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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 some materials cannot be deposited on particular substrates? what factors do affect sputter deposition?

Why some materials cannot be deposited on particular substrates? what factors do affect sputter deposition? Particularly, on which wafers we cannot deposit titanium nitride?
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Vibrations in Stones and Crystals

I have read studies done that indicate certain sounds can either disrupt or reinforce the molecular structure (I think this is the terminology used) of living organisms. This is based on the idea that ...
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Why can a nitrogen-vacancy center be viewed as a basic unit of a quantum computer?

I was on the Wikipedia page for Nitrogen-Vacancy Center and in the first paragraph the following statement is made: An individual N-V center can be viewed as a basic unit of a quantum computer, and ...
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What happens if I replace an IR laser diode with CD burner laser diode in green laser pointer

I was wondering what happens if CD burner photons hit the crystal NdYO4 and KTP 780 nm wave length where original 808 nm IR pumper diode. I am confused with NdYO4 crystal I know that KTP is a ...
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Physical Interpretation of Energy-wavenumber Graphs

Consider an energy-wavenumber graph, typical in solid state physics, like the one below. I can follow the mathematics in the derivations with a KP model. But I don't understand the physical ...
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Claim that DeBroglie relation doesn't work in crystal

In this Wikipedia article on Position and Momentum Space, https://en.wikipedia.org/wiki/Position_and_momentum_space there is a claim that "the de Broglie relation is not true in a crystal" in the ...
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Using Brillouin zones to write Hamiltonian and find momenta values

This is a homework problem that I have spent a large amount of time on..I will try my best to simplify the questions down to conceptual ones, but I will also write more or less that whole question ...
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A one-dimensional periodic structure is the simplest type of photonics crystal and any such one-dimensional system has a band-gap?

My textbook says the following: A one-dimensional periodic structure, such as a multilayer film (a Bragg mirror), is the simplest type of photonics crystal, and Lord Rayleigh showed that any such ...
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Intensity of x-ray difracted on a crystal

Suppose we have an X-ray tube R which emits X-rays of intensity $I_s(\lambda)$, obeying the Kramers' law. The X-rays then come to the cubic crystal K under the angle $\vartheta$, where diffraction ...
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Reciprocal lattice points and diffraction peaks

I am having a issue with the concept of what this question is asking. Question For a FCC crystal describe all the reciprocal lattice points corresponding to the two diffraction peaks. Here is my ...
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35 views

Basis function of $\Gamma_2$ irrep of point group $T_d$?

From Properties of the Thirty-Two Point Groups (Koster, et. al.), the basis function of the $\Gamma_2$ irrep of the point group $T_d$ is $l_xl_yl_z$, where $l$ is the angular momentum operator. ...
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Is polarization matrix always diagonalizable?

In chapter 31 of Feynman lectures Vol 2, he covers polarization , polarization tensor and its diagonalisation, he proves that for a crystal, the tensor matrix is symmetric hermitian and hence ...
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Slater-Koster parameter for SC

I want to use SK method to calculate the interatomic matrix element for $P_{y}$ and $P_{z}$ for the nearest, second and third neighbors in simple cubic crystal. based on paper written by Slater-Koster ...
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Spectrum of sinusoidal potential

In 1D quantum mechanics problems, the energy spectrum is often determined by the limits of the potential at $\pm$ infinity. Generally, the spectrum is continuous non-degenerate when energy is above ...
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Mossbauer effect: neglectable recoil or absolute no recoil?

I stumbled on the Mossbauer effect. From the wikipedia article, I cannot tell for sure if the momentum of recoil is really zero, or only neglectable. From what I do (think I) understand, the ...
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Phase Matching in a Non linear crystal

I am working with Second Harmonic Generation using a LBO crystal. My pump beam is 795nm and I want to generate blue light using Collinear SHG in LBO. I have perused a lot of resources on the internet ...
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Unitary matrix that transforms Bloch wavefunctions of k-points connected by crystal symmetries

In the following link https://docs.abinit.org/theory/wavefunctions/#symmetry-properties, there's Eqn. (8) that describes for degenerate states how wavefunctions of k-points connected by symmetry $\...
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Scattering on crystals beyond Ewald and Bragg

So I whenever we consider the diffraction and scatting using crystals, powders, basically anything crystalline in the lab using X-rays we get a bunch of theories and models. The most simple one would ...
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How does a basis affect the nearly free electron model?

Lets say I have a monatomic chain of atoms in which the electrons are nearly free. I know how to solve this, we end with energy gaps at the Brillouin zone boundaries. Now lets say every other atom ...
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Two Dimensional Self-Reciprocal BravaisLattice

I've been reading Quantum States of Atoms Molecules and Solids by Morrison et al. for a condensed matter course. They make the claim that all 2D Bravais lattices are self-reciprocal, but I'm having ...
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Figure Description of Equilibrium in a Crystal Lattice

I am reading an Introductory Semiconductor Physics by Parker. The textbook states the following: The ionic crystal itself is formed by the ions coming together in an equilibrium configuration. ...
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What does it mean for a wavevector to terminate?

In the question we are told that the amplitude of a wave after being diffracted through a crystal is: $$ S\propto e^{i\mathbf{k\cdot r_D}}\sum_n e^{i(\mathbf{k-k_0)\cdot r_n}} $$ where $k_0$ is the ...
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How to find the structure factor for the BCC lattice?

why is the value of structure factor zero when value of exponential is -1?
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Honeycomb lattice Brillouin zone structure and direct lattice periodic boundary conditions

One way to construct the Brillouin zone of the Honeycomb lattice is by obtaining the standard Wigner-Seitz cell by constructing the perpendicular bisectors of the reciprocal lattice vectors and ...
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Symmetry Operation in Reciprocal Space

I have a set of k points spanning the entire Brillouin zone and I want to reduce it to the irreducible BZ. So for reduction, I use the point group symmetry operation. To verify, I use quantum espresso ...
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How is the point symmetry group of real space related to the reciprocal space?

I am taking a course of solid state physics. My teacher asked me that. I have been looking for the answer in the book Solid State Physics by Ashcroft & Mermin, and also in the book of Ibach & ...
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Effect of complex refractive index on reflectivity in a periodic structure?

I'm studying the effects of absorption in a 1D photonic structure with repeating alternate layers (a Distributed Bragg Reflector). To include absoprtion effects, the refractive index is defined as $...
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Solid state physics, meaning of momentum notated G in photon-phonon collision?

I have a problem in momentum conservation in the scattering of photon with phonon.In the process the momentum conservation is written as k'=k+G+q.where k'=wave vector of scattered photon,k=wave vector ...
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What is a ferroelectric metal?

I was reading online about ferroelectricity, and came upon the topic of ferroelectricity in metals. The main cited paper is the one below by Anderson and Blount in the 1960's Symmetry Considerations ...
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Representative Volume Element for crystals

I am trying to average the tensor properties of crystals with different types of unit cells. Due to symmetry elements for different crystals, the integration over a limited volume should be enough, ...
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35 views

Origin of XRD Peak Asymmetry

I have been doing an introductory XRD experiment in which we measure the crystal spacing of a simple lattice (LiF) and as usual obtained data for intensity against two theta. Ideally the peaks should ...
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Can we call a hexagonal system with two different atoms as inversion symmetric?

Graphene is two-dimensional honeycomb crystal lattice with the two Carbon atoms in its unit cell. Clearly, it is inversion symmetric. But, suppose we have two different atoms in the hexagonal system ...
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Inversion applicable to three-dimensional lattices only

I have just started my first course in solid state physics and while studying symmetries, Inversion is defined as "A point operation which is applicable to three-dimensional lattices only. This ...
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Wigner Seitz cell

While searching the difference between primitive cell and unit cell I have seen that "Primitive unit cells contain only one lattice point, which is made up from the lattice points at each of the ...
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Momentum Space Representation of the Tight Binding Hamiltonian

I am trying to represent the tight-binding Hamiltonian \begin{equation} \hat{H}_{TB} = \sum_{\sigma} \sum_{\alpha,\beta} \sum_{\mathbf{R}_1,\mathbf{R}_2} t^{\alpha,\beta}_{\mathbf{R}_1,\mathbf{R}_2} \...
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Density of states in Frequency Space vs K Space

Why do we use the density of states in frequency space when the density of states in k space is one state per unit k cubed (in 3 dimensions0?
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Single Crystal Growth- Czochralski process

Cz process operates with two opposite rotations (melt and seed's rotations). How these rotations prevent growing imposed by other facets' directions (Other than that perpendicular to the axis of ...
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Bond order correlation function

I am trying to compute the bond order correlation function, $g_6$. It is defined based on the bond order parameter: $$\psi_6(x_i) = \frac{1}{N_i}\sum_{i=1}^{N_i}{\exp(i6\theta_i^j)}$$ where $\theta_i^...
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Does the sequence of the $n$th Brillouin zones converges to any particular geometrical form?

I am currently studying solid state physics and we just saw the construction of the Brillouin zones. My question is the following: Does the sequence of the $n$th Brillouin zones converges to any ...
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Number of allowed (phonon)wave vectors in a poliatomic-basis lattice?

Lets say that my crystal is of size $N=N_1N_2N_3$ , this is the typical textbook example and after that they say that the number of allowed wavevectors is N. But tbh I dont really know if they are ...
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Reduced wave vector using Bloch's theorem

In every solid state physics book it says that the wave vectors appearing in Bloch's theorem can be confined to the first Brillouin zone and provide a hint on how to show this. Most of the times this ...
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Is there a mathematical way to find the lattice points in a crystal?

In my solid state physics class we need to be able to determine the number of lattice points per cell of various Bravais lattices. For example, the orthorhombic which has 4 lattice points per cell. I ...
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A computation problem on reciprocal lattice

I am reading David Tong’s lecture notes on Application of Quantum Mechanics. My confusion is about the following paragraph: Consider a function $f(\vec{x}) $, suppose $f(\vec{x})=f(\vec{x}+\vec{r})$...
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Drawing reciprocal lattice structures

I am currently trying to understand why and how reciprocal lattice relates to the diffraction plane, so I did some research on Wiki about reciprocal lattice, but I seem to be stuck as I would like to ...
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How does one construct the $n$th Brillouin Zone in a rectangular lattice geometrically?

What are the general rules of constructing the Brillouin Zone in a rectangular lattice geometrically? While the construction of the 1st and 2nd Brillouin zone is rather simple, starting to construct ...
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Terminology Trouble with respect to lattice structures

I am having an issue understanding terminology in a chemistry text book I am reading. I am reading about lattice structures and it keep interchanging with the word 'basis'. So for context, it ...
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Wave scattering by crystals

The structure factor is defined as (assuming orthogonal axes): $$S_{(hkl)} = \sum_{j \in \mathcal{U}} f_j \exp\{2\pi i (hx_j+ky_j+lz_j)\},$$ where $\mathcal{U}$ is a unit cell of the lattice and the ...
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Reciprocal lattice of fcc or bcc

If we want to find reciprocal vectors/points in reciprocal space of a bcc or fcc lattice we often use the non-primitive lattice vectors of the ordinary cubic (reciprocal) lattice. Looking at families ...
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Lattice structure of diamond

The previous question was about whether diamond can be described by an ordinary cube lattice instead of a FCC lattice. I now know that this is possible since we can still get the whole crystal in this ...
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A homogeneous isotropic liquid and a perfectly periodic crystal lattice

A homogeneous and isotropic liquid or a perfectly periodic crystal lattice which one has higher symmetry. I was thinking that both have same order of symmetry as if I am at a lattice point and ...