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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Using Fractional Coordinates to define Plane Cuts

Say I have a none cubic Unit Cell with all its atomic positions defined fractionally (x, y, z defined as some fraction of the a, b, and c lattice vectors). Effectively, viewed in this way the atoms ...
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Book recommendation: Does anybody know a book adopting a more intuitive approach to the topic of Crystal Vibrations (phonons) than the Book by Kittel?

I have tried Simon's 'Oxford Solid State basics' and Kittel 8th edition but I am not impressed by both (I mean the content covered through Chapters 4 and 5 in Kittel)
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Atomic coordinates of NbS2 monolayer

In a monolayer $NbS_2$, the $Nb$ atoms are packed in trigonal prismatic coordination with $S$ atoms above and below, and the unit cell consists of a single $Nb$ and two $S$ atoms. Does someone know ...
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Find the fraction of Miller indices for which FCC crystals scatter

I have been running into some problem (which I have essentially run down into a maths problem) with Miller indices: I have the lattice structure factor for scattering $$S \propto \sum_{j}e^{2\pi i(...
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Limit on number of basis vectors for a d-dimensional lattice?

is there a limit to how many basis vectors one can have when decorating a d-dimensional lattice? For example, if I have a crystal structure in 2D that has an underlying lattice, is it permissible to ...
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If the lattice parameter is changed from $a$ to $a/2$ in 1D lattice chain then how the graph will change for optical and acoustical?

If the lattice parameter is changed from a to a/2 in 1D lattice chain for two different atom then how the graph will change for optical and Acoustical branch? How will the dispersion relation change?
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No solution to Bragg's law?

Bragg's Law provides a description for the diffraction peaks we observe when x-rays are incident on a crystal structure. We observe these diffraction peaks because the wavelength of the incident x-...
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How can I determine the number of broken bands per unit area in a crystal on the (111), (110) and (100) planes?

How many dangling bonds per surface atom are there at each of these surfaces;(100),(111), and (110)? Is there any formula to calculate dangling bond per surface atom other than visualizing in your ...
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Is it possible to make invisibility cloak in real? [closed]

I am a materials science undergraduate student. I have a question out of curiosity if it is possible to make a material that can completely make things invisible? What are the problems we will ...
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Why is the translational symmetry broken?

In the book Condensed Matter Field Theory by Altland, on page 5, it is given that $$H[\pi, \phi]=\int d x\left(\frac{\pi^{2}}{2 m}+\frac{k_{\mathrm{s}} a^{2}}{2}\left(\partial_{x} \phi\right)^{2}\...
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Radiation damage in a crystal

Take a single crystal as close to the ideal as possible, say, Si, GaAs, or SiGe, etc. Immerse the crystal in some fixed rate ionizing radiation and measure the radiation damage it has caused to the ...
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Are ionic crystals, band insulators?

Ionic crystals are considered as electrical insulators. Is there a proof that they are insulators from the point of view of electronic band theory? In other words, is there a proof that ionic crystals ...
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Most symmetric unit cell in a two-dimensional arrangement

Consider the two dimensional structure below, where two atoms A (white) and B (black) are displayed like a brick wall. I need to find the most symmetric primitive unit cell of this structure and the ...
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Problem with the value of $Z$ for a $C2 /c$ cell

I have a unit cell with C2/c symmetry that contains 4 molecules (Z = 4) as shown in the image that I attach. The unit cell in question is a base-centered monoclinic cell. I have 8 points of the ...
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Different ways to defining Fourier transform of a lattice model

I have a Kagome 2D lattice as shown in the figure below: There are three atoms in one unit-cell A, B, and C (shown in circle). An interaction Hamiltonian can be $$H = H_1+H_2+H_3\equiv -t\sum_{\...
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The interaction of an ion with all ions in KCL crystal structure deducing its relationship as $𝑈_𝑖 = −|𝛼| 𝑒 ^2 /𝑅 + 𝛽 𝐵_𝑛 / 𝑅^𝑛$

please, if someone can answer this question? deduce the relationship of the interaction of an ion with all ions in KCL crystal structure as $𝑈_𝑖 = −|𝛼| \frac{𝑒^2}{𝑅} + 𝛽 \frac{𝐵_𝑛}{𝑅^𝑛}$
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Why phonons are Goldstone modes?

I read this in the lecture notes by David Tong: "Gapless excitations often dominate the low-temperature behaviour of a system, where they are the only excitations that are not Boltzmann ...
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Whta's are the defferences between conventional transmission electron tomography and scanning electron microscope Focused ion beam?

I'm begining in Electronic microscopy ( Transmission electronic microscopy and scanning electron microscopy) i was reading an article related to this and i found this information: Since the twisted ...
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Relation between roughness of a p-n junction and interatomic spacing

Question:Can we take one slab of p-type semiconductor and physically join it to another n-type semiconductor to get p-n junction? Answer:No! Any slab, howsoever flat, will have roughness much larger ...
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What is a “half-convergence angle”?

What is the definition of the half-convergence angle of an incident electron beam? I have been asked the value for a half-convergence angle for an electron beam of diameter 381 pixels and on the [$000$...
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Method to increase density of $k$-points

I've been working on a simulation for some time and I have seem to hit a stone wall. Basically I want to plot the spectral function: $A(\boldsymbol{k},\omega) $. I set $\omega=0$ to look at the ...
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What is a simple example illustrating the concept of “commensurate” and “incommensurate” order in condensed matter physics?

In a wide range of contexts in condensed matter physics, e.g this paper, the concepts of commensurate and incommensurate orders are invoked to describe particular ordered phases. I think I have some ...
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Generating more $k$-points in simulation

I'm hoping someone can help me out with generating more $k$-points so that I can get some higher resolution plots. Some background: First, I am doing a simulation on an $N\times N$ lattice with PBCs. ...
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Why do atoms arrange themselves in a regular fashion to form crystals?

This questions has been hovering in my mind for a long time. Why would something which does not have life would to be in such a beautiful neighborhood, while the world is so much disordered. What ...
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Lattice unit cells

Just wondering if anyone had any links to good web based interactive models of lattice unit cells? Especially primitive unit cells? The one I used to use was built with flash so it no longer works :( ...
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What are these geometric patterns on ice?

In a winter day, I noticed the water frozen inside a canal in our building. As you see there are very nice geometric patterns formed by the ice, with specific angles. What is the physical ...
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Describing complex Bravais lattice as a simple Bravais lattice with a basis

Recently I started to read about solid state physics, and as an introduction to analyzing the problem of electrons in crystals with periodic potential, I started to learn about Bravais lattice. I've ...
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Closed formula for neighbors in FCC lattice

I wonder if there is a close formula for the sequence of distances of neighbor shells in an FCC lattice, i.e. a formula of the form $d_n = a f(n)$ where $a = \frac{A}{\sqrt{2}}$ is the nearest-...
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Finding the K-Path of High Symmetry Points in the Brillouin Zone

I am trying to understand how to find the K-Path of high symmetry points in the 1st Brillouin Zone. Can someone explain to me what does $\Gamma-X-U \space|\space K-\Gamma-L-W-X $ mean for the case of ...
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Bravais lattice point groups

I'm trying to describe Bravais lattice point groups as permutations of lattice points. In doing so, I encounter a problem: I can only find descriptions of Bravais lattice point groups in terms of ...
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Why does the kinematic theory of diffraction for crystals predict the reflectivity will grow larger than 1?

Kinematic diffraction for perfect crystals is based on a few assumptions (neglecting multiple scattering, far field, etc.) some of which become less valid as the crystal thickness is increased. ...
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Writing Basis for the unit cell

I'm following The oxford solid state basics By S. Simon. I'm sort of confused, How he has written the basis in different places? The definition that is given goes like this: The description of ...
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Is there a place online to look for lattice structures and constants for most (if not all) of the crystals constituted of single element?

For example, if I want to look for lattice structure and constants (unit cell side lengths, angles) of the Bismuth crystal, where should I go for? It is more important for me to know the cell ...
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Finding the number of particles per unit area along a given plane

We are given a problem in our class that goes like this: In a simple cubic lattice constant $0.287$ nm, the number of atoms per $\text{mm}^2$ along the plane $111$ is $2.11\times 10^{13}$ $1.73\...
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What are typical resonant frequency ranges of large crystals?

I want to measure the resonant frequency of a crystal about 1 inch long using a transducer and a contact mic. What frequency ranges should I select to be able to measure a variety of different ...
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Why does $P21/c$ space group have $2/m$ point group symmetry?

In wikipedia, it says $P21/c$ has $2/m$ symmetry. https://en.wikipedia.org/wiki/Monoclinic_crystal_system But in its space group diagram, there is no 2-fold rotation or mirror planes http://img.chem....
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The difference between two edge dislocations, ⊥ and ⊤

The edge dislocation is denoted by ⊥, if the dislocation line lies below the half-plane, and ⊤ if it lies above the half-plane. How do you differentiate between them? You can always rotate the crystal ...
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Can we use Neumann's principle for microscopic properties?

Neumann's principle states if a crystal is invariant with respect to certain symmetry elements, any of its physical properties must also be invariant with respect to the same symmetry elements. We ...
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Energy of cubic dipole lattice

Consider a single dipole in a cubic box with periodic boundary conditions, or an infinite cubic lattice/grid of parallel dipoles. Is there a simple expression for the energy?
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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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Is it possible for the Kagome lattice to have edges of different lengths?

Is it possible for the edges of the Kagome lattice to be of different lengths? In other words, in the attached picture, is it possible to have $x\neq y$? If so, how will be the shape of that network? ...
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What is two adjacent planes in a crystal? [closed]

I want to resolve the problem of the book, introduction to solid state physics, 2nd, Kittel. the problem is Consider a plane $hkl$ in a crystal plane. (a) Prove that the reciprocal lattice vector $\...
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Understanding the phonon

It is said that the phonon is the equivalent of the photon in Solid state physics. I cannot see how,when i try to give an interpretation to the phonon. What i am trying to say is the following: If we ...
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How is ECR (Electron Counting Rule) done in a structure?

I've been told how to apply the ECR to GaAs{001}(2×4) in my lectures but it makes no sense to me and I don't seem to be able to find any other sources that explain this. (This is a further question on ...
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Finding coupling between crystal sites related by symmetry

Say I have a crystal and the coupling between sites is described by the following local, model Hamiltonian (a spin 1/2 system): $$ \hat{H}_{i,j} = J \bf{S}_i\cdot\bf{S}_j+\bf{d}\cdot\left[\bf{S}_i\...
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Bloch's theorem for a lattice with sublattices

Bloch's theorem states the following: suppose we have a Hamiltonian $$ H = \frac{p^2}{2m} + V(x) $$ where $V(x + a) = V(x)$, then the wavefunctions take the form $\psi_k(x) = e^{ikx} u_k(x)$ and $u_k(...
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Painfully confused on free electron in an “empty” lattice

I'm trying to study some aspects of solid-state that have always bothered me and I am truly stuck on this conceptual boundary. We take the discrete spatial frequency Fourier Transform to arrive at the ...
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Rotation of crystal structure to match with match another structure of same compound/polymorph

Say, I have two crystal structures of a particular organic molecule, the crystal structures are basically identical, apart from a rotation and redefinition of the lattice vectors/angles, a simple ...
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Ewald summations and series convergence

Does anyone have a explanation of why the direct summation of the coulomb interactions between the ions of a crystal structure which might be conditionally convergent is mathematically allowed to be ...
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Which is the correct GaAs{001}(2×4) structure?

When trying to understand the GaAs 2x4 surface reconstruction, I came across the following statement: "Because the periodicity of the surface has doubled (compared to the bulk periodicity) in the ...

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