An ionic conductor is studied by measuring its ionic conductivity as a function of…

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 Point defects, dislocations and alloys

Problem

An ionic conductor is studied by measuring its ionic conductivity

\sigma

as a function of temperature. The product

\sigma T

(which removes the mobility prefactor's explicit

1/T

) is measured at four temperatures, two in the intrinsic (high-temperature) regime, where the vacancy concentration is set by thermal Schottky disorder, and two in the extrinsic (low-temperature) regime, where a fixed concentration of aliovalent impurities pins the vacancy concentration. Data in the intrinsic regime:

\sigma T=1.63\times10^{5}\,\mathrm{S\,m^{-1}\,K}

T=800\,\mathrm{K}

and

5.93\times10^{3}\,\mathrm{S\,m^{-1}\,K}

T=700\,\mathrm{K}

. Data in the extrinsic regime:

\sigma T=20.1\,\mathrm{S\,m^{-1}\,K}

T=400\,\mathrm{K}

and

1.36\,\mathrm{S\,m^{-1}\,K}

T=350\,\mathrm{K}

. ((a)) Using the two intrinsic points, find the slope of

\ln(\sigma T)

against

1/T

and hence the activation energy governing this regime. ((b)) Using the two extrinsic points, find the activation energy governing that regime. ((c)) Identify these two activation energies with

E_S/2+E_m

and

E_m

, and hence find the Schottky formation energy

E_S

and the vacancy migration energy

E_m

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