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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What happens when we cut the crystal perpendicular to its optical axis?

In many optic experiments, it's always mentioned to cutting the crystal perpendicular to the optic axis, but why? cuz nothing change at all! I'm going to add a picture for clarity:
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Non-invertibility of crystallographic pole figure

In Group Theory by Morton Hamermesh, while explaining the pole figure and its stereographic projection, it is clear to me that we will get same angle between crystal sample faces if we scale all ...
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What is a basis actually is and how it differs from primitive unit cell?

I have some questions about primitive unit cell and basis. These are: Is the basis the smallest identical fragment of a crystal which repeats in a pattern throughout the crystal? Or can it be an ...
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Algorithm to find out the local translation vectors in a distorted lattice structure for materials simulation

For example, I have a set of atomic position data of an lattice structure with BCC, but some parts of the structure are distorted by the thermal perturbation or rotated due to the material defects (...
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What is the difference between normal surfaces and index ellipsoid in crystal optics?

What is the difference between normal surfaces and index ellipsoid in crystal optics? Why does the normal surfaces have two shells but the index ellipsoid have only one? And how to analyze light ...
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What does planar quadratic fluorine coordination refer to?

In the paper Magnetic and Crystal Structure of Copper (II) Fluoride, I do not understanding the following sentence: "The layer type structure with planar quadratic fluorine coordination of $Cu^{2+...
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Ghost Imaging with SPDC?

I am studying the field of quantum imaging and in particular ghost imaging. For example here (https://royalsocietypublishing.org/doi/10.1098/rsta.2016.0233) we know that according to Klishko model, we ...
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Reading a graph for dispersion relation of normal modes in 3D lattice

I'm trying to interpret graphs of this type. In this example, dispersion relation $\omega = \omega(k)$ for some waves corresponding to lattice vibrations in GaAs are shown. What is uncomprehensible to ...
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On reciprocal lattice properties

One of the properties of the reciprocal lattice vector is shown in the following Theorem. For any family of lattice planes separated by a distance $d$ there are reciprocal lattice vectors $\mathbf{G}...
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Tight-Binding method and orthogonality of Bloch functions

Tight binding summary When computing the electronic bands of a crystal in the tight-Binding approximation, the standard way to do it is to construct Bloch solution as $$ \Psi_n(\vec{r}, \vec{k}) = \...
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How to understand the tight binding chain?

I am wondering how to extend the mono-/di-atomic chain models here, say $Q_{diatomic}$ to describe behaviors of electrons in solids. (References: https://www.physics.rutgers.edu/grad/601/CM601/...
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What are normal modes (accoustic/optical modes) in 1d diatomic chain?

Q0: What are normal modes (accoustic/optical modes) in 1d diatomic chain? According to What are normal modes? and wiki, The most general motion of a system is a superposition of its normal modes. 'The ...
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Can oxides of uranium be used to color aluminium oxide based gemstones, or diamonds?

Rubies and sapphires are chemically equivalent to the mineral corundum, with the exception of transition metal impurities that impart different colors to the aluminium oxide. Uranium is not a ...
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Are scattering of electrons in Drude theory and scattering in wave scattering (XRD, etc.) the same/similar?

Background: How will crystal orientation affect the mobility? I am reading solid state physics, and I am confused by 'scattering (time)'. Is scattering in scattering time $\tau$ in the calculation of ...
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What is crystal orientation?

Related: How will crystal orientation affect the mobility? (I separate one question out. I wrote my understanding of the concept there, but I am not sure if it is accurate.) We know that crystal ...
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How will crystal orientation affect the mobility?

[Refined:] We know that crystal orientation will affect the mobility Mobility Dependence on Crystal Orientation and Strain Engineering. What is crystal orientation? Is there a basic textbook/lecture ...
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How do we calculate the effective mass?

In a band structure calculation, the dispersion relation for electrons is found to be $$\epsilon_k = \beta\, (\cos k_xa+ \cos k_ya+ \cos k_za) \quad ,$$ where $β$ is a constant and a is the lattice ...
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On Miller indices

In the book Solid-state physics, Ashcroft and Mermin provide a somewhat derivation of them starting from the reciprocal lattice: The Miller indices of a lattice plane are the coordinates of the ...
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Open boundary condition in hubbard model

In case of open boundary condition, crystal momentum is not a good quantum number anymore. I mean we can construct an $N×N$ matrix in position basis and diagonalize it to obtain the eigenvalues, but ...
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Electron Diffraction Pattern (spot in the center)

So in the diffraction pattern of an electron beam (or an electron) in a polycrystaline material we observe rings and a central spot . What's exactly the central spot? Is it not diffracted electrons ...
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How does amorphous $\rm SiO_2$ crystallize?

I know crystalline $\rm SiO_2$ changes its crystalline structure depending on temperature, but what happens to amorphous $\rm SiO_2$ if you heat it up? I could find nothing on this topic. Is it ...
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What is $B(N)$ crystal structure? What does this nomenclature stand for

Is it basic cubic with 20 atoms? I can't find the explanation for this nomenclature online. Maybe I could find it in a textbook, but if someone answers it here, other people can just google it.
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How to understand crystal momentum, its relation to translational symmetry, Noether theorem, and to symmetry breaking/Landau-Ginzburg theory?

This question continues from my another question How to understand critical points of the Brillouin zone, (in)direct bands of transition-metal dichalcogenides?, and is related to Is crystal momentum ...
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How to calculate the mass for phonon vacuum fluctuations?

I am studying this paper, the precise content of which isn't relevant for the question. In there, the authors consider quantized bulk vibrations in a diamond. As usual when quantizing such systems, ...
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How to understand critical points of the Brillouin zone, (in)direct bands of transition-metal dichalcogenides?

In the paper Optical and Excitonic Properties of Atomically Thin Transition-Metal Dichalcogenides, it is said: 'Such calculations indicate that the direct gap occurs at the high-symmetry K and K′ ...
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What is the reduced mass of a diamond unit cell?

I am reading this paper to study so-called collapse models. However, the paper isn't really relevant to understand the problem here. In the paper, the authors are considering a bulk vibration (optical ...
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About Volterra's displacement equation on dislocation: cancellation of a surface integral on stress

In the theory of dislocations, the displacement induced by a dislocation in an anisotropic solid media can be expressed by Volterra's displacement equation as follows: $$ u_j(\mathbf{x}) = \int\int\...
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Density states of phonons with different speed at different directions:

I was trying to get the density of states $g(v)$ for phonons which have $2$ polarizations transversally, and $1$ polarization longitudinally. My approach: $$dN = \frac{1}{8} 4 \pi n^2 dn, \lambda = c/...
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Difference in crystal shapes of Soidum Chloride (NaCl) and Potassium Chloride?

According to this website, 1. https://en.crystalls.info/Sodium_chloride 2. https://en.crystalls.info/Potassium_chloride. The Sodium Chloride (NaCl) crystallizes among various other shapes into ...
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Why Hamiltonian for a Solid is periodic in Bloch Theorem?

It is as simple as the title and more general to Bloch theorem treatment. In any periodic infinite solid lattice, we say that the potential will be periodic. This makes sense, but how do we know that ...
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Surface effect on non-symmorphic symmetries when applied to tensors

I am curious about the effect that a surface has on a non-symmorphic symmetry. To be concrete, assume that we have a crystal with symmetry-group $G$, which contains non-symmorphic elements $\{R|\tau_R\...
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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 is the catch behind the simple expression and explanation of Bragg's Law?

Consider how the topic of scattering by periodic crystal structures is covered in most books: Start by treating the crystal structure as a periodic potential and use Fermi's Golden Rule to show that ...
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Can polychromatic light be produced from monochromatic light after passing through a crystal in transmission spectroscopy?

I have an optical setup where monochromatic light (573.5nm) is passed through a cuprous oxide crystal (Cu2O). This light is then passed through a monochromator, but the output light is actually ...
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Jone calculus in crystal optics and electro-optic sampling

Assume a linearly polarized light passing through a retardation crystal and a quarterwave plate and the angle between the linear light and the principal axis is 45 degrees. The question is to ...
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Where do valence and conduction bands lie in periodic barrier structure?

If we represent a periodic barrier structure as : Where would valence bands and conduction bands lie wrt to these barrier structure? Should not the conduction bands lie above barrier and valence ...
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Can a diamond lattice be deformed to have a site-avoiding mirror symmetry?

I'm working on an argument that relies heavily on the presence of site-avoiding mirror symmetries, i.e. mirror symmetries that do not fix any lattice sites. It's possible to deform the lonsdaleite ...
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Are Bloch states scattering states?

Bloch states can't be bound states because they spread out like all over the lattice and could be defined by $ \psi = e^{ikr} \space u(r)$ where $u(r)$ is a periodic function with lattice constant/s ...
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Miller index and intersects

How intersects between a plane and unit cell are $a/h, b/k, c/l$? Let me say miller indices of the give plane are (hkl) and lattice transitional vectors are (a,0,0), (0,b,0), (0,0,c). As you may know, ...
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Drawing reciprocal space phonon vectors

I'm a bit unsure about how the crystallographic directions work with phonon momentums and reciprocal space. If I have a phonon that's travelling in some direction $[abc]$ in a cubic structure, I ...
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Why does a lattice have to have an inversion center?

Indeed all lattices have inversion symmetry, but my teacher said a lattice has to have an inversion center: why? If a lattice doesn't have inversion symmetry, what would happen?
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What kind of material could be used as a diffraction grating for Xrays?

I'm trying to design a home-built X-ray fluorescence spectrometer with the following layout: Building the X-ray tube is relatively simple, however I'm uncertain what material could be used as the '...
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What's the crystal orientation of this YBCO sample?

I recently purchased this YBCO crystal. The epitaxial thin film composition is described as <100> YBCO and the package it arrived in describes it as "orientation: (100) with edge (100)"...
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Diffraction pattern for a cosine crystal

I have a 2D square crystal which has a continuous potential $U(\vec r)$. It stretches to infinity. I want to find the diffraction pattern for this crystal. The potential I use is $$U(\vec r )=U(x \hat ...
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How can salt "grow" up the wall of a vial with very salt water?

In my kitchen I have a vial with very salt water, and some food coloring. It's been left to slowly dry out for a year or so. Recently, salt (presumably) started growing up the walls of the vial. Does ...
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Are reciprocal lattice basis vectors parallel to their corresponding real lattice basis vectors?

So I had a question asking to find the angle between b* and (113) plane normal in a tetragonal unit cell. I know that the angle between two plane normals are given by: My thinking was that if I know ...
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How to unfold electronic bands? How do the reduced/extended schemes work? Confusion regarding the quasi-momentum

One of the simplest models for electronic band structures is a tight binding model on a one dimensional chain with spacing $a$, one atom per cell and interactions only for nearest neighbours. This ...
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Brillouin zone integration and delta function

Many BZ integrals of interest are related to the spectral function $$ G(\omega) = \int_{BZ}\frac{F(\mathbf{k})d\mathbf{k}}{\omega - \omega(\mathbf{k}) + i\eta} \tag{1} $$ where $\omega(\mathbf{k})$ ...
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Do all particles oscillate with same frequency in a crystalline solid?

For the reference : lecture notes In the derivation for the displacements in an oscillating monoatomic crystal the notes assume an $\omega$ (angular frequency) and $k$ ( wavenumber) that is the same ...
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Fourier transform of the crystal lattice

I am trying to show that the Fourier transform (not the Fourier series) of a crystal lattice can only be non-zero at the points of the reciprocal lattice. For this I have tried to describe the lattice ...
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