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Of covalent bonds and muon catalyzed cold fusion.

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A hydrogen molecule consists of two protons held together by a covalent bond. One way to think of such bonds is to imagine that there is only one electron is directly involved as shown below. The bonding electron only spends 1/7 of its time between the protons, making the bond, the other 6/7 of the time the electron shields the two protons by 3/7 e– each, reducing the effective charge of each proton to 4/7e+.

We see that the two shielded protons will repel each other with the force of FR = Ke (16/49 e2 /r2) where e is the charge of an electron or proton, r is the distance between the protons (r = 0.74Å = 0.74×10-10m), and Ke is Coulomb’s electrical constant, Ke ≈ 8.988×109 N⋅m2⋅C−2. The attractive force is calculated similarly, as each proton attracts the central electron by FA = – Ke (4/49) e2/ (r/2)2. The forces are seen to be in balance, the net force is zero.

It is because of quantum mechanics, that the bond is the length that it is. If the atoms were to move closer than r = 0.74Å, the central electron would be confined to less space and would get more energy, causing it to spend less time between the two protons. With less of an electron between them, FR would be greater than FA and the protons would repel. If the atoms moved further apart than 0.74Å, a greater fraction of the electron would move to the center, FA would increase, and the atoms would attract. This is a fairly pleasant way to understand why the hydrogen side of all hydrogen covalent bonds are the same length. It’s also a nice introduction to muon-catalyzed cold fusion.

Most fusion takes place only at high temperatures, at 100 million °C in a TOKAMAK Fusion reactor, or at about 15 million °C in the high pressure interior of the sun. Muon catalyzed fusion creates the equivalent of a much higher pressure, so that fusion occurs at room temperature. The trick to muon catalyzed fusion is to replace one of the electrons with a muon, an unstable, heavy electron particle discovered in 1936. The muon, designated µ-, behaves just like an electron but it has about 207 times the mass. As a result when it replaces an electron in hydrogen, it forms form a covalent bond that is about 1/207th the length of a normal bond. This is the equivalent of extreme pressure. At this closer distance, hydrogen nuclei fuse even at room temperature.

In normal hydrogen, the nuclei are just protons. When they fuse, one of them becomes a neutron. You get a deuteron (a proton-neutron pair), plus an anti electron and 1.44 MeV of energy after the anti-electron has annihilated (for more on antimatter see here). The muon is released most of the time, and can catalyze many more fusion reactions. See figure at right.

While 1.44MeV per reaction is a lot by ordinary standards — roughly one million times more energy than is released per atom when hydrogen is burnt — it’s very little compared to the energy it takes to make a muon. Making a muon takes a minimum of 1000 MeV, and more typically 4000 MeV using current technology. You need to get a lot more energy per muon if this process is to be useful.

You get quite a lot more energy when a muon catalyzes deuterium fusion or deuterium- fusion. With these reactions, you get 3.3 to 4 MeV worth of energy per fusion, and the muon will be ejected with enough force to support about eight D-D fusions before it decays or sticks to a helium atom. That’s better than before, but still not enough to justify the cost of making the muon.

The next reactions to consider are D-T fusion and Li-D fusion. Tritium is an even heavier isotope of hydrogen. It undergoes muon catalyzed fusion with deuterium via the reaction, D+T –> 4He +n +17.6 MeV. Because of the higher energy of the reaction, the muons are even less likely to stick to a helium atom, and you get about 100 fusions per muon. 100 x 17.6 MeV = 1.76 GeV, barely break-even for the high energy cost to make the muon, but there is no reason to stop there. You can use the high energy fusion neutrons to catalyze LiD fusion. For example, 2LiD +n –> 34He + T + D +n producing 19.9 MeV and a tritium atom.

With this additional 19.9 MeV per DT fusion, the system can start to produce usable energy for sale. It is also important that tritium is made in the process. You need tritium for the fusion reactions, and there are not many other supplies. The spare neutron is interesting too. It can be used to make additional tritium or for other purposes. It’s a direction I’d like to explore further. I worked on making tritium for my PhD, and in my opinion, this sort of hybrid operation is the most attractive route to clean nuclear fusion power.

Robert Buxbaum, September 8, 2022. For my appraisal of hot fusion, see here.

The Brexit, Trump, Johnson anti-crash

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Before Brexit, I opined, against all respectable economists, that a vote for Bexit would not sink the British economy. Switzerland, I argued, was outside the EU, and their economy was doing fine. Similarly, Norway, Iceland, and Israel — all were outside the EU and showed no obvious signs of riots, food shortages, or any of the other disasters predicted for an exited Britain. Pollsters were sure that Britain would vote “No” but, as it happened, they voted yes. The experts despaired, but the London stock market surged. It’s up 250% since the Brexit vote.

Lodon stock market prices from January 2016 through the Brexit vote, August 2016, to the Boris Johnson election, August 2019. The price has risen by more than 250%.

A very similar thing happened with the election of Trump and of Boris Johnson. In 2016 virtually every news paper supported Ms Clinton, and every respectable economic expert predicted financial disaster if he should, somehow win. As with Brexit, the experts were calmed by polls showing that Trump would, almost certainly lose. He won, and as with Brexit, the stock market took off. Today, after a correction that I over-worried about, the S+P index remains up 35% from when Trump was elected. As of today, it’s 2872, not far from the historic high of 3049. Better yet, unemployment is down to record levels, especially for black and hispanic workers, and employment is way up, We’ve added about 1% of adult workers to the US workforce, since 2017, see Federal Reserve chart below.

Returning to Britain, the economic establishment have been predicting food shortages, job losses and a strong stock market correction unless Brexit was re-voted and rejected. Instead, the ruling Conservative party elected Boris Johnson to prime-minister, “no deal” Brexiter. The stock market responded with a tremendous single day leap. See above

Ratio of Civilian Employment to US Population. Since Trump’s election, we’ve added about 1% of the working age US population to the ranks of the employed.

You’d think the experts would show embarrassment for their string of errors. Perhaps they would save some face by saying they were blinded by prejudice, or that their models had a minor flaw that they’ve now corrected, but they have not said anything of the sort. Paul Krugman of the New York Times, for example, had predicted a recession that would last as long as Trump did, and has kept up his predictions. He’s claimed a bone rattling stock crash continuously for nearly three years now, predicting historic unemployment. He has been rewarded with being wrong every week, but he’s also increased the readership of the New York Times. So perhaps he’s doing his job.

I credit our low un-employment rate to Trump’s tariffs and to immigration control. When you make imports expensive, folks tend to make more at home. Similarly, with immigration, when you keep out illegal workers, folks hire more legal ones. I suspect the same forces are working in Britain. Immigration is a good thing, but I think you want to bring in hard-working, skilled, honest folks to the extent possible. I’m happy to have fruit pickers, but would like to avoid drug runners and revolutionaries, even if they have problems at home.

I still see no immediate stock collapse, by the way. One reason is P/E analysis, in particular Schiller’s P/E analysis (he won a Nobel prize for this). Normal P/E analysis compares the profitability of companies to their price and to the bond rate. The inverse of the P/E is called the earnings yield. As of today, it’s 4.7%. This is to say, every dollar worth of the average S+P 500 stock generates 4.7¢ in profits. Not great, but it’s a lot better than the 10-year bond return, today about 1.5%.

The Schiller P/E is an improved version of this classic analysis. It compares stock prices to each company’s historic profitability, inflation adjusted for 10 years. Schiller showed that this historic data is a better measure of profitability than this year’s profitability. As of today, the Schiller P/E is 29.5, suggesting an average corporate profitability of 3.5%. This is still higher than the ten-year bond rate. The difference between them is 2%, and that is about the historic norm. Meanwhile, in the EU, interest rates are negative. The ten year in Germany is -0.7%. This suggests to me that folks are desperate to avoid German bank vaults, and German stocks. From my perspective, Trump, Johnson, and the Fed seem to be doing much better jobs than the EU bankers and pendents.

Robert E. Buxbaum, August 16, 2019.

Less than 1 year to the crash

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Stock market crashes happen for a reason, and generally the reason is that owning stock is seen as less profitable than owning bonds, gold, guns, or hundred-dollar bills stuffed into one’s mattress. For this essay, I thought I might explain the reasoning behind the alarm bells that virtually every economist has been sounding. For the last year and a half they’ve been sure a severe correction is imminent. The reason has to do with price and predictions of profitability.

Let’s begin with Nobel Laureate economist, Paul Krugman of the New York Times. He has been predicting severe job losses, and a permanent stock collapse since Trump’s election in November 2016. Virtually every week he announces that the end is near, and every month the economy looked better. A lesser man would give up, but he has not. Why? Mostly it’s his hatred of all things Trumpian: Krugman can not accept that Trump could avoid destroying the economy, and con not imagine that any investor would see things otherwise.

Apparently some folks felt otherwise, and caused unemployment to drop and the market to rise. but then, in September 2017, Krugman’s dire predictions were echoed by Robert Schiller, 2013 Nobel winner, and author of a textbook the majority of schools use to teach market analysis. Robert Schiller, has argued that valuations are extremely expensive. “This stock market bears striking similarities to that of 1929. “The market is about as highly priced as it was in 1929,” “In 1929 from the peak to the bottom, it was 80 percent down. And the market really wasn’t much higher than it is now in terms of my CAPE [cyclically adjusted price-to-earnings] ratio. So, you give pause when you notice that.”

What Schiller is referring to is his particular version of the price to earnings ratio, the price of the average stock share divided by the amount of the average earnings per share. Schiller’s CAPE version uses the ten-year, inflation-averaged earnings, rather than today’s earnings, and finds the ratio is high, as the graph below shows. When he made these comments, this ratio was 25, nearly as high as the 1929 peak. The ratio is now higher, 32.74, higher than it stood on “Black Tuesday.” Why this number is important is that the profitability of a stock-share is merely the inverse of the Price/ Earnings ratio. The current ratio, 32.74 suggests that the average dollar’s worth of shares will return about 3.05% (1/32.74 = 3.05%). By comparison, one could buy a five-year treasury bond and get 2.96%. That’s hardly less, and federal bonds are totally safe. More alarming yet, the Federal Reserve has indicated that it will continue to raise interest rates at planned rate of 1%/year for at least the next year. At some point, people will decide bonds are the far better bargain, and will exit stocks en-mass. And then it’s crash-city, or so the theory goes.

The Schiller Price to Earnings ratio as of July 27, 2018. It suggests a crash is past due.

The Schiller Price to Earnings ratio as of July 27, 2018. It suggests a crash is past due.

Shown above is a historical plot of Schiller’s particular version of the price to earnings ratio based on the S+P 500 index, with data going back to 1880. It’s argued that his version using a ten-year, trailing average of corporate profits, is better than the non-adjusted, one year P/E ratio: the version you find in the newspapers. In the newspaper version, the peaks don’t show up until just after the crash because company profits tend to spike along with prices. In this version, profits can’t exactly spike, and  stock crashes show up as valuation peaks. The crash is seen as a consequence to high values of the Schiller P/E.  In terms of CAPE, we are at a more dangerous spot than in 1929. We are more exuberant than in 2008, or when Alan Greenspan warned of irrational exuberance. Schiller: “you give pause when you notice that.”

Schiller Price to earnings ratios are a good predictor of future stock prices. We are past the end of this chart, suggesting a significant loss of stock value ahead.

Schiller Price to earnings ratio plotted versus 20 year stock return. The higher the Schiller P/E, the lower the return. We are past the end of this chart suggesting we should expect a significant loss of capital value.

Stock pull-backs are sometimes gradual, as in 1968 through 1982, but more often the pullback is sudden, a crash. People typically expect a stock return in excess of bonds of 2% or so. They sometimes accept less, and sometimes demand more. Schiller calls the cause “animal spirits.” The fear is that investors will suddenly go back to the historical norm and demand of stocks 2% more return than the 3.05% they get from bonds. If they’d suddenly demand a 5.05% return on stocks to balance, the stock prices would fall by 40%. If the crash happened now, it would take a 40% drop in stock prices to raise the earnings ratio to 5.05%. But if they wait a year, until after the Fed raised the interest rate to 3.5%, we’d expect a greater pull-back 50% or so, a major crash. As early as last year, Schiller has advised moving out of US stock into foreign stocks, particularly European, noting that the US market was  the most expensive in the world. I don’t agree that Europe is a safe haven, but agree that a crash is likely given current return rates, snd the treasury plan to raise interests by 1% over the next year.

Schiller claims that the reason the recession has not hit so far is that people trust Trump. I would not have expected a comment like that from a Yale economist, especially given the constant carping from the TV news. Still Schiller may be on to something. The stock market went up dramatically after the Trump election. There are some advantages to a narcissist president. It also seems Trump’s tariffs are helping to provide jobs, as I predicted. In this quarter, the GDP rose at an impressive 4.1% rate. Gains came even where you’d expect otherwise. US soybean exports rose by 9600% despite a boycott from China. If the economy keeps going like this it might be as much as a year before the correction. A likely scenario is that the Fed raises interest rates, growth slows to 2.5% or less, and with bond interest rates at 3.5% people will get out of stocks in a big way. My expectation is that China will suffer too, and with it Europe. With luck, the Fed will then lower interest rates to 2%, or so. In my opinion interest rates should matches the inflation rate, more or less. I don’t know why the Federal Reserve does not do this, but instead swings its interest rates from very high to low, now aiming for a far excess of inflation rate. I suspect it’s mistake, one that we will pay for soon.

Robert Buxbaum, July 29, 2018. My only other stock analysis post was on bitcoin, In December 2017 I thought it had gone about as far as it would go. Shortly there-after bitcoin value crashed. I hope I don’t cause a crash

Much of the chemistry you learned is wrong

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When you were in school, you probably learned that understanding chemistry involved understanding the bonds between atoms. That all the things of the world were made of molecules, and that these molecules were fixed proportion combinations of the chemical elements held together by one of the 2 or 3 types of electron-sharing bonds. You were taught that water was H2O, that table salt was NaCl, that glass was SIO2, and rust was Fe2O3, and perhaps that the bonds involved an electron transferring between an electron-giver: H, Na, Si, or Fe… to an electron receiver: O or Cl above.

Sorry to say, none of that is true. These are fictions perpetrated by well-meaning, and sometime ignorant teachers. All of the materials mentioned above are grand polymers. Any of them can have extra or fewer atoms of any species, and as a result the stoichiometry isn’t quite fixed. They are not molecules at all in the sense you knew them. Also, ionic bonds hardly exist. Not in any chemical you’re familiar with. There are no common electron compounds. The world works, almost entirely on covalent, shared bonds. If bonds were ionic you could separate most materials by direct electrolysis of the pure compound, but you can not. You can not, for example, make iron by electrolysis of rust, nor can you make silicon by electrolysis of pure SiO2, or titanium by electrolysis of pure TiO. If you could, you’d make a lot of money and titanium would be very cheap. On the other hand, the fact that stoichiometry is rarely fixed allows you to make many useful devices, e.g. solid oxide fuel cells — things that should not work based on the chemistry you were taught.

Iron -zinc forms compounds, but they don't have fixed stoichiometry. As an example the compound at 60 atom % Zn is, I guess Zn3Fe2, but the composition varies quite a bit from there.

Iron -zinc forms compounds, but they don’t have fixed stoichiometry. As an example the compound at 68-80 atom% Zn is, I guess Zn7Fe3 with many substituted atoms, especially at temperatures near 665°C.

Because most bonds are covalent many compounds form that you would not expect. Most metal pairs form compounds with unusual stoicheometric composition. Here, for example, is the phase diagram for zinc and Iron –the materials behind galvanized sheet metal: iron that does not rust readily. The delta phase has a composition between 85 and 92 atom% Zn (8 and 15 a% iron): Perhaps the main compound is Zn5Fe2, not the sort of compound you’d expect, and it has a very variable compositions.

You may now ask why your teachers didn’t tell you this sort of stuff, but instead told you a pack of lies and half-truths. In part it’s because we don’t quite understand this ourselves. We don’t like to admit that. And besides, the lies serve a useful purpose: it gives us something to test you on. That is, a way to tell if you are a good student. The good students are those who memorize well and spit our lies back without asking too many questions of the wrong sort. We give students who do this good grades. I’m going to guess you were a good student (congratulations, so was I). The dullards got confused by our explanations. They asked too many questions, and asked, “can you explain that again? Or why? We get mad at these dullards and give them low grades. Eventually, the dullards feel bad enough about themselves to allow themselves to be ruled by us. We graduates who are confident in our ignorance rule the world, but inventions come from the dullards who don’t feel bad about their ignorance. They survive despite our best efforts. A few more of these folks survive in the west, and especially in America, than survive elsewhere. If you’re one, be happy you live here. In most countries you’d be beheaded.

Back to chemistry. It’s very difficult to know where to start to un-teach someone. Lets start with EMF and ionic bonds. While it is generally easier to remove an electron from a free metal atom than from a free non-metal atom, e.g. from a sodium atom instead of oxygen, removing an electron is always energetically unfavored, for all atoms. Similarly, while oxygen takes an extra electron easier than iron would, adding an electron is energetically unfavored. The figure below shows the classic ion bond, left, and two electron sharing options (center right) One is a bonding option the other anti-bonding. Nature prefers this to electron sharing to ionic bonds, even with blatantly ionic elements like sodium and chlorine.

Bond options in NaCl. Note that covalent is the stronger bond option though it requires less ionization.

Bond options in NaCl. Note that covalent is the stronger bond option though it requires less ionization.

There is a very small degree of ionic bonding in NaCl (left picture), but in virtually every case, covalent bonds (center) are easier to form and stronger when formed. And then there is the key anti-bonding state (right picture). The anti bond is hardly ever mentioned in high school or college chemistry, but it is critical — it’s this bond that keeps all mater from shrinking into nothingness.

I’ve discussed hydrogen bonds before. I find them fascinating since they make water wet and make life possible. I’d mentioned that they are just like regular bonds except that the quantum hydrogen atom (proton) plays the role that the electron plays. I now have to add that this is not a transfer, but a covalent spot. The H atom (proton) divides up like the electron did in the NaCl above. Thus, two water molecules are attracted by having partial bits of a proton half-way between the two oxygen atoms. The proton does not stay put at the center, there, but bobs between them as a quantum cloud. I should also mention that the hydrogen bond has an anti-bond state just like the electron above. We were never “taught” the hydrogen bond in high school or college — fortunately — that’s how I came to understand them. My professors, at Princeton saw hydrogen atoms as solid. It was their ignorance that allowed me to discover new things and get a PhD. One must be thankful for the folly of others: without it, no talented person could succeed.

And now I get to really weird bonds: entropy bonds. Have you ever noticed that meat gets softer when its aged in the freezer? That’s because most of the chemicals of life are held together by a sort of anti-bond called entropy, or randomness. The molecules in meat are unstable energetically, but actually increase the entropy of the water around them by their formation. When you lower the temperature you case the inherent instability of the bonds to cause them to let go. Unfortunately, this happens only slowly at low temperatures so you’ve got to age meat to tenderize it.

A nice thing about the entropy bond is that it is not particularly specific. A consequence of this is that all protein bonds are more-or-less the same strength. This allows proteins to form in a wide variety of compositions, but also means that deuterium oxide (heavy water) is toxic — it has a different entropic profile than regular water.

Robert Buxbaum, March 19, 2015. Unlearning false facts one lie at a time.