The tag has no usage guidance.

learn more… | top users | synonyms

8
votes
1answer
280 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 ...
7
votes
0answers
481 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
votes
0answers
35 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 ...
3
votes
0answers
64 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 ...
3
votes
0answers
142 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
votes
0answers
187 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 ...
2
votes
0answers
28 views

Crystals in piezoelectricity

I was reading about piezoelectricity and crystals and found such a statement (on Wikipedia) : For example, a 1 cm3 cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage ...
2
votes
0answers
40 views

Proof that magnetic Bloch waves are almost periodic in the reciprocal index

I would like to prove that the magnetic Bloch waves change by a phase factor if you shift their crystal momentum by a reciprocal lattice vector. That is, if $u_{n,\mathbf{k}}(\mathbf{r})$ is a Bloch ...
2
votes
0answers
16 views

What is crystal “supermodulation”?

I am researching the pair density wave in cuprates, and during my reading I came across a term "crystal supermodulation". I believe it relates to BSCCO. Can anyone give me a definition or give me a ...
2
votes
0answers
42 views

Estimate Uncertainties in Rietveld Refinement

I have the output of an x-ray diffraction experiment made on a thin film. Here I report the output of the experiment (I analyzed those data using powdercell and coloured regions have been excluded ...
2
votes
0answers
190 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 ...
2
votes
0answers
137 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
votes
0answers
111 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
235 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
vote
0answers
27 views

Process of x-ray crystallography

This is a pretty basic question but I would just like some confirmation of what I suspect is true. As I understand it, the basic idea behind x-ray crystallography is that we take our crystal and hit ...
1
vote
0answers
42 views

Coulomb potential of a periodic crystal in reciprocal space

Usually the Coulomb potential (electron-electron interaction) can be Fourier transformed (aside from prefactors) like that: $$ \frac{1}{|\vec r_1 -\vec r_2|} = \int \frac{\text d ^3 k}{(2\pi)^3} ...
1
vote
0answers
65 views

Activation energy of luminescence

Assuming that activation energy is constant for some range of temperature, it can be determined from the slope of the plot: $$\ln{I}=A-\frac {E_a}{k_bT}$$ where $I$ - intensity , $E_a$ - activation ...
1
vote
0answers
61 views

Four dimensional Bravais lattice

I am wondering if there are any reference on four dimensional Bravais lattice and their primitive vectors, even an example will help.
1
vote
0answers
37 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 ...
1
vote
0answers
62 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?
1
vote
0answers
62 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
vote
0answers
294 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 ...
1
vote
0answers
233 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
vote
0answers
113 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
139 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
vote
0answers
416 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
vote
0answers
47 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
376 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
votes
0answers
15 views

How to determine the basis of any crystal

In the following example, I have a rutile TiO2. Here the basis of O with respect to Ti is (0.3*x, 0.3*y, 0*z), where a,b,c are the lattice vectors. So in order to build a crystal, I need the basis and ...
0
votes
0answers
10 views

What is temperature dependence (Schottky defects)?

The problem requires us to use the following property to determine the temperature dependence: For a system in thermal equilibrium in a heat bath at temperature $T$ the Helmholtz free energy is a ...
0
votes
0answers
37 views

Calculating potential energy per ion of an one dimensional ionic crystal

The problem states to calculate "the potential energy, per ion, for an infinite 1D ionic crystal with separation $a$"; the crystal is a 1D lattice of alternating charges, likes so: ...
0
votes
0answers
5 views

Whether raman spectroscopy is dependent on crystallographic orientation

If I have three bars of Si, and each has the (100) (110) and (111) surface pointing up at the laser respectively, will I get a different raman spectra for each of them? In my opinion, I shouldn't ...
0
votes
0answers
6 views

Electrode configuration when radially poling piezoelectric material?

All the information on the web I have come across WRT poling piezoelectric material usually assumes a uniform field (such as between two plates). I would like to pole a cylinder so that the reverse ...
0
votes
0answers
17 views

How to understand the simplified tight-binding representation on square lattice?

I have read a paper in this website:http://cmt.nbi.ku.dk/student_projects/bsc/Haider_Moradi_BSc_thesis.pdf I am curious about how to understand the simplified tight-binding representation on square ...
0
votes
0answers
27 views

Solving Bloch Waves for Potentials with Few Fourier Components

Suppose we have a potential in 1D $$U(x) = 2A\cos(\frac{2\pi}{a} x)$$ Let $G_\alpha$ be reciprocal lattice coordinates $$G_\alpha = \frac{2\pi \alpha}{a},\;\;\;\;\alpha\in \mathbb{Z}$$ As in Ashcroft ...
0
votes
0answers
17 views

What are gyrotropic crystals?

I am reading a paper about spin photocurrents that talks about gyrotropic crystals, but I do not find any good explanation what gyrotropy is or how to find out whether a crystal belongs to the ...
0
votes
0answers
20 views

How would the fermi energy of an element inside of crystal affect its fermi level?

If I had a substitutional crystal of nickel atoms inside of a copper fcc lattice, how would this affect the Fermi level of the material?
0
votes
0answers
38 views

Double groups in Crystallography

I'm currently studying double point groups and their applications in condensed matter physics. Let me start by giving you the definition of the double group that is used in my textbook: Let $G$ be a ...
0
votes
0answers
51 views

Energy Oscillations in a One Dimensional Crystal?

Can anyone help me find articles on similar topics "Energy Oscillations in a One Dimensional Crystal" (I have links to one article on this subject)? article, that I have Especially interested in ...
0
votes
0answers
30 views

Reciprocal Plane diagram of body-centered cell?

I was reading that the reciprocal lattice of a body-centered cell (BCC) is simply the face-centered cell(FCC), right? Would each of the reciprocal lattice vectors be the FCC lattice vectors, but with ...
0
votes
0answers
30 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
112 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 ...
0
votes
0answers
373 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, ...
0
votes
0answers
24 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
0answers
80 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
0answers
66 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 ...
0
votes
0answers
47 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 ...
0
votes
0answers
28 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
votes
0answers
84 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 ...
0
votes
0answers
38 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 ...