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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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Cesium chloride crystal structure

Cesium chloride has a cubic structure with eight $Cs$ atoms at each corner of each cube and one $Cl$ in the middle of the cube. It is stated in my solid state book that this crystal cannot be ...
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FCC and BCC lattice

Some crystals can be described by a FCC lattice or BCC lattice. For example diamond can be described as a FCC lattice with two basis vectors. Is it also possible to describe it using an ordinary cube ...
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Can we / should we use the Pauli principle to explain band structure?

Checking the wikipedia article on band structure, I got caught in major doubts... They try to give an intuitive explanation of the band structure relying heavily on Pauli exclusion Principle: if a ...
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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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Viscosity table or diagram for melts of oxides

Is there a table or diagram to relatively determine which oxides have low 'melt-viscosity' (i.e relatively flow readily when melted)? Is it possible to determine such property based on phase diagrams ...
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What is the relationship between directions in reciprocal and real space of a photonic crystal?

I am reading "Photonic crystals - molding the flow of light" by Joannopoulos et al. (available on-line). The figures below are reproduced from there. This is a diagram of a triangular lattice of air ...
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Group velocity in different dimensions

I am given the following equation for the group velocity in one-dimension: $$v_g = \frac{d\omega}{dk}.$$ In solid state physics one has $-\pi/a \leq k \leq \pi/a$ for a one-dimensional lattice with ...
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How are the orientations and cuts of crystal substrates determined?

I have been looking at piezoelectric crystals, LiNbO3 primarily, so piezoelectric devices. But I have had trouble understanding the cuts and orientations that are referred to with the rotated cuts. ...
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What are the allowed wavenumbers in the finite size system?

Usually, we introduce wavenumber $\textbf{q}$ by Fourier transform, for example, an operator $A_{\textbf{q}}=1/\sqrt{N}*\sum_{i}e^{i \textbf{q}\cdot \textbf{r}_{i}}A_{i}$, where $N$ is number of sites,...
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Why does first photonic band go to zero at the centre of the Brillouin zone?

I have been plotting photonic band diagrams of various geometries recently and I identify if it is correct by looking if it goes to zero at the Brillouin zone centre, $\Gamma$. I realised early on ...
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What is the irreducible Brillouin zone for a rhombic unit cell?

So I realised that the rhombic unit cell is in fact not the same as a hexagonal unit cell. (I thought they both gave hexagonal lattices but the rhomic unit cell with two rods gives a honeycomb lattice ...
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Wave Superposition on a crystal

Does the principle of superposition apply for electromagnetic waves on a crystal? So I know that the principle applies for any wave but I don't understand why some books say that doesn't apply for ...
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Phase matching and the index ellipsoid

I've seen analytically all the process that brings to the condition for the phase matching (after I'll use PM) in an isotropic crystal, which is $n(\omega)=n(2\omega)$. My teacher hasn't shown it ...
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What would happen if we had a crystal structure but only gravitational interactions?

The idea is simple. Let's say we arrange similar bodies (call them planets, ions, anything) in an infinite crystal structure, but the only possible interactions are gravitational interactions. A ...
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Negative Miller indices and parallel planes

The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. https://en.m.wikipedia.org/wiki/Miller_index Does this mean, that parallel planes are generally ...
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TEM diffraction analysis- imaging artifact or distorted crystal structure

I've got some "nanobeam" diffraction data from TEM (transmission electron microscope). Analysis is a challenging because I forgot the golden rule... I didn't measure a "standard". Hence, I don't know ...
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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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Analytic derivation of honeycomb lattice Brillouin zone

My goal is to analytically derive the first Brillouin zone of the honeycomb lattice. Geometrically it's clear how to do this by just finding the space on the lattice nearest to a particular point of ...
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Why do quantum memories have to be so cold?

I understand that currently, atomic qubits, or just atomic ensembles are kept near absolute zero, in order to try to create an ideal gas structure. For higher temperatures the individual ions will ...
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Points of symmetry in $k$-space

Can you relate a point in the reciprocal space with a vector in real space? How do I find the family of planes that represent a point of symmetry in the Brillouin zone? For example, germanium has ...
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How to estimate the mobility of atoms implanted in the interstitials and/or vacancies of a crystal?

I would like to compare the likelihood for implanted helium atoms to move from interstitials/vacancies of a crystal versus neon atoms. I read in the literature that He atoms located in interstitials/...
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How is the a Fermi surface different from a Fermi sphere?

How is a Fermi surface (a surface in reciprocal space separating the occupied electron states from unoccupied states at $T=0$) different from a Fermi sphere? Is Fermi sphere a special case of Fermi ...
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What is the difference between the structure factor of a crystal and of that liquid phase?

What is the difference between the structure factor of a crystal and of that liquid phase? Why the graph has smooth behaviours for liquid?
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Spacing of atoms in a cubic meter [closed]

I want to figure out the spacing between neighbouring atoms in a cubic meter of a large amount of 10^17 atoms were placed in perfect cubic structures within the cubic meter. I’m not sure how to go ...
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Using Miller indices to determine interference from a particular plane in a crystal lattice

In terms of x-ray diffraction from crystals. I was wondering how you can use the miller indices to determine whether there will be constructive or destructive interference from a particular plane in ...
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Could spacetime have crystalline properties?

Space-time is currently modeled as a continuous manifold. However, space-time shares many features in general relativity that mimic a fluid-like thing. Fluids are certain states of matter and under ...
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Does a crystal only belong to a unique crystal system?

I wonder whether a specific crystal (e.g. cubic diamond) only belongs to a unique crystal system (7 in total, see the wikipedia page). The question is from an observation that the unit cell of the ...
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How can I tell the cubic structure of different crystals?

So I have a couple of crystals I am analysing (LiF RbCl NaCl...) and I have the x ray diffraction patterns for them. How do I determine the different structures of these crystals as I need to ...
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X-Ray Diffraction for Crystal Structures

So I was carrying out an XRD experiment and found that I only got peaks for the (2 0 0) and (4 0 0) lattice structures. I was wondering why there aren't any peaks for the (1 0 0) and (3 0 0) lattice ...
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How to determine if a calculated Raman mode in a crystal is active or not?

I have used an ab initio electronic structure code to calculate the harmonic Raman spectrum of a (molecular) crystal. However, no use of symmetry has been made, and it might well be that some of the ...
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Does translational symmetry imply some sort of rotational symmetry? Do all crystals have at least one rotation axis?

We know that crystals (not including quasicrystals) have periodic structures. That is, they all have a translation invariant vector. My question is, do all crystals necessarily have a rotation axis? ...
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Diffraction peaks and Miller indices

How do we find out if a diffraction peak is observable using miller-indices?
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Transverse field Ising model - why is the sum restricted to half of the Brillouin zone?

I am reading Coleman's "Introduction to many-body physics" and am working on problem 4.2, which involves calculating the spectrum of the transverse-field Ising model. We start with the Hamiltonian $...
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Why does a ionic crystal polarize more at low frequencies rather than at high ones?

And if there was a difference if the propagational mode of the electric field in the crystal is longitudinal or transverse.
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Working with Reciprocial Lattice

In solid matter physics the lattice structure can equivalently be described via standard Bravais modelling but also by considering it's reciprocial lattice. Mathematically the reciprocial lattice can ...
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Quasiperiodicity of the Fibonacci chain

I am interested in finding an intuitive way to show that the Fibonacci chain is quasiperiodic (and not simply random). Or put differently, how can I tell from just looking at a given chain whether or ...
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Can the periodicity in k-space of the electronic band structure be understood as a result of aliasing?

Discrete sampling in the case of phonons In the case of phonons in periodic solids, the picture is quite intuitive. The motion of the atoms in the lattice is described as a continuous wave (amplitude ...
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BCC to FCC lattice conversion

In the book Condensed Matter Physics by Marder I have read that an FCC lattice can be obtained by expanding a bcc lattice along one axis by a factor of $\sqrt{2}$. How can I get that mathematically?
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Symmetry of the dielectric tensor

In the book Principles of Optics by Max Born, in chapter XIV, the rate of change in the electric energy density $w_{e}$ is generalised to \begin{equation} \frac{dw_{e}}{dt} = \frac{1}{4\pi}\sum_{kl}\,...
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Irrep corresponding to a rotation, what's the definition?

My character tables for point group $T$(Schönflies-notation but easily convertible into other point group notations) tell me that the rotation around the $z$-axis, $R_z$ (the $z$-direction ...
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Isn't end-centered monoclinic same as monoclinic?

monoclinic is simply an extruded parallelogram. If we place end centers on parallelogram faces then taking half of both diagonals and same height as before as 3 basis, its the same. That's what I ...
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Even/odd number of electrons per primitive cell and conductivity

In this pdf it says Because the number of electron states in a Brillouin zone is twice the number of primitive cells in a Bravais lattice (the factor two comes from spin), the zone can be ...
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How many electrons are in the $k$-space?

Let's assume we have a metal cube with edge length $L$ and in its volume $L^3$ are $N$ conduction electrons. The components of the wave vector are quantized. i.e. $k_x=m\cdot (2\pi/L)$ where $m=0,\pm ...
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Schottky defect effect on density

Schottky defects occurring means that atoms move from internal sites of a crystal to the edge of the crystal. This increases the volume of the crystal slightly, which in turn decreases its density. ...
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Conservation of quasimomentum in second quantization

I'm trying to work out the expression for the matrix elements in Section VI of this paper (PRA 72, 053604). There is a point I need to expand the contact interaction term $\hat{V} = U \int dr\,\, \...
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Laser induced damage in BBO crystal

Does the repetition rate [Hz] of a IR (1035 nm) pulsed laser play a role in the damage threshold of a BBO crystal?
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Calculate the Macroscopic Electric Field from the Microscopic Electric Field

In standard textbooks, such as Classical Electrodynamics by Jackson, the microscopic electric field $E_{micro}$, varying on the length scale of atoms, is connected with the macroscopic electric field $...
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Switch from sum to integral in non-Cartesian coordinates

when I do the BZ integral in honeycomb lattice numerically I need to calculate: $$\left| {\begin{array}{*{20}{c}} {\frac{{\partial {k_x}}}{{\partial {{k'}_1}}}}&{\frac{{\partial {k_y}}}{{\partial {...
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How to cleave a perovskite single-crystal in vacuum?

I am trying to cleave the lead-halide perovskite in vacuum to study its intrinsic electronic properties using photoelectron spectroscopy, since it is difficult to remove surface adsorption without ...
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How to identify the basis of a crystal?

I'm having some difficulty identifying, geometrically, the basis of crystals. I have two particular examples. The first one, CaF2, I know we have a Ca at (0,0,0) and 2F, one at (1/4, 1/4, 1/4) & ...