The real part of the permittivity of a polar crystalline solid ('compound Z') has…

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

The real part of the permittivity of a polar crystalline solid ('compound Z') has been measured at four widely separated frequencies:

\varepsilon_1=60

f=1\,\mathrm{kHz}

;

\varepsilon_1=20

f=100\,\mathrm{GHz}

, with the dielectric loss (

\varepsilon_2

) maximum located at

f=3\,\mathrm{GHz}

;

\varepsilon_1=4

f=100\,\mathrm{THz}

(infrared); and

\varepsilon_1=4

f=500\,\mathrm{THz}

(visible). ((a)) Identify the polarisation mechanism responsible for each of the two successive drops in

\varepsilon_1

, in order of increasing frequency, and for the value that remains on the highest-frequency plateau. ((b)) Using the loss-peak frequency, find the relaxation time

\tau_D

of the mechanism responsible for the first drop. ((c)) Read off

\varepsilon_\infty

from the highest-frequency plateau and state the refractive index it implies. ((d)) On cooling towards a temperature

T_0

, the zone-centre transverse optical phonon responsible for the drop between

100\,\mathrm{GHz}

and

100\,\mathrm{THz}

is followed by neutron scattering:

\omega_{TO}^2

falls linearly to zero as

T\to T_0

, and the mode remains an underdamped, propagating peak at every temperature studied down to

T_0

. Say whether the transition at

T_0

is displacive or order-disorder, and justify the answer from the described spectrum.

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