Paul Joseph Steinhardt is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences.
Paul Steinhardt
Steinhardt at University of Pennsylvania
The electron diffraction pattern for icosahedrite, the first natural quasicrystal, obtained by aiming the electron beam down a fivefold axis of symmetry. The patterns correspond perfectly (up to experimental resolution) with the fivefold patterns first predicted by Paul Steinhardt and Dov Levine in the 1980s for an icosahedral quasicrystal.
Girih tile quasicrystal pattern on right half of spandrel at Darb-e Imam Shrine
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
Potential energy surface for silver depositing on an aluminium–palladium–manganese (Al–Pd–Mn) quasicrystal surface. Similar to Fig. 6 in Ref.
Girih-tile subdivision found in the decagonal girih pattern on a spandrel from the Darb-i Imam shrine, Isfahan, Iran (1453 C.E.). A subdivision rule to construct perfect quasi-crystalline tilings has been identified
Atomic image of a micron-sized grain of the natural Al71Ni24Fe5 quasicrystal (shown in the inset) from a Khatyrka meteorite fragment. The corresponding diffraction patterns reveal a ten-fold symmetry.
Electron diffraction pattern of an icosahedral Ho–Mg–Zn quasicrystal