# One-dimensional model of the quasicrystalline alloy

@article{Burkov1987OnedimensionalMO, title={One-dimensional model of the quasicrystalline alloy}, author={Sergei Burkov}, journal={Journal of Statistical Physics}, year={1987}, volume={47}, pages={409-438} }

A one-dimensional chain of atoms of two types is investigated. It is proven exactly for the model of attracting hard spheres that if the ratio of the numbers of atoms of the two types is irrational, then the state of absolutely minimal energy is quasicrystalline. The quasicrystalline state is also investigated in the case of the Lennard-Jones interatomic potential. All the microscopic values (interatomic spacing, electronic density, etc.) are shown to be quasiperiodic functions varying on…

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## References

SHOWING 1-10 OF 17 REFERENCES

### Quasicrystals: a new class of ordered structures

- Physics
- 1984

A quasicrystal is the natural extension of the notion of a crystal to structures with quasiperiodic, rather than periodic, translational order. We classify two- and three-dimensional quasicrystals by…

### Fractal structure of the equilibrium crystal shape

- Physics
- 1985

The equilibrium crystal shape of the classical crystal at zero temperature is found in the framework of the model suppressing the atomic distorsions. In this model the interaction between two atoms…

### Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

- Materials Science
- 1984

We have observed a metallic solid (Al-14-at.%-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations. Its diffraction…

### Devil's staircase and order without periodicity in classical condensed matter

- Materials Science
- 1982

The existence of incommensurate structures proves that crystal ordering is not always the most stable one for nonquantum matter. Some properties of structures which are obtained by minimizing a free…

### On the properties of monolayers of adsorbed atoms

- Physics
- 1978

The structure of monolayers adsorbed on solids is investigated and the consequences of particular force laws explored. The dipole-dipole interaction is assumed to predominate and a model is developed…

### Exact models with a complete Devil's staircase

- Physics
- 1983

The author describes two exact models which exhibit a complete Devil's staircase which can both be calculated explicitly with the same method. The first one is a discrete Frenkel-Kontorova model (an…

### Modulated structure of the NC-type (N = 5.5) pyrrhotite, Fe1−xS

- Materials Science
- 1982

The modulated structure of the NC-type pyrrhotite Fe1 - xS with x = 0.09 has been determined. The analysis is based on a four-dimensional space group, Wpna21qq1, and an anharmonic modulation model…