SSW_S2013_10

So last time we had talked briefly, or not last time but several times ago, about thermal expansion problems in dissimilar metal bonding. And here's a little table that I found in my notes. Aluminum alloys are about 2 × 10⁻⁵. This is in 10⁻⁶ per degree Kelvin. So 2 × 10⁻⁵ per degree C, per degree Kelvin, whichever, and most metals are in that range. Some of the cast irons only half of that. Titanium alloys are only half of that. There are some tungsten [tellurium?] alloys that are very low, but they melt at high temperatures, and in fact they're similar to some of the ceramics. In fact, silicon is somewhere around this six.

And so if we're talking about die-attach for ceramics, they sometimes make copper-tungsten composites to try to match the coefficient of thermal expansion of silicon. Very expensive, very heavy. There's a company that makes aluminum silicon carbide composites that have like 60 volume percent silicon carbide and 40 volume percent aluminum. The only way you can do that with powders, if you just took round powders and had them as perfect packing density, I think you only get something like 60% and you'll never get perfect packing density. They actually go with a double-sized powder, dual-sized powder. So they're not circular powders, but if you just consider circular powders, you can say what's the largest particle that will fit between the spheres. Actually you should be doing a tetrahedron here, right? Three-dimensional. But nonetheless they actually have a bimodal size distribution, and you can calculate — I think this is 0.16 times the diameter of the larger particle or something like that. So they actually mix them together like that so they can get maximum packing density to match the coefficient of thermal expansion.

Not quite as important in silicon because silicon is not terribly brittle, but gallium arsenide, like on your cell phones and stuff, which they need for the higher frequency of cell phone operation — gallium arsenide will crack just from bonding even at room temperature. You don't have to worry about the thermal cycling and stuff. So they actually have to use things like these aluminum silicon carbide substrates for dissimilar material bonding. As far as that goes, diamond, silica — this is quartz — diamond and quartz and carbon fibers can be in order of magnitude or more smaller.

There are some low expansion, we call invar alloys. Invar for invariant, meaning low coefficient of thermal expansion. And they're down in this range too. Fairly pricey. They're high in nickel and molybdenum as I remember, and molybdenum is very expensive. But in any case there's about two and a half orders of magnitude. What's a half order of magnitude? It's three, because 3.16 squared is 10. Okay. Or the square root of 10 is three, roughly. 3.16. So on the geometric scale, three is half an order of magnitude. Okay. But in any case, you got two and a half orders of magnitude from 1 to 300 here. It's interesting that rubbers have the highest coefficients of thermal expansion of any material that we deal with. So that's one of the major problems in dissimilar metal bonding.

Another thing I mentioned was the problem — this is several lectures ago — of trying to do cold bonding of some of these integrated circuits in the old days, or transistors and whatnot. [Tom produces a power transistor.] So here we have — so here's a — this is a power transistor. Here's a silicon chip on a copper substrate. It's threaded into a base and it's got a lead coming off that's soldered on here. And we might talk about that later. [Tom produces another component.] Here's another power electronics component. You got some — I don't even know what this one is, but you got some heavy copper pieces and some leads coming in here to whatever this active component is.

And I mentioned that in order to encapsulate these things in the old days, and even today sometimes, they would use indium. This is when we were talking about cold pressure welding and I told you that indium had the highest oxide-to-metal hardness ratio and therefore you could form a cold bond. So this would be the lid of one of these packages, which might look something like this. [Tom produces a large diode.] This one is actually not bonded that way. This is just a big diode. This is like a 1000 amp diode. Okay. So it's got a big piece of PN silicon inside and big copper bases and here's the external lead coming in. But you have to seal that from the environment because the contacts inside will otherwise corrode. You got a lot of dissimilar materials and you get galvanic corrosion.

[Tom produces a 1 kW transistor.] This is a 1 kilowatt transistor. Okay. So, it's actually got three leads. You got a lead here, and a lead here, a lead here, a lead here, and a lead here. You can tell which ones are the high current leads compared to the low current emitter. But in any case, you have to make these bonds, and some of these bonds you can make because it's complex in packaging all this together. Some of them can be braze joints, some could be solder joints. Some of them may need to be a cold joint, in which case you basically would have your substrate. You might have a lid. In this case, they're actually showing an electrical resistance weld. This is the lid of the can. Here's your silicon in here. And you're actually going to come down here and squeeze and pass current through here and make a resistance spot weld which later looks like this.

Okay, there. It's a nickel-plated mild steel weld. And they really didn't make a weld. They still got the nickel there, but nonetheless, it's sort of a diffusion bond. It's sort of an activated diffusion bond, if you will. Okay. A nickel plate to keep the iron from oxidizing. And here's your activated bond. You ended up with two nickel surfaces which are just cold pressure forging together. Here's another version of cold pressure welding for aluminum-copper packages. Aluminum-copper don't really weld well because they form intermetallics. Again, your lid, you got some sort of components in here. You put a little projection on here. You come in with force. In this case, it's just force. You see the rounded electrode. Why do we have a rounded tip electrode? To get the shear at the interface, right? I've got to get shear interfacial sliding to extrude out or slide out those impurities. And there's what the joint looks like. You can see the projection was probably this width and it's been folded over. And there's your real bond in here. This is not quite as good a bond over here because it didn't get lots of shear.

And here's another one. I don't know if I can show this one very — how well I can show it without messing up the picture, but essentially you have some electrodes and you — this is an ultrasonic, I think. Actually resistance seam weld, but you can do it ultrasonically too. And when you're all done, you end up with a bond that looks like this. Okay. There's what's at the interface here. Nickel-iron-cobalt lid to package wall joint produced by series electrode. So they're heating it up. The nickel-iron-cobalt is basically the invar alloy, the low coefficient of thermal expansion alloy. They also sometimes do micro arc welding. There's a little micro arc weld on these things, and hopefully you have room that you don't heat up the whole thing and destroy your semiconductor while you're doing that. So anyway, there's lots of different ways, but indium is one of those that can be easily cold welded.

So, okay, any questions? We've been talking about soldering. Those are just kind of cleaning up some things. We've been talking about cold welding. We talked about Young's equation. There are several things we ought to talk about in terms of wetting. You need to get wetting. The whole soldering and brazing process occurs because metals have high surface energy. Okay? They have higher surface energy than any other material by a factor of two or three. Remember that's because you have bonding from several layers deep. Whereas covalent and ionic, it's really just the top surface layer of atoms. Metals, it's the top two or three surface layers. And so you get surface energy contribution from like three times the volume of material.

Well, that means if you can get a liquid metal to wet a solid metal by cleaning the contamination, you will have a very low interfacial energy. Because what you end up with is — you start out with the solid metal, which could be copper, it could be anything else, and you'll put a drop of a liquid metal on top, and you want it to flow across the surface by Young's equation. Except Young's equation only occurs at equilibrium, but that's why it's hard to understand it. But the way you'll get an interfacial energy here between the liquid and the solid — that's, this interfacial energy here will be very low because you got metal bonds, and metals like to satisfy each other's bonds. That gives you a low effective surface energy. And the ceramic fluxes or the organic fluxes have higher interfacial energies, and that's why the metal wants to undermine them and flow across underneath them. The metal's heavy compared to these organics or the molten ceramic fluxes. You don't use barium chloride as a flux because it can be heavier than some of your metals. But you use fluxes that are light and will be displaced by surface tension and the cleaning action of the flux. So that's why soldering and brazing work.

I'm not saying there aren't soldering and brazing processes for ceramics. There are, but they're actually where you actually get a chemical reaction between the metal and the ceramic that gives you a very low interfacial energy. There are not really soldering operations for ceramics. If you can come up with a ceramic solder, the world will beat the path to your door. But in fact, because soldering occurs below 450° centigrade, you don't have as much thermal energy to drive these reactions. In brazing, you can go up to a thousand degrees and you now can have reactive metal components. Like — well, we've worked and other people have worked on trying to come up with a solder which might be tin-titanium. So it might be 95% tin and 5% titanium. Okay. And that will be reactive because the titanium forms a titanium oxide with the ceramic. Okay? But in fact, you have to go to pretty high temperatures, well above the melting point of the tin to do this. In fact, you have to go up to like 600 C usually, which is really in the brazing range, even though you're ending up with a joint that has a melting point in the soldering range. So you have to have that extra temperature to drive the chemical reactions to get things started where the titanium is going to react with the ceramic. So you can get a reactive wetting by forming compounds at the surface.

And in fact I'll show you some of that later. I'm going to talk a little bit about the requirements of a flux and then give you some examples. Someday maybe I'll find some book or some handouts that will allow you to see some of this. [Tom writes on the board.] But you have to have chemical activity in your flux. This is the requirements of flux. It has to be able to react with the surface. And the next one is, has to have spreading. Stability. And the fourth, it should be non-corrosive, at least in the environment it's going to serve. So these are four requirements of your flux if you're going to be doing soldering. And some of these are written very specifically into some military soldering specs for military hardware and electronics.

So the first example that I'll give you is oxalic acid. It turns out that if I want to solder — and the eutectic here is 183 C and it's 37% lead and [63% tin] — acid... you just take a piece of copper, take a torch underneath it to heat it up, put a little solder on the surface, and you put oxalic acid as the flux on top. You'll find as you heat it up, the oxalic acid will start to boil. And then you will see, just as you get to about 183, the solder starts to melt and it starts to flow, but it doesn't get very far. It just stops. It's got a good contact angle, but the problem is oxalic acid boils at 182 C. So this is a problem of thermal stability. It is an acid. It'll clean off the copper oxides. Remember I showed you the wetting test, freshly clean copper, you can get it to flow within less than a second. Well, the flux here will clean it, but then it vaporizes off at the same time it's starting to do its cleaning action, and so it just doesn't stick around to finish the job. So oxalic acid doesn't work.

Another one is glucose. Good old sugar. Okay, acts as a flux, and it will, it can remove some of the copper tarnish, but no spreading. It will essentially — in this one I probably could — you take a copper plate and you'll have your glucose and you'll have your lead-tin on copper. And I probably ought to be able to develop one of these, but supposedly you heat this whole thing up. You get to the melting point of lead-tin. The lead-tin balls up and you can take that little lead-tin ball and run it around the surface, but it has no good contact angle. And so it just remains as a ball. And you'll have a little track. If you take that little ball and you run it around the surface of the copper, you can make a little line of tinned-lead copper without the lead-tin spreading out. So this has a problem of no spreading activity.

So if I'm talking about the requirements of the flux, I've got oxalic acid has no thermal stability. Glucose has no spreading ability. And the last one is abietic acid. Has anyone ever heard of abietic acid before? Okay, abietic acid is an organic acid and it's got a chemical formula that looks terrible. Okay, it's three benzene rings with a bunch — you know, I can't even tell you. I'm not enough of an organic chemist to tell you. Well, here, put it up here. It looks something like that. Okay, that's abietic acid. So I can't even tell you exactly what types of bonds those are. Abietic acid actually is fairly good in a lot of ways. If it's fairly clean copper, you will wet the whole surface quite well and you'll get a good solder joint. But sometimes if your tarnish — low tarnish this is okay as a flux, high tarnish on your copper it's just no good. Because abietic acid will form a copper abietate. So you actually clean the surface of the copper oxide, but it can't be very — it's not a very strong acid. It's used in printing inks. Don't ask me why, but it's often used in printing inks. But at high tarnish, there's not enough activity to clean the surface. So if I go back to my requirements of the flux that it have chemical activity, it doesn't have enough chemical activity.

But if you add just the least little bit of hydrochloric acid to this, it'll wet beautifully. And in fact, this is the basis of all the rosin-base fluxes. What's rosin? Anybody know? Pine tap. Pine tar, tap. So if you go down Georgia and you go out walking in the forest — it's a pine forest — and you look at the trees, and there's this little kind of gold colored material dripping down on the outside of the bark of the trees. It's called rosin. It's the tar, or the juice, the blood of the tree, or whatever you want to call it. And there's a number of uses for rosin. You can bake potatoes in it. Makes the best baked potatoes. Go to Texas Roadhouse. You can tell the different texture. When I was growing up in Atlanta, the next door neighbor used to rosin-bake potatoes on the weekends. Okay. He had a vat of rosin. He'd wrap everything in aluminum foil. He'd put the potato in there and you get this nice fluffy mashed potato — as long as the aluminum foil is nice and tight and you don't get a rosin-tasting potato.

It turns out you can do just as well by just having a vat of hot oil and French-frying the whole potato. And you don't even have to wrap it in aluminum foil. You just throw it — you clean the surface, you know, throw it in the oil, and it will sink to the bottom. And when it pops to the top, it's done. Now, it might take 40 minutes to French-fry a whole potato. But you take that and you open that up and you put the butter on it, it just melts right through there. It's nice fluffy potato. Go to Texas Roadhouse. Look at the skin of the baked potato. It's a little different cuz it's French-fried. Okay. I made about 20 pounds of rosin-baked potatoes for Thanksgiving last year. Okay. Not rosin-baked, I did oil-baked. I was frying turkeys. So I figured, hey, before I fried the turkey, I'd fry some potatoes.

So anyway, abietic acid has the ability to eat off some copper oxide. It has a wonderful surface angle. It spreads well. It has thermal stability. It doesn't have enough chemical activity. If you add a little bit of hydrochloric acid to it or an amine hydrochloride — it can be an organic chloride — just a little bit of chlorine will replace that copper oxide with a copper chloride which then dissolves in the abietic acid rosin flux. So what they talk about in the soldering literature — it may say that you will flux your circuit board with water-white rosin. Now, that little gold stuff coming down the tree is gold because it's got all kinds of junk in it. Okay? But if you distill your rosin, you can get what's called water-white. And water-white actually still is somewhat gold, but if you drop it into a bath of water and quench it from a molten condition, it'll form little white globules as it expands and stuff as it is quenched. So it's called water-white rosin. Many of your military specifications require that you use a chloride-free water-white rosin. You can have what they call — actually might as well go back a little bit.

If you go to specifications for fluxes somewhere in here — this is a handout that you have on solders and soldering. Here we go. So here's a little table. It's hard to read at the top. Various metals. If you want to solder to platinum, gold, copper, silver, tin plate, solder plate — these are easy to solder. You can use rosin fluxes, non-activated, no hydrochloric acid, because these things don't have heavy oxides if the copper is freshly cleaned. And these other things, you basically just melt the surface so you get rid of any oxides. Mildly activated — so if the copper is tarnished a little bit more. Inactivated is — this is — mildly activated is a little bit of chloride, and then activated is a fair amount of chlorides mixed in with the rosin.

Turns out lead, nickel, brass, bronze, rhodium — these are less easy to solder. Why would brass be more difficult to solder than copper? What's the difference, copper and brass? It's got — brass got zinc. Turns out zinc oxide is more stable than copper oxide. And so abietic acid doesn't work very well unless you put a lot of chlorine in there. Then you form zinc chlorides. In fact, zinc chloride fluxes are great fluxes in of themselves for soldering. You get down here to stainless steels and aluminum and bronzes and you find it's getting hard to solder these things. Very difficult to solder. You're going to have to use precoating if you're going to do wave soldering of stainless steel on some circuit board, which we don't usually do. Or precoating could be — you could tin plate the chromium or the stainless steel — or you're going to have to use a zinc chloride flux, which — I'm going to show you why it's so corrosive. The aluminum bronzes have an aluminum oxide coating, very difficult to solder to, and I'll show you something about that. Beryllium and titanium, they're just not solderable. Below 450 C, you don't have enough temperature to break down the titanium oxide or the beryllium oxide. So, you can throw zirconium in here. A lot of your refractory metals with very stable oxides just can't solder them because below 450, some things you just can't get rid of that oxide very easily.

Student: So when you solder something — you don't actually correctly, you know, you don't use the flux correctly — you just kind of solder like, you know, like a sixth grader would. You just dump a drop of solder on and it sticks a little bit but it's going to break off. Is that just a temporary mechanical [bond]?

Sure. Yes. It's mechanically locked. It's basically an adhesive bond, and if you flick it with your fingernail, it's able to fall off. Okay. But it won't have a good contact angle either. Okay. You can tell by just a simple inspection. In fact, they have automatic solder inspection systems which are vision systems, and all they're doing is looking for the contact angle. Okay? They've got an image analysis software, or they'll come in with a laser light and they'll look how the — a line of laser light, how it — what's the profile of that solder joint. If it doesn't show a good low contact angle, you automatically reject it. So there are automated inspection systems, and I'll show you why in a little bit, why you need those.

So some things are not solderable. It turns out there is a way to solder aluminum, and it's called a reaction flux, which is a terrible name because it doesn't react. That's the point, okay, of how it works. The other ones are — you can have chemical dissolution, which is abietic acid. You're dissolving the copper oxide in the rosin. Okay, it becomes copper abietate. Okay, you can have chemical reduction. So you can use hydrogen or chlorides, and you're basically forming copper chlorides, or does — reducing — the hydrogen, or the hydrogen takes the oxygen off the copper and leaves metallic copper.

A reaction flux for aluminum is tin chloride or zinc chloride. And essentially what happens, as you heat up, the aluminum oxide will actually break up the surface because of difference of coefficient of expansion between the aluminum oxide surface and the aluminum underneath. Now, if you do that with regular aluminum in the air — you know, we got the Langmuir 10⁻⁸ atmosphere-seconds — you just fill in those cracks and grow the oxide back. But if you've got a flux of tin chloride or aluminum chloride, you actually get a chemical reaction, and I've just written it for tin here. The tin replaces the aluminum to form aluminum chloride gas. Aluminum trichloride is a gas, and it deposits tin metal. So now I'm soldering a tinned silver, and these little islands of aluminum oxide float away on the solder bath. So if you now have — you have the flux that keeps the air from reforming and bridging — aluminum oxide cracks up the aluminum oxide. You have some solder come in here, and the aluminum oxide floats away, and you end up with a solder joint.

The problem is tin chloride and zinc chloride are extremely hygroscopic. If you leave this solder out for 4 hours in Cambridge exposed to the air — or, not the solder, but the flux — it's no longer any good. It will pick up enough moisture from the air that the tin reacts with the moisture to form tin oxide and water. Okay? Or — and hydrochloric acid, I guess. So tin oxide and hydrochloric acid — you no longer have any fluxing capability. You just destroyed your tin chloride or your zinc chloride. Okay. So I once soldered up something — some aluminum for a demonstration back when I was an assistant professor. This is a few years ago, before you were born. And I got some of this aluminum soldering flux and everything worked great until — and I went and did my little demonstration in class on slip planes. It had to do with deformation and stuff. And the next year I took it off the shelf and it just fell apart in my hands, cuz I had some blind joints and I'd left some of the flux on the inside. Air got on the inside, attacked the solder flux that was the residue, and just corroded the joint within a year. So I had to redo it and make it out of steel and weld it up. Anyway, it was a mess. And now it weighs a ton when I'm trying to do the demonstration for the students. Actually, I haven't done it for 30 years cuz it does weigh a ton.

But nonetheless, there is a reason why chlorides are so harmful for soldering. And I guess I can write it on the board, but I thought I had something here that actually gave you the formula. I guess I'll just write on the [board]. There is an International Institute of Welding classification for soldering fluxes. They call it resin-type flux, which is actually rosin, or you can have a synthetic resin. It can be organic, water-soluble, or not water-soluble. It can be not activated — means no halogens. Doesn't have to be chlorine. It could be fluorine. It could be bromine. We don't usually use iodine for other reasons. And then three is not halogen-activated. There are ways to activate fluxes with organics that will reduce the copper oxide. And the flux form can be liquid, solid, or paste. So there's a classification here, and you can specify a type one flux 23A. Okay? So it'd be a liquid, not halogen-activated, resin-type. Okay.

Is there a question anyway? But let me show you what happens. And unfortunately, this is not quite as intuitive as it used to be for students. It used to be intuitive because if you ever did any maintenance on your car battery, you would see this white deposit that forms on the lead terminals of your car battery. Except now I can hear it. I guess I'll have to write it down for you. Okay. If you form — well, you have some lead oxide on the terminals of your car battery, and this used to be the old types of unsafe terminals that you had a little post of lead sticking up and you had a clamp and you just clamp to it. Now we actually have a stainless steel screw cast into the lead terminal and you just tighten the screw up against the flat piece of lead. You can get the same thing, but they actually have rubber boots and stuff to keep the moisture out. And I'll show you why you want to keep the moisture out.

If you have some chlorides, such as road salt, that will form a lead chloride plus water. [Lead] chloride will react with the CO₂ and moisture in the air to form a lead [carbonate] here. And it regenerates the hydrochloric acid. So this thing just runs around in a circle. This chemical reaction spinning off lead carbonate. It's not lead oxide that forms on — it is lead oxide that forms on your terminals. But if you have any chlorides left over, such as New England road salts that splash up onto your lead battery in your engine compartment, you will actually form this white lead carbonate growing at the anode. Corrosion occurs at the anode. So your positive terminal will grow this white scum, and you can go to an auto parts store and they'll sell you these little jellies that you can put on there that will essentially dissolve the lead carbonate. Essentially, you're doing something that's trying to tie up the chloride. But if you can keep the chloride away, you don't have a problem.

Well, now you can see why if you don't clean off your flux residue, or you use a halogen-activated flux and you don't clean it off completely, very small amounts of chlorine just lead to corrosion in the air. And in fact, if you're talking about very small solder joints such as you have on some sort of printed circuit board where your joints are very small, it doesn't take more than a year's worth of corrosion — because the joints are so thin and so small — and all of a sudden you've corroded away your joint. So a significant problem in making circuit boards is a way to encapsulate the semiconductor and those joints to keep the moisture out. Okay? You'd love to run them in a vacuum, but that's not very economical to run your cell phone in a vacuum. Okay. Although a lot of what goes into the cell phone — oh, no, that's never — okay, that's another problem.

Let me show you another kind of — I told you that no one has really come up with a solution. They want to get the lead out of solder because they've decided that children are growing up stupid in this country because there's lead contamination everywhere. I don't think that's why they're growing up stupid. I think it's genetic. Their parents were stupid and they are stupid. But anyway, so if you look at this — this is tin solders, tin-lead, tin-silver, tin-indium, tin-bismuth — this is the excess temperature for tin-base solders for the spreading ratio. So this is how much it flows.

For lead-tin, you have to have an excess temperature of about — what's going on here? That's a funny scale. Anyway, yeah, of about 10° centigrade. It'll spread out a factor of 10 over its original area if you give it 10° centigrade above 183 C. If we're talking the eutectic solder, tin-silver, that's a little bit pricey, but you've got to have three times that. Tin-indium, you got to have a 50 to 75° excess temperature. Even though tin-indium melts at like 156° centigrade, you got to get up to 225 C before it really starts to flow. This really gets back to some of these activities that I just erased. Okay, the spreading activity, the chemical reaction of these other things is not as — anywhere near as good as lead-tin. And if you look, these are indium-base. Indium-based solders all have high superheats, if you will. If you look at lead-base — well, here's lead-tin. And even the other lead-based solders are nowhere near as good as lead-tin. If you look at bismuth-base, okay, or if you look at silver-base — silver-tin and lead-tin are the two that flow close to the melting point without too much superheat. And that means if I'm doing wave soldering or anything like that, they're much better.

Now, a lot of people when they first started looking for lead-free solders looked at bismuth alloys. Okay? And I remember going to — there was a hundred million dollars a year being spent on coming up with tin-bismuth, or primarily tin-bismuth. And bismuth was cheaper than lead. Okay. Does anyone have any idea why bismuth — by a choice of bismuth-tin would be such a terrible choice? Because it would destroy the recyclability of a billion tons of steel each year. It turns out you can get lead out of steel. You can oxidize it out when you remelt the steel. You cannot get bismuth out of steel. And bismuth goes to the grain boundaries of the steel. Where does the majority — or not the majority, actually probably the largest single fraction, not the majority — of steel recycling come from? Automobiles. And there are electrical solder joints in automobiles. And these people wanted to get the lead out of automobiles by — well, they've never replaced the lead acid battery. That's another thing we can talk about. We're still using lead acid batteries, but that's sort of localized and you can unbolt it and send that to the battery recycling center. But solder joints, they're all through the car. You're going to have someone go in there and take out all the solder joints in a car before you try to recycle it? It cost a fortune to recycle it.

There is no way that we have in the way we make steel today that can take out lead contamination or bismuth contamination. You can't oxidize it out. You oxidize out the iron before you oxidize out the bismuth. Okay? Iron oxide is much more stable than — in a lead bath, than a little bit of bismuth oxide. So I used to look at this and roll my eyes and say these people don't understand the systems implications of what they're trying to do. So it turns out, I think nowadays in the last 10 years, a lot of people have figured that out. And the system that most people are using are not even these systems. They have — well, they actually tend to be tin-antimony systems, which are not even on here. Where's my tin systems? My tin systems. Okay. They don't even list tin-antimony.

Now, they first got the lead out of plumbing. I think it was like 1978, the Commonwealth of Massachusetts changed the plumbing code, and you could not use lead-based solders in your plumbing for your household potable water. And they had to go to — they first went to tin-silver, and you can see why they did. And it was pricey, but it's only 5% silver, and silver wasn't quite as expensive back then as it is now. But they then went to tin-antimony, which has got like anywhere from 3 to 10%. And some of them are tin-antimony-copper. You put a little copper in there, raises the melting point a little bit. But anyway, tin-antimony — but there's a problem with that. If you talk to a plumber — and soldering, remember, is not just the way we make electrical connections. It's the way we make plumbing joints.

And lead-tin was wonderful because if I had a gap between 1,000th and 4,000ths on that clearance, gap clearance, the lead would fill it. It flows in very well into very thin joint. It also will bridge the gap of a 4,000ths or 5,000ths inch joint. 10,000ths inch joint, no, it's just going to all flow away. Forget it. You got a problem. But up to 1 to 4,000ths gap on the radius, it will flow in and it will stay there until it solidifies and you end up with a solid joint. And so it used to — you talk to nowadays an old plumber, because — but when they used to plumb up the system, they would then fill it up with air or with water, and they'd go and do a leak check, and if it's a lead-tin system, you never had a leak. Or if you had a leak, it was one out of 200 joints. With the tin-silver or tin-antimony type solders they use today, tin is very fluid. It's great on a 1,000ths thick joint, but typically these things have — you know, if you're just talking about a copper pipe going into a copper elbow that's deformed to shape it and form it, they've easily got 4,000ths clearance in terms of normal process manufacturing variation. And when they solder up the whole system and they go do the leak check, they may have 10% leaks, which they got to go back and fix, but it adds a cost, okay, to that whole thing. And so back in the 1980s, the plumbers were just cursing this requirement that you get rid of lead-tin solder, because lead-tin had some very nice properties.

Okay. Some of this is just sort of catching up a number of different topics. Here on solders, we're going to get into — tomorrow I will be lecturing and we'll get into electronic packaging and stuff. But this is something which — this is a general principle, not just — oops — of what it costs to do repairs at different stages of the manufacturing process. And note this repair cost is on a log scale. So if you're doing pre-solder visual testing, you're looking to see if the solder all got placed where it's supposed to be before you put it into the wave solder or the furnace or whatever that's going to melt the solder. And it doesn't cost you much to spot where you forgot to put the solder before you make the joint.

If you are now doing a post-solder inspection, the price goes up by more than a factor of 10. It costs about 10 bucks to find the bad joint on the circuit board, repair it. Okay. Systems testing — if you now put this all into some bigger something or other, whether it's size of a bread box or whether it's size of a relay rack, you're now talking something on the order of $50. You might find the circuit, you got to pull it out of the rack, you got to reassemble it, and so now the price goes up. If you do it as a field repair, it might cost you three, $400 to send a technician out there to find it and hand-solder it. Okay? But this is not just soldering. This is just in general. You talk about virtually any type of manufactured product. If you catch the defects early on, it's about an order of magnitude difference at each one of these steps. So, what people learned is quality control is important.

And I guess the last thing I'll do before we go — I need to give you that. We can talk about it a little bit. Before I — rather than going into something new, let me just tell you a story about pagers. Back around 1990, pagers — the pager business, there had been pagers back in the 1980s, but that business initially of pagers got sent to Asia. But in 1990 or so, 1989, Motorola was very innovative, down in Boynton Beach, Florida. They decided to bring the pagers back to manufacture them, assemble them in the United States. It turns out today, I'm sure pagers — this is all done on software on a chip, but chips weren't as powerful back then. They weren't as inexpensive 25 years ago. And there were like four or five components, cuz every pager has to have a different frequency that's being paged, right? So there are like four or five different components.

And if you ordered a pager in the United States, it would be six weeks in 1988 for you to get your pager, because they'd have to send the order to Asia, have the thing go in line for production, be produced, shipped back — 6 weeks before you get your pager. Motorola decided that they could have a plant in Florida that might cost more to assemble, but they could get the pager to you within 3 to 5 days of ordering, because you didn't have to do all this stuff across the Pacific Ocean. And they streamlined their billing procedure so that if you ordered, the order went immediately to Chicago, and then from Chicago it went immediately by computer to Boynton Beach, and got in line for production within a very short time. Plus, they built an automated assembly line that took a lot of the handwork that they were doing in Asia. And so this whole thing was automated. It was assembly line — I saw it, wasn't much bigger, maybe twice the size of this room. Okay, it wasn't all that expensive. And so they brought the pagers back, and they had this competitive advantage that they could get you your pager within a week rather than 6 weeks.

Well, it turns out there was another significant advantage to the guy at Motorola who had conceived of all of this. He said, "We will not have a rework area." Okay, so I told you the post-solder repair. The rule of thumb in the industry was 6% of your product had to be reworked. And he said, "I'm not going to build a room to do rework. If it doesn't work, we throw it out." And people said, "You're going to kill your profitability." He says, "Nope. We're going to fix the problems before they show up." And so they didn't build it. Everybody said it was going to be a disaster. Turns out they fixed the problems and they had almost no rework. And so this rule of thumb in the industry, if you always build in 6% rework — that was what was determining the 6% rework. It was a self-fulfilling prophecy. People — they had engineers who would fix the process until they got to 6% and the rework area wasn't overloaded, and then they would quit fixing that process and go on to some other fire. But when they had no rework area, they would keep on fixing the process. And this is when they first started talking about six sigma quality control and things.

But I'll tell you the exact same thing happened in a Ford plant, a Ford Mustang plant. Turns out at the end of the line of assembling the vehicles, they filled them up with — they're filled up with gas, and a guy was supposed to get in there, turn the key, and drive it out to the lot to be loaded onto the railroad cars, etc. If the car didn't start when he turned the key, they had a little tow motor vehicle come and pull the car out to the repair area to figure out why the engine wouldn't start. New plant manager came in. He says, "No more tow motors." They said, "What do you mean?" He said, "If it doesn't start, you push it all 250 yards to the repair area." Well, you want to know something? The guys who had to push the cars made sure — those engineers made sure — that the cars started every time, and all of a sudden they were all starting. So once they gave them the proper incentive — either push it or start it — okay, the problems went away. So anyway, so it works not just in soldering but in Ford Mustangs. So, see you tomorrow.