Tag: Cal’s Coffee

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

Confluence

On By rolcottIn Astronomy, Astronomy: Multi-messenger, General: Fun Stuff, UncategorizedLeave a comment

“My usual cup of — Whoa! Jeremy, surprised to see you behind the counter here. Where’s Cal?”

“Hi, Mr Moire. Cal just got three new astronomy magazines in the same delivery so he’s over there bingeing. He said if I can handle the pizza place gelato stand he can trust me with his coffee and scones. I’m just happy to get another job ’cause things are extra tough back on the rez these days. Here’s your coffee, which flavor scone can I get for you?”

“Thanks, Jeremy. Smooth upsell. I’ll take a strawberry one. … Morning, Cal. Having fun?”

“Morning, Sy. Yeah, lotsa pretty pictures to look at. Funny coincidence, all three magazines have lists of coincidences. This one says February 23, 1987 we got a neutrino spike from supernova SN 1987A right after we saw its light. The coincidence told us that neutrinos fly almost fast as light so the neutrino’s mass gotta be pretty small. 1987’s also the year the Star Tours Disney park attractions opened for the Star Wars fans. The very same year Gene Roddenberry and the Paramount studio released the first episodes of Star Trek: The Next Generation. How about that?”

“Pretty good year.”

“Mm‑hm. Didja know here in 2025 we’ve got that Mercury‑Venus‑Jupiter-Saturn‑Uranus‑Neptune straight‑line arrangement up in the sky and sometimes the Moon lines up with it?”

“I’ve read about it.”

“Not only that, but right at the September equinox, Neptune’s gonna be in opposition. That means our rotation axis will be broadside to the Sun just as Neptune will be exactly behind us. It’ll be as close to us as it can get and it’s face‑on to the Sun so it’s gonna be at its brightest. Cool, huh?”

“Good time for Hubble Space Telescope to take another look at it.”

“Those oughta be awesome images. Here’s another coincidence — Virgo’s the September sign, mostly, and its brightest star is Spica. All the zodiac constellations are in the ecliptic plane where all the planet orbits are. Planets can get in the way between us and Spica. The last planet to do that was Venus in 1783. The next planet to do that will be Venus again, in 2197.”

“That’ll be a long wait. You’ve read off things we see from Earth. How about interesting coincidences out in the Universe?”

“Covered in this other magazine’s list. Hah, they mention 1987, too, no surprise. Ummm, in 2017 the Fermi satellite’s GRB instrument registered a gamma‑ray burst at the same time that LIGO caught a gravitational wave from the same direction. With both light and gravity in the picture they say it was two neutron stars colliding.”

“Another exercise in multi-messenger astronomy. Very cool.”

“Ummm … Galaxy NGC 3690 shot off two supernovas just a few months apart last year. Wait, that name’s familiar … Got it, it’s half of Arp 299. 299’s a pair of colliding galaxies so there’s a lot of gas and dust and stuff floating around to set off stars that are in the brink. If I remember right, we’ve seen about eight supers there since 2018.”

“Hmm, many events with a common cause. Makes sense.”

“Oh, it’s a nice idea, alright, but explain V462 Lupi and V572 Velorum. Just a couple months ago, two novas less than 2 weeks apart in two different constellations 20 degrees apart in the sky. Bright enough you could see ’em both with good eyes if you were below the Equator and knew where to look and looked in the first week of June. My skywatcher internet buddies down there went nuts.”

“How far are those events from us?”

“The magazine doesn’t say. Probably the astronomers are still working on it. Could be ten thousand lightyears, but I’d bet they’re a lot closer than that.”

“On average, visible stars are about 900 lightyears away. Twenty degrees would put them about 300 lightyears apart. They’re separated by a slew of stars that haven’t blown up. One or both could be farther away than that, naturally. Whatever, it’s hard to figure a coordinating cause for such a distant co‑occurrence. Sometimes a coincidence is just a coincidence.”

Adapted from images by
IAU and Sky & Telescope magazine
(Roger Sinnott & Rick Fienberg)
CC BY 3.0

~ Rich Olcott

Why A Disk?

On By rolcottIn Astronomy: Stellar Science, Cosmology, UncategorizedLeave a comment

Late Summer is quiet time on campus and in my office. Too quiet. I head over to Cal’s coffee shop in search of company. “Morning, Cal.”

“Morning, Sy. Sure am glad to see you. There’s no‑one else around.”

“So I see. No scones in the rack?”

“Not enough traffic yet to justify firing up the oven on such a hot day. How about a biscotti instead?”

“If it’s only the one it’s a biscotto. Pizza Eddie’s very firm on that. Yeah, I’ll have one.”

“Always learning. By the way, a photo spread in one of my astronomy magazines got me thinking. How come there’s so much flat out there?”

“Huh? I know you’re not one of those flat‑Earthers.”

“Not the planets, I mean the way their orbits go all in the same plane. Same for most of the asteroids and the Kuiper belt, even. Our Milky Way galaxy’s basically flat, too, and so are a lot of the others. Black hole accretion disks are flat. You’d think if some baby star or galaxy was attracting stuff from everywhere to grow itself, the incoming would make a big globe. But it’s not, we get flatness. How come?”

“Bad aim and angular momentum.”

“What’s aim got to do with it?”

“Suppose there’s only two objects in the Universe and they’re closing in on each other. If they’re aimed dead‑center to each other, what happens?”

“CaaaRUNCH!!!”

“Right. Now what if the aim’s off so they don’t quite touch?”

“Oh, I know that one … it’ll come to me … yeah, Roche’s limit, it was in an article a few months ago. Whichever’s less dense will break up and all the pieces go like Saturn’s rings. Which are also flat, by the way.”

“In orbit around the survivor, mm‑hm. The pieces can’t fall straight down because they still have angular momentum.”

“I know about momentum like when you crash a car if you go too fast for your brakes. Heavier car or faster speed, you get a worse crash. How does angle fit into that — bigger angle, more angular momentum?”

“Not quite. In general, momentum is mass multiplied by speed. It’s a measure of the force required to stop something or at least slow it down. You’ve described linear momentum, where ‘speed’ is straight‑line distance per time. If you’re moving along a curve, ‘speed’ is arc‑length per time.”

“Arc‑length?”

“Distance around part of a circle. Arc‑length is angle in radians, multiplied by the circle’s radius. If you zip halfway around a big circle in the same time it took me to go halfway around a small circle, you’ve got more angular momentum than I do and it’d take more force to stop you. Make sense?”

“What if it’s not a circle? The planet orbits are all ellipses.”

“It’s still arc‑length except that you need calculus to figure it. That’s why Newton and Leibniz invented their methods. A falling something that misses a gravity center keeps falling but on an orbit. Whatever momentum it has acts as angular momentum relative to that center. There’s no falling any further in without banging into something else coming the other way and each object canceling the other’s momentum.”

“Or burning fuel if it’s a spaceship.”

“… Right. … So anyway, suppose you’ve got a star or something initially surrounded by a spherical cloud of space junk whirling around in all different orbits. What’s going to happen?”

“Lots of banging and momentum canceling until everything’s swirling more‑or‑less in the same direction and closer in than at come‑together time. But it’s still a ball.”

“Gravity’s not done. Think about northern debris. It’s attracted to the center, but it’s also attracted to the southern debris and vice-versa. They’ll meet midway and build a disk. The ball‑to‑disk collapse isn’t even opposed by angular momentum. Material at high latitudes, north and south, can lose gravitational potential energy by dropping straight in toward the equator and still be at the orbitally correct distance from the axis of rotation.”

“That’d work for stuff collecting around a planet, wouldn’t it?”

“It’d even work for stuff collecting around nothing, just a clump in a random density field. That may be how stars are born. Collapsing’s the hard part.”

~ Rich Olcott

Look, Look Again, Then Think

On By rolcottIn Astronomy, UncategorizedLeave a comment

Cathleen and I are sharing scones and memories when Vinnie trundles up to our table. “Glad I got you two together. I just ran across a couple news items and I need some explanations.”

“Astronomy AND Physics in the same news items? Do tell.”

“They’re only one paragraph each and read like someone wrote ’em before their morning coffee. They’re both about that big black hole they’ve been taking pictures of.”

“The one in our galaxy or the M87* supermassive black hole in the Messier‑87 galaxy?”

“The second one, Cathleen. This item says it shot out a jet traveling faster than light.”

<sigh> “Pop‑sci journalism at its worst, right, Sy? I know the work that’s based on and the academic reports don’t say that. Good observations leading to less flamboyant conclusions.”

“Maybe it was supposed to be a bigger article but the editors cut it down badly. That happens. I’m sure it’s not really a superluminal jet—”

“Superluminal’s faster‑than‑light, right?”

“Right, Vinnie. Sorry to get technical. Anyway, it’s an illusion.”

“Ah geez, it’ll be frames again, right?” <eyes suddenly open wide> “Wait, I got it! I betcha it’s about the time difference. Take a blob in that jet, it’s flying out at near lightspeed. Time dilation happens when relativity’s in the game, me and Sy talked about that, so blob‑frame seconds look like they take longer than ours do. We see the blob cramming a lightsecond of distance traveled into less than one of our seconds and that’s superluminal. Am I right, Sy?”

“Right answer to a different question, I’m afraid. You’re straight on the time dilation but it doesn’t apply to this situation. Something happening within the blob’s frame, maybe a star blowing up or something weird metabolizing in there, Special Relativity’s time distortion hijinks would show us that action taking place in slow motion. But this superluminal blob claim hinges on how the blob’s whole frame moves relative to ours. That motion isn’t superluminal but it can look that way if conditions are right. As I understand it, the M87* jet qualifies. Your bailiwick rather than mine, Cathleen.”

“Actually it is a frames thing, Vinnie, but timeframes, not spacetime. Those blobs move too slowly in our sky to watch in real time. We take snapshot A and then maybe a few years later we take snapshot B and compare. Speed is the ratio of distance to time. We need the A‑B distance in 3‑D space to compare to the known time between snapshots. But we can’t see the blob’s trajectory in 3‑D. All we can capture is its 2‑D arc C‑B across an imaginary spherical shell we call the sky. If the M87* jet were perpendicular to our line of sight the C‑B image on the sky‑sphere would match the 3‑D path. Multiply the image’s angle in radians by the distance to M87* and we’re done.”

“We’re not done?”

“Nope. This jet points only 20° away from our direct line of sight. I’ll spare you the trigonometry and just say that distance A‑B is about 3 times longer than C‑B.”

“So we measure C‑B, triple the angle and multiply by the M87* distance. No problem.”

“Problem. That tripling is what makes the blob’s A‑B journey appear to go faster than light. Three times 0.4c equals 1.2c. But you missed something important. Your arithmetic assumed you could use a simple ‘M87* distance’. Not in this case, because the blob moves towards us at close to lightspeed. Visualize two concentric sky‑spheres. The outer one’s radius runs from us to the blob’s location at A‑time. The inner sphere’s radius runs to the blob’s location at B‑time. The B‑sphere is our reference frame. The light we saw at A‑time had to travel from the outer sphere to the inner one before we could register the C‑B image.”

“Can’t be very far.”

“We’re talking years at lightspeed, so lightyears, so significant. A properly illusion‑free A‑B travel calculation must include the A‑C travel time in the denominator of the distance/time ratio. The true kilometers per second come out well below lightspeed. Oh, and relativity’s not involved.”

“Dang, Cathleen, it was such a cool illusion.”

~ Rich Olcott

Sharpening The Image

On By rolcottIn Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

“One coffee, one latte and two scones, Cal. Next time is Cathleen’s turn. Hey, you’ve got a new poster behind the cash register. What are we looking at?”

“You like it, Sy? Built the file myself from pics in my astronomy magazines, used the Library’s large‑format printer for the frameable copy. Came out pretty well, didn’t it, Cathleen?”

“Mm‑hm. Sy, you should recognize the pebbly-looking one. It’s granules at the bottom of the Sun’s atmosphere. The image came from the Inouye Solar Telescope at Haleakala Observatory on Maui, probably Earth’s best ground‑based facility for studying the Sun. I showed the image to your niece in that phone call. For scale, those granules of super‑heated rising gas are each about the size of Texas.”

“My magazine article didn’t mention Texas but it said there’s about ten million granules. What it was mostly about was the IST and its resolution. Those edges in the picture are as narrow as 18 miles across. It’s that good ’cause the beast has a 4‑meter mirror, which used to be amazing, but they made it even better with active and adaptive optics.”

“Hmm. It’s obvious that the bigger the mirror, the better it is for catching photons. If someone’s going to build a big mirror they’re going to put it behind a big aperture, which is important for resolving points that are close together. But what are ‘active and adaptive optics’ and why did you say that like they’re two different things?”

” ‘Cause they are two different things, Sy. Different jobs, different time‑scales. Gravity here on Earth can make a big mirror sag, and the sag changes depending on where the machine is pointed and maybe part of it gets the wrong temperature. Active optics is about keeping the whole mirror in the right shape to focus the photons where they’re supposed to go. There’s a bunch of actuators rigged up to give adjustable support at different points behind the mirror. The astronomer tells the system to watch a certain guide point and there’s a computer that directs each actuator’s pushing to sharpen the point’s image.”

“And adaptive optics?”

“That’s about solving a different problem. Stars twinkle, right, and the reason they twinkle is because of the atmosphere. One part refracts light one way, another part maybe warmer or with different humidity sends the light another way. Everything moves second to second. By the time a light‑wave gets down to us it’s been jiggled a lot. Adaptive optics is a small mirror, also with a lot of actuators, placed up in the light path after the primary mirror. Again with a guide point and a computer, the little mirror’s job is to cancel the jiggles so the scope’s sensors see a smooth wave. Adaptive works a lot faster than active, which sounds backwards, but I guess active came first.”

“The granules must be in the Sun’s disk somewhere. The other two images look like they’re on the edge.”

“That’s right, Sy. The bottom one is from the Solar Dynamic Observatory satellite a few years ago. That’s not visible light, it’s EUV—”

“EUV?”

“Extreme UltraViolet, light‑waves too short even for hydrogen so it’s mostly from iron atoms heated to millions of degrees. SDO had to be a satellite to catch that part of the spectrum because the atmosphere absorbs it. Of course, up there there’s no need for active or adaptive optics but imaging EUV has its own problems.”

“How tall is that photogenic tree?”

“It’s a prominence. The article said it’s about twenty times Earth’s diameter.”

“What about the pink one?”

“That’s new, Cathleen, from another Maui telescope. Adaptive optics were in play but there’s a problem. If you’re probing inside the corona there’s no fixed guide point. The team focused their adjustment system on corona features where they were a few seconds ago. The article said the process was ‘tricky,’ but look at the results. The loop is about the size of Earth, and those fine lines are about the width of Vancouver Island. They discovered details no‑one’s ever seen before.”

Top left: Schmidt et al./NJIT/NSO/AURA/NSF;
Top right: NSO/AURA/NSF under CC A4.0 Intl license;
Bottom: NASA/SDO

~ Rich Olcott

Why Those Curtains Ripple

On By rolcottIn Astronomy: Planetary Science, Physics: Electromagnetism, UncategorizedLeave a comment

I’m in the scone line at Cal’s Coffee when suddenly there’s a too‑familiar poke at my back, a bit right of the spine and just below the shoulder blade. I don’t look around. “Morning, Cathleen.”

“Morning, Sy. Your niece Teena certainly likes auroras, doesn’t she?”

“She likes everything. She’s the embodiment of ‘unquenchable enthusiasm.’ At that age she’s allowed.”

“It’s a gift at any age. Some of the kids in my classes, they just can’t see the wonders no matter how I try. I show them aurora photos and they say, ‘Oh yes, red and green in the sky‘ and go back to their phone screens. Of course there’s no way to get them outside late at night at a location with minimal light pollution.”

“I feel your pain.”

“Thanks. By the way, your aurora write-ups have been all about Earth’s end of the magnetic show. When you you going to do the rest of the story?”

“How do you mean?”

“Magnetism on the Sun, how a CME works, that sort of thing.”

“As a physicist I know a lot about magnetism, but you’re going to have to educate me on the astronomy.”

Plane‑polarized Lorentz (electromagnetic) wave
 Electric (E) component is red
 Magnetic (B) component is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)
Licensed under CC ASA3.0 Unported

“Deal. You go first.”

<displaying an animation on Old Reliable> “We’ll have to flip between microscopic and macroscopic a couple times. Here’s the ultimate micro — a single charged particle bouncing up and down somewhere far away has generated this Lorentz‑force wave traveling all alone in the Universe. The force has two components, electric and magnetic, that travel together. Neither component does a thing until the wave encounters another charged particle.”

“An electron, right?”

“Could be but doesn’t have to be. All the electric component cares about is how much charge the particle’s carrying. The magnetic component cares about that and also about its speed and direction. Say the Lorentz wave is traveling east. The magnetic component reaches out perpendicular, to the north and south. If the particle’s headed in exactly the same direction, there’s no interaction. Any other direction, though, the particle’s forced to swerve perpendicular to both the field and the original travel. Its path twists up- or downward.”

A charged particle traversing a Lorentz wave

“But if the particle swerves, won’t it keep swerving?”

“Absolutely. The particle follows a helical path until the wave gives out or a stronger field comes along.”

“Wait. If a Lorentz wave redirects charge motion and moving charges generate Lorentz waves, then a swerved particle ought to mess up the original wave.”

“True. It’s complicated. You can simplify the problem by stepping back far enough that you don’t see individual particles any more and the whole assembly looks like a simple fluid. We’ve known for centuries how to do Physics with water and such. Newton invented hydrodynamics while battling the ghost of Descartes to prove that the Solar System’s motion was governed by gravity, not vortices in an interplanetary fluid. People had tried using Newton‑style hydrodynamics math to understand plasma phenomena but it didn’t work.”

<grinning> “I don’t imagine it would — all that twistiness would have thrown things for a loop.”

“Haha. Well, in the early 1940s Swedish physicist Hannes Alfven started developing ideas and techniques, extending hydrodynamics to cover systems containing charged particles. Their micro‑level electromagnetic interactions have macro‑level effects.”

“Like what?”

“Those aurora curtains up there. Alfven showed that in a magnetic field plasmas can self‑organize into what he called ‘double layers’, pairs of wide, thin sheets with positive particles on one side against negative particles in the other. Neither sheet is stable on its own but the paired‑up structure can persist. Better yet, plasma magnetic fields can support coherent waves like the ones making that curtain ripple.”

“Any plasma?”

“Sure.”

“Most of the astronomical objects I show my students are associated with plasmas — the stars themselves, of course, but also the planetary nebulae that survive nova explosions, the interstellar medium in galactic star‑forming regions, the Solar wind, CMEs…”

“Alfven said we can’t understand the Universe unless we understand magnetic fields and electric currents.”

~ 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

Xanax For Molecules

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

Vinnie plops down by our table at Cal’s Coffee. “Hi, guys. Glad you’re both here. Susan, Sy here says you’re an RDX expert so I got a question.”

“Not an expert, Vinnie, it’s just one of a series of compounds in one of my projects. What’s your question?”

“How come the stuff is so touchy but it’s not touchy? You can shoot a bullet into a lump of it, nothing happens, but set off a detonator next to it and WHAMO! Why do we need a detonator, and what’s in one anyway?”

“Sy, what sets off an H‑bomb?”

“An A‑bomb. You need a lot of energy in a confined region to crowd those protons enough that they fuse.”

“And what sets off an A‑bomb?”

“Hey I know that one, Susan, I saw the Oppenheimer movie. You need some kind of explosives going off just right to cram two chunks of plutonium together real fast so they do the BANG! thing instead of just melting. Wait! I see where you’re going — little explosions trigger big explosions, right?”

“Bravo! You’ve got the idea behind activation energy.”

“Geez, another kind of energy?”

“Yes and no, Vinnie. Enthalpy and its cousins are about the net change when something happens. We can use them to predict how a complex reaction will settle down, but they don’t tell us much about the kinetics, how fast things will happen. Think for a minute about those H‑bomb hydrogen atoms. What prevents them from fusing?”

“I guess under normal conditions they’re too far apart and even when they get close their electron clouds push against each other.”

<Sketching on a paper napkin> “Fair enough. Okay, here’s what the potential energy curve looks like, sorta. There’s hydrogen atom A over there at the right-hand end of the curve. B‘s a second hydrogen on the left and heading inwards. With me?”

“So far.”

“Right. Now, B comes roaring in with some amount of kinetic energy and hits the potential energy bump where those electron clouds overlap. If it has enough kinetic energy to overcome that barrier, it keeps on going. Otherwise it bounces back with the kinetic energy it had maybe minus some that A picked up in the recoil.”

“So the first barrier is the electron‑electron repulsion, but the potential dips in the middle where the clouds merge and that’s where molecules happen.”

“Right, Sy. But then there’s the second barrier as B‘s positive charge encounters A‘s. Inverse‑square law and all that, it’s an enormous hurdle. Visualize lots of Bs with different kinetic energies running up against that wall again and again until finally, if the pressure’s high enough, one gets past and the fusion releases more energy than the winning B had originally. The higher the wall, the fewer Bs hit As per unit time and the slower the reaction.”

“Looking at the before‑and‑afters, the reaction only happens if energy’s released, but how fast it goes is that barrier’s fault.”

“Perfect, Vinnie. Take RDX, for example. You’re right, it’s touchy. If you’ve got the pure stuff, never look at it cross‑eyed unless you’re behind a blast shield. Lots of energy released, very low energy of activation.”

“But like I said, you can shoot a gun at it, no effect.”

“That wasn’t pure RDX, it was probably some version of C‑4.”

“Yeah, C‑4, don’t know any of the details.”

“C‑4’s explosive is RDX, but it’s also got some plasticizer for that putty consistency, and a phlegmatizer. I love that word.”

“Phlegmatizer? That’s a new one for me.”

“It’s an additive to keep the explosive calm — phlegmatic, get it? — until it gets excited on purpose, which is the detonator’s job.” <scribbling on a stack of paper napkins> “Okay, here’s that same activation energy curve, an RDX particle on the right, and an incoming shock wave. The gray region is the phlegmatizer, usually paraffin or a heavy oil. Think of it as a shock absorber, absorbing or deflecting the shockwave before it can activate the explosive. A detonator’s designed to activate and erupt so quickly that its shock peak arrives before the phlegmatizer can spread it out.”

“Like they say, timing is everything.”

~ Rich Olcott

Tightening Up Fast And Loose

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

Cal brings out a fresh batch of scones. He’s tonging them onto the racks when I suddenly get a whiff of mocha latte. I glance back and there’s Susan Kim, grinning at me. “Hi, Sy. Grab your scone and a table. I have a bone to pick with you.”

A few moments later we’re seated. Cal’s coffee’s especially smooth today. “Okay, what’s the bone?”

“You’re playing fast and loose with your enthalpy definition. Yes, there’s change in temperature times entropy, enthalpy’s thermal component, and an expansion‑contraction component you called pressure‑volume. But it’s just sloppy to call what’s left ‘the chemical portion.’ What it is, really, is the combination of every other kind of energy something has that some process could extract. Chemical reactions are just one piece.”

“Strong words, coming from a chemist. What else should be packed in there?”

“Radioactivity, for one. It’s a heat source that doesn’t depend on chemical reactions. Atom for atom, a nuclear disintegration can yield millions of times more energy than a chemical reaction does. Trouble is, radioactive atoms only break down when they feel like it so the energy’s all random heat. I’m sure there’s a bunch of other non‑chemical ways to increase something’s apparent enthalpy.”

“Hmm. Challenge accepted. … It’s all about which process will extract some kind of energy from your something. How about the something’s a tightly‑wound spring? No, wait, that’s chemical, because the energy’s stored in stretched metal‑metal bonds.”

“No, I’ll accept spring tension because there’s no change in chemical composition during the unwind process. What’s another one?”

“Ah. Easy. Kinetic energy if the something’s flying through the air to hit something else.”

“Now you’re cooking. Gravitational potential energy if it’s falling down. Oh, suppose it’s magnetized and goes through a conductive loop on the way down?”

“Nope, doesn’t count. The object’s kinetic energy would produce a jolt of electrical potential in the loop, but it’s own magnetization wouldn’t change. Nice, that distinction sharpens the point — what you count as enthalpy’s third component depends on which change process you’re talking about. If there’s no chemical change, then the chemical part of the internal component of the enthalpy change is zero. In the early days of thermodynamics, for instance, everyone was working on steam. Water may corrode your equipment over the long term, but otherwise it’s just hot water molecules becoming not‑as‑hot water molecules and there’s no change in internal energy. The only energy terms you have to think about are pressure‑volume and temperature‑entropy. That’s why they defined it that way.”

“Which one wins?”

“Hmm?”

“You’ve pared enthalpy changes down to just two kinds of energy. I’ve got to wonder, which one has the bigger contribution?”

<pulls up a display on Old Reliable> “This is just for the water‑steam system, mind you. Vinnie was surprised. It’s all based on specific heat measurements so visualize one kilogram of liquid water.”

“A liter, right.”

“The line labeled ‘Mechanical’ is the amount of energy you’d get by expanding that kilogram from 0°C up to the temperatures laid out on the x‑axis. No significant expansion up near boiling temperature, then it follows the Ideal Gas Law, PV=nRT. At atmospheric pressure and in this temperature range the expansion relative to 0°C runs about 200 kilojoules per kilogram.”

“And the ‘Thermal’ line?”

“That’s lab‑measured heat capacity values I pulled from the CRC Handbook, each multiplied by the corresponding temperature in kelvins. That’s the amount of energy our kilogram of water molecules holds just by being at the temperature it’s at. The gas makes a nice straight line, at least in the range before heat shatters the molecules.”

“That’s what, fifteen or sixteen times more energy than the mechanical part? Wow! You know, back in Physical Chemistry class they just threw around lots of confusing thermodynamics formulas but never put numbers to them. I had no idea the entropy effect could just swamp whatever else.”

“Numbers do make a difference.”

“This clarifies something I didn’t understand back then. Entropy’s about randomness, right, and a gas molecule can be in more locations in a large volume than in a small one. V=nRT/P says volume rises linearly with temperature and that’s the linear rise in your chart.”

~ Rich Olcott