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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Mathematical definition of a Wigner–Seitz cell

Let $\mathfrak{A}$ be a Bravais lattice generated by the primitive vectors $a_1,a_2,a_3$. We know that the Wigner–Seitz cell of a lattice point is the region of space that is closer to that point than ...
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Electrons' distribution inside bands

If you consider a crystal of silicon made by $N$ atoms, you know that there will be a valence band with $4N$ possible levels of energy for electrons and a conduction band with $4N$ possible levels of ...
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What does the blue directions indicate?

This is with close reference to the X ray diffraction.I do not understand what it means to highlight a particular direction as blue when the incident light can diffract in all directions.Please help.
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Geometrical proof of number of lattice points in 3D lattice

It is well known that number of lattice points in three-dimensional (3D) objects of simple cubic lattice, body-centered cubic lattice, and face-centered cubic lattice are 1, 2, and 4, respectively (...
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Proof of Bloch's Theorem

I'm reading the book Solid State Physics by Ashcroft and Mermin. In its second proof of Bloch's Theorem on p.137, the periodic potential $U(\mathbf{r})$ and the wavefunction $\psi(\mathbf{r})$ both ...
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Integration domain of fourier series expansion on lattice

In solid state physics we define the Fourier expansion of a lattice periodic function $f$ as $$f\left(\vec{k}\right)=\sum_{\vec{R}_n} f_{\vec{R}_n} \mathrm{e}^{\mathrm{i}\vec{R}_n\cdot\vec{k}}$$ where ...
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How to determine interplanar spacing for BCC/FCC crystals?

I have a query as to how interplanar spacing in fcc and bcc can be determined. In line with the known formula, $$d_{hkl} = \frac{a}{\sqrt{h^2+k^2+l^2}}$$ for a crystal with Miller indices (1 1 0), ...
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Angular positions of points on a pole figure

I have to integrate a certain physical property of a crystal within a section of orientation space, Say between the space bound by directions <100>, <110> and <111> and so on. How can I ...
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A fast and automated way to check if symmetry (space group) operations preserve a lattice

Consider the simple cubic lattice. There are symmetry operations which preserve the lattice symmetry such as translations and rotations around certain axes. There are also symmetry operations that do ...
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Basic band structure reading

In band diagrams (e.g. GaAs below), symmetry points are sometimes indicated with a numerical index. I first thought it was the band index in the Bloch function (so two electrons with the same wave ...
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Are atoms in a perfect crystal lattice indistinguishable?

So I was reading a wikipedia article about the third law of thermodynamics, and was intrigued by the following sentences: Suppose a system consisting of a crystal lattice with volume V of N ...
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Crystal lattice Fourier coefficient

In solid state physics we have a periodic function over the lattice as $$f(\boldsymbol{r})=\sum_{\boldsymbol{G}}f_{\boldsymbol{G}}\mathrm{e}^{2\pi i\boldsymbol{G}\cdot\boldsymbol{r}}$$ where $$\...
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Why is silicon absorbing visible light?

Here it is shown that silicon absorbs visible light: but the band gap energy for direct transitions is 3.6 eV which does not match to this absorption coefficient. Instead, the band gap energy for an ...
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Focusing a Gaussian beam into a nonlinear crystal

Boyd analyzes in his book (Boyd's book), section 2.10.3, the case of harmonic generation using a focused Gaussian beam and he mentions that an analytic solution can be evaluated for certain special ...
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Understanding the Born-Mayer binding potential for ionic crystals

what was supposed to be a simple question, turned out to be a conundrum. I am asked to plot the Born-Mayer potential energy for a single pair of positive and negative ions. The potential energy is ...
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How to know the symmetry (point group) of crystal field in a material?

As an example, Let's consider a material $Ba_{2}YMoO_{6}$,(ref:PRB 81,224409), the space group of this material is Fm3m, the crystal structure is shown below (https://journals.aps.org/prb/abstract/...
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Compared to natural gem formation, does the decreased pressure when forming flame fusion gems affect crystal structure (different system entropy)?

Do the synthetic gems (flame fusion type) have the same crystal structure as a natural gem or is it a less perfect crystal lattice? Because they are not formed at the same pressures I'm wondering how ...
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Space group for vector fields with fractional periods in subspaces

Consider a periodic system of 3-dimensional vector fields, the corresponding Hamiltonian is a 3-by-3 hermitian matrix: $$ H(\mathbf{r})=\begin{pmatrix} a(\mathbf{r}) & 0 & d(\mathbf{r})\\ 0 &...
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Sonority of metals [closed]

Is there any reasonable atomic theory which can provide a rational reason for the existence of sonority in metals? Almost all the non-metals do not exhibit sonority. Can it be correlated to the ...
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Does pseudospin break the crystal symmetry?

Pseudospin is a concept to describe a superposition of two quantum states. Sometimes, I see a pseudospin texture in the momentum space which breaks a crystal symmetry. A simple example is the ...
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For what choice of the basis atoms origin the Structure Factor is real?

I have a Cuprite Structure: Now, given that I described this structure as a Simple Cubic lattice with a 6 atoms basis, I have to choose the origin for these basis atoms such that the structure ...
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Cutting silicon wafers using sound?

I've heard about using particle accelerators to shoot particles a specific distance into a wafer to split it and it got me thinking, can we do the same with sounds? Link to a page talking about the ...
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Metal-Insulator from number of atoms in the basis

I have an issue understanding what A&M means while saying this in chapter 12: It is a reassuring exercise to go through the periodic table looking up the crystal structure of all insulating ...
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In band gap theory, why can we use periodic boundary conditions

In band gap theory, why can we use periodic boundary conditions when finding the wave function of free electrons in a conductor? Why do you think it is smoothly connected at both ends of the conductor?...
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Crystal Field Theory (CFT) in $s$-$p$ orbitals system

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals (Source: wiki). My doubts: Is it possible to have CFT effect in ...
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Why does silicon have 6 phonon modes instead of 24?

As is known, silicon has a structure made up of two intertwined face-centered cubic (FCC) lattices, with bases $[000]$ and $[\frac 1 4,\frac 1 4,\frac 1 4]$. This equates to $\frac{1}{8}\cdot 8 + \...
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Berry Curvature in a hexagonal lattice

I am having troubles to understand the concept of the Berry curvature in a hexagonal lattice. What I know is: The Berry curvature $\Omega_n (\vec{k})$ for the $n$-th band reads \begin{equation} \...
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Role of d-band in metals

I have seen that in many publications authors discuss the metals in the d-block of the periodic table (often called 'transition metals') separately from other metals (e.g. alkali metals and aluminum). ...
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Steinhardt order parameter and radial distribution function

Is there a relation between the probability distribution of Steinhardt order parameter for BCC and FCC and their radial distribution function? In the picture we see the probability distributions of ...
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68 views

How do we determine refractive index of a photonic crystal?

Normally, refractive index of a medium is defined as $$n=\frac c{v_\text{p}},$$ where $c$ is the speed of light in vacuum, and $v_\text{p}$ is the phase speed of light in the medium. Phase speed is ...
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Can anyone recommend a book on sigma phase?

I am looking for a book in Solid State Physics where I could find a systematic approach to sigma-phase (closed packed structures) and high-entropy alloys. So far, I have only found published papers on ...
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Conventional unit cells and Bravais lattices

Conventional unit cell is defined in the following: A definition of a conventional unit cell of a lattice is one that contains the same point group symmetries as the overall lattice and is the ...
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How many atoms are in the primitive unit cell for diamond?

The primitive unit cell for diamond is pictured (the parallelepiped inside the cube). How many atoms are in the unit cell? My first guess is 3.5 and i know this must be wrong as the number of atoms in ...
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Are there any crystallographic effects we can see in the reflection of visible light from metal surfaces?

I started thinking about this in a discussion in comments. One can start by thinking of the reflection of visible light by most metals as similar to the reflection of radio waves in that it's an ...
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What is the lattice vector description of diamonds structure for a conventional fcc unit cell?

I understand how diamond has a conventional fcc unit cell with 4 extra atoms in it's basis. I also know that we can construct a primitive lattice cell using the lattice vectors: $\pmatrix{\frac{1}{2} ...
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Solids are crystalline or amorphous. Where do polymers fit in?

Traditionally, solids are classified as being either crystalline (well-ordered, periodic lattice structure at large spatial scales) or amorphous (disordered structure). A well-ordered polymer is a ...
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Vibrations in Stones and Crystals [closed]

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 [closed]

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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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 ...