A hydrogen-bonded crystal

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Dielectric and optical properties of solids · Dielectric and optical properties of solids

Solid State Physics, Ch Dielectric response, local fields and ferroelectricity

Problem

A hydrogen-bonded crystal, structurally similar to KH2PO4\mathrm{KH_2PO_4}, undergoes a ferroelectric transition at Tc=110 KT_c=110\,\mathrm{K}. Dielectric loss measurements at T=118 KT=118\,\mathrm{K} (above TcT_c) show a single peak in ε2(ω)\varepsilon_2(\omega) centred on a frequency fp=2.1 GHzf_p=2.1\,\mathrm{GHz}, and no separate resonance is seen anywhere between this peak and the highest phonon frequencies of the lattice. ((a)) Identify the functional form this loss peak obeys and extract the associated relaxation time τD\tau_D. ((b)) State which mechanism, displacive or order-disorder, this spectrum points to, whether it settles the question on its own, and what further measurement would.

Browse the problem library