comes along, people use it, and they don't necessarily understand it. So welding is often applied as an art, and along with that, relatively few people have been trained in welding. It is an interdisciplinary field. There are materials engineers who, like myself — I went to work for a steel company, and they said, "You're a welding engineer." I had never taken a welding course in my life, but all of a sudden I was a welding engineer. And I met many physicists whose manager would call them in and say, "You're now a welding engineer." They took physics classes. They didn't know anything about welding. And you can kind of see how they kept reinventing the wheel, because they took what they knew from physics and tried to apply it to welding. It doesn't always work. The physics of welding is a little different than what you learn in the classroom.
There are very few people trained in welding in this country. There's one school that gives a four-year degree from a regular university — Ohio State University, which has had a welding engineering department for the last 60 years, though that department is now folded in with a couple of others. Highest-paid students in the School of Engineering at Ohio State. Industry wants them. If you go to the former Soviet Union, they had the Paton Institute in Kiev. For political reasons, the Paton Institute used to get huge amounts of money from the Soviet government. It's an institute of 10,000 people studying welding, though they study a lot of other things too, like casting.
Professor Paton — I think he just passed away a year or two ago — his father had weld-repaired Soviet tanks during World War II and got them back to the front to fight Hitler. He was a hero of the Soviet Union. After the war, under the Stalin regime, the son took over in the 40s and 50s this Paton Welding Institute named after the father. It's kind of fuzzy whether it's named after the father or the son. Professor Paton was head of the Ukrainian Academy of Sciences, and in the former Soviet Union all the research money from the central government came through the Academy of Sciences and was divvied up. There were only seven people on the Soviet Academy of Sciences, and Professor Paton was one of those seven. The Ukraine was the largest and most financially successful of all the provinces in the former Soviet Union, so they got more research money than any other province, because Professor Paton represented Ukraine, and when the money came to the Ukraine, he gave most of it to his institute. Corruption at its best.
So they had a huge welding institute and they developed technologies like — if you've ever read The Hunt for Red October or seen the movie, they had titanium submarines. My first research project, in 1977, was from the US Navy to weld titanium for submarines. [Tom holds up a 1977-era titanium weld sample.] This probably belongs in the Smithsonian. We were welding 1-inch-thick titanium for submarines. The United States wanted to build titanium submarines. We never built one, other than the deep-sea research vessel Alvin that went down and found the Titanic. The Navy built that as part of a prototype program to learn to weld titanium for bigger ships, because titanium submarines have the same strength-to-weight ratio advantage that aircraft and fast-moving vehicles need. You want high strength-to-weight so you can dive deeper and, hopefully, if you lose power, pop to the surface rather than sink to the bottom — because if you sink to the bottom, everything gets crushed, including the people inside.
The Soviets actually built a titanium submarine. [Tom holds up a weld made at Oregon Graduate Center.] This is a weld made at Oregon Graduate Center by one of the processes developed by Dr. Gurevich at the Paton Institute, because the Soviets spent hundreds of millions of dollars. We couldn't justify building the titanium submarine or spending the money to do the research, but the Soviets were under a different economic system and were driven by military needs much more than we are. It turns out their titanium submarine was somewhat of a disaster, and within two or three years they all just parked them in the harbor because they were developing leaks. The US Navy asked me, "How did the Soviets solve the creep-fatigue interaction of the titanium?" Titanium has this problem: if you put it under continuous compressive stress, even at room temperature or seawater temperature, it will start to slowly creep. Then if you flex it, there's an interaction, and the cracks grow ultra-fast. In 1980, when we learned about the Soviet Alfa subs, I went to some workshops and they said, "How'd they solve the problem?" I said, "I don't know." It turns out they didn't. They built these submarines and they had cracks. They had to park them.
But anyway, the US Navy's never built them for various reasons, mostly economic. With the poor training in this country, we produce about 40 to 100 welding engineers a year. Maybe 40 at Ohio State. There's Ferris State College in Michigan, and LeTourneau College in Texas. Some of these are more like two-year colleges than four-year colleges. The Soviets supposedly produced 5,000 welding engineers a year. Welding engineers are at a premium here. Most of the people in welding are just misplaced metallurgists or physicists or civil engineers, because their boss came to them after a major failure that cost the company tens or hundreds of millions of dollars and said, "We're going to study welding and we're going to fix these problems." It's not a question of not knowing what the problem is — in most cases, we actually know what the problem is. It's just that the people working on it didn't know what the problem was.
§5. The limits of joining: aluminum cars, composite tanks, and the value of a pound [20:23]
So welding is poorly trained for, and applied as an art often before we know the science behind it. Basically, I've made my career by trying to figure out the science behind what people have been applying as an art. When Comfort Adams started the American Welding Society in 1921 after being in charge of building ships in World War I, he came up with the AWS motto: "to foster the art and science of welding." So they admit it's an art.
The last thing I wanted to mention is that our ability to join a material limits the usefulness of the material. [Tom holds up two pieces of aluminum sheet metal.] Here are a couple of pieces of aluminum sheet metal that came out of the automotive research labs — this one at Chrysler, this one at Ford. These people have been trying to build all-aluminum vehicles for 80 years. We built an all-aluminum Duesenberg in the 1930s. And Mellon, of Mellon Bank — I can't remember his first name — was one of the richest men in the United States. He was on the board of Alcoa, and he had this luxury vehicle made out of all aluminum, but only he could afford it.
Twenty years ago I used to hear that because of the increase in the price of gasoline, steel was on its way out, and in a few years we'd all be driving aluminum automobiles. Actually, one of the reasons I wrote that paper on the future of metals was because in the early 90s you'd go to a conference and people would say, "Well, we're not going to be using metals anymore. It's all going to be ceramics." They were trying to make internal combustion engines out of ceramics — they wouldn't have to cool them, they could just take the heat themselves. So I came up with this plot, a fracture mechanics plot of steel versus titanium versus aluminum versus plastics and composites and ceramics. If you study this plot, you want to be way up here, and steel has better properties by an order of magnitude compared to titanium and aluminum. The properties of steel are much better. It's also less expensive.
I also talked about ceramics, because people would say we're going to use these other materials and steel is a dying material. It's not a dying material. I used to say, "In 20 years we'll still be driving steel cars." People said, "What about the all-aluminum Audi?" If you go buy an Audi, it'll be all aluminum — high performance, lightweight. And what will you pay for it? $100,000. If you buy a Ford Taurus, you'll pay $20,000 or $25,000. In the mid-90s I started saying anyone can build a $100,000 vehicle out of aluminum, but building a $20,000 vehicle out of aluminum is a lot more difficult. That's still true today. Twenty-five years ago I predicted we'd still be driving steel cars in 20 years, and here it is 25 years later and we are. All it took was understanding something about joining technology and the cost of materials.
We also couldn't use ceramics because it was hard to join them. We can join them now — if you're willing to pay the price. [Tom holds up a piece of the X-33 space plane hydrogen tank.] Here's a piece of the X-33 space plane. This is all composite — Nomex, which is the same thing as Kevlar but from a different manufacturer than DuPont. You can buy this foam Nomex, which is like Kevlar — fire-resistant. The suits for firemen are made of Nomex; you pay $300 for a jacket rather than $100 because it won't burn very well in a fire. Carbon fiber composites, adhesively bonded. They built this structure on a fast track. It has a foamed adhesive joint through here. They built two of these. That was supposed to be the liquid hydrogen tank for the X-33 space plane. They built them at about $50 million apiece, and they weighed about 4,000 pounds — so it cost about $12,000 a pound to fabricate. What I'm holding is less than an ounce; it's not even $1,000 worth of product.
So most materials can be joined if you're willing to pay the price. But the advantage of steel is it's much cheaper. I handed out last time "Materials for the 21st Century" — that article is my Cliff's Notes version. I was on this committee. They didn't like what I said, so they put all my stuff in the appendix. This is where we talked last time about the relative cost of materials: materials are 10 to 20% of the cost, fabrication — forging, machining, joining — is 20 to 40%.
I also talk about the value of a pound saved over the life of the vehicle. With gasoline at $1 to $2 a gallon — you can see this is a little bit old — you'll save $2 over the 100,000-mile life of a car for every pound you take out. At $4 a gallon, you'd need to go 200,000 miles. The price of the car has gone up since then, too. For an aircraft, they have vice presidents determining how many magazines can be carried, because over the life of the vehicle every pound costs $200. They don't carry very many magazines in first class anymore. American Airlines used to have essentially a clean aluminum skin with no paint, because paint has weight, and at $200 a pound for all those gallons of paint on the fuselage, just to make it look pretty, it adds up.
Over the life of a spacecraft, that piece I just sent around, $20,000 a pound is what it costs to get payload up into space. So you can afford to pay $12,000 a pound for your liquid hydrogen tank — if it works. Except it didn't. But that's another story. Ships and railroads are at about 20 cents a pound as the value of a pound saved. So the ability to join things limits the usefulness of the material, and the cost or value of the material limits the usefulness of what we're using it for.
§6. Show-and-tell: bulletproof glass, gas pipe, laser welds, brazed diamond tips [29:44]
That's the introduction about materials. If we talk about different products — [Tom passes a metal-wood golf club around.] Here's a metal wood.
[Tom passes a piece of bulletproof glass around.] Here's a piece of bulletproof glass. It's not just glass — it has glass in it, three layers, and a layer of polycarbonate, all adhesively bonded. The adhesively bonded joints have to be void-free, because otherwise you're looking at a bubble. The major military vehicles actually have something almost five inches thick, and the presidential limousine also has something about five inches thick, so it can take a shaped-charge weapon, an anti-tank round. It's laminated material — just to make transparent armor.
[Tom holds up a section of plastic gas pipe.] Gas pipe. They used to make gas pipes that run down the street out of steel, but after 30 or 40 years it corrodes, and now you have gas leaking into the soil and you can blow up homes. Now they use plastic — they weld plastic pipe. Very corrosion resistant, but it also fails, and it can fail at the joints. We'll talk about some of that. We talked last time about soldering. I passed around one of the semiconductor chips — an old Pentium chip from the 1995 era. I don't have the newest ones, but the technology of tape-automated bonding is the same, and we'll go through the soldering techniques.
[Tom passes a laser-welded aluminum part around.] This is a laser weld. These are little prototype welds. This one came from a factory in California where they would fill this with explosive — for the canopy of a fighter jet. If you lost electrical power and needed to eject, you don't want to try to eject right through the polycarbonate canopy, because you'll just kill yourself — you won't break the polycarbonate. You also can't rely on having electricity to operate things. So they have a percussive explosive: instead of transferring energy to bolts that hold the canopy on, they have a little aluminum tube filled with explosive, and you can hit the end of it and eject the canopy, then eject yourself. Laser-welded aluminum.
[Tom passes a brazed diamond-tip asphalt tool around.] Here's a brazing example. This is part of a tip for reclaiming asphalt from the street. You may have seen them late at night on the highway — a great big machine with a bunch of these tips going around in circles, beating up the asphalt so they can resurface the road. The tip is usually made out of tungsten carbide, which is one of the hardest materials we know, but you can get a much better life if you use sintered diamond. The black stuff there, about a centimeter across, is sintered diamond. It has to be brazed. So you have to learn how to braze it so it doesn't fail as it beats up the road to reclaim the asphalt.
[Tom holds up a diffusion-bonded titanium part.] We use diffusion bonding. This is a piece of titanium that was part of the development project for the F-21 [F-22] jet fighter. One of the students who was in the class gave this to me — he had recovered it when he was working at Pratt & Whitney research labs, and they were developing the engine and the joining technology of how to put together the jet engine. That's a type of diffusion bonding.
I've got lots of little trinkets up here, and we'll pass them around as we get to these things. So welding is used for all kinds of manufactured products. In a sense, this is a manufacturing course. In another sense, it's a course where I want to prove to you that you already know the answer. You learned in high school chemistry and physics, and someone just has to show you how to think through the problem. Any questions before I start the first subject, which is cold welding?
§7. Why don't two atoms bond when you touch them together? The Lennard-Jones potential [35:19]
So if we go to cold welding — but even more basic: if I take two materials and just touch them together, they don't bond, right? Why don't they bond? There are two fundamental reasons, and throughout the next 11 lectures we're going to keep coming back to these two fundamental reasons why things don't bond when you stick them together.
The first one is: you can think of welding and joining as the opposite of lubrication. In lubrication, you don't want things to bond. What do we do in lubrication to keep things from bonding? We put a film of oil in there, or we put some grease in there. We contaminate the surface with something else that doesn't want to bond. It turns out most materials, if they're clean, want to bond. If I bring two atoms together in an ultra-high vacuum and stick them together, they will bond with considerable force — equivalent strength of 2 million PSI. We don't have anything on Earth, even solid single-crystal diamond, that's that strong. But if I just talked about the bond strength of two atoms, perfectly clean, just brought in contact with each other, they would bond.
Why is that? If you took 3.091 — how many of you took 3.091? One, two, three. Did you learn the Lennard-Jones potential in 5.11? Okay, fine. [Tom puts up an overhead.] Let me show you the Lennard-Jones potential. I'm using some of my old lecture notes. The Lennard-Jones potential is nothing more than the energy potential between two atoms — that's what these little green things are — at some radius. There's some inter-atomic spacing. In a simple cubic system, it's the lattice parameter. In body-centered cubic it's the square root of 3 over 2 times the lattice parameter; in FCC it's the square root of 2 over 2 times the lattice parameter. But in any case, there's some inter-atomic separation, and there's some energy of attraction — as something is far away, you bring it in, you reach a minimum of energy, and then it starts repelling as you get closer.
A student asked me about 15 years ago, "Well, you say it's 2 million PSI — how do you get that?" You go to the Lennard-Jones potential, which you find in any physical chemistry text. The energy is something over r to the n power minus something over r to the m power. One's attractive and one's repulsive. The attractive force is minus a over r to the sixth, and the repulsive force is even greater. Not the energy — the force is the derivative of the energy. The force is zero at the equilibrium spacing; at the equilibrium spacing, it doesn't have anything trying to pull it one way or the other, so the force goes to zero. That's also the minimum of the energy of the Lennard-Jones potential. It's called the Lennard-Jones potential because these quantum mechanics guys in Britain in the 1920s — I don't know if it was one Lennard-Jones with a hyphenated name, or two people. But in any case, there are these potentials for bringing two atoms together.
If you integrate the area under the force curve to pull them apart — F times d, F times dr from zero to infinity — you'll come up with a force to separate those two atoms. I did this for iron, and we'll talk about it later, but you get about 2 million PSI.
§8. Dislocations: why real metals are ten times weaker [41:33]
But in fact, most materials don't have anywhere near that strength. Real iron might have one-tenth that strength. Why is it so much weaker? Student: Defects — dislocations. Right.
You've heard how dislocations were discovered, haven't you? There were two guys. There was Egon Orowan, who was in Hungary at the time as a professor in an institute and later came to MIT as a professor of mechanical engineering. The other was Polanyi — I can't remember his nationality, but I think he was in Britain at the time. People in the 1930s were trying to understand why metals — the physicists had done quantum mechanics, Lennard-Jones had come along in the 1920s, they had done this type of calculation, and they said, "Oh, metals have a strength of 2 million PSI." And people said, "No, they don't."
So in the 1930s they said, "We must have crystal defects that weaken the material." It was Orowan and Polanyi, both independently, who came up with dislocations before we ever saw them. When did we first see dislocations? Not until we got electron microscopes. The first guy to demonstrate them was someone in the 1950s who did very fancy etching techniques on lithium bromide crystals. He could show movement of dislocations — he could etch the dislocations, stress the material, re-etch, and see the movement of the etch pits.
Egon Orowan told the story of how he learned about a dislocation. [Tom tears a sheet from a pad of paper to demonstrate.] He had a very big office with a great big Persian rug. He was working in his office and the cleaning lady came in and noticed that the rug needed to be moved about three or four inches. He said, "I'll help you." She said, "No, I don't need any help." So he watched her. She put a little fold in the rug, like this, and she kicked it across the room, and when she was done the rug had moved a couple of inches. Orowan looked at this, and he thought about it some more.
I used to rip telephone books, but the problem is they're now using plastic-improved paper, so it doesn't rip as easily as the old brittle paper. If you take a telephone book and put a dislocation in it like that, and then you stretch it, you can break it one page at a time. You're just putting a dislocation in and bending it. I put the U in it, I grab it tight, and when I straighten it out, the top page is in tension but all the others are loose. By bending it, I'm ripping one page at a time. That's a dislocation. Analogies are never perfect — I'm not dealing with atoms, I'm dealing with paper. But I used to love the old MIT telephone directories — then they improved the paper, and now we don't even have telephone directories. Science marches on.
So people predict tremendous strengths, and in the 1950s they actually found single crystals of iron. They grew iron whiskers and they had a screw dislocation right up the middle with no edge dislocations — a perfect crystal except for the screw dislocation. If you pull parallel to a screw dislocation, what's the force on the screw to move the dislocation? Zero. If you pulled an edge dislocation in tension, it'd be just like the cleaning lady in Hungary that showed Orowan about dislocations. But a screw dislocation — if you look at the Burgers vector — does anyone study dislocations anymore? I had to take a whole graduate course in dislocations. It was horrible. If you actually study dislocations, you find that a material might lose 90% of its strength because of the movement of dislocations.
§9. Bucky balls, nanotubes, and the trap of forgetting history [46:35]
Today we have great physicists who wanted to win the Nobel Prize for discovering bucky balls — three-dimensional carbon structures. [Tom holds up a diamond-structure model.] This is the structure of diamond. Bucky balls are essentially hollow spheres with sp3 hybrid bonding. They calculated the strength of carbon-carbon bonds and found these should be 3 million PSI, and we're going to be able to make composites out of bucky fibers — nano fibers. That's true — as long as you don't have any defects in those carbon nanotubes. What's the probability of having a defect in a carbon nanotube? Pretty high. If you make them at absolute zero, you can make them without defects, but at any temperature above absolute zero, statistical mechanics will prove to you you'll have some vacancies. And if you have some vacancies, you're going to find they're not as strong as you thought.
So in the last 25 years, the physicists and many materials scientists have sold a billion dollars worth of research on carbon nanotubes, because in theory they're super strong. But who has ever measured the strength of a carbon nanotube? No one. We did measure the strength of asbestos fibers — about 700,000 PSI. Iron whiskers, about 1.2 million PSI. They're not quite as strong as we calculate, but people have been running around selling schlock in materials science because they can't remember history. There was a guy up at Harvard named George Santayana — anybody ever heard of George? He was a philosopher, famous for the quote that those who cannot remember history are condemned to repeat it.
The materials scientists and the physicists — someone won a Nobel Prize for discovering bucky balls, and just a couple years ago someone won a Nobel Prize for forming these flat sheets of bucky films [graphene]. They're all saying, "Oh, this is going to save the world. We will have things that are 10 times as strong." Yes, if they are defect-free. They're not defect-free. So they're actually going to be one-tenth as strong, or one-fifth as strong, when we make them in high quantity, and people are going to be disappointed. So don't invest in carbon nanotubes for structural applications. I'll see you again tomorrow.