Quasicrystals, explain those terms please!

Jamalll

I have been reading this article and google-ing and still nothing, so here it goes

What is:

-P-type icosahedral?

-Tsai-type quasicrystal?

-1/1 cubic approximant?

-six-dimensional lattice parameter a_6D?

-why has (this is example) powder X-ray diffraction spectrum just 2 high peaks (at some angles), and why are they called 111112 and 011202 (underlined line should be above letters) and what does it mean?

Many thanks..

M Quack

Icosahedral means that the quasicrystal has the symmetry of an icosahedron, i.e. of a soccer ball.

P-type probably means primitive (as opposed to I=body centered and F=face centered, not sufe if F-type QC exist)

Tsai discovered a different type of QC that has 10-fold symmetry in one plane and periodic in the direction perpendicular to the plane (IIRC). These are called decagonal QC.

Approximants are periodic crystals with similar local structure to a quasicrystal.

The Bragg reflections of QC can be indexed in 6-dimensional reciprocal space. Hence you get 6 Miller indices rather than the usual 3 (HKL).