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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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Why must solids in equilibrium become crystalline?

In Landau's Statistical Physics's analysis of solids, he begins with the remark that solids are caracterized by their atoms' small oscillations about equilibrium positions. However, he states that ...
Lourenco Entrudo's user avatar
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Brillouin zone(s) the Fermi surface lies within

I'm trying to understand how you can calculate which Brillouin zone(s) the fermi surface lies within. The way that seems reasonable for me is to: 1: Calculate the fermi radius. 2:Look in the "...
lilted's user avatar
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Translational invariance $\neq $ Galilean invariance?

I have the impression that some literature say that Galilean invariance is broken by a uniform lattice. That is, although a uniform lattice like a tight binding model is translationally invariant, it ...
poisson's user avatar
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Quantization into Phonon in a multi-basis crystal

I am quite frustrated in quantizing the vibration of a multi-basis crystal. The specific point that confuses me is the potential term, which hinders me from decoupling the Hamiltonian as the sum of HO-...
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Why do cryogenic temperatures usually result in higher conductivity, even (sometimes) superconductivity, but otherwise nonconductive Wigner crystals?

Wigner crystals are all the rage in the news, since around the start of the pandemic... But at what temperatures (and pressures?) do these cold materials create a nonconducting 'Wigner crystal' rather ...
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Is the Choice of Bravais Lattice for a Crystal Always Unique?

I was wondering if the choice of the Bravais lattice for a given crystal is always unique. It seems to me that, as long as we change the basis, there could be multiple possible choices. For example, ...
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Structure factor correct calculation

I have a set of 2D points and wish to test it for hyperuniformity. As I've learned from papers, the good idea is to calculate structure factor $S(\mathbf {q})$ and test it for $$\lim _{\mathbf {q} \to ...
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How to call ellipse packing structures?

My research group and I are trying to figure out what is the correct terminology for two different packing structures of 2D ellipses. The two structures are displayed below as Structure A and ...
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Reciprocal lattice for non-bravais lattices

In crystallography, when dealing with a lattice that is not a Bravais lattice, from my understanding, we sometimes chose a bravais lattice and consider the "misbehaving" atoms as "...
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Free electron in weak periodic potential (Graphene)

I am trying to model the potential of 2-D graphene monolayer as a sum of delta functions. I don't know where to begin. Also, after defining it, I also wish to obtain the energy gap and fermi surfaces. ...
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How are 3 Principle Sections possible in a crystal even when there is only one optical axis and all must contain it?

While studying polarization in calcite crystals, I came across that there are 3 possible principle sections in the rhombohedral crystal. But the conditions are that each section must be perpendicular ...
Gauransh 21HPH2625's user avatar
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How do you determine the basis of a crystal structure? [closed]

Consider this Cuprite unit cell like in the picture. I am first thinking that this is a body centered cubic cell, with the atom in the center and the surrounding copper atoms as the basis, hence five ...
Vro's user avatar
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Help with Parametrizing Path Through High-Symmetry Points in 2D Hexagonal Brillouin Zone

I'm currently working on a project involving the calculation of band structures for a 2D hexagonal lattice, and I need some guidance on how to properly parametrize a path that covers the high-symmetry ...
Felipe Cubillos Pérez's user avatar
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What is the unit cell and the bravais lattice of a perovskite?

First year PhD. student here. I keep trying to wrap my head around what kind of bravais lattice and how does the unit cell of a perovskite look? I am specifically interested in bismuth ferrite (BiFeO3)...
Andrew's user avatar
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'Polarization' of waves in crystal lattice

The vibrations in crystal are modelled as sound waves in debye model of specific heat. The density of states function for these vibrational modes is multiplied by 3 because of allegedly 3 '...
Mr. Wayne's user avatar
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How to find Euler angles for orientation of Single crystals with respect to Lab Frame?

I have a monoclinic C2 space group single crystal sample glued to a tenon plate. I know the surface normal direction and the edge plan of the crystal. Also, I know the XY plane of the tenon plate. How ...
Shiva Agarwal's user avatar
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Phonon dispersion and what wave it represents

To start things off, I'm doing a semestral project on phonons and I'm to find a dispersion relation of a crystal (with the use phonopy). I chose to do hexagonal boron nitride. From my understanding, ...
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Are there any materials known to be harder than diamond under high pressure as of April 2024?

This is a variation of this question where I asked if materials under high pressure can break standard pressure density records. I am curious about materials that become superhard under very high ...
Sidharth Ghoshal's user avatar
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Reproduce band structure Kagome fermi-hubbard - Python

I am trying to reproduce figure 5c) of https://arxiv.org/pdf/2002.03116.pdf in Python. So I would like to plot the band structure of a Fermi-hubbard defined in a Kagome lattice. The eigenvalues are: $\...
relaxon's user avatar
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Why are there triclinic and monoclinic lattices, but biclinic is never mentioned?

When classifying the Bravais lattices we have the triclinic (point group ${\rm C_i}$) and the monoclinic $({\rm C_{2h}})$ cases, but we do not see the "biclinic" case listed. Why not? It ...
Jos Bergervoet's user avatar
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Why is Wigner-Seitz cell considered primitive?

During the lecture I listened, as well as in the internet, in Wikipedia for example, unit cell was defined as the parallelepiped spanned by the translation vectors. Primitive cell was defined as the ...
Максим Неважно's user avatar
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Is the difference between cubic and hexagonal diamond structure in 2 dimensions or 3 dimensions?

I was reading the book Solid State Physics by Charles Kittel. It was explained that the difference between Cubic F or FCC and the Hexagonal Closed Packed structure or the HCP was as follows - (Please ...
Vatsal Sharma's user avatar
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What happens when slip direction is the same as applied force?

Using the equation $$ \tau R = \sigma y \cos \left( \phi \right) \cos \left( λ \right) \tag{1} $$ means that when the angle $\phi$ between the tensile axis and slip plane normal is $90$, $\cos \left( ...
Thyla's user avatar
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Born–von Kármán (BvK) Supercell

I have come across in the literature Born–von Kármán (BvK) Supercell, which are described as a unit cell that is repeated periodically. However, say in a calculation that is derived using a BvK ...
L_J's user avatar
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Why don't all metals have closed pack structures?

A lot of times, in my materials classes, metal atoms' behavior during deformation is described like a bunch of stacked balls. In my introduction to material class, our professors explained that metals ...
asker's user avatar
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Ultra-strong nanocrystalline metal without transition to superplasticity

It is known that a decrease in the grain size of a polycrystalline metal to 1 micron is accompanied by an increase in its strength by several orders of magnitude (super-strength) almost to the ...
Ванек Огонек's user avatar
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3 answers
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Why is an FCC lattice the reciprocal lattice of a BCC Lattice?

This can, of course, be calculated mathematically. However it is difficult for me to believe that this is a pure mathematical coincidence. Perhaps I don't understand reciprocal lattices the way I ...
Ambica Govind's user avatar
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0 answers
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Transforming the diamond structure Raman tensor to [111] crystal orientation

I'm writing my physics bachelor on the Raman scattering effect in solids. I'm trying to evaluate the scattering intensity response to varying polarization angle. This is the well known linear ...
Eslam Aboelfadl's user avatar
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Brillouin Zone Corresponding to Unit Cells

I was reading the book 'The Oxford Solid State Basics', Book by Steven H. Simon. The section explaining Brillouin zones had this paragraph in it Each Brillouin zone has exactly the same total area (...
Harshdeep Chhabra's user avatar
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Plane Wave in a Periodic Lattice

From Introduction to Superconductivity; Second Edition; A.C. Rose-Innes and E. H. Rhoderick; Page 3 Electrons have, of course, a wave-like nature, and an electron travelling through a metal can be ...
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Why do lattice structures absorb more photon frequencies than single atoms?

I'm trying to understand why the liquid-like structure of glass is necessary for it to be transparent.
bansheenocturno's user avatar
1 vote
1 answer
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Interpretation of velocity in the de Broglie wavelength of an electron in a crystal

The de Broglie wavelength of a free electron is $\lambda = h/mv$ whre m is the free electron mass, and v is the velocity. Often in introductory solid state physics literature (review articles, lower-...
intraband's user avatar
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2 votes
2 answers
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2D primitive unit cells

The answer given says that 2 & 3 are primitive unit cells.How can a hexagon be a primitive unit cell.Can someone explain?
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3 votes
2 answers
156 views

Entropy of Schottky defects

We have a crystall with $N$ atoms. A Schottky defect is one of the atoms leaving their points in the lattice and going to the surface with $N' = cN^{2/3}$ possible atom places. I want to compute the (...
Jahi02's user avatar
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8 votes
2 answers
262 views

What may have caused these bizarre frost patterns on my car windows?

I went to my car a couple days ago in the morning, and I was amazed at the patterns I found on all the side windows, shown in the attached picture. No amount of googling revealed anything similar, so ...
Gregory Beaudoin's user avatar
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1 answer
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Compensation of polarization-dependend frequency offset of a passive optical cavity

I have a passive optical cavity used as an OPO for the generation of squeezed states in pulsed regime, schematized in the following figure. The crystal used to generate squeezing is a KDP (C1), which ...
edsu's user avatar
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1 vote
0 answers
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Can hydrogen be stored in the crystalline structure of ice?

I recently read that when ice freezes to form hexagonal crystals, the space within the hexagon is in fact a vacuum. Could this space potentially be used to store burnable hydrogen gas? If so, would ...
Robert Goddard-Wright's user avatar
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Exactly solvable Schrödinger equations on the circle?

Are there any (famous?) periodic potential functions in 1d, $V(x) = V(x+L)$, so that the Schrödinger equation with periodic boundary conditions $\psi(x)= \psi(x+L)$ is exactly solvable? I can do it if ...
Upasker's user avatar
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3 votes
1 answer
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Band theory of solids: Kronig–Penney model parameters question

In the Kronig–Penney model, we assume that the periodic potential of the crystal is modeled as a square well. The period of the potential is $d$, where $d=a+b$. $a$: the width of the zero potential ...
Nero's user avatar
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Does the energy output of a piezoelectric material increase when its dielectric constant is incressed?

According to the output voltage equation, the output of a piezoelectric material increases when its dielectric constant is increased. But it reduces the coupling constant. Since that can we directly ...
Kavindu Lochana's user avatar
1 vote
0 answers
73 views

Group Velocity at the Boundary of the Brillouin Zone

I'm having trouble understanding why the dispersion relation $\omega(\vec{q})$ is extremal at the boundaries of the first Brillouin zone. I understand why the dispersion relation is symmetric around ...
Tomas Noguera's user avatar
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0 answers
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Are there any nonlinear crystals or other transparent materials that can produce anti-Stokes, phase matched, frequency shift of laser light?

While some nonlinear crystals can convert incoming laser light into harmonics, thus for example doubling the light frequency, are there any crystals or other transparent materials that can reduce the ...
Jimski's user avatar
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Understanding Wyckoff Position of Apatite group

I was learning about Wyckoff position, and one of the simplest example was of $ZrO_{2}$. For Zr and O, the Wyckoff positions are 4a and 8c and belongs to space group Fm-3m. Now from the Wyckoff ...
Anshul Sharma's user avatar
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Can continuous translation of Wigner crystal be described by charge neutral density excitations?

In a two-dimensional electron gas (2DEG), under conditions where electron-electron interactions predominate over kinetic energy contributions, the ground state is a Wigner crystal. This crystalline ...
aj_01100110's user avatar
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How can Miller indices be calculated for this reoccuring scenario?

Miller indices are very simple and straightforward for most planes. However, I see a problem for a plane that goes through the coordinates origin. In such a case, the Miller indices should be $(\infty,...
100xln2's user avatar
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About a restatement of the Bloch theorem

In the Introduction to Solid State Physics written by Charles Kittel, chapter 7, restatement of the Bloch theorem, Kittel says the wave function can be represented as follows: $$\psi_k(x) = \sum_G C(k-...
ranger's user avatar
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1 answer
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Brillouin Zone Summation

If one has the following summation: $$\frac{1}{A}\sum_{\vec{k}} F(\vec{k})$$ which is taken over all k-space and $A$ is the area of the unit cell from the system itself. I want to them limit this to ...
L_J's user avatar
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Picturing a normal mode of vibration of the monoatomic lattice in 1D that is either in-phase nor completely out-of-phase

For a monoatomic lattice of $N$ atoms in one-dimension, the ratio of the displacements of two consecutive atoms at the $(n+1)$th and the $n$th site is given by $$\frac{u_{n+1}}{u_n}=e^{ika}$$ where ...
Solidification's user avatar
1 vote
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Unique lattice constant using X-ray diffraction

I recently learned about X-diffraction methods to analyse crystal lattices. One important law in this is the Bragg condition $$\lambda = 2d\sin(\theta).$$ I understand that $d$ is the distance between ...
Space junk's user avatar
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2 answers
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Symmetry of Crystalline Lattice

In the book Solid State Physics by Kittel, it is written in Bravais Lattice's definition that "the arrangement of atoms in the crystal looks the same when viewed from the point r as when viewed ...
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