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2answers
61 views

How many are the points which are $n$th nearest to a certain point in a hexagonal lattice

Suppose there are infinite points arranged as hexagonal lattice. The question is the one as the title. First we choose a point called $A$. Then when we count the $n$th nearest points to $A$, what ...
0
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2answers
77 views

Bragg diffraction and lattice planes

Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation. From the illustration below we see that we get constructive ...
4
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1answer
149 views

Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
4
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1answer
308 views

What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare ...
3
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1answer
62 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
3
votes
1answer
61 views

How can one reasonably theoretically model polycrystalline materials?

Many techniques are taught in advanced solid state courses but they are almost all derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you ...
1
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1answer
27 views

Difference in electrons excitation in Au (111) between perpendicular and diagonal orientation?

In Au (111) single crystalline as shown in attached file, is there a difference the way electrons are excited when they are excited from perpendicular and diagonal orientation as shown in the figure ...
1
vote
1answer
18 views

Why Nitrides have internal polarization?

Why GaN has internal polarization? I know that in wurtzite crystal structure, the atomistic bonds are not equivalent and as a result there appears a net dipole and consequently a polarization. But ...
0
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1answer
36 views

At which gravitational acceleration would a diamond crystal lattice break down?

Gravitational acceleration can be upto infinite (which is at the Event Horizon of a Black Hole). On which least acceleration, would crystal lattice of diamond break down? Update: Please, don't apply ...
0
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1answer
91 views

Coordinate system for crystallographic groups

In the International Tables for Crystallography for each crystallographic group an asymmetric unit is supplied (mathematicians call this a fundamental domain of the group). This region is a bounded ...
0
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1answer
26 views

Why can the twin plane be uncoincide with the composition plane in reflection twin?

In the book Elements of X-Ray Diffraction, p67, I found the following sentence: In the case of a reflection twin, the composition plane may or may not coincide with the twin plane. But I think ...
0
votes
1answer
71 views

Graphene has a honeycomb lattice - true or false?

In my grand ignorance I would state that graphene has a honeycomb lattice. Some tend to agree with me and some others do not. I'm curious to know what members of the SE community think is the right ...
0
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1answer
130 views

Reciprocal Lattice of a non-bravais lattice

Is a reciprocal lattice defined for non-Bravais lattices? I'm trying to work out one for HCP structure and not figuring it out.
-2
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1answer
595 views

Why do phonons cause excellent heat conduction in diamonds?

Phonons are the quantum of lattice vibrations in crystals and are not to be confused with photons, the gauge bosons of the electromagnetic force. Apparently, they contribute to heat conduction, but I ...
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0answers
390 views

Does positronium have a stable crystalline phase?

This is a long shot, but while the 100YSS conference is going on at Houston, i haven't been able to get a grip on myself and think in other, more mundane and short-term rewards as normal people do. ...
4
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0answers
30 views

What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of ...
4
votes
0answers
164 views

Crystal momentum and the vector potential

I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase ...
3
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0answers
90 views

Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
3
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0answers
135 views

Bandgap Spacing in Photonic Crystals

I am doing some self-study on photonics and have encountered the following question: We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic ...
3
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0answers
255 views

Does a thermally expanding torus experience internal stress?

I'm trying to learn continuum mechanics and thermo-mechanics. As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic ...
2
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0answers
24 views

What is the the real world interpretation of the high dimensionality of quasicrystals?

One of the examples of the problems of 5-fold symmetry is that pentagons tiled on a 2D plane do not completely fill that plane, leaving voids. This may be solved by "folding" it into 3D space, and ...
2
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0answers
115 views

Lattice theory in mathematics and physics

I have undertaken a project examining lattice model and trying to construct algorithm that could work on all lattice (in physical sense, or crystal structure). I notice there is a branch in ...
2
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0answers
81 views

The boundary between polycrystalline and crystalline

My current understanding of solid crystalline-like materials (please correct me if I'm wrong!) is that it is a continuum in terms of crystallinity, from amorphous (basically no periodicity) to single ...
2
votes
0answers
174 views

Discrete sum over an exponential with imaginary argument, considering only every second lattice site?

Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g., A-A-A-...-A-A (total of N sites) ...
1
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0answers
30 views

Crystallography: relationship between side length and radius of atom

For a FCC the relationship between the radius and the side length 'a' is 4r=(2)^.5 a And this is derived by drawing a diagonal across one of the faces of the unit cell. However, is this meant to be ...
1
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0answers
103 views

Pseudocubic unit cells: how to construct one?

I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation ...
1
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0answers
52 views

How does a liquid crystal on Silicon affect the phase of incident light?

When a polarized light beam is directed to a phase-only LCoS system how is the phase modulated ? What is the physical effect behind ? Does voltage modulation has an impact on birefringence ?
1
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0answers
152 views

Bloch's theorem and Bloch's state

The question is not so much about the theorem, but more about what it means in this context: see this link. So yes, because of Bloch's theorem the Hamiltonian eigenstates in a crystalline system can ...
1
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0answers
57 views

What is the physical meaning of group velocity for elastic waves through crystals?

In a chapter about phonons they define group speeds for elastic waves in crystals as the derivative of the dispersion relation: $$v_g = \frac{d{\omega}}{d{k}} $$ I wonder though how they come to ...
1
vote
0answers
94 views

Is there a derivation of all possible Bravais lattices in 2D and 3D?

Do any of you know a (possibly elegant) derivation of all possible Bravais Lattice and the Crystallographic Group of Lattices in 2 and 3 dimensions? Group theory /abstract nonsense approaches are ...
1
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0answers
306 views

How to demonstrate that there are just 14 types of Bravais lattice?

Is it possible to demonstrate that there are just 14 types of Bravais lattice without the knowledge of group theory?
1
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0answers
45 views

pressure required for displacing a single electron off a crystal

I need to know this for my project- "power generation using the pressure applied on a keypad of a mobile electronic device". How much pressure does it take to displace a single electron off its ...
1
vote
0answers
300 views

What defines the thickness of a Nomarski prism?

Lets say I want to design a Nomarski prism that would split the ordinary and extraordinary beam by an angle of 0.32 mrad. I used a raytracer to find the internal angle between the quartz wedges. ...
0
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0answers
8 views

Phase Diagram of Polymorphs vs. Binding Energy

Phase diagrams show how various polymorphs are favored at specific temperatures and pressures. I am interested in a 3-axis diagram showing the binding energy on the third axis. Ideally there would ...
0
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0answers
11 views

How many unique crystal faces does a given unit cell have?

I am not sure how to best approach this problem. "A diamond crystal is composed of an enormous number of cubic unit cells that are stacked to produce crystal faces. Stacking of cubes to produce an ...
0
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0answers
11 views

Binding forces in crystalline solids

I am referring to rocks in this instance. Individual crystals grow together in an igneous rock as it solidifies. I know that the SiO4 tetrahedron is the basic building unit of silicate minerals, and ...
0
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0answers
25 views

Quantization in a 2D quasicrystal?

let be the Schroedinger equation with a potential in a quascristal $$ -( \partial _{x}^{2}+ \partial _{y}^{2}) \Psi (x,y)+ V(x,y)=E_{n} \Psi (x,y) $$ if we were in a crystal we could impose the ...
0
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0answers
14 views

What are some structures which minimize surface stress upon expansion

Intro I am currently researching into a problem involving the cyclical expansion and contraction of a 3 layered structure comprised of an internal metal encased by another metal encased in an outer ...
0
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0answers
29 views

Mixed-Alloy materials

Short version: Is it a physical problem (crystal structure/grains/redox/etc.) or just a logistics problem (keeping the solutes from homogenizing, molten/solid/temperature related problems) that keeps ...
0
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0answers
17 views

3-dimensional quasicrystals

As is well known, quasicrystals (i.e. their diffraction patterns) show patterns which can be deciphered and understood via the use Penrose tilings (and aperiodic tilings of the plane in general). ...
0
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0answers
39 views

Which metal will be on the surface after solidification?

I know that there are some metals that just "like" to be on a surface, so if I make an alloy of such metal and some other metal, the first one will be on the surface after solidification of initially ...
0
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0answers
49 views

How can I get the lattice constant of a salt?

This is probably a very dummy question, but I am not able to solve it on my own. Given that the radius of $Li^+$ ions is 76 picometers, and the radius of $F^-$ is 133 pm, I would expect the size of a ...
0
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0answers
34 views

Transmissivity of Liquid Crystals in the near-infrared range

The gist of my query is in the title. I have been searching for papers and studies that could provide transmission curves (in nematic liquid crystals) across the visible to near-IR range (or from ...
0
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0answers
20 views

How to derive the exponential distribution for the Pool-Frenkel effect?

For the Pool-Frenkel effect, the external electrical field $E_{ext}$ reduces barrier by a potential energy amount $U_{ext}(r_{m})$, where $r_{m}$ is the distance maximizing the total potential enrgy ...
0
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0answers
48 views

Diffusion coefficient of a crystal

I've been trying to work this out so I can give a hand waving argument for one of the effects I'm observing on the fly and I find myself going down a rabbit hole that seems way too complicated for ...
0
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0answers
163 views

Bragg's law in photonic crystals

So in photonic crystals when looking at diffraction the refraction of light has to be taken into account. I am told this would lead to the "photonic bragg's law" which is $$n \lambda = ...
0
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0answers
36 views

Type-II SHG of linearly polarized light

It's possible to perform type-II frequency doubling of unpolarized light in suitable nonlinear crystals. But for a single beam of linearly polarized input light, is it still possible to do type-II ...
0
votes
0answers
17 views

Impurities involved in nucleation centres

When magmas begin to crystallise, a first step is the formation of a crystal nucleus around an impurity (nucleation centre), whereby a few of the right atoms get together to form a speck of a crystal. ...
0
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0answers
71 views

Bragg's law - intensity “sensitivity” to lattice spacing or scattering angle

I don't understand this sentence (emphasis added): A consideration of Bragg's law (nλ = 2dsinθ), i.e. the relationship between scattering angle (θ) and the interplanar spacing (d) shows that if ...
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0answers
181 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec ...