Category: Chemistry

Flipping An Edge Case

On By rolcottIn Chemistry, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Why’s the Ag box look weird in your chart, Susan?”

“That’s silver, Eddie. It’s an edge case. The pure metal’s diamagnetic. If you alloy silver with even a small amount of iron, the mixture is paramagnetic. How that works isn’t my field. Sy, it’s your turn to bet and explain.”

I match Eddie’s bet (the hand’s not over). “It’s magnetism and angular momentum and how atoms work, and there are parts I can’t explain. Even Feynman couldn’t explain some of it. Vinnie, what do you remember about electromagnetic waves?”

“Electric part pushes electrons up and down, magnetic part twists ’em sideways.”

“Good enough, but as Newton said, action begets reaction. Two centuries ago, Ørsted discovered that electrons moving along a wire create a magnetic field. Moving charges always do that. The effect doesn’t even depend on wires — auroras, fusion reactor and solar plasmas display all sorts of magnetic phenomena.”

“You said it’s about how atoms work.”

“Yes, I did. Atoms don’t follow Newton’s rules because electrons aren’t bouncing balls like those school‑book pictures show. An electron’s only a particle when it hits something and stops; otherwise it’s a wave. The moving wave carries charge so it generates a magnetic field proportional to the wave’s momentum. With me?”

“Keep going.”

“That picture’s fine for a wave traveling through space, but in an atom all the charge waves circle the nucleus. Linear momentum in open space becomes angular momentum around the core. If every wave in an atom went in the same direction it’d look like an electron donut generating a good strong dipolar magnetic field coming up through the hole.”

“You said ‘if’.”

“Yes, because they don’t do that. I’m way over‑simplifying here but you can think of the waves pairing up, two single‑electron waves going in opposite directions.”

“If they do that, the magnetism cancels.”

“Mm‑hm. Paired‑up configurations are almost always the energy‑preferred ones. An external magnetic field has trouble penetrating those structures. They push the field away so we classify them as diamagnetic. The gray elements in Susan’s chart are almost exclusively in paired‑up configurations, whether as pure elements or in compounds.”

“Okay, so what about all those paramagnetic elements?”

The angular portion of the lowest-energy spherical harmonic modes
Credit: Inigo.quilez, under CCA SA 3.0 license

“Here’s where we get into atom structure. An atom’s electron cloud is described by spherical harmonic modes we call orbitals, with different energy levels and different amounts of angular momentum — more complex shapes have more momentum. Any orbital hosting an unpaired charge has uncanceled angular momentum. Two kinds of angular momentum, actually — orbital momentum and spin momentum.”

“Wait, how can a wave spin?”

“Hard to visualize, right? Experiments show that an electron carries a dipolar magnetic field just like a spinning charge nubbin would. That’s the part that Feynman couldn’t explain without math. A charge wave with spin and orbital angular momentum is charge in motion; it generates a magnetic field just like current through a wire does. The math makes good predictions but it’s not something that everyday experience prepares us for. Anyway, the green and yellow‑orange‑ish elements feature unpaired electrons in high‑momentum orbitals buried deep in the atom’s charge cloud.”

“So what?”

“So when an external magnetic field comes along, the atom’s unpaired electrons join the party. They orient their fields parallel to the external field, in effect allowing it to penetrate. That qualifies the atom as paramagnetic. More unpaired electrons means stronger interaction, which is why iron goes beyond paramagnetic to ferromagnetic.”

“How does iron have so many?”

“Iron’s halfway across its row of ten transition metals—”

“I know where you’re going with this, Sy. It’ll help to say that these elements tend to lose their outer electrons. Scandium over on the left ionizes to Sc3+ and has zero d‑electrons. Then you add one electron in a d orbital for each move to the right.”

“Thanks, Susan. Count ’em off, Vinnie. Five steps over to iron, five added d‑electrons, all unpaired. Gadolinium, down in the lanthanides, beats that with seven half‑filled f‑orbitals. That’s where the strength in rare earth magnets arises.”

“So unpaired electrons from iron flip alloyed silver paramagnetic?”

“Vinnie wins this pot.”

~ Rich Olcott

Was Ramses Pharaoh-magnetic?

On By rolcottIn Chemistry, UncategorizedLeave a comment

Kareem puts in another couple of chips. “Hold your horses, Cal. The conversation‘s just getting interesting.”

Vinnie raises him a few chips. “Hey, Mr Geology. Just how rare are these lanthanide rare earths? And if they’re metals, how come they’re called earths?”

Source

“Not that rare.” <pulls up an image on his phone> “Here’s a quick abundance chart for the lanthanides and a few other elements averaged over all of Earth’s continental crust. Cerium’s more abundant than copper and 350 times more common than lead. Of course, that’s an average. Lanthanide concentrations in economically viable ores are much higher, just like with copper, lead, tin and other important non‑ferrous metals.”

“Funny zig-zag pattern there.”

“Good catch, Cal. Even‑number elements are generally more abundant than their odd‑numbered neighbors. That’s the Oddo-Harkins Rule in action—”

“ODDo-Harkins, haw!”

“You’re—” <Susan’s catches Vinnie’s frown and quickly drops few chips onto the pile> “Sorry, Vinnie. You’re not the first person to flag that pun. Two meteorite chemists named Giuseppe Oddo and William Harkins developed the rule a century ago. We’re pretty sure the pattern has to do with how stars fuse even‑numbered alpha particles to build up the elements heavier than hydrogen and helium. As to why the rare earths are called earths, back when Chemistry was just splitting away from alchemy, an ‘earth‘ was any crumbly mineral. Anybody heard of diatomaceous earth?”

Cal perks up. “Yeah, I got a bag of that dust in my garden shed to kill off slugs.”

“Mm‑hm. Powdery, mostly silica with some clay and iron oxide. The original ‘earth’ definition eventually morphed to denote minerals that dissolve in acid” <grin> “which diatomaceous earth doesn’t do. A few favorable Scandinavian mines gave the Swedish chemists lanthanide‑enriched ores to work on. Strictly speaking, in metallic form the lanthanides are rare earth metals, not rare earths, but people get sloppy.”

Eddie pitches in some chips. “So they’re <snort> chemical odd‑ities. Why would anyone but a chemist care about them?”

<sigh> “Magnetism.” <shows her laptop’s screen> “Here’s a chart that highlights the elements that are most magnetically active. The lanthanides are that colored strip below the main table. Chemically they’d all fit into that box with the red circle. They’re—”

“Wait, there’s more than one kind of magnetism?”

“Oh, yes. The distinction’s about how an element or material interacts with an external magnetic field. Most elements are at least weakly paramagnetic, which means they’re pulled into the field; diamagnets push away from it. Diamagnetic reaction is generally far weaker. Manganese is the strongest paramagnet, about 70 times stronger per atom than the strongest diamagnet, bismuth. Then there’s iron, cobalt and nickel — they do ferromagnetism, which means their atoms interact so strongly with the field that they get their neighbors to join in and make a permanent magnet.”

Schematic of a Gouy Balance

“How does anyone find out whether the field’s pulling or pushing?”

“Good question, Cal (you owe the pot, by the way). Basically, the idea is to somehow weigh a sample both with and without a surrounding field. Tammy’s lab down the hall from me has a nice Gouy Balance setup which is one way to make that measurement. The balance stands on a counter over a hole that leads down to a hollow glass tube that guards against air currents. There’s also a big powerful permanent magnet down there, mounted on a hinged arrangement. Your sample hangs on a piece of fishline hooked to the balance pan. Take a weight reading, swing the magnet into position just below the sample, read the weight again, do some arithmetic and you’re done. A higher weight reading when the field’s in place means your sample’s paramagnetic, less weight means it’s diamagnetic.”

“Why does that Ag box look weird in your table, sort of half‑brown and half‑gray?”

“That’s silver, Eddie. It’s an edge case. The pure metal’s diamagnetic but alloy a sample with even a small fraction of some ferromagnetic atoms and you’ve made it paramagnetic. Magnetism’s one test that people in the silver trade use to check if a coin or bar is pure. How that works isn’t my field. Sy, it’s your turn to bet and explain.”

~ Rich Olcott

That Lump in The Table

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

The Acme Building Science and Pizza Society is back in session. It’s Cal’s turn to deal the cards and the topic. “This TV guy was talking about rare earths that China’s got a lock on and it’s gonna mess up our economy, but he didn’t say what they are or why we should care about them. What’s goin’ on?”

Vinnie passes but Susan tosses a chip into the pot. “The rare earths are oxides of the lanthanide elements—”

“Wait, they’re from the planet that the Strange New Worlds engineering prof is from?”

“Put in a chip, Vinnie, you know the rules.” <He does.> “No, they have nothing to do with Pelia or her home planet. She’s a Lanthanite, these elements are lanthanides. Although these days we’re supposed to call them lanthanoids because ‑ides are ionic compounds like oxides.”

It’s not Kareem’s turn yet but he chuckles and flips in a chip. “Funny. The geology community settled on meteoroids as rocks floating in space, meteors when they flash through the sky, and meteorites when they hit the ground. I don’t think there’s such a thing as a meteoride. Sorry, Susan, go on.”

“As a matter of fact, Kareem, I once did a high‑rated downhill mountain bike path in Arizona called the Meteoride. Once. Didn’t wipe out but I admit I used my brakes a whole lot. Where was I? Oh, yes, the lanthanides. They’re a set of fourteen near‑identical twins, chemistry so similar that it took decades of heroic effort by 19th‑century Swedish chemists in the long, cold Swedish nights to separate and identify them.”

Benfey‘s “Periodic Snail” Image by DePiep under CC BY-SA 3.0

“Similar how?”

“They all act like aluminum.” <pulls laptop from her purse, points to two stickers on its lid> “You’ve all at least heard of the Periodic Table, right? Back in the mid-1800s, the chemists had isolated dozens of chemical elements, enough that they could start classifying them. They didn’t know what atoms were yet but they had developed ways to measure average atomic weights. Some theorists played with the idea of arranging elements with similar chemistries according to their atomic weights. Mendeleev did the best job, even predicting three elements to fill empty slots in his tabulation. These guys in the lime green row and the pale pink bulge were his biggest puzzlement.”

“Why’s that? They’re all spread out nice.”

“Because like I said, Vinnie, they all have pretty much the same chemistry. Aluminum’s a soft silvery metal, oxidizes readily to a 3+ ion and stays there. Same for almost all the lanthanides. Worse yet, all their atoms are nearly the same size, less than 8% difference from the largest to the smallest.”

“Why’s that make a difference?”

“Because they can all fit into the same crystalline structure. Nineteenth‑century chemistry’s primary technique for isolating a metallic element was to dissolve a likely‑looking ore, purify the solution, add an organic acid or something to make crystalline salts, burn away the organics, add more acid to dissolve the ash, purify the solution and re‑crystallize most it. Do that again and again until you have a provably pure product. All the lanthanide ions have the same charge and nearly the same size so the wrong ions could maliciously infiltrate your crystals. It took a lot of ingenious purification steps to isolate each element. There were many false claims.”

Kareem contributes another chip. “Mm‑hm, because geology doesn’t use chemically pure materials to create its ores. Four billion years ago when our planet was coated with molten magma, the asteroids striking Earth in the Late Heavy Bombardment brought megatons of stone‑making lithophile elements. The lanthanides are lithophiles so random mixtures of them tended to concentrate within lithic silicate and phosphate blobs that later cooled to form rocky ores. Industry‑scale operations can tease lanthanides out of ores but the processes use fierce chemicals and require close control of temperature and acidity. Tricky procedures that the Chinese spent billions and decades to get right. For the Chinese, those processes are precious national security assets.”

Cal’s getting impatient. “Hey, guys, are we playing cards or what?”

~ Rich Olcott

Why No Purple?

On By rolcottIn Chemistry, Physics: Light and RelativityLeave a comment

<ding/ding/ding> <yawn> “Who’s texting me at this time of night?”

This better be good.

Hi, Uncle Sy. Did I wake you up?

At this hour? Of course you did, Teena. What’s going on?

Oh, I’m sorry. I didn’t realize what time it is. I’ve been deep into my Chemistry homework. There’s a question here that I don’t understand and I thought you could help me with. Please?

Well, I’m awake. What’s the question?

This isn’t quite what they ask but it’s what I’m stuck on. Is energy stepwise or continuous?

Whoa! That’s not really an either‑or proposition. Energy is continuous, but the energy differences that atoms/molecules respond to are stepwise. You get continuous white light from hot objects like stars and welding torches.
If white light passes a hydrogen atom, the atom will only absorb certain specific frequencies (frequency is a measure of energy).

The rest bounce off, creating the atom’s…line spectrum?

Yes, except they don’t bounce off, they pass by.

The more energy/heat fire has, the further down the EM spectrum its light goes: red, orange, yellow, blue, white. Is that correct?

Mostly, though the usual sequence read ‘upward’ in energy is radio, microwave, infrared, red, orange, yellow, green, blue, violet, ultraviolet, X-rays, gamma rays.
White is an even mixture of all frequencies.

I was focusing on the visible section for a reason.

Mmm?

So, there’s red, orange, yellow, and blue fire in order of how much heat it has, why does it skip purple and green? A normal fire can reach red, orange, yellow just fine with the only difference being heat, but why can’t fire be green or purple without throwing chemicals in it?

Ah, what you’re really looking at is variation in fuel/air mixture (and possibly which fuel — I’ll get to that).
A rich methane mixture (not much oxygen, like a shuttered Bunsen burner) doesn’t get very hot, has lots of unburnt carbon particles and looks orange. Add more oxygen and the flame gets hotter, no more soot particles, just isolated CO, CO2, and water molecules, each of which gets excited to flame temp and then radiates light but only at its own characteristic frequencies. Switch to acetylene fuel and the flame gets hotter still because C2H2+O2 reactions give off more energy per molecule than CH4+O2. Now you’re in plasma temperature range, where free electrons can emit whatever frequency they feel like.

How about sunsets and campfires?

Sunsets are a whole other thing — the sun’s white light is transformed in various ways as it filters through dust and such in the atmosphere. Anyway, no flame or atom/molecule excitation in a sunset

But it all comes down to how much energy the light source “has”, right? That’s what I think I remember from physics. And what about campfires? In the center of the fire you have blue flame, and the further from the center the closer to red flame you get, but it still skips green!

Yes, but in each of these cases the *source* is different — soot particles, excited molecules, plasma.

???

The campfire has several different processes going on. Close in, the heated wood emits various gases. The gases reacting with O2 *are* the flame, generally orange to yellow from excited molecules but you can get blue where the local ventilation forms a jet and brings in extra oxygen for an efficient flame. Further out it’s back to red-hot soot.

OK

To your original question — this is a hypothesis, but I suspect the particular atoms and molecules emitted from untreated burning wood simply don’t have any strong emissions lines in the green region. I know there aren’t for any hydrogen atoms — look up “Balmer series” in wikipedia.

Thanks for talking me through this. I understand it better now. Continuous spectrums come from hot electrons, but line spectrums come from different atoms or molecules. Right?

*spectra
Right.
As you said, you could throw in copper or sodium salts to get those blue and golden colors.

I figured there had to be some way to go about it – I’ve seen lots of green and gold (YAY CSU!) fireworks. G’night, Uncle Sy.

G’night, Teena.
Now get to bed.

~ Rich Olcott

  • Thanks to Alex, who wrote much of this.

Rows, Columns And Freedom

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

“Geez, Sy. You know I hate equations. I was fine with the Phase Rule as an arithmetic thing but you’ve thrown so much algebra at me I’m flummoxed. How about something I can visualize?”

“Sorry, Vinnie, the algebra was just to show where the Rule came from. Application’s not in my bailiwick. Susan, it’s your turn.”

“Sure, Sy, this is Chemistry. Okay, Vinnie, what’s the Rule about?”

“Degrees of freedom, but I’m still not sure what that means. ‘Independent intensive variables’ doesn’t say much to me.”

“Understandable, seeing as you don’t like equations. Visualize a spreadsheet. There’s an ‘Energy’ header over columns A and B. The second row reads ‘Name’ and ‘Value’ in those two columns. Then one row each for Temperature and Pressure.”

“This is more like it. Any numbers in the value column?”

“Not yet. They’ll be degrees of freedom, maybe. Next, ‘Components‘ in cell C1, ‘Name’ in C2 and then C rows, one for each component.”

“Do we care how much of each component?”

“Not yet.* Next visualize a multi‑column ‘Phases‘ header over one column for each phase. The second row names the phase. Below that there’s a row for each component. The whole array is for figuring how each component spreads across the phases assuming there’s enough of everything to reach equilibrium. With me?”

“A little ahead, I think. Take one of Kareem’s lava pools on Io, for instance. It’s got two components, iron and sulfur, and two molten phases, iron‑light 5:95 floating on top of iron‑heavy 60:40. Phase Rule says the freedom degrees is C–P+2=2–2+2, comes to 2 but that disagrees with the 6 open boxes I see.”

“But the boxes aren’t independent. Think of the interface between the two phases. One by one, atoms in each phase wander across to the other side. At equilibrium the wandering happens about as often in both directions.”

Adapted from Walder and Pelton
Click image to expand

“That’s your reversibility equilibrium.”

“Right, thermodynamics’ classic competition between energy and entropy — electronic energy holding things together against entropy flinging atoms everywhere. Pure iron’s a metallic electron soup that can accept a lot of sulfur without much disturbance to its energy configuration. That means sulfur’s enthalpy doesn’t differ much between the two environments and that allows easy sulfur traffic between the two phases. On the other hand, pure sulfur will accept only a little iron because iron disrupts sulfur‑sulfur moleular bonding. Steep energy barrier against iron atoms drifting into the 95:5 phase; low barrier to spitting them out. Kareem’s phase diagram for atmospheric pressure shows how things settle out for each temperature. There’s a neat equation for calculating the concentration ratios from the enthalpy differences, but you don’t like equations.”

“You’re right about that, Susan, but I smell weaseling in your temperature‑pressure dodge.”

Water’s phase diagram

“Not really. You’ve read Sy’s posts about enthalpy’s internal energy, thermal and PV‑work components. Heat boosts entropy’s dominance and tinkers with the enthalpies.”

Meanwhile, I’ve been tapping Old Reliable’s screen. “I’m playing water games over here. Maybe this will help clarify the freedom. Water can be ice, liquid or vapor. At high temperature and pressure, the liquid and gas phases become a single phase we call supercritical. Here’s a sketch of water’s phase diagram. Only one component so C=1 … and a spreadsheet summarizing seven conditions.

“The first four are all at atmospheric pressure, starting at position 1 — just water vapor in a single phase so P=1, DF=2. We can change temperature and pressure independently within the phase boundaries. If we chill to point 2 liquid water condenses. If we stop there, on the boundary, we’re at equilibrium. We could change temperature and still be at equilibrium, but only if we change pressure just right so we stay on that dotted line. The temperature‑pressure linkage constraint leaves us only one degree of freedom — along the line.”

“Ah, 3 and 5 work the same way as 1 but for liquid and solid, and 4‘s like 2. The Fixed ones—?”

“One unique temperature‑pressure combination for each equilibrium. No freedoms left.”

  • * Given specific quantities of iron and sulfur, chemists can calculate equilibrium quantities for each phase. Susan assigned that as a homework problem once.

~ Rich Olcott

The Quest for Independents

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

The thing about Vinnie is, he’s always looking for the edges and loopholes. He’d make a good scientist or lawyer but he’s happy flying airplanes. “Guys, I heard a lot of dodging when you started talking about that Gibbs Rule. You said it only works when things are in equilibrium. That’s what Susan was talking about when she said Loki Lake on Io ain’t an equilibrium ’cause there’s stuff getting pumped in and going away so the equations don’t balance. I got that. But then you threw in some other excepts, like no biology or other kinds of work. What’s all that got to do with the phases and chemistry?”

“They’re different processes that drive a system away from equilibrium. Biology, for example. Every kind of life taps energy sources to maintain unstable structures. Proteins, for instance — chemically they’re totally unstable. Oxidation, random acid‑base reactions, lots of ways to degrade a protein molecule’s structure until its atoms wind up in carbon dioxide and nitrogen gas. Your cells, though, they continually burn your food for energy to protect old protein molecules or build new ones and DNA and bones and everything. I visualize someone riding a bicycle up a hillside of falling bowling balls, desperately fighting entropy just to keep upright.”

“Fearsome image, Susan, but it fits. From a Physics perspective, dumping in or extracting any kind of work disrupts any system that’s at equilibrium. The Phase Rule accounts for pressure-volume energy because that’s already part of enthalpy—”

“Wait, Sy, I don’t see pressure‑volume or even ‘PV‘ in
  ’degrees of freedom=components–phases+2‘.”

“That’s what the ‘2′ is about, Vinnie. If it weren’t for pressure‑volume energy, that two would be a one.”

“C’mon.”

“No, really. ‘Degrees of freedom’ counts the number of intensive properties that are independent of each other. Neither temperature nor pressure care about how much of something you’ve got, so they’re both intensive properties. Temperature’s always there so that’s one degree of freedom. If PV energy’s part of whatever process you’re looking at, then pressure comes into the Rule by way of the enthalpies we use to calculate equilibrium situations. I guess you could write the Rule as
  DF=C–P+1T+1PV.“

“That’s not the way we learned that in school, Sy. It was
  DF=C–P+1+N,
with ‘N’ counting the number of work modes — PV, gravitational, electrical, whatever fits the problem.”

“How would you do gravitational work on an ice cube, Kareem?”

“Wouldn’t be a cube, Vinnie, it’d be a parcel of Jupiter’s atmosphere caught in a kilometers‑high vertical windstream. Water ice, ammonia ice, ammonium polysulfide solids, all in a hydrogen‑helium medium. A complicated problem; whoever picks it up will have to account for gravity and pressure effects.”

“Come to think of it, the electric option is getting popular and Kareem’s iron‑sulfur system may be a big player. My Chemistry journals have carried a sudden flurry of papers about iron‑sulfur batteries as cheap, safe alternatives to lithium‑based designs for industry‑sized storage where low weight isn’t a consideration. Battery voltage is intensive, doesn’t care about size. Volt’s extensive ‘how much’ buddy is amps. Electrical work is volts times amps so it fits right in with the Rule if I write
  DF=C–P+1T+1PV+1VA
A voltage box with sulfur electrodes on one side and iron electrodes on the other would be way out of equilibrium.”

“But why components minus phases? Why not times? What if it comes out negative? What’d that even mean?”

Water’s phase diagram

“Fair questions, Vinnie. Degrees of freedom counts independent properties, right? You’d think the phases‑components contribution to DF would be P*C but no. The component percentages in C must total 100%. If you know all but one percentage, the last percentage isn’t independent. Same logic applies to the P phases. That leaves (C–1) and (P–1) independent variables. For the P phases P*C drops to P*(C–1) variables. But you also know that each component is in equilibrium across all phases. Each equilibrium reduces the count by one, for C*(P–1) reductions. Do the subtraction
  P*(C–1)–C*(P–1)=C–P
You’re left with only C–P quantities that can change without affecting other things. If the result’s negative it’ll constrain exactly that many other intensive variables, like with water’s triple point.”

~ Rich Olcott

Water Rites

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Vinnie pulls a chair over to our table, grabs some paper napkins for scribbling. “You guys know I hate equations, but this Phase Rule one is simple enough even I can play. It says ‘degrees of freedom’ equals ‘components’ minus ‘phases’ plus 2, right? Kareem’s phase diagram has a blue piece with a slush of iron crystals floating in an iron‑sulfur melt. There’s two components, iron and sulfur, two phases, crystals and melt, so the degrees come to 2–2+2=2 and that means we get to choose any two, you said intensive properties, to change. Do I got all that straight, tell me more about degrees and what’s intensive?”

Phase diagram for the iron:sulfur system
Adapted from Walder and Pelton
Click image to expand

“Good job, Vinnie, and good questions. Extensive properties are about how much. In Kareem’s experiment, he’s free to add iron or sulfur in whatever quantities he wants. By contrast, intensive properties don’t care about how much is there. The equilibrium melt’s iron:sulfur ratio stays between zero and one whatever the size of Kareem’s experiment. The ratio’s an intensive property. So are temperature and pressure. If he kept his experimental pressure constant but raised the temperature, I expect some of the crystals would dissolve. That’d lift the iron:sulfur ratio.”

“How about raising the pressure, Kareem?”

“I suspect that’d squeeze iron back into the crystalline mass, but I’ve not tried that so I don’t know. Different materials behave different ways. Raising the pressure on normal water ice melts it, which is why ice skates work.”

Susan suddenly pulls her tablet from her purse and starts fiddling with it.

“Fair enough. Okay, in your diagram’s top yellow piece where it’s all molten, there’s still 2 components but one phase so the Rule goes 2–1+2=3. You’re saying 3 degrees means you can choose whatever temperature, pressure and mix ratio you want and it’d still be molten.”

“You’ve got the idea, Vinnie. What I’m really interested in, though, is what happens when I add more components. To model Io’s lava pools I need to roll in oxygen and silicon from the surrounding rocks. I’m looking at a 4‑component situation which could have multiple phases and things are complicated”

Vinnie’s got that ‘gotcha’ glint in his eye. “Understood. But how about going in the other direction? If you’ve got only one component then you could have either 1–2+2=1 or 1–3+2=0. How do either of those make sense?”

Susan shows a display on her tablet. “As soon as Kareem mentioned ice I figured this phase diagram would come in handy. It’s for water — single component so there’s no variation along a component axis, just pressure and temperature.”

“Kareem had to read his chart to us. Now it’s your turn.”

“Of course. By convention, pressure’s on the y‑axis, temperature’s along the x‑axis. The pressure range is so wide that this chart uses a logarithmic scale which is why the distances look weird. Over there on the cold side, there’s two kinds of ice. Ice Ic has a cubic crystal structure. Warm it up past 240K and it converts to a hexagonal form, Ice Ih. That’s the usual variety that makes snowflakes.”

“TP!” <snirk, snirk>

“Cal, please. That’s water’s Triple Point, Vinnie’s 1–3+2=0 situation where all three phases are in equilibrium with each other so there’s no degrees of freedom. The solid‑liquid and liquid‑vapor boundaries are examples of Vinnie’s 1–2+2=1 condition — only one degree of freedom, which means that equilibrium temperature and pressure are tightly linked together. Squeeze on ice, its melting point drops, so we ice skate on a thin film of liquid water. Normal Boiling Point holds at standard atmospheric pressure but if you heat water while up on a balloon ride it may not get hot enough to hard‑boil those eggs you brought for the picnic.”

“What’s going on in the gray northeast corner?”

“CP‘s the Critical Point at the end of the 1–2+2=1 line. The liquid-vapor surface disappears. No gas or liquid in the container, just opalescent supercritical fog. There’s only one phase; temperature and pressure are independent. Beyond CP you’re in 1–1+2=2 territory.”

~ Rich Olcott

Surf Lake Loki? No, Thanks.

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Vinnie’s been eavesdropping (he’s good at that). “You guys said that these researcher teams looked at how iron and sulfur play together at a bunch of different temperature, pressures and blend ratios. That’s a pretty nice chart, the one that shows mix and temperature. Got one for pressure, like the near‑vacuum over Loki’s lava lake on Io?”

“Not to my knowledge, Vinnie. Of course I’m a lab chemist, not a theoretical astrogeochemist. Kareem’s phase diagram is for normal atmospheric pressure. I’d bet virtually all related lab work extends from there to the higher pressures down toward Earth’s center. Million‑atmosphere experiments are difficult — even just trying to figure out whether a microgram sample’s phase in a diamond anvil cell is solid or liquid. Right, Kareem?”

“Mm‑hm, but the computer work’s hard, too, Susan. We’ve got several suites of software packages for modeling whatever set of pressure-temperature-composition parameters you like. The problem is that the software needs relevant thermodynamic data from the pressure and temperature extremes like from those tough‑to‑do experiments. There’s been surprises when a material exhibited new phases no‑one had ever seen or measured before. Water’s common, right, but just within the past decade we may have discovered five new high‑pressure forms of ice.”

“May have?”

Artist’s concept of Loki Patera,
a lava lake on Jupiter’s moon Io
Credit: NASA/JPL-Caltech/SwRI/MSSS

“The academics are still arguing about each of them. Setting aside that problem, modeling Io’s low‑pressure environment is a challenge because it’s not a lab situation. Consider Cal’s pretty picture there. See those glowing patches all around the lava lake’s shore? They’re real. Juno‘s JIRAM instrument detected hot rings around Loki and nearly a dozen of its cousins. Such continual heat release tells us the lakes are being stirred or pumped somehow. Whatever delivers heat to the shore also must deliver some kind of hot iron‑sulfur phase to the cooler surface. That’ll separate out like slag in a steel furnace.”

“It’s worse than that, Kareem. Sulfur’s just under oxygen in the periodic table, so like oxygen it’s willing to be gaseous S2. Churned‑up hot lava can’t help but give off sulfur vapor that the models will have to account for.”

I cut in. “It’s worse than that, Susan. I’ve written about Jupiter’s crazy magnetic field, off‑center and the strongest of any planet. Io’s the closest large moon to Jupiter, deep in that field. Sulfur molecules run away from a magnetic field; free sulfur atoms dive into one. Either way, if you’re some sulfur species floating above a lava lake when Jupiter’s field sweeps past, you won’t be hanging around that lake for long. Most likely, you’ll join the parade across the Io‑to‑Jupiter flux tube bridge.”

Susan chortles. “Obviously not an equilibrium. It’s a steady state!”

“Huh?” from everyone. Cal gives her, “Steady state?”

“Chemical equilibrium is when a reaction and its reverse go at equal rates, right, so the overall composition doesn’t change. That’s the opposite of situations where there’s a forward reaction but for some reason the products don’t get a chance to back‑react. Classic case is precipitation, say when you bubble smelly H2S gas through a solution that may contain lead ions. If there’s lead in there you get a black lead sulfide sediment that’s so insoluble there’s no re‑dissolve. Picture an industrial vat with lead‑contaminated waste water coming in one pipe and H2S gas bubbling in from another. If you adjust the flow rates right, all the lead’s stripped out, there’s no residual stink in the effluent water and the net content of the vat doesn’t change. That’s a steady state.”

“What’s that got to do with Loki’s lake?”

“Sulfur vapors come off it and those glowing rings tell us it’s giving off heat. It’s just sitting there not getting hotter and probably not changing much in composition. There’s got to be sulfur and heat inflow to make up for the outflow. The lake’s in a steady state, not an equilibrium. Thermodynamic calculations like Gibbs’ phase rule can’t tell you anything about the lake’s composition because that depends on the kinetics — how fast magma comes in, how fast heat and sulfur go out. Kareem’s phase diagram just doesn’t apply.”

~ Rich Olcott

Phases And Changes

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

“Okay, so the yellow part of your graph is molten iron and sulfur, Kareem. What’s with all the complicated stuff going on in the bottom half?”

“It’s not a graph, Cal, it’s a phase diagram. Mmm… what do you think a phase is?”

“What we learned in school — solid, liquid, gas.”

“Sorry, no. Those are states of matter. Water can be in the solid state, that’s ice, or in the liquid state like in my coffee cup here, or in the gaseous state, that’d be water vapor. Phase is a tighter notion. By definition, it’s an instance of matter in a particular state where the same chemical and physical properties hold at every point. Diamond and graphite, for example, are two different phases of solid carbon.”

“Like when Superman squeezes a lump of coal into a diamond?”

“Mm-hm. Come to think of it, Cal, have you ever wondered why the diamonds come out as faceted gems instead of a mold of the inside of his fist? But you’ve got the idea — same material, both in the solid state but in different phases. Anyway, in this diagram each bordered region represents a phase.”

Phase diagram for the iron:sulfur system
Adapted from Walder and Pelton

“It’s more complicated that that, Kareem. If you look close, each region is actually a mixture of phases. The blue region, for instance, has parts labeled ‘bcc+Liquid’ and ‘fcc+Liquid’. Both ‘bcc’ and ‘fcc’ are crystalline forms of pure iron. Each blue region is really a slush of iron crystals floating in a melt with just enough sulfur to make up the indicated sulfur:iron composition. That line at 1380°C separates conditions where you have one 2‑phase mix or the other.”

“Point taken, Susan. Face it, if region’s not just a straight vertical line then it must enclose a range of compositions. If it’s not strictly molten it must be some mix of at least two separate more‑or‑less pure components. That cool‑temperature mess around 50:50 composition is a jumble when you look at micro sections of a sample that didn’t cool perfectly and they never can. The diagram’s a high‑level look at equilibrium behaviors.”

“Equilibrium?”

“‘Equi–librium’ came from the Latin ‘equal weight’ for a two-pan balance when the beam was perfectly level. The chemists abstracted the idea to refer to a reaction going both ways at the same rate.”

“Can it do that, Susan?”

“Many can, Cal. Say you’ve got a beaker holding some dilute acetic acid and you bubble in some ammonia gas. The two react to produce ammonium ions and acetate ions. But the reaction doesn’t go all the way. Sometimes an ammonium ion and an acetate ion react to produce ammonia and acetic acid. We write the equation with a double arrow to show both directions. Sooner or later you get equally many molecules reacting in each direction and that’s a chemical equilibrium. It looks like nothing’s changing in there but actually a lot’s going on at the molecular level. Given the reactant and product enthalpies Sy’s been banging on about, we can predict how much of each substance will be in the reaction vessel when things settle down.”

“Banging on, indeed. You’re disrespecting a major triumph of 19th‑Century science. Before Gibbs and Helmholtz, industrial chemists had to depend on rules of thumb to figure reaction yields. Now they just look up the enthalpies and they’ can make good estimates. Gibbs even came up with his famous phase rule.”

“You’re gonna tell us, right?”

“Try to stop him.”

“The Gibbs Rule applies to systems in equilibrium where there’s nothing going on that’s biological or involves electromagnetic or gravitational work. Under those restrictions, there’s a limit to how things can vary. According to the rule, a system’s degrees of freedom equals the number of chemical components, minus the number of phases, plus 2. In each blue range, for instance, iron and sulfur make 2 components, minus 2 phases, plus 2, that’s 2 degrees of freedom.”

“So?”

“Composition, temperature and pressure are three intensive variables that you might vary in an experiment. Pick any two, the third is locked in by thermodynamics. Set temperature and pressure, thermodynamics sets the composition.”

~ Rich Olcott

A Lazy Summer Day at 1400°C

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Susan Kim and Kareem are supervising while Cal mounts a new poster in the place of honor behind his cash register. “A little higher on the left, Cal.”

“How’s this, Susan? Hey, Sy, get over here and see this. Ain’t it a beaut?”

“Nice, Cal. What’s it supposed to be? Is that Jupiter in the background?”

“Yeah, Jupiter all right. Foreground is supposed to be a particular spot on its moon Io. They think it’s a lake of molten sulfur!”

“No way, from that picture at least! I’ve seen molten sulfur. It goes from pale yellow to dark red as you heat it up, but never black like that.”

“It’s not going to be lab-pure sulfur, Susan. This is out there in the wild so it’s going to be loaded with other stuff, especially iron. But the molten sulfur I’ve seen in volcanoes is usually burning with a blue flame. I guess the artist left that out.”

“No oxygen to burn it with, Kareem. Why did you mention iron in particular?”

“Yeah, this article I took the image from says that lake’s at 1400°C. I thought blast furnaces ran hotter than that.”

I’ve been looking things up on Old Reliable. “They do, Cal, typically peaking near 2000°C.”

“So if this lake has iron in it, why isn’t the iron solid?”

“Same answer as I gave to Susan, Cal. The iron’s not pure, either. Mixtures generally melt or freeze at lower temperatures than their pure components. Sy would probably start an entropy lecture—”

“I would.”

“But I’m a geologist. Earth is about ⅓ iron. That’s mixed in with about 10% as much sulfur, mostly in the core where pressures and temperatures are immense. We want to understand conditions down there so we’ve spent tons of lab time and computer time to determine how various iron‑sulfur mixtures behave at different temperatures and pressures. It’s complicated.” <brings up an image on his phone> “Here’s what we call the system’s phase diagram.”

“You’re going to have to read that to us.”

Adapted from Walder and Pelton
Click image to expand

“I expected to. Temperature increases along the y‑axis. Loki’s temp is at the dotted red line. Left‑to‑right we’ve got increasing sulfur:iron ratios — pure iron on the left, pure sulfur on the right. The idea is, pick a temperature and a mix ratio. The phase diagram tells you what form or forms dominate. The yellow area, for instance, is liquid — molten stuff with each kind of atom moving around randomly.”

“What’s the ‘bcc’ and ‘fcc’ about?”

“I was going to get to that. They’re abbreviations for ‘body‑centered cubic’ and ‘face‑centered cubic’, two different crystalline forms of iron. The fcc form dominates below that horizontal line at about 1380°C, converts to bcc above that temperature. Pure bcc freezes at about 1540°C, but add some sulfur to the molten material and you drive that freezing temperature down along the blue‑yellow boundary.”

“And the gray area?”

“Always a fun thing to explain. It’s basically a no‑go zone. Take the point at 1400°C and 80:20 sulfur:iron, for instance. The line running through the gray zone along those red dots, we call it a tie line, skips from 60:40 to 95:5, right? That tells you the 60:40 mix doesn’t accept additional sulfur. The extra part of the 80:20 total squeezes out as a separate 95:5 phase. Sulfur’s less dense than iron so the molten 95:5 will be floating on top of the 60:40. Two liquids but they’re like oil and water. If you want a uniform 80:20 liquid you have to shorten the tie line by raising the temp above 2000°C.”

“All that’s theory. Is there evidence to back it up?”

“Indeed, Sy, now that Juno‘s up there taking pictures. When the spacecraft rounded Io last February JunoCam caught several specular reflections of sunlight just like it had bounced off mirrors. At first the researchers suspected volcanic glass but the locations matched Loki and other hot volcanic calderas. The popular science press can say ‘sulfur lakes’ but NASA’s being cagey, saying ‘lava‘ — composition’s probably somewhere between 10:90 and 60:40 but we don’t know.”

Artist’s concept of Loki Patera,
a lava lake on Jupiter’s moon Io
Credit: NASA/JPL-Caltech/SwRI/MSSS

~ Rich Olcott