The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
1answer
24 views

The proof of a discrete Fourier identity in quantum field theory

On page 25, in the book Quantum Field Theory for the Gifted Amateur by Tom Lancaster and Stephen. J Blundell, it states the following: We impose periodic boundary conditions forcing ...
0
votes
0answers
14 views

Any good reference on crystal optics?

I am primarily interested in the birefringence phenomenon. Any good reference? I want something above the general physics level.
0
votes
0answers
11 views

Why are reciprocal lattice vector periodic, and time-frequency not?

k-space vectors are related to each other by $k=k'+G$, where $G$ is the reciprocal lattice vector $G=2\pi/a$. This means that the frequency of oscillation in real space of a plane wave $e^{ikx}$ is ...
0
votes
0answers
32 views

Definition of Fourier Transform on a Lattice

I am reading a book(EDIT: the book is Czyholls theoretical condensed matter physics, though i am not sure if there is an english version) where for periodic functions $f(x_l+L)=f(x_l)$ the Fourier ...
4
votes
1answer
72 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 ...
0
votes
1answer
29 views

can ice crystals be molded into a structural shape in space

I know that water exposed to vacuum space first boils and then turn into vapor (sublimates) . Is it possible re use this vapor say inside a pressurized membrane, to mold it into a solid ice structure, ...
0
votes
1answer
146 views

Does graphene have a honeycomb lattice?

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 ...
1
vote
1answer
30 views

Density of particles in hexagonal lattice

I need to calculate, in a 2D hexagonal lattice of point particles in which the nearest neighbours are a distance apart $a$, what's the density of particles. What I really need is, if $\rho$ is the ...
1
vote
1answer
37 views

Why is graphene stronger than graphite?

Why is graphene stronger than graphite when graphene is just a single layer while graphite is multiple layers of graphene? And can't we say that diamond and coal also consist of layers of graphene as ...
1
vote
1answer
25 views

Is graphene on a sticky tape strong enough to compete with my hand stretching it?

As we know we can make graphene using sticky tape so after we make graphene on a sticky tape will that thin sheet of graphene on a sticky tape be strong enough to compete with my hand trying to ...
1
vote
2answers
76 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
votes
2answers
157 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 ...
0
votes
0answers
22 views

Why do some materials have a negative coefficient of thermal expansion in all directions?

Those materials are especially ceramic-glasses. I've found some studies about how does it happens in one dimension (for example a nanocrystalline has a silica helix that works like twisting spring, ...
1
vote
0answers
23 views

Sum in the reciprocal lattice

I have to use this property but I don't understand at all the deduction, so I was wondering if someone could help me. We have a crystal lattice with vectors to each atom from one of them $R_j$, and ...
0
votes
1answer
223 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.
1
vote
1answer
192 views

Atomic nearest neighbor notation

I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: Do you mean NN, NNN, etc., or NN, 2NN, 3NN? ...
3
votes
1answer
107 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, ...) ...
2
votes
1answer
92 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 ...
0
votes
0answers
19 views

Constructing uniform mesh in reciprocal space?

This is a bit of a mental exercise for me to get comfortable with the math of reciprocal spaces since I am going to start doing some research that requires knowledge of reciprocal spaces. Let's say I ...
0
votes
1answer
113 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 ...
4
votes
1answer
171 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 ...
1
vote
1answer
37 views

What is the importance of reciprocal lattice?

Reciprocal lattice is the diffraction plot of a crystal. Now with the STM instrument we can get the get the topology of the crystal, so what is the importance of reciprocal lattice or the Brillouin ...
0
votes
1answer
19 views

If Ionic crystals are heated up, where does the energy go?

Ionic crystal are poor conductors of heat, due to lack of delocalised electrons. So if they are heard up where does the heat go? Does it get dumped in the potential well created by interatomic ...
2
votes
1answer
35 views

Getting the ($hkl$) Miller indices from the angle of incidence of a light ray

I was given an X-ray diffraction lab this week. We measured the count rate for different angles $2\theta$ of the rotation of the detector. From these measurements we plotted a graph of 2theta vs the ...
0
votes
1answer
26 views

Path length requirement for diffraction problem [closed]

The following question has been asked in a problem sheet I have been asked to answer: "The above diagram relates to the path lengths of radiation, with an angle of incidence, θ, reflecting off ...
0
votes
0answers
36 views

In which direction along a GaN (wurtzite) crystal are only Ga atoms being observed?

So, if you have an electron microscope image of a GaN crystal, and that it shows only white dots which represent Ga atoms. No nitrogen atoms are seen in the image. Along which direction is this ...
0
votes
1answer
30 views

Building a Crystal Radio Questions

I have been reading several books and articles about building a crystal radio and the explanations about the inner workings of the circuit seem vague. All articles and books mention the coil and the ...
1
vote
1answer
335 views

If my lattice has an atomic basis, do I also find the reciprocals of the basis vectors to get the reciprocal crystal structure?

That is what my crystal structure looks like. The blue atoms sit on every lattice point (basis vector of $\{0,0\}$) and the red atoms have basis vector of $\left\{{2\over3},{1\over3}\right\}$. The ...
46
votes
1answer
5k views

Is it possible to “see” atoms?

As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals. The image: How can we ...
11
votes
2answers
610 views

Are synthetically-produced diamonds as hard as natural diamonds?

I was having a discussion with my friend about the intrinsic worthlessness of diamonds (DeBeers and whatnot) and how synthetic diamonds haven't caught on, again because of the marketing/propoganda ...
0
votes
0answers
40 views

Reciprocal to determine Miller indices

If we know the reciprocal space basis of a BCC lattice \begin{align}b_1=\frac{2\pi}{a}(\vec{x}+\vec{y}),b_2=\frac{2\pi}{a}(\vec{z}+\vec{y}),b_3=\frac{2\pi}{a}(\vec{x}+\vec{z})\end{align} how do we ...
5
votes
1answer
348 views

Born-Oppenheimer Approximation equivalent to Tensor-product ?

If you have a wave function $\Psi$ of a system consisting of an electron and the vibrational modes of the crystal, THEN we represent the wavefunction $\Psi%$ to be in the Hilbert Space formed by the ...
0
votes
0answers
34 views

crystal momentum conservation

Electrons on 1D chain interacting with each other $$ H = \sum_{k_4,k_3, k_2, k_1} V(k_4-k_1) c_{k_4}^{\dagger}c_{k_3}^{\dagger}c_{k_2}c_{k_1}\delta_{k4+k3=k2+k1;\text{mod}~G}$$ where $G$ is ...
2
votes
1answer
55 views

How is periodic potential approximation justified in semiconductor physics?

In semiconductor physics the usual approximation is that of infinite crystal. This seems to allow one to write Hamiltonian for electron subsystem (in adiabatic approximation) as having periodic ...
1
vote
3answers
62 views

Why are $2\pi$ factors included in the definition of the reciprocal lattice?

I would like to know where the $2\pi$ factors are coming from in the formula for reciprocal vectors in reciprocal lattices. For example, in a simple cubic lattice the primitive vectors are given by ...
2
votes
2answers
127 views

FCC lattice as a stack of triangular lattices

According to Marder, Condensed Matter Physics, Chapter 2: Within the planes normal to the vector [1,1,1], the atoms of an fcc lattice lie in a two dimensional triangular lattice However, he does ...
1
vote
0answers
34 views

Is there an intuitive reason for why the reciprocal lattice of FCC is BCC and vice versa?

This can be proved using formulae for generating reciprocal lattice vectors from direct lattice vectors. But does this result have more to it than meets the eye?
0
votes
1answer
73 views

How to prove Bloch function is periodic in reciprocal lattice?

How to prove Bloch function is periodic in reciprocal lattice? I saw in some textbooks this formula: $$ \Psi_{\mathbf{k}} (\mathbf{r}) = \sum_{\mathbf{G}} ...
7
votes
0answers
236 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 ...
0
votes
0answers
11 views

magnetization of a infinite crystal lattice

Cosider a infinite crystal lattice with right face end at infinity and left face end at origin.my question is, consider this crystal is made of material which can be magnetized and if you magnetize ...
12
votes
2answers
158 views

Why do crystals grow in preferred directions?

I want to know why snowflakes (and other crystals) grow symmetrically and I find the leading answer to the established question to be entirely unsatisfactory. When water freezes, you get ice. ...
2
votes
1answer
40 views

neglect of lattice potential for conduction electrons

Why is it true that in nearly free electron compunds, complete neglect of the lattice potential is usually a good approximation as long as one considers crystal momenta remote from the boundaries of ...
4
votes
1answer
339 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 ...
2
votes
1answer
70 views

planewave Ansatz for modelling phonon dispersion in crystals

From Ashcroft's "Solid State Physics", for one-dimensional monatomic Bravais lattice, the equations of motion of ions are: \begin{equation} M\ddot u(na)=-K[2u(na)-u([n-1]a)-u([n+1]a)] \end{equation} ...
2
votes
1answer
45 views

Zero Diffraction Plates: Why do they give such low diffraction signals?

In our laboratory we use silicon plates named "Zero Diffraction Plates". They are named so because they give extremely low diffraction signals in an XRD instrument (reflection mode). But how are these ...
2
votes
2answers
103 views

What limits the doping concentration in a semiconductor?

Si and Ge can be blended in any ratio, $\mathrm{Si}_x\mathrm{Ge}_{1-x},\ 0\le x\le 1$. So do InxGa1-x. So what exactly causes doping impurities inside Si/Ge/etc. to saturate at $\sim 10^{-19}\ ...
9
votes
4answers
17k views

Why does ice have a lower density than water?

Can someone explain me why is ice lighter than water? As I know, all solids are usually heavier than the liquids (correct me if I am wrong).
1
vote
1answer
25 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 ...
2
votes
2answers
497 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
0
votes
1answer
48 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 ...