Past exam of the condensed matter physics course of the University of Oxford / 2012 / 1 / d

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- Solution d

Solution

The high-pressure lattice constant follows from its first

(100)

reflection:

a_{P} = \frac{0.154 nm}{2 s i n 14.8 5 ^{\circ}} = 0.30044 nm .

Conserve the number of NaCl formula units. The low-pressure conventional unit cell contains four, whereas the high-pressure cell contains one. The volume per formula unit changes from

a_{0}^{3} /4

to

a_{P}^{3}

, so

\frac{V _{P}}{V _{0}} = 4 (\frac{a _{P}}{a _{0}})^{3} ≃ 0.605.

The sample contracts by about

39.5%

. Comparing

a_{P}^{3}

directly with

a_{0}^{3}

would compare different amounts of material.

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