# Tag Info

248

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 below except for a small opening. If the freezing rate is high enough the expansion of ice under the surface will increase pressure (since the ice is less dense ...

96

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 play around with, like its constituents (protons, electrons) in particle accelerators. The size of atoms is of the order 0.1 nanometres (of course, there is a ...

32

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 are one of the first systems studied via computer simulation and one of the first big surprise was that by increasing pressure, they are able to crystallize from ...

30

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 electromagnetic interactions such as bremsstrahlung or pair production (the former goes as $M^{-5}$ at fixed energy). This makes it possible to use protons to image ...

25

They do. It is easiest to do show this in two dimensions. I used to demonstrate this on an overhead projector, with lead shot in a transparent CD-case. It is probably better to use smaller spheres (more spheres) than marbles. The other classic demo is with bubble rafts, which can also demonstrate the movement of dislocations. In three dimensions, it is ...

23

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 with the usual concept of crystals, whose whole structure can be represented by spatially replicating the unit cell. Is the time crystal an addendum to the ...

22

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 has the precise form it has. Let $F[f]$ denote the Fourier Transform of $f$, and let $\boldsymbol P=-i\boldsymbol \partial$ denote the momentum operator. We ...

21

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 get down to the center of the trap, where the trapping potential is at its minimum, with the mutual repulsion between the ions. This usually results in an ...

21

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 essentially exclusively from this work; think of it as an introduction to/summary of parts of this work that will hopefully segue into the whole thing. So, in my ...

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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 support nonlinear effects of even order. The reason for this is that adding an even harmonic to the fundamental will yield an asymmetric dependence of the ...

18

Due to the crystal structure of the solid phase of water, the molecules arrange themselves in a rigid, ordered fashion and end up being, on average, farther apart from each other (than they are in the liquid phase), and thus less dense. Less dense things float because of buoyancy.

13

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 temperature, and the rate of cooling to room temperature). -Materials Science and Engineering: An Introduction 9th, Wiley, Calister, Rethwisch Look up phase ...

11

Proton crystallography is typically not 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 to penetrate through the same amount of material as other particles (electron/photon/neutron) it needs to be accelerated to much higher energy, but it is that ...

10

Indeed this is a handy counter example to people who, not understanding the second law, claim that evolution is impossible on the basis that entropy decreases (nevermind that by this misunderstanding life itself would be impossible as well). The growing crystal is not a closed system: it exchanges energy and matter with the surrounding environment, and this ...

10

The laboratory made diamonds are as good as the naturally found ones. It is the same crystal structure. They are not used much as gemstones, (2% of the market) because of the objections of the diamond industry which relies on mined diamonds and dominates the markets. Gem-quality diamonds grown in a lab can be chemically, physically and optically ...

10

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 the substance in question. For example, for water ($H_2O$), 1 mole equals 18 grams. To get this number, remember that hydrogen ($H$) has an atomic mass of $1$....

10

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 dynamic instability (chaos) resulting from the non-linear phenomena of solidification and dendrite formation as a function of temperature and humidity variations in ...

10

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 you said Gamma for (0,0,0) etc. The important thing to realize as far as the group theory, is that the group of the wavevector at the Gamma point has the full ...

10

"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 packed (3D) configuration. In a real life scenario we may not immediately see that. That is so because of friction between marbles at their point (or rather area) ...

10

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, states. If you cool a sample rapidly, it loses energy too rapidly to explore more than a tiny neighborhood of its state space, and produces non-crystalline states. ...

8

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 $$\begin{pmatrix} b_{1x} & b_{1y} \\ b_{2x} & b_{2y} \end{pmatrix} \begin{pmatrix} a_{1x} & a_{2x} \\ a_{1y} & a_{2y} \end{pmatrix} = 2\pi \begin{... 8 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, but which however does not oscillate with the same period but shows oscillations which a different period T'=kT with k>1 integer, i.e., which ... 8 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. If marbles were confined in a way that did not impose hard boundary conditions, then they would almost always form perfectly crystalline arrangements. A ... 7 You are comparing apples with oranges. \vec k has the unit 1/\mathrm{Length}, and \vec r has the unit \mathrm{Length}. It is true that every lattice and reciprocal lattice contain the origin. When the lattice is cubic with lattice constant 1, the real and the reciprocal lattice are indeed completely identical, but this is of no importance ... 7 Let I \sim \sum_{\vec R} e^{i\left(\vec{k'}-\vec{k}\right)\vec R} \int_{V_{UC}} d^3r \Psi^*_{n\vec{k}}\left(\vec r\right) \Psi_{n'\vec{k'}}\left(\vec r\right) The term \sum_{\vec R} e^{i\left(\vec{k'}-\vec{k}\right)\vec R} gives you a \sim \delta(\vec{k} - \vec{k'}) term. Now, you have : \Psi^*_{n\vec{k}}\left(\vec r\right) \Psi_{n'\vec{k'}}\left(\... 7 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 others) as of the encyclopedia's publication in 1988-1999. 7 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 structure. Formed from ice Ih by compressing it at temperature of 190–210 K. When heated, it undergoes transformation to ice III. Ice III A tetragonal ... 7 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 fittings for some electron beam optics, I soon learned to either use different metals, or sprinkle a bit of dry molybdenum disulfide on the joints to dirty them ... 7 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\rangle = i\hbar|\psi\rangle$$On the position basis, this is$$[x,P_x]\psi(x) = (xP_x - P_xx)\psi(x) = i\hbar\psi(x) and it follows that a position basis ...

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