Questions tagged [crystals]
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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Strange ice found in my garden
This morning I found a really strange ice formation in my garden. I can't figure out how it appeared, because there was nothing above. The night was particularly cold (Belgium).
To give an idea, it ...
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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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What is the smell after quartz is rubbed together?
When I rub quartz together, it glows due to triboluminescence but it also creates a burnt smell. What causes that smell?
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Why are snowflakes flat?
There have been many questions and excellent answers in this community about the symmetry of snowflakes, e.g., here and here. There is however one aspect of snowflakes that does not seem clearly ...
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Understanding time crystals
In very recent publications, two groups in Maryland (paper: "Observation of a Discrete Time Crystal") and Harvard (paper: "Observation of discrete time-crystalline order in a disordered dipolar many-...
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Is crystal momentum really momentum?
Almost every solid state physics textbook says crystal momentum is not really physical momentum. For example, phonons always carry crystal momentum but they do not cause a translation of the sample at ...
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Why no proton microscopes? Proton diffraction; or proton scattering experiments? Proton crystallography?
I am asking a (relatively) 'low-energy' question here, not about things like the Large Hadron Collider...
There are tons of articles everywhere, including such places as Wikipedia and ScienceDirect, ...
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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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Why don't marbles naturally arrange themselves like a crystal?
Most solids are crystalline in nature because the energy released during the formation of ordered structure is more than that released during the formation of disordered structure such that the ...
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"Lack of inversion symmetry" in crystal?
Apparently (first paragraph of this article) the lack of inversion symmetry is some crystals allows all sort of nonlinear optic phenomena.
Now. Does anyone know of an intuitive or just physical ...
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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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Why are phonons quantized?
I'm a third year physics major taking an introductory subject on condensed matter physics. I'm trying to understand the concept of phonons in a 1D lattice.
I understand the classical treatment of (1D) ...
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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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Notations for high symmetry points in the 1st Brillouin zone
I am trying to understand how I should interpret the letters like Г,K,M,T etc., that are usually there in the electronic band structure diagrams.
So, let's assume we have graphene with its hexagonal ...
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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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Does positronium have a stable crystalline phase?
I wonder if there is a way to stabilize and store positronium in a way that the mass of storage device is negligible to the antimatter fuel
It is known that excited Ps atoms with high n (rydberg or ...
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Can two atoms be a crystal?
In the physics literature, you can often find the term "two-ion crystal", when talking about two ions that are confined in a e.g. Paul trap. How is this possible? Shouldn't a crystal be a structure ...
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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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Why is crystalline graphite black yet shiny?
I am unable to find images of pure crystalline graphite with high confidence, but based on various sources I believe that it should actually be both black and shiny, in the sense that it reflects much ...
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Why is Fourier space called as momentum space?
If I take a periodic wavefunction $\psi\left(\vec{r}\right)$ and then take the Fourier space dispersion of the wave function as defined below
$$
\psi(\vec{k})=\iiint_{-\infty}^{+\infty}\psi\left(\vec{...
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Why are Bloch waves so successful at explaining behavior of electrons in crystals?
The solutions to the time independent Schrodinger equation for a periodic potential are Bloch waves of the form
$$\psi(r) = u(r)e^{ik.r}$$
where $u(r)$ is a periodic function with the same periodicity ...
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How strong is electron degeneracy pressure?
I'm trying to get some specific numbers for electron degeneracy that I can understand, using a concrete example.
Take for example this portion of carbon crystal:
Exactly how much energy would be ...
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Is it possible for a crystal to have different structures at different temperatures?
For instance, suppose it is a 50-50 alloy of two metals that is BCC at room temperature $T_0$. If I raise (or lower) the temperature, is it possible for the bonds in the crystal to rearrange and form ...
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How to prove Bloch function is periodic in reciprocal lattice?
How to prove Bloch function is periodic in reciprocal lattice?
I saw in some textbooks this formula:
$$
\Psi_{\mathbf{k}} (\mathbf{r}) = \sum_{\mathbf{G}} c_{\mathbf{k}+\mathbf{G}}e^{i(\mathbf{k}+\...
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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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Does a cube under high pressure transform into a ball?
Will a material in the shape of a cube, under high pressure, crumble into the shape of a ball?
One would expect that there will develop strains and stresses, after which the corners crumble and ...
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Why haven't we found thermal superconductors?
First of all I want to apologize if this is a stupid question. I'm a layman who's merely very interested in physics, without a degree to my name.
I was trying to research electric superconductors ...
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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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Why do oxides form amorphous films instead of crystalline films?
If I oxidize a metal at room temperature, say aluminum, why does it form an amorphous material instead of crystalline $\rm Al_2O_3$?
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What's the difference between a time crystal and a system undergoing periodic motion?
What's the difference between a time crystal and a system undergoing periodic motion? My understanding of a crystal is that it is a rigid body with a spatially periodic structure. Is any system ...
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What exactly is Crystal Momentum, $\hbar k$?
The title says it all really.
Does this mean that the crystal is moving?
From my notes, I read that
The effect of an external force on an electron in the crystal is to
change the crystal momentum $\...
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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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How many optical and acoustical branches are in a primitive cell?
I am reading Introduction to Solid-State Physics (by Kittel) and I don't understand how he counts the optical and acoustical branches in a primitive cell.
It says that if there are $p$ atoms in a ...
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Can someone explain LO-TO Splitting?
LO-TO splitting occurs in an ionic (i.e. polar) solid such as GaAs or NaCl. What happens is that the degeneracy of the transverse optical (TO) and longitudinal optical (LO) phonons at $k=0$ is broken ...
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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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Fourier transform of almost-periodic lattice?
For a perfectly periodic lattice of atoms, the density can be written as a Fourier series like any other periodic function. This Fourier representation is very useful, because it can be connected to ...
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What causes this frost pattern on my windshield?
I was walking back to my car yesterday when I noticed the frost on the back windshield formed these long "straight" lines:
The temperature was about -10C and I was wondering what the ...
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Why a mono-atomic crystal layer (2D) can't be stable?
According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist!
Of course, this theory was disapproved in 2004 (example: graphene).
What is the general definition of ...
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Conventional unit cell and point group symmetries?
A definition of a conventional unit cell of a lattice is one that contains the same point group symmetries as the overall lattice and is the smallest such cell.
I can understand how a (infinite) ...
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Is the phenomenon of geometrical frustration in condensed matter physics related to some kind of topological invariant?
Edit (attempt to clarify my question a little bit):
I’m not thinking geometrical frustration should be necessarily associated to a topological invariant in a direct way, but maybe local geometrical ...
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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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Why do 3D Wigner crystals form a bcc rather than an fcc lattice?
When an electron gas has low enough density, the electons' Coulomb repulsion can be strong enough relative to their kinetic energy that they spontaneously form a Wigner crystal. Since the electrons ...
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Significance of Dirac cones in condensed matter physics
In condensed matter physics, Dirac cones can be found in graphene, topological insulators, cuprates, and iron-pnictides. This means that electrons behave as massless particles near the Dirac points.
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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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Reciprocal lattice in 2D
So, I learned that I can create a reciprocal lattice from direct lattice, using the following formulas:
$$b_1=\frac{2\pi (a_2 \times a_3)}{a_1.(a_2\times a_3)}$$
$$b_2=\frac{2\pi (a_3 \times a_1)}{...
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Is it possible to reassemble a perfectly cleaved crystalline solid?
This is a purely theoretical question about "perfect" solids under "perfect" conditions.
Assume you have a crystalline solid with a perfect crystal lattice (i.e. no defects). Let's imagine a cube of ...
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Distance between adjacent planes in a crystal
This question has been asked before, but there doesn't seem to be a decent answer.
Many sources state that " For cubic crystals with lattice constant a, the spacing d between adjacent (ℓmn) lattice ...
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Dissatisfied with textbook explanations for why $\vec k$ in Bloch's theorem can be restricted to thefirst Brillouin Zone (BZ)
By Bloch's theorem, all the eigenfunctions of a Hamiltonian with a periodic potential $$U({\vec r}+{\vec R})=U({\vec r})$$ can be chosen to have the form $$\psi_{n{\vec k}}({\vec r})=e^{i{\vec k}\...
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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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