A metallic glass is modelled

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

A metallic glass is modelled, for the purposes of this calculation, by putting all N=12N=12 nearest neighbours of a given atom on a single thin spherical shell at r0=2.85 A˚r_0=2.85\,\mathrm{\AA}, so that g(r)−1=N4πnar02 δ(r−r0),g(r)-1=\frac{N}{4\pi n_a r_0^2}\,\delta(r-r_0), where nan_a is the mean atomic number density. ((a)) Substitute this model into S(Q)=1+4πna∫0∞r2[g(r)−1]sin⁡QrQr drS(Q)=1+4\pi n_a\displaystyle\int_0^\infty r^2[g(r)-1]\dfrac{\sin Qr}{Qr}\,dr and show that it collapses to S(Q)=1+Nsin⁡Qr0Qr0S(Q)=1+N\dfrac{\sin Qr_0}{Qr_0}. ((b)) Evaluate S(Q)S(Q) at Q=2.20 A˚−1Q=2.20\,\mathrm{\AA^{-1}}. ((c)) A real measured g(r)g(r) has this peak broadened rather than being a delta function. State which two features of the measured peak give NN and r0r_0, and what limits the precision of each.

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