Movement of atoms in solids

Factual Questions
1

As I understand it, atoms and molecules are (nearly always) moving and bouncing around. When a material is solid, it’s because the atoms have slowed enough to get caught against each other in an invisible net of mutual attraction. But, where we might often visualize this like spherical metal magnets all clumped together, the fact that you can warm up and cool down solid materials would say that they’re still bouncing around - just constrained in territory - not rigidly and immobily touching one another.

My questions:

Is there any sort of pattern to this movement? In space, for example, things tend to line up their movement into disks. I would think that the forces around the atoms would push and pull the atoms surrounding themselves in such a way as to set up patterns of movement.

(Assuming that those patterns exist.) Do those patterns have any ramifications on the physics of the object? For example, if the atoms end up in small, spinning circles then would that have any gyroscopic effects? If they’re bouncing back and forth in a straight line - like little pistons - is that going to have any effects on how it moves in particular directions or how robust the material is from shock in certain directions?

2

A lot of materials do have particular alignment of the molecules and atoms within.
Atoms align into molecules. Then the molecules often align in relation to other molecules.
Crystal structures have very definite, repeating alignments alignments.
One ramification of alignments can be magnetism. You can use a magnet to align some molecules of a metal, to make it magnetic.

3

That’s what crystals are. Like a diamond. The pyramid shape of the carbon atom repeats itself.

Graphite is also Carbon that joins together to form rings, these rings slide over each other like sheets

4

You are asking about phonons, which are quantized vibrations of a crystal lattice.

Phonons are fundamental to just about all solid state based phenomena, including transistors, superconductors, and lasers.

5

That’s a pattern in how they arrange themselves relative to one another, not a pattern in their movement. E.g. if I stick a bunch of children in movie theater chairs then they’re going to be seated in nice, ordered rows and columns - that doesn’t mean that they’re not moving around, flailing their arms and kicking.

If you can warm up and cool down a crystal then the atoms are moving faster and slower, relatively. They’re still - as I understand it - in their position in the lattice, they’re just squirming around at different speeds inside their little space.

It’s this seat-squirming movement that I was curious about.

A phonon does seem to be the answer.

6

It’s hard to tell what effect they have from the Wikipedia article, it mostly seems to be going through the math of their movement. (From the graphics and some logic, I’ll spitball that they’re usually moving in ellipses and tend to set up wave patterns between themselves.)

An elliptical movement pattern would, I think, create gyroscopic effects? Or, at this scale, does that not matter?

7

The movements don’t tend to create patterns, really. They’re small relative to the separations atoms have to achieve to break bonds or shift their arrangements around – when they get to this scale, we call it “melting” and it stops being a solid.

There are, I understand, patterns in movements for very small pieces of solids. I’m a bit out of my depth here, but, as I understand, this is the reason that very thin pieces of solids melt at significantly lower temperatures. I hope somebody that knows what they’re doing comes along and straightens this out…

8

The movements are random. There are a lot of particles in even a small piece of a solid and even if you could line them all up almost perfectly, infinitesimal differences would lead to chaotic results.

9

Phonons are essentially a method by which energy can travel through the crystal lattice. Other particles (electrons, holes, etc.) can create, absorb, and exchange the phonons, which from a quantum mechanical view are also particles (bosons).

The simplest example is a (BCS) superconductor. Two free electrons in a metal become correlated through a phonon, creating a single cooper pair, held together by an attractive force created by their interaction through the lattice (the phonon).

10

Here is a paper saying that harmonic waves and such occur due to “lattice vibration”.
"in a crystal , the vibrations of atoms are not independent of each other. "

Lattice Vibrations - Engineering LibreTexts.

For example, it says the lattice vibrations will send up electrical resistance due to high temperature.

11

Then there’s

Measures the effect of gamma rays hitting atoms in a lattice.

12

Do you know about time crystals?:

13

OP may be interested in molecular vibrations?

14

You shouldn’t picture atoms held rigidly together by little rods, but you mostly can picture them as being held together by little springs. The bonds are strong enough that the arrangement of the atoms don’t change relative to other atoms, but they do still jiggle in place.

As for phonons, what’s really fun is that if you get enough of them in an object, the individual phonon particles act like a gas, and you can describe the pressure and density of that gas as a function of position and time. Which, in turn, means that you can get sound waves in that gas: Sound whose medium of vibration is, itself, also sound. This is called “second sound”.

15

Undoubtedly the source for the 1965 play that later won the Pulitzer Prize, The Effect of Gamma Rays on Man-in-the-Moon Marigolds.

16

No, that’d be from the horticultural practice of exposing a whole bunch of seeds to radiation, to induce a whole bunch of random mutations, in the hopes that one or two of those mutations might be something that you can sell as a new variety. Which practice, by the way, dates back the better part of a century, and is not legally considered “GMO”.

17

@Sage_Rat, the balls-and-springs picture @Chronos described is the correct one. If you want to introduce another layer of complexity to this picture, thinking about phonons is jumping the gun. You first need to understand collective behavior – vibrational “modes”.

If we work in 2D for visualization simplicity, first imagine four unmovable objects (X) supporting a movable object (O) with identical, suitably stiff springs to keep the movable object fairly close to its home, like this:

    X
    |
X---O---X
    |
    X

(Aside: Ignore the italics in that diagram. The dashes apparently do that, which I do not want in “preformatted” text. Oh well.)

The “O” in the middle can jiggle up and down, and it can jiggle side to side, and it can do both at the same time. If it does both at the same time, it might follow a diagonal path if the up/down oscillation and the left/right oscillation are in perfect phase with one another, or it might follow an elliptical path if they aren’t. Stop me here if you want more details on this part. Else…

Now imagine that the immovable objects are themselves other movable objects connected by springs to yet more movable objects, forming a huge lattice extending in all directions:

   |   |   |   |   |
 --O---O---O---O---O--
   |   |   |   |   |
 --O---O---O---O---O--
   |   |   |   |   |
 --O---O---O---O---O--
   |   |   |   |   |
 --O---O---O---O---O--
   |   |   |   |   |

Now if we look at a single object (atom) in this lattice, it sort of follows the same rules as before, except how compressed or stretched its springs are depends on what the four neighbors are up to. If those neighbors happen to be currently vibrated/displaced up and to the right, then our atom stuck in between them will be pulled that way. Or flipping the story, if our current atom vibrates right, the atoms around it will feel a push or pull from that.

So, the atoms are all still just vibrating around their little home, but the precise motion is made more complicated due to the interconnection throughout the lattice.

So looking at a single atom could lead to very complex motion given the connection to all the neighbors (and the neighbors’ neighbors, etc.), but zooming out to look at the entire lattice as a whole leads to a dramatical simplification. When you have a collection of things that individually behave in a sinusoidal way (i.e., simple oscillations), the collective behavior throughout the whole system also exhibits sinusoidal behavior, but at a macro level and with a set of system-specific frequencies possible. A 1D picture of oscillation “modes” in a vibrating string is here at Wikipedia and gives you something to visualize.

The remarkable simplification is that each mode (“harmonic”, “overtone”, whatever you want to call it) can be thought of as a separate thing now. And they can – and typically do – co-exist. You can have some vibration in mode number 17 and some vibration in mode number 138 and some vibration in mode number 2 – all at the same time. On the one hand, this is just a relabeling of the same complicated motion we would see examining individual atoms. On the other hand, since the modes each have a set frequency and spatial pattern, they provide the more relevant picture for connecting the interior motion to the outside world.

Stop me here if useful. Else…

All that is a prerequisite to worrying about phonons. In short, when you examine all this with atoms or molecules – for which quantum mechanics is relevant – you still get these oscillation modes at certain frequencies, but those modes become quantized. You can’t have arbitrary energy stored in mode number 138 or 72. You can only have discrete levels of energy. And those discrete, quantum mechanical excitations of the lattice are phonons.

I hope I have shown that phonons aren’t really a direct answer to the question “How does an atom move?” Side note: I introduced quantum mechanics only at the end, but it affects even the first “single atom” picture. I just skipped quantizing that part of the story.

In summary:

An atom is bound to its neighbors and moves in approximately a sinusoidal way in all allowed directions, and in doing so can follow various elliptical paths, except all that is subject to quantum mechanical caveats. Also, the atom’s neighbors all do the same, and thus an individual atom’s motion is made much messier by the collective behavior of all the atoms. But, that messiness can be abstracted away by thinking about vibrations across the entire lattice. Those macro vibrations have a clean interpretation as vibrational modes with specific frequencies and spatial patterns, and those are also subject to quantization, and those quantized modes are called phonons.

Unrelated to the above, but note that time crystals require a periodic perturbation (e.g., an incoming light wave). So, these aren’t standalone crystals that oscillate their structure spontaneously with time. However, in the static presence of a dynamic (and periodic) perturbation, they take on crystal properties in the time dimension.

18

Well so, my question would be - and I suspect that the answer is “no” - whether this elliptical movement forms the basis of inertia? Gyroscopes are rigid in space. A messy collection of things moving in ellipses would have a resistance to movement in more-or-less all directions and it would take energy to overcome that.

19

Gyroscopes have interesting properties when rotated due to the stored angular momentum, but they don’t offer any special “resistance” to linear motion. So, I’m not seeing the connection you are proposing. That is, if you have a spinning gyro on your desk, you can push it across your desk just the same as it it were not spinning.

20

They don’t want to change the angle of the plane on which they’re spinning and trying to rotate that plane requires energy. (Linear changes don’t matter but rotational do.)

Given an imperfect world and jelly-like objects that aren’t truly rigid - just sort of wobbling around on springs against each other - linear movement of macroscopic objects is probably nigh-impossible. Any attempt at movement would seem likely to cause some rotational force as well?