Along a five-fold axis of icosahedral

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Solids without a lattice: glasses and quasicrystals

Problem

Along a five-fold axis of icosahedral Al70Pd21Mn9\mathrm{Al_{70}Pd_{21}Mn_9}, electron-diffraction spots lie at scattering vectors given by the six-dimensional generalisation of the Fibonacci indexing, Q=Q0(n1+n2φ)Q=Q_0(n_1+n_2\varphi), with the remaining four of the six integer indices equal to zero for reflections along this row (n3=n4=n5=n6=0n_3=n_4=n_5=n_6=0), where φ=(1+5)/2=1.618\varphi=(1+\sqrt5)/2=1.618. Measurements along this row give Q0=0.550 A˚−1Q_0=0.550\,\mathrm{\AA^{-1}} and a spot at Q=1.440 A˚−1Q=1.440\,\mathrm{\AA^{-1}}. ((a)) Find the two non-zero integers (n1,n2)(n_1,n_2), each between −3-3 and 33, that index this spot. ((b)) Write the full six-index label of the reflection.

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