# Tagged Questions

Crystals are solid material whose constituents, such as atoms, molecules or ions, are *arranged in a highly ordered microscopic pattern*, a crystal lattice that extends with regularity in all directions. Use for all crystallography and ordered structure topics.

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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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) ...
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### 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 ...
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### 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
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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}) = u_{\...
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### 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 ...
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### 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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### How does crystal lattice explain electrical conductance?

From http://education.jlab.org In a metal, the atoms are arranged in a crystal-like configuration. ... Now, in a metal, the valence band is relatively close to the conduction band - ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### Notation in crystallography

I'm trying to comprehend the proof that for a crystal with translational symmetry only 1,2,3,4 or 6 rotational axes exist. The proof I'm trying to follow however uses a weird notation I haven't seen ...
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### How can crystal symmetry operations be used to reduce the number of unique properties of a solid?

Can anyone please give an example or a reference which shows how crystal point groups and symmetry operations can be used to reduce the number of parameters describing the property of a crystal, ...
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### Dispersion in crystall for a random direction

Lets say one get a dispersion of electrons or phonons from this website: http://www.matprop.ru Usually dispersion in particular directions is drawn: as for wurtzite crystall it is A to L, L to U and ...
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### How to experimentally identify the exposed face of a crystal?

After depositing a material (e.g, TiO2) on a substrate, what methods can I use to check whether the material is crystalline, and what face (e.g, 001, 101, etc..) of the crystal is exposed?
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### Deformation in the nematic phase of a liquid crystal survived in solid state

Does anyone know if I cool a liquid crystal with a deformed nematic phase quickly it will preserve the deformation in the crystal lattice? I didn't never see that in classical books on liquid crystals....
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### 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.
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### 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 ...