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1answer
127 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 ...
0
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1answer
22 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 ...
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2answers
138 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
70 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 ...
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2answers
74 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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1answer
196 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.
3
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1answer
98 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, ...) ...
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0answers
29 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 ...
2
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1answer
76 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
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1answer
107 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
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1answer
165 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 ...
0
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1answer
21 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
319 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 ...
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1answer
4k 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 ...
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2answers
566 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
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0answers
34 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 ...
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1answer
343 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 ...
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0answers
33 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
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1answer
49 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 ...
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3answers
57 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
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2answers
120 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 ...
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0answers
30 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
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1answer
56 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}} ...
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0answers
232 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 ...
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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
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2answers
148 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
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1answer
39 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
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1answer
334 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
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1answer
59 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
36 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
78 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
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4answers
15k 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
24 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
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2answers
445 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
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1answer
45 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 ...
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0answers
10 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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1answer
35 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 ...
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1answer
74 views

Why are (most) solids periodic?

Is there a rigorous proof that periodic arrangements minimize the energy of a group of particles?
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0answers
24 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 ...
1
vote
1answer
41 views

Crystal structure of Silicon

From what I was reading, Silicon has a FCC unit cell but they also said that the Silicon atoms form a tetrahedron at 109 degrees from each other. Then they said that the tetrahedron is formed by ...
0
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0answers
15 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 ...
1
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1answer
40 views

Can I tear apart a pipe with magnetostriction? And how big field should I use?

As I know, with magnetostriction we can "stretch" its unit cell. The stronger is the field, the more it expands the cell. Using alternating current in coils that induce magnetic field we can stretch ...
0
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0answers
27 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
votes
1answer
59 views

How corner atom of a cube is shared by 8 atoms? [closed]

Since each atom is at the corner of a cube and 8 cubes meet at each corner. Therefore each atom is shared by 8 cubes. But I don't visualize it, so please tell how I Visualize it.
0
votes
1answer
46 views

Crystal lattices in solid state

I found this problem in Christman's book fundamental of solid state physics What is the Miller index for a plane parallel to both $3\vec{a}+\vec{c}$ and $\vec{b}$, in any lattice?
2
votes
1answer
90 views

Help needed to understand the dispersion curve of a 1D lattice with diatomic basis

I am trying to understand the dispersion curve (as shown below) of a 1D lattice with diatomic basis. Here are my questions: Can both optical and acoustic branch of phonon simultaneously exist in ...
2
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2answers
856 views

How many atoms exist within a continuum body?

Materials, such as solids, liquids and gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have cracks and discontinuities. However, certain physical ...
2
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1answer
161 views

Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ ...
0
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1answer
86 views

Calculating number of atoms per cell in a crystal. Nonsense question in class

I don't agree at all with this question, and I think my teacher does not understand his topic. I hope you can prove me wrong. The question was this one: Potassium crystallises in a Body Centered ...
3
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1answer
114 views

Can you explain why crystals form without thermodynamics?

I know that the basic reason that solid crystals form is because it's the lowest energy configuration (i.e. this). I am looking for an intuitive explanation for this process, one that does not involve ...