250 votes
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Strange ice found in my garden

Congratulations, you found an inverted pyramid ice spike, sometimes called an ice vase! The Bally-Dorsey model of how it happens is that first the surface of the water freezes, sealing off the water ...
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98 votes
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Is it possible to "see" atoms?

This entirely depends on what you mean by "see". Let me start of by noting: As per my knowledge, atoms are small beyond our imaginations No. Atoms are quite big compared to certain other things we ...
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  • 14.9k
33 votes

Why no proton microscopes? Proton diffraction; or proton scattering experiments? Proton crystallography?

What do protons offer that electrons and photons don't? Well, mass: $$ \frac{M_p}{m_e} \approx 1837 $$ What that means is that protons can travel through large $Z$ materials without undergoing ...
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  • 24k
32 votes

Why don't marbles naturally arrange themselves like a crystal?

Interaction between marbles is very similar to the hard sphere (HS) interaction model i.e. a pair-wise potential energy which is zero if spheres do not overlap and $+\infty$ elsewhere. Hard spheres ...
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27 votes
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Understanding time crystals

The key idea is that time crystals are externally driven at a certain frequency, but they respond at a different (in fact, slower) frequency. First of all, terminology: what does it have in common ...
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24 votes
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Why are snowflakes flat?

The most comprehensive, rigorous work I have ever seen on snowflake formation is Dr. Kenneth Libbrecht's (free) book Snow Crystals (I've linked to its location on the Arxiv). This answer will pull ...
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23 votes
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Why is Fourier space called as momentum space?

As per my username, I feel it is partially my responsibility to address this question. I said it before and I'll say it again: The Fourier Transform is not an accident. There are countless reasons it ...
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21 votes
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"Lack of inversion symmetry" in crystal?

The presence or absence of inversion symmetry in a medium has a direct impact on the types of nonlinear interactions that it can support; specifically, media which do have inversion symmetry cannot ...
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21 votes
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Can two atoms be a crystal?

Coulomb crystals are the structures formed by ions in a trap when they are sufficiently cold: once they stop jiggling around, they come down to equilibrium positions which need to balance the need to ...
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20 votes
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Why no proton microscopes? Proton diffraction; or proton scattering experiments? Proton crystallography?

Proton crystallography is not typically done because protons have a very shallow penetration depth compared to electrons, photons/x-rays, or neutrons with the same energy. This means that for a proton ...
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  • 6,020
17 votes

Why doesn't classic mechanics hold the concept of identical particles?

Classical physics has the concept of identical particles. What it doesn't have is the concept of indistinguishable particles. Informally, the difference is as follows: Man can not tell identical ...
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  • 24k
16 votes

Why do atoms arrange themselves in a regular fashion to form crystals?

To put it in simple terms: In the case of metals, surrounding the nucleus of each atom is a cloud of electrons. While some of the electrons occupy clouds that are spherically symmetric, other clouds ...
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16 votes
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Why do oxides form amorphous films instead of crystalline films?

This is because the volume occupied by an Al2O3 molecule is different from that occupied by two Al's. This volumetric mismatch means that you can't retain the crystalline lattice of the Al across the ...
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14 votes
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Notations for high symmetry points in the 1st Brillouin zone

For any crystal, the First Brillouin Zone is found using the Wigner-Seitz construction for the reciprocal lattice. The high-symmetry points are labeled by certain letters mainly as a convention--like ...
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13 votes
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Is it possible for a crystal to have different structures at different temperatures?

The microstructure of an alloy depends on such variables as the alloying elements present, their concentrations, and the heat treatment of the alloy (i.e., the temperature, the heating time at ...
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11 votes
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Why do crystals grow in preferred directions?

Broadly speaking, the reason why a snowflake forms a flat crystal with 6-fold symmetry (as opposed to a sphere) is due to a combination of the underlying symmetry (order) of the ice crystal and a ...
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11 votes
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What's the difference between a time crystal and a system undergoing periodic motion?

A crystal is a system which spontaneously breaks the translation symmetry of the underlying physical laws. Similarly, a time crystal is a system which is subject to a periodic driving with period $T$,...
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10 votes

How many atoms exist within a continuum body?

The number of atoms (or molecules) in a body is given by Avogadro's constant, or $6.022 \times 10^{23}$ per mole. A mole is the amount of material, in grams, equal to the atomic or molecular mass of ...
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10 votes
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Reciprocal lattice in 2D

You don't need to. In fact, you can work directly in 2D and solve things explicitly, since the condition for the reciprocal basis that $b_i\cdot a_j = 2\pi\delta_{ij}$ reads in matrix notation $$ \...
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10 votes

Why don't marbles naturally arrange themselves like a crystal?

"So if we take different marbles in a box and shake it then shouldn't they arrange themselves in order to get to a low energy state?" They certainly do - they will adopt a hexagonal (2D) or close ...
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10 votes

Why don't marbles naturally arrange themselves like a crystal?

You should study annealing. Vastly oversimplifying: If you cool the sample slowly enough, it retains enough energy long enough to explore its state space and find very low entropy, crystalline, ...
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9 votes
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Can electrons have energies between valence and conduction bands?

This is similar to asking if an electron, in say a hydrogen atom, can occupy an energy level somewhere in between the $n=1$ and $n=2$ levels. In this instance, and in the context of your question, the ...
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  • 25.6k
8 votes

Is it possible for a crystal to have different structures at different temperatures?

Yes, it is very possible. Even water goes through such different structures Two lines in particular from the wikipedia article on Ice: Ice II A rhombohedral crystalline form with highly ordered ...
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  • 43.1k
8 votes

Why don't marbles naturally arrange themselves like a crystal?

As HolgerFielder and Pieter said in their answers, marbles do form crystalline arrangements. Notice, though, in Holger Fielder's illustration that the arrangement is much less ordered near a boundary....
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  • 24.1k
7 votes

How many of the 230 crystallographic groups are realized in nature?

According to Fizicheskaya Entsiklopediya (Physical Encyclopedia, in Russian, http://www.femto.com.ua/articles/part_2/3634.html ), no real crystals had been found for 4 space groups (Pcc2 and three ...
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7 votes
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The Correct Statement of the Third Law of Thermodynamics

The hamiltonian of a perfect crystal can be approximated at low temperature as the sum of harmonic oscillator hamiltonians. In 1D we have $$H = \sum_{i=1}^N \frac{p_i^2}{2 m} + \frac 1 2 m \omega^2 \...
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  • 15.5k
7 votes

Is it possible to reassemble a perfectly cleaved crystalline solid?

For example, see cold or contact welding of ultraclean, similar metallic surfaces under ultrahigh vacuum conditions. After a few such experiences with what I thought were cleverly designed friction ...
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  • 7,069
7 votes

Why is Fourier space called as momentum space?

but is there some other reason for calling it momentum space? The canonical commutation relation for the position and momentum operators is (in one dimension) $$[X, P]|\psi\rangle = (XP - PX)|\psi\...
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  • 2,088
7 votes
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Fourier Transform and Lattices

$f(X)$ is a periodic function that has a Fourier series. In other words, $f(X)$ is a periodic function and so its Fourier transform has a spectrum at only discrete values of q. Still the transformed ...
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