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1answer
400 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.
0
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1answer
155 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
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 ...
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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 ...
1
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1answer
44 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 ...
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1answer
14 views

Can a piezoelectric material only vibrate at one frequency?

Given a material X with piezoelectric properties which is used in a ultrasonic transducer, what determines the working frequency of said transducer? If hypothetically such a transducer is specified ...
4
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1answer
189 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, ...) ...
1
vote
1answer
157 views

Point group symmetries and unit cell

I was wondering if the unit cell (of a given lattice) had to have every point group symmetries of the lattice it defines ? I guess there is no unique way to define a unit cell and that it may not have ...
0
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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: ...
5
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1answer
201 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 ...
2
votes
1answer
286 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? ...
1
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1answer
154 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
0
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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 ...
2
votes
2answers
131 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 ...
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 ...
0
votes
1answer
153 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 ...
2
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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 ...
1
vote
1answer
24 views

3D Bravais Lattices in terms of $\mathbb{Z}^3$

I am looking at the definitions of Bravais Lattice on Wikipedia and I find that I can describe many of them in terms of a mathematical lattice $\mathbb{Z}^3$. cubic $\mathbb{Z}^3$ body-centered ...
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2answers
303 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 ...
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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
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1answer
21 views

Are There Any Theories To Explain Why Ice Freezes in Orthogonal Patterns on Surfaces Such as Glass

If one examines the following image: One will notice that the ice is freezing in this characteristic criss-cross pattern. Are there any theories to explain this behavior? I've seen this on car ...
0
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1answer
32 views

How do atoms scatter X-rays?

I am learning the theory behind X-ray diffraction but I have a question. According to the textbook I am using, X-ray tubes (in diffractometers) produce near monochromatic X-rays. In other words, they ...
0
votes
1answer
25 views

How can we prove that each point (hkl) in the reciprocal lattice corresponds to a set of lattice planes (hkl) in the real space lattice?

In crystallography, we always speak about the direct and reciprocal lattice spaces. One property about these spaces in mentioned here, as follows: Each point (hkl) in the reciprocal lattice ...
0
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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 ...
2
votes
1answer
52 views

Space group setting of a crystal structure

I was reading a PDF of a crystal phase in order to draw its structure, when I noticed that it was, apparently, ambiguously described. The PDF lists two descriptions of the monoclinic structure: 1) ...
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 ...
3
votes
3answers
332 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}\ ...
2
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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 ...
1
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0answers
28 views

Twin and Detwin Crystals [closed]

Hello i would like to ask , what are twin and detwin monocrystals? what has to do with their crystalographic symmetry? any consequences ? any image also would be really helpfull! Thank you
2
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2answers
307 views

Software to calculate and visualize reciprocal lattice

I am currently preparing XRD experiments for an epitaxial thin film on a silicon wafer. I am looking for software (Win oder Mac) to calculate the reciprocal lattice from the cell parameters and ...
1
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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 ...
6
votes
1answer
82 views

Reduce integration over crystal to integration over unit cell

I am wondering when I can reduce integrals over a periodic crystal to a an integral over the unit cell. Especially I consider the following two-electron integral $$ I=\langle \varphi_i \varphi_j | V | ...
0
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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
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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 ...
1
vote
2answers
299 views

Volume of Brillouin zone is the same as Fourier primitive cell?

In Kittel's solid state text, problem 2.3, he says that the volume of the Brillouin zone is the same as a primitive parallelepiped in Fourier space. Somehow I can't see why this is true. Can someone ...
0
votes
1answer
298 views

Why are HCP materials brittle whie FCC materials are ductile?

Why are hexagonal close packed materials brittle, While face centered cubic is ductile. Is it related to crystal planes?
0
votes
1answer
46 views

crystal structure of metals

I am studying solid state physics and I'm a complete newbie in that sense. I know that semiconductors and group IV elements bond themselves in the FCC structure with covalent bonds which satiate the ...
5
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2answers
1k views

Why do some things crystallize? (And others don't, for that matter.)

Ice, for example, will form a crystal when frozen under certain circumstances. Why is this the case for ice? While on the subject of water crystallization, why do snowflakes usually form in base 6 ...
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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
2answers
169 views

Non-uniqueness of the k-vector in Bloch state

How to understand that Bloch wave solutions can be completely characterized by their behaviour in a single Brillouin zone? Given Bloch wave: \begin{equation*} \psi_{\mathbf{k}}(\mathbf{r}) = ...
0
votes
1answer
45 views

Might a diamond with impurities (doped) be less brittle than a pure diamond?

Diamonds are extremely hard (resistant to pressure) but quite brittle (susceptible to shock). Sufficient impurity will compromise hardness, but I am finding it difficult to find out the effect on ...
0
votes
1answer
36 views

Could a flat battery make a watch run fast?

My watch used to keep good time but as of about a month ago it runs fast (gains about 5 mins per day). Could a flat battery be responsible, or is this physically impossible? It's a quartz crystal ...
0
votes
3answers
154 views

Primitive unit cell of fcc

When I consider the primitive unit cell of a fcc lattice (red in the image below) the lattice points are only partially part of the primitive unit cell. All in all the primitive unit cell contains ...
1
vote
3answers
137 views

Any scientific basis behind “crystal energy”? [closed]

I always hear people talking very loosely about the terms "vibration" and "energy" in relation to crystals. Is there any scientific basis in "crystal energy" or is it purely metaphysical ...
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4answers
36k views

Why does ice have a lower density than water?

Can someone explain me why is ice less dense than water? As I know, all solids are usually denser than the liquids (correct me if I am wrong).
1
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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 ...
3
votes
3answers
510 views

Jet turbine blades from single crystals, how are they formed?

I know about nothing about crystals, although I do know a bit more about jet turbine engines, and I definitely know that you don't want the fan blade hitting the fan housing. The reason given in the ...
4
votes
1answer
329 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 ...
0
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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?
1
vote
1answer
33 views

How do phonons affect the work function?

How do phonons affect the work function? Could phonons that are directed towards a single atom, such as in a body-centered cubic crystal, increase the amount of thermal excitation and thus decrease ...