24
votes
How much pressure would it take to compress a block of solid steel into one-tenth the original volume?
The basic answer is "Perfectly achievable pressures, but not for very long (with lasers, it's even legal)"
Metal is perfectly happy to shrink if you squeeze it hard enough. This is in fact ...
- 584
22
votes
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Why haven't we found thermal superconductors?
In an electrically insulating crystaline solid, heat is mostly transferred by phonons rather than by photons. What provides thermal resistance is phonon scattering via impurities or umklapp ...
- 53.2k
19
votes
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Why can you hammer a hole into an underwater ceramic cup?
First some background.
Glass and ceramics are stiff, but not totally rigid. Thin sheets are surprisingly flexible. To break a sheet of glass along a straight line, you scratch a line along the surface....
- 38.6k
17
votes
How much pressure would it take to compress a block of solid steel into one-tenth the original volume?
The basic answer is "no, you cannot." Consider that if you have enough pressure to compress an "incompressible" steel to one tenth its volume, the surfaces doing the pressing ...
- 48.9k
13
votes
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Why can't the charge carriers leave the conductor?
Fundamentally they can't leave because they are attracted to the fixed positively charged atomic nuclei in the material.
This results in the work function, meaning an amount of energy required to free ...
- 27.6k
13
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How much pressure would it take to compress a block of solid steel into one-tenth the original volume?
The bulk modulus of steel is 160 GPa, meaning that if it were linear, it would take 160 GPa to compress it twice. The pressure at the center of Jupiter is up to 7 TPa, which would be sufficient to ...
- 231
11
votes
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Forbidden vs. allowed transitions
Allowed and Forbidden transition is the language related to the selection rules. If we look at it from the point of view of Fermi Golden rule:
$$
w_{i\rightarrow f}=\frac{2\pi}{\hbar}\left|V_{if}\...
- 58.7k
9
votes
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Density functional theory: logical steps from Hohenberg-Kohn theorems to Kohn-Sham equations
1. The Hohenberg-Kohn Theorems:
I think the first part of your question does indeed summarize well the Hohenberg-Kohn theorems. Apart from some minor details (such as that $V$ is unique up to an ...
- 7,931
8
votes
What force attracts electrons so that they cannot leave the conductor?
As pointed out in the comments, electrons are bound in metals both by electrostatic and quantum mechanical interactions. Your intuition is correct, though: if the electric field is strong enough, the ...
- 3,008
8
votes
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Explaining Ohm's Law and Conductivity's constance at particle level
First of all, the $E$ one uses in these formulas are macroscopic , and describe accurately only the forces on macroscopically small, yet microscopically large bodies, i.e, a large collection of charge ...
- 702
8
votes
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When the energy in a conductor is not carried by the electrons, how resistances warm up?
You need more than just the Poynting vector, you need all of Poynting’s theorem$$\frac{du}{dt}+\nabla\cdot \vec S + \vec J\cdot \vec E =0$$
The Poynting vector describes the flow of energy from one ...
- 100k
7
votes
Landau tubes and Fermi sphere
My understanding is that the question is about figure like this one (taken from thread What's the coordinate of the Landau tube?):
Magnetic field does not change the number of electronic states or ...
- 58.7k
7
votes
Why can you hammer a hole into an underwater ceramic cup?
I'm 99% sure the answer is that it is not possible to hammer a hole into a ceramic cup using a nail, regardless of whether the cup is underwater or not.
This is not just because a ceramic cup is ...
- 34k
7
votes
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Band theory of solids: Kronig–Penney model parameters question
Now my question is, what does $k$ represent here? I know that it is the wave number. However, isn't $k=\frac{2\pi p}{h}$ (De broglie formula)?
It depends on what you mean by $p$. If you mean the ...
- 69.1k
7
votes
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One-dimensional tight-binding model with two different hoppings in the limit the hoppings are equal
Here's a way in which we can make sense of the limits in a physical situation in which the limit $t_1\to t_2$ should yield the first Hamiltonian. We could think of the atomic species as being the ...
- 7,704
6
votes
Are there phonons in air?
TL;DR: What differs phonons from photons is that phonons require presence of a medium, where the movement of the medium constitutes a field to be quantized. Photons are electromagnetic waves - they do ...
- 58.7k
6
votes
Understanding a sum in the Bravais lattice
It's just a generalisation of the discrete Fourier transform in higher dimensions. You have for $N$ a positive integer and $m$ integers modulo $N$:
$$
\sum_{n=0}^{N-1} e^{i2\pi mn/N} = N\delta_m
$$
...
- 11.5k
6
votes
Explaining Ohm's Law and Conductivity's constance at particle level
Your analysis is based on the false premise that the mobile electrons which are being accelerated by an electric field do not interact with anything.
On a simple model can can think of a copper $(Z=29)...
- 96.1k
6
votes
Would two substances, with different specific heat capacities, have different average kinetic energies at the same temperature?
Assuming no phase change, all energy was converted to K.E. (kinetic energy).
This is actually incorrect.
The average thermal energy per internal degree of freedom is $\frac{1}{2}k_B T$ where $k_B$ is ...
- 100k
6
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Why can you hammer a hole into an underwater ceramic cup?
EDIT: I should have watched the video first. Scroll to the end for additional remark.
Supposition:
For a ceramic bowl to fracture the fracturing must start at the rim.
The center of the bowl is a ...
- 20.9k
6
votes
When the energy in a conductor is not carried by the electrons, how resistances warm up?
In the Poynting model, the current produces a magnetic field that, in part, guides the energy flow. In the Drude model, the current is composed of electrons, whose collisions with something (lattice ...
- 20.9k
5
votes
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Do some gases have short range order?
When faced with terminology-related problems, a general warning is to double-check the conventions in the specific area of research.
In Condensed Matter Physics, short-, intermediate-, or long-range ...
4
votes
Why does lattice potential scattering cause band gaps?
You need to look at the potential in momentum space. The Fourier transform gives:
\begin{align}
\hat V(k) &:= \int dx V(x) e^{-ikx} \\
&= 2\pi\left(V_0\delta(k)+V_1\left(\delta\left(k-\frac{2\...
- 11.5k
4
votes
Accepted
Why can't valence electrons conduct electricity?
To be clear, valence band electrons (or lack thereof, i.e. holes) can and do carry current, you might find this answer useful. A band that is completely filled doesn't carry current. Here is a proof, ...
- 13.5k
4
votes
Accepted
What force attracts electrons so that they cannot leave the conductor?
A conductor consists of positively charged ions, forming a lattice, and negatively charged electrons, which are free to move within a conductor. The net charge is zero, and so the net force is ...
- 58.7k
4
votes
Accepted
Vortices in a Superconductor: triangular lattice VS other geometries
The vortex lines in a superconductor (or a neutral superfluid) form a regular crystal. Just like in a solid the precise arrangement depends on the interaction between the vortices, and is the one that ...
- 18.7k
4
votes
Why is the attraction of ions near the surface stronger than the repulsion of electrons?
Why don't you fly apart into your constituent atoms? The same logic applies: the nuclei repel each other, as do the electrons. Why does the attraction between the nuclei and electrons dominate?
One ...
- 20.9k
4
votes
Why is the specific heat of conductors and insulators not same at high $T$?
The Dulong-Petit law says that at high temperatures, the molar heat capacity of a solid substance approaches $3R$, regardless of whether it is an electrical conductor or insulator. It is a ...
- 69.1k
4
votes
Density functional theory: logical steps from Hohenberg-Kohn theorems to Kohn-Sham equations
Chapter 5 of Robert van Leeuwen's notes provides the missing links that I was looking for. This is one of references that was kindly recommended by Tobias in a comment.
For the benefit of future ...
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4
votes
Restoring force in a crystal
Your argument with Gauss' law is incorrect, but a correct treatment can lead to a similar contradiction.
From central symmetry, the other ions apply a net zero force on the ion when it is in its site. ...
- 11.5k
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