Zirconium, #40

The metallic element Zirconium is twice as abundant in the earth’s crust as either copper or zinc. It it ten times more abundant than lead. Zirconium is not found in nature in its native state. It is always bound up in compounds, the most common of which is zircon, a neo-silicate, ZrSiO4.

Zircon is hard and dense and can be cut and polished as a semi-precious gemstone. It is also used directly in many commercial applications such as refractories, metal molds, and laboratory crucibles. About 60 million tonnes are mined annually. Of that quantity about one million tonnes of pure zirconium metal is extracted.

Zirconium metal is resistant to corrosion and thus used as an alloying agent. Pure zirconium is used as cladding for nuclear reactor fuels.

Cubic zirconia is the synthetic oxide form (ZrO2) of zirconium. It is used as a substitute for diamonds. The natural form of zirconia is too rare and thus it has to be made in the lab.

Zirconium is not a biologically active metal and humans consume a few milligrams of it every day in their food and water.

Here’s a zircon specimen from Crystal Classics Fine Minerals:


No, not the Hoagy Carmichael song. I mean literal stardust—the stellar debris that makes up the stuff of the universe. At least the universe we know about!

Astronomy Picture of the Day (or APOD to its aficionados) is the best site on the internet. Today they gave us a genesis story from the Book of Chemistry:

We are all stardust. Everything is. We only share our atoms with the earth and other living things. They don’t belong to us. We are like words on a Scrabble board. Assembled and displayed for oh-so-brief a time and then broken down and scrambled up again.

This fact alone should liberate humankind from prejudice. We are all just dust devils. We swirl into existence and swirl out again in the blink of an eye. We all have the same origin. We all have the same fate. And, to reiterate, we are all made of the same stuff, and none of that stuff is ours in any sense of the word. It’s just a temporary organization that results in something amazing.

The Book of Genesis has its own creation story, of course:

Then the Lord God formed a man from the dust of the ground and breathed into his nostrils the breath of life . . . (2:7 NIV)

There’s that dust again. Dust is an old Saxon word and similar words appear in Norse and German. It can mean “smoke” or “vapor” as well as “meal-dust” (the fine debris from grinding grain).

We’ve been re-watching Breaking Bad and we were treated to Mr. White asking his class “what is the subject of chemistry about?” One student suggested “it’s about chemicals.” But Mr. White said, “no, it’s about change.”

Next time you are dusting think about the stuff you are sweeping away as the foundation materials of a future world!


There are fourteen possible calendars. How so, you ask? Take this notion that we have 52 weeks in a year. 52 x 7 = 364. That means a year is really 52 weeks plus one day.

That one day could be any of seven possible days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday. There’s no rule that says a year has to start on a particular day of the week!

If a year starts on a Sunday then the next year will start on a Monday, and the year after that on a Tuesday, then Wednesday, et cetera.

That’s where we get seven possible calendars. One for each day of the week. January 1st can fall on M, Tu, W, Th, F, Sa, or Su.

How do we get to fourteen? Easy: 7 x 2 = 14.

Not all years are 365 days. Some are 366 days. We call them Leap Years. The Leap Years add another wrinkle. We need a Leap Year version for each of our seven possible calendars. Thus there are fourteen.

You can re-use your calendars. Sounds weird, I know, but it’s true. Look up “Perpetual Calendar” in the almanac. Or go to this website.

2023 is classified as “Calendar 1.” This is arbitrary of course. But it makes sense as the year starts on Sunday and is not a Leap Year. Calendar 2 starts on Monday, Calendar 3 on Tuesday, you get the drift. Calendar 8 is, naturally, the Leap Year variant of Calendar 1.

Your old 2006 and 2017 calendars will work for 2023.

Your old 2022 calendar (Calendar 7) will work in 2033 and again in 2039.

The earth takes its own time traveling around the sun. It doesn’t care about our time-keeping schemes. We have to adjust to the physical reality. Plus there’s more than one way to measure a “year.” If you reckon a year by the stars, that is, you wait for the sun to return to the same place relative to its stellar background, that takes 365.2563 days give-or-take a few decimals. This is known as a sidereal year and is based on the idea of a fixed frame of reference, in this case the background constellations. The other way is to use geometry. If the sun moves 360 degrees—one complete revolution—relative to some starting point, that’s a tropical year. It’s about 356.2422 days from solstice to solstice. That’s 20 minutes shorter than the sidereal year. That extra 1/4 day (~0.25) or so is why they add a Leap Day every four years.

Myself, I count years from birthday to birthday. My year starts and ends on November 13th!

Happy New Year, everyone.

Oxygen, #8

Oxygen is the third-most abundant element in the Solar System after Hydrogen and Helium. Oxygen makes up about 50% (by weight) of the Earth’s crust and about 20% (by volume) of the atmosphere.

Of course we all know that animals need oxygen for respiration. You can live for a month (maybe) without food. A few days without water. But mere minutes without oxygen.

Oxygen supports combustion. We’ve all blown on a flame to help it grow. Metabolism is not much different than combustion. We eat carbohydrates and they “burn” slowly in our gut, releasing energy and by-products like carbon dioxide.

In a pure oxygen environment a small spark could become a conflagration. Even the pipes and vessels used to contain gaseous or liquid oxygen could be consumed in a fire if one got started. It may be essential for life but it can also be a killer!

Oxygen is highly reactive and will combine readily with most things. Many of our important ores are oxides and they require a lot of energy to reduce them to base metals. Smelting iron ore into steel is the largest use of commercial oxygen. Added to the mix in the blast furnace it scrapes away carbon and sulfur impurities from the iron by forming, you guessed it, the oxides CO and SO2.

And then there’s that stuff we hear a lot about: antioxidants. We are supposed to eat blueberries by the sackful to prevent cancer and other maladies. What’s up with that?

Oxygen, in gaseous form, is diatomic. That is, two atoms combine to make an O2 molecule. This is the good stuff we need to live. Unfortunately once we get this molecule in our system it gets ripped apart and the individual oxygen atoms and ions form new combinations. The free radicals created cause serious damage to cells and tissues. What is necessary to life is also toxic.

Fortunately we have stuff like this:

That’s a model of Vitamin C, also known as ascorbic acid. This is a dietary antioxidant. The others are Vitamin A and Vitamin E. These help to inhibit oxidation and to clean up free radicals. Cells have their own antioxidants like glutathione and there are enzymes like superoxide dismutase (SOD) that are also antioxidants. Living things have systems for utilizing oxygen and for cleaning up the mess, too.

Antioxidant dietary supplements are worthless. It’s more important to eat well and be sure you get the necessary nutrients (like Vitamins A, C, and E!) from regular foods. A healthy metabolism also means that your body’s own scheme for coping with oxygen toxicity will function properly.

Many years ago I attended a lecture by a famous biochemist (Bruce Ames, inventor of the Ames Test). It was a fascinating and wide-ranging talk that covered nutrition, cancer, aging, toxicity and related topics. The audience was particularly interested in diet and in the Q-and-A afterwards one frustrated listener (it was a deep, information-dense event) asked the equivalent of “what does it all mean?” We were feeling a little overwhelmed and wanted to walk away with some straightforward, simple things we could do to stay healthy.

He told us to remember “what our mothers always said.” That is, “don’t smoke, don’t drink too much, cut down the sweets, and eat your vegetables.”

Sounds good to me!


We live in a time dominated by economics and economists. Every politician subscribes to a particular economic orthodoxy, even they have only a superficial grasp of it, because they need talking points. And those talking points are inevitable: jobs and growth. And trade, of course. Since NAFTA everyone talks about trade.

Ultimately everything comes down to economic growth. If the Soviet Union could have generated similar economic growth to the United States and its NATO allies it would still be functioning. Alas, the planned economy could not compete with the free market and the whole mess collapsed upon itself.

If you want growth you have to have a capitalist system. And we want growth. We want our wealth to increase, both individually and as a nation. Growth is the solution to every social problem. If worker productivity grows then the economy will grow and there will be more investment in the future and we will all get richer. Anything that gets in the way of economic growth is bad. Anything that sustains or encourages it is good.

I don’t mean to be simplistic but we rarely dispute the need for growth, so I won’t. Not this time. There are plenty of folks out there who think maybe continuous growth is a bad thing, especially for the environment, and they have arguments worth looking at. But I’m not going to do that. I’m just going to think about growth.

When I want to understand something I try to measure it or put a number on it. Lots of things are not amenable to numerical analysis but growth is obviously something that requires numbers. I remember my mom and dad marking my height on the wall and each year we’d see how much I grew from last year. I didn’t need numbers to see the change of course but I was measuring nonetheless.

How do we measure growth? I’ll give you one easy way. It’s one of those very few things from high school math class that you can actually use.

It’s called the Rule of 72. Sometimes you will see it called the Rule of 70 but it doesn’t really matter. The Rule of 72 (or 70) is a quick estimator. A rule of thumb. (If you wanna be fancy, call it a “heuristic” instead.)

We’ll use 72. This is a handy number because it is divisible by 12 and there are 12 months in a year. And the Rule of 72 is about time, and years is a unit of time.

Let’s say you put money in something like a Treasury note or a CD and you get 4% interest rate. How fast will your money grow? The Rule of 72 says “divide 72 by the rate” so that’s what we’ll do.

72 divided by 4 (from the 4% interest rate) is 18. That means your money will DOUBLE in 18 years!

What the Rule of 72 tells us is the DOUBLING TIME of any quantity expressed as a percent growth rate. (Note that 70/4 = 17.5 which is pretty close. You can use either 70 or 72 as either is a handy estimate.)

Let’s say your candidate for President argues that the country needs to grow the economy by 3% every year. Let’s take a quick look at that.

72 divided by 3 is 24. (70/3 = 23.3)

What the candidate is saying is that the economy should be TWICE AS BIG AS IT IS NOW in 24 years. Is that what you want? I’m not saying this is a good or bad political position. I’m saying we should all understand the implications. Do we want our economy to double in size in 24 years?

When you see something expressed as a rate percentage you are looking at a phenomenon called “fractional growth.” That means that over each time period the original amount will grow by the same fraction. That fraction is the same (4/100 in the case of 4%) but since the amount keeps growing the amount of new growth added on keeps growing. We know this as compound interest. This is the Holy Grail of capitalism. Here’s what steady fractional growth looks like:

Don’t you want your money to do this?

When you learn the growth equation in algebra class they use examples like bacteria growing in a petri dish because bacteria double (one splits into two) in a predictable way. So you get these nice graphs. Look how fast the population grows after the fifth hour! The growth rate is constant, but the amount added on in each interval increases rapidly. You learn this stuff in the chapter about “exponential functions.”

I once heard a speaker (a physics professor teaching science teachers) say “the greatest shortcoming of the human race is the inability to understand the exponential function.” (Albert Bartlett)

Growth can be good and growth can be bad. But the most important thing is to get a handle on what growth means. Now you have a tool for estimating the DOUBLING TIME of anything that grows at a constant rate. Doubling is a nice, intuitive way to visualize quantities.

Note that 72 can be divided by 36, 24, 18, 12, 9, 8, 6, 4, 3, and 2 so it is a handy number for quick math in your head. 70 is divisible by 14, 10, 7, 5 and 2 so it’s really a matter of how precise you want to get. The actual number is approximately 69.3 (that’s the natural logarithm of 2 times 100) and you can use that with your calculator. Of course the internet is chock full of websites with interest calculators and any spreadsheet program (like Excel) will have the exponential functions built in if you need an accountant’s level of precision.

But most of us don’t need that. We just need a “quick and dirty” estimate. That’s the Rule of 72—high school math you can actually use in real life!

Quick quiz: the world’s population is growing 1.2% per year. How many years will it take at this rate for the world’s population to double?

Copa Mundial, finals edition

I said previously that they should just call the World Cup the Western Europe/South America championship tournament. And what happened? Argentina will be playing France in the finals!

Argentina is a world football powerhouse. They were World Cup champions in 1978 and again in 1986. They’ve also been runners-up in 1930, 1990, and 2014. France is also a big name in international soccer. They are the defending champions having won the prize four years ago. They were also champions in 1998. They were runners-up in 2006 and have two third-place finishes in 1958 and 1986.

So this year’s final is a heavyweight bout. All the minnows and surprise teams have been eliminated. I won’t get to see a Morocco vs. South Korea final!

That’s what I wanted. I wanted a new champion or at least a champion from somewhere other than Western Europe or South America.

But this showdown is what a lot of football fans expected as well as what they wanted. These are two great, accomplished squads with superstar players. The outcome is too close to call. At one site I saw that Argentina was favored 9-to-5 (1.8/1) to win and France was listed at 21-to-13 (1.6/1)! Everyone is anticipating a close match. The semifinal games were unfortunately a bit lopsided but the previous round (the quarterfinals) produced some excellent contests.

I don’t have the soccer nous to make a prediction and I frankly don’t care who wins. I expect to watch the final and all I hope is that it is a tight, well-played event THAT GETS DECIDED IN REGULATION and does not degenerate to fookin’ penalty kicks! But if I have to make a prediction I will say that it goes to double overtime and gets decided in a shoot-out.

We can get back to baseball when this is all over.

Tantalum, #73

Tantalus was a Greek god who pissed off Zeus and was thus punished, like Sisyphus, with eternal anguish. Tantalus was made to stand in a pool of water that would recede when he bent to drink. A laden fruit tree branch hung over his head and it would recede from his grasp if he tried to eat. Thus the poor fellow was “tantalized” forever! He earned it: he killed his son Pelops and tried to feed him to the Olympians (Greek gods are hella weird!) but got busted. Pelops was the father of Atreus who was the father of Agamemnon and Menelaus. You might have heard about those guys and a little thing called the Trojan War.

The guy who discovered Tantalum (Anders Ekberg in 1802) named it so because the metal was resistant to acid. Even in an acid bath the metal would not absorb the solution or get saturated.

These days the element is used (in powdered form) to make capacitors. In the old days capacitors were called condensers. Many of the terms first used in electronics had a mechanical origin. Plumbing analogies abounded when describing electric circuits. The forerunner of the transistor—the triode vacuum tube—had parts known as the gate, source, and drain. These days the corresponding parts of the transistor are the base, emitter, and collector.

Capacitors are key elements in modern circuits. They are generally used as filters, sensors, and in tuning and switching applications. Needless to say there are hundreds of millions of them in existence, perhaps billions, as they are used in almost every electronic device.

Tantalum is mined with cobalt and is thus a conflict mineral. The Democratic Republic of the Congo is the chief source. Worldwide demand is about 2000 metric tons per year. Tantalum ores have not been mined in the U.S. since 1959.

Here’s some tantalum “caps” you can buy at Wal-Mart:

Return of the Jetti

The world needs copper and lots of it. There are only so many places for copper mines. Mining is a messy business and leaves a lot of waste material behind. Here’s the thing: that’s a framing problem. Instead of calling the stuff that’s left behind “waste” we should call it a “potential resource.” Enter the Jetti.

Jetti Resources is an American company (headquartered in Boulder, CO) that extracts copper ore from mine waste. Mines dig ore. The ore has to be high-grade, that is, containing an economically obtainable fraction of the desired material. Miners dig up the good stuff and leave the low-grade stuff behind.

That’s nuts. All that rock had to be moved at one point. It took huge amounts of time and energy to do that and the result is a big pile of rock that’s seemingly no good to anyone. Instead of digging new holes, it’s time to re-visit the holes we’ve already made and see if we can do a better job.

Economically feasible extraction from low-grade sulfide ores is sometimes called the Holy Grail of copper mining. Jetti claims to have a hydro-metallurgical process for doing just that. Sulfide ores are usually reduced via a pyro-metallurgical process otherwise known as roasting in a furnace. The chemical leaching that Jetti is using is less energy-intensive and can work with poor quality ore material that would not be suitable for the traditional methods. They claim they have doubled copper production at their test site in Pinto Valley in Arizona.

Capitalism is a great system for extracting wealth from the earth. But it comes at a cost. Those costs are called “externalities” by economists but you know them better as waste, environmental disruption, and pollution. We accept these “externalities” as the price of doing business. You want gasoline for your car? Well that’s fine, we can supply that, but we’ll sully your air and water in the process and ask you to accept that as a “trade-off.” This is where economics veers off into bullshit. We don’t have the right to “trade-off” our air and water and the rest of our ecosystem! We need a new way of thinking about how to get what we need and how to do it sustainably. We need to get rid of the notion of waste. I remember a nuclear engineer telling me once that burying nuclear materials (by-products of fission reactors) deep in the earth was a mistake. “What if we need to get to that stuff?” he would ask me. “That’s not nuclear waste, that’s a nuclear resource!” Regardless of how you feel about nuclear power you have to appreciate his attitude. It took a tremendous technological effort to isolate and create those fuels—why then do we throw them away?

The Jetti people aren’t going to save us. And I don’t know enough about markets and technology to guess about the company’s future. But they are on to something. Luxury car-maker BMW seems to think so, too. They just dumped a bunch of money in Jetti’s lap. BMW wants to electrify their fleet. They say that half their cars will be EVs by 2030. That’s going to take a lot of copper!

Copa Mundial

There have been 21 World Cups since 1930. This one is the 22nd. Eight nations have hosted the trophy. Five of those countries are from Western Europe: Germany (4), Italy (4), France (2), Spain (1), and England (1). That’s twelve of the twenty-one winners. South America has produced the other nine winners: Brazil (5), Argentina (2), and Uruguay (2).

So it’s not the World Cup. It’s the Western Europe-v.-South America soccer tournament!

No Asian team has ever won. Nor has an African team. This year we will see Senegal reach the knockout phase (the final 16 teams). Other teams like Japan, Ghana, Cameroon, Iran, and Tunisia are still in the hunt. North America (USA-Canada-Mexico) has never had a winner. This year both Mexico and USA are still in contention. Perennial favorites like Brazil and France are expected to take the trophy home this year, however. The big countries with a long history of competition are most likely to win. We will probably get another repeat champion—one of the “elite eight” past winners.

The 2026 World Cup will feature 48 teams, up from the usual 32. FIFA (world football’s governing body) recognizes over 200 nations! Maybe by 2030 (the 100th anniversary of the World Cup) we’ll get a winner that hasn’t won before. Or maybe we’ll get a surprise in Qatar this time. I think that would be a good thing for the “World” Cup, don’t you?

Nickel, #28

The United States nickel, or five-cent piece, is made of an alloy called cupronickel. It’s 75% copper and 25% nickel. These days the melt value of the coin exceeds the face value. According to coinapps.com I can get six cents for my nickel! Apparently this is not allowed. You can’t melt US-minted coins and sell the metal.

Nickels aren’t very useful or convenient any more. Neither are most coins but we still pound out billions of them each year.

The element Nickel—atomic number 28 and symbol Ni—is used in a lot more things than coins. Mostly it is alloyed with iron (in small quantities) to make stainless steels. Alnico magnets (Al-Ni-Co, aluminum-nickel-cobalt) are another important use. And we are all familiar with Ni-Cd or “nicad” (nickel-cadmium) rechargeable batteries. We can’t get through the day without using steel products and portable electronics.

Worldwide 2.7 million metric tons of nickel were produced in 2021. That’s up from 1.6 M in 2010. Indonesia and the Philippines are the top exporters. China is the largest consumer as they have a massive steel industry.

Nickel is a shiny, durable, and corrosion-resistant metal. It is substituted for silver and is also used to electroplate other metals to provide a tougher, more attractive finish. Nickel compounds can be very colorful and some make lovely solutions in the test tube.

Here’s a nickel for your thoughts: