The first peak of the measured Ge-O partial radial distribution function of vitreous…

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

The first peak of the measured Ge-O partial radial distribution function of vitreous

\mathrm{GeO_2}

(neutron diffraction, room temperature) is centred at

r=1.73\,\mathrm{\AA}

. Integrating

4\pi r^2 n_O\,g_{\rm GeO}(r)

over this peak gives a coordination number of

4.05

, with a

\pm4\%

statistical uncertainty in the peak area from counting statistics. Crystalline

\mathrm{GeO_2}

(the quartz-like polymorph) has each Ge atom coordinated by 4 oxygen atoms. ((a)) State the nearest-neighbour Ge-O distance read from this

g(r)

. ((b)) Quote the coordination number with its uncertainty, rounded to a sensible number of figures. ((c)) Say whether the glass result is consistent with the tetrahedral, network-forming coordination expected from Zachariasen's rules.

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