The measured resistivity of three copper samples of different purity is given at and at

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Electronic transport in solids

Condensed Matter Physics, Ch Real crystals: vacancies, dislocations and the strength of metals

Problem

The measured resistivity of three copper samples of different purity is given at

300\,\mathrm{K}

and at

20\,\mathrm{K}

, a temperature low enough that the vibrational part has essentially died away. Data in units of

10^{-8}\,\Omega\,\mathrm{m}

: sample A has

\rho_e(300\,\mathrm{K})=1.72

and

\rho_e(20\,\mathrm{K})=0.02

; sample B has

1.90

and

0.20

; sample C has

3.10

and

1.40

. ((a)) Using Matthiessen's rule, find the vibrational part

\rho_{e,{\rm vib}}(300\,\mathrm{K})=\rho_e(300\,\mathrm{K})-\rho_{e,0}

for each sample, taking

\rho_{e,0}\approx\rho_e(20\,\mathrm{K})

, and say what the three values have in common. ((b)) Rank the three samples by purity, using the residual resistance ratio

\rho_e(300\,\mathrm{K})/\rho_{e,0}

. ((c)) Taking Chapter 8's pure-copper mean free path of

38\,\mathrm{nm}

300\,\mathrm{K}

as a baseline, estimate the low-temperature mean free path of the purest sample.

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