Crystals are solid material whose constituents, such as atoms, molecules or ions, are *arranged in a highly ordered microscopic pattern*, a crystal lattice that extends with regularity in all directions. Use for all crystallography and ordered structure topics.

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Is it possible to “see” atoms?

As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals. The image: How can we ...
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Why does ice have a lower density than water?

Can someone explain me why is ice less dense than water? As I know, all solids are usually denser than the liquids (correct me if I am wrong).
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Why do crystals grow in preferred directions?

I want to know why snowflakes (and other crystals) grow symmetrically and I find the leading answer to the established question to be entirely unsatisfactory. When water freezes, you get ice. Ice,...
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Are synthetically-produced diamonds as hard as natural diamonds?

I was having a discussion with my friend about the intrinsic worthlessness of diamonds (DeBeers and whatnot) and how synthetic diamonds haven't caught on, again because of the marketing/propoganda ...
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470 views

What are some predictions from string theory that say some crystalline materials “will end up in one of many lowest-energy ground states?”

I am referring to this recent "news feature" by Zeeya Merali from Nature magazine www.nature.com/uidfinder/10.1038/478302a. Here is the specific quote: "To make matters worse, some of the testable ...
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Crystal momentum and the vector potential

I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase ...
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Is it possible for a crystal to have different structures at different temperatures?

For instance, suppose it is a 50-50 alloy of two metals that is BCC at room temperature $T_0$. If I raise (or lower) the temperature, is it possible for the bonds in the crystal to rearrange and form ...
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How strong is electron degeneracy pressure?

I'm trying to get some specific numbers for electron degeneracy that I can understand, using a concrete example. Take for example this portion of carbon crystal: Exactly how much energy would be ...
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Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
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Are there materials that get softer with temperature decrease?

Could be there material that begins melting/softening when it's temperature is lowered? I would say no, but I've seen enough physics to know that not always life is so easy. Moreover I think I've ...
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How many of the 230 crystallographic groups are realized in nature?

All of them or only a subset? This is a famous and fundamental result in solid state physics.
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Transparency of materials

Is transparency of material has something to do with inter- or intra-molecular bonding? E.g. both graphite and diamond are carbon, but graphite is opaque and diamond transparent.
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Does positronium have a stable crystalline phase?

This is a long shot, but while the 100YSS conference is going on at Houston, i haven't been able to get a grip on myself and think in other, more mundane and short-term rewards as normal people do. ...
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How does the process of freezing water remove salt?

How does freezing water to make ice remove whatever salts were in the water to begin with?
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Entropy and Crystal Growth

I was reading about growing single crystals and I'm a little confused about this - In most crystal growing processes, a "seed crystal" is used, and the rest of the material crystallizes on the seed ...
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FCC-to-BCC phase transition in NaCl, Buckingham or Lennard-Jones potentials?

Background The transformation from B1 (face centered cubic (FCC) type) to B2 (body centered cubic (body centered cubic (BCC) type) structures is one of the best documented high pressure phase ...
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Reduce integration over crystal to integration over unit cell

I am wondering when I can reduce integrals over a periodic crystal to a an integral over the unit cell. Especially I consider the following two-electron integral $$ I=\langle \varphi_i \varphi_j | V | ...
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Is it possible to have annealing without creep?

Annealing can repair a material by allowing atoms to find the minimum energy state; since solids have a surface tension this process will allow cracks to fuse and reverse fatigue. However, annealing ...
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If pencil tip is heated why doesn't it write?

Why doesn't a pencil write if its tip is heated in a candle flame?
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Why do some things crystallize? (And others don't, for that matter.)

Ice, for example, will form a crystal when frozen under certain circumstances. Why is this the case for ice? While on the subject of water crystallization, why do snowflakes usually form in base 6 ...
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Born-Oppenheimer Approximation equivalent to Tensor-product ?

If you have a wave function $\Psi$ of a system consisting of an electron and the vibrational modes of the crystal, THEN we represent the wavefunction $\Psi%$ to be in the Hilbert Space formed by the ...
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226 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
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84 views

Neutron diffraction on Salty Ice VII

Can someone explain in layman's term how this figure shows the presence of Cl and Li ions in Ice VII ? What can we deduce about the crystal from this data ? The whole figure and caption are ...
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Lattice parameters and basis vectors of crystal lattice structures

Does someone know where I can find lattice parameters and basis vectors of crystal lattice structures (Strukturbericht Designation) for different materials? In particular I am searching the lattice ...
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What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of Weaire–...
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108 views

What physical phenomenon occured in this experiment?

I noticed a strange behavior of my experiment. I have a glass container with a fully saturated solution of CuSO4, which I use to grow CuSO4 crystals, by waiting for the water to evaporate. Recently I ...
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The Correct Statement of the Third Law of Thermodynamics

The Third Law of Thermodynamics can be stated in various ways, one of which is: The entropy of a perfect crystal at absolute zero is exactly equal to zero. Is this true for only "perfect ...
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Topological Insulators: is HgX a special case?

I got confused by reading this article: Francois Virot, Roland Hayn, Manuel Richter, and Jeroen van den Brink. “Engineering topological surface-states: HgS, HgSe and HgTe.” arXiv preprint arXiv:...
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How does crystal lattice explain electrical conductance?

From http://education.jlab.org In a metal, the atoms are arranged in a crystal-like configuration. ... Now, in a metal, the valence band is relatively close to the conduction band - ...
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Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
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317 views

Difference in chemical potential in supersaturated solutions

I have been more or less struggeling to understand an equation that is apparently used in almost all books covering crystals in any way. Basically every book that I have found explains the following: ...
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366 views

Anisotropic refractive index with isotropic components?

In relation to my question here I wanted to make sure that my physical argument was not flawed. Anisotropic properties, (especially refractive index) is characteristic of a well-ordered solid (...
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Origin of Laue equations?

The Bragg condition (by Bragg in 1913) can be derived by the Laue equations that is making use of the Miller indices and all the latice/crystal stuff (so basically it's bringing Bragg's law to more ...
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What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare ...
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Does a thermally expanding torus experience internal stress?

I'm trying to learn continuum mechanics and thermo-mechanics. As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic ...
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How can one reasonably theoretically model polycrystalline materials?

Many techniques are taught in advanced solid state courses but they are almost all derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you ...
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Jet turbine blades from single crystals, how are they formed?

I know about nothing about crystals, although I do know a bit more about jet turbine engines, and I definitely know that you don't want the fan blade hitting the fan housing. The reason given in the ...
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What limits the doping concentration in a semiconductor?

Si and Ge can be blended in any ratio, $\mathrm{Si}_x\mathrm{Ge}_{1-x},\ 0\le x\le 1$. So do InxGa1-x. So what exactly causes doping impurities inside Si/Ge/etc. to saturate at $\sim 10^{-19}\ \...
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The 2011 Nobel Prize in Chemistry

As far as I understand a new pattern of crystal growth has been found experimentally. How does it relate to the known 2D and 3D nucleation and growth of crystals? The dominating theory of crystal ...
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Can you explain why crystals form without thermodynamics?

I know that the basic reason that solid crystals form is because it's the lowest energy configuration (i.e. this). I am looking for an intuitive explanation for this process, one that does not involve ...
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Interpretation Born-Von Karman boundary conditions

The cyclic Born-Von Karman boundary condition says that if we consider a one dimensional lattice with length $L$, and if $\psi(x,t)$ is the wavefunction of an electron in this lattice, then we can say ...
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Molecule vs Crystal

Feynman mentions in his lectures: ...the concept of a molecule of a substance is only approximate and exists only for a certain class of substances. It is clear in the case of water that the ...
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How to make a single crystal silicon wafer?

How can I make a single crystal silicon wafer? What are the tools needed? What is the most diffcult part? Can I make it at home or at school lab? I am now interested on Czochralski process where you ...
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516 views

Nature of tetragonal distortion in Jahn-Teller effect

I am wondering: If I have a regular octahedron as my starting point, oriented along the x-y-z axis, and now Jahn-Teller suggest I elongate or compress along the $z$-axis, what happens along the other ...
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1answer
42 views

Honeycomb Bravais Lattice with Basis

I just had my second solid state physics lecture and we were talking about bravais lattices. As far as I understand a Bravais lattice is an infinite network of points that looks the same from each ...
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Are there any electro-optic crystals that are also pyroelectric but not birefringent?

As the title says, a crystal that is electr-optic and pyroelectric can it be non-birefrigent?
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How to write the Fröhlich Hamiltonian in one dimension?

I am currently working on a (functional) analysis problem refining Pekar's Ansatz (or adiabatic approximation, as it is called in his beautiful 1961 manuscript "Research in Electron Theory of Crystals"...
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Where are the ice rings in X-ray crystallography located?

I threw this image of one of my protein crystal's diffraction pattern (not the greatest) on a poster, and was wondering where (what reciprocal dimension) the ice rings are located as it might be a ...
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Why do we still get sharp scattering spots with quasi-crystal?

In a quasi-crystal, there is no translational invariance. This means there is no delta-function in the Fourier transform. But to get a sharp scattering spot, we need a delta function. Physically, ...
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What determines Phonon - Phonon collisions?

I was in Solid State Physics lecture yesterday and we BRIEFLY went over what causes phonons to collide with one another. Things such as crystal imperfections, boundaries, Temperature, but I was ...