Questions tagged [quasicrystals]

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3
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0answers
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Are quasicrystals always self-similar?

The diffraction patterns of quasicrystals very often display self-similarity ie. similarity under length scaling, thus relating them to fractals. My question is: Do they always display self-...
5
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1answer
138 views

Quasiperiodicity of the Fibonacci chain

I am interested in finding an intuitive way to show that the Fibonacci chain is quasiperiodic (and not simply random). Or put differently, how can I tell from just looking at a given chain whether or ...
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0answers
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Is there a quasicrystal whose properties don't change with any amount of rotation about a specific axis?

Suppose you have a quasicrystal where each layer has the wall paper group of a square tiling and is the same as the layer below it except that layer is rotated counterclockwise from the previous layer ...
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0answers
163 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 ...
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2answers
844 views

Quasicrystals - Projections from higher dimensional regular crystal lattices

Why are quasicrystals projections from higher dimensional regular crystal lattices? See for example wikipedia: »Mathematically, quasicrystals have been shown to be derivable from a general ...
3
votes
1answer
67 views

Why do we still get sharp scattering spots with quasi-crystal?

In a quasi-crystal, there is no translational invariance. This means there is no delta-function in the Fourier transform. But to get a sharp scattering spot, we need a delta function. Physically, ...
23
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1answer
1k views

Why do quasicrystals have well-defined Fourier transforms?

I was recently reading about quasicrystals, and I was really surprised to learn that even though they do not have a periodic structure, and only have long range order in a very different sense to the ...
19
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2answers
2k views

Literature on fractal properties of quasicrystals

At the seminar where the talk was about quasicrystals, I mentioned that some results on their properties remind the fractals. The person who gave the talk was not too fluent in a rigor mathematics ...
16
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3answers
2k views

Phonons in non-crystalline media

Do sound waves in a gas consist of phonons? What about a glass? Or other non-crystalline materials such as quasicrystals? How does the lack of translational symmetry affect the quantization of the ...