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Molecules and Crystals

Problem 6.187

Evaluate the propagation velocity of acoustic vibrations in aluminium whose Debye temperature is \(\Theta=396 \mathrm{~K}\).

Reveal Answer
 6.187. v≈kΘ/ℏ6π2n03=3.4 km/s, where n0 is the concent-  ration of the atoms. The tabulated values are: v∥=6.3 km/sv⊥=3.1 km/s\begin{aligned} &\text { 6.187. } v \approx k \Theta / \hbar \sqrt[3]{6 \pi^{2} n_{0}}=3.4 \mathrm{~km} / \mathrm{s}, \text { where } n_{0} \text { is the concent- }\\ &\text { ration of the atoms. The tabulated values are: } v_{\|}=6.3 \mathrm{~km} / \mathrm{s}\\ &v_{\perp}=3.1 \mathrm{~km} / \mathrm{s} \end{aligned}
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