PHY3202 Solid State Physics Problemsheet 2 - PHYSICS DEPARTMENT PHY32M2 SOLID STATE PHYSICS Tutorial sheet 2 Mechanical and thermal properties 25th

PHY3202 Solid State Physics Problemsheet 2 - PHYSICS...

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PHYSICS DEPARTMENT PHY32M2 SOLID STATE PHYSICS Tutorial sheet 2: Mechanical and thermal properties 25 th October 2018 e = 1.602 × 10 - 19 C h = 1.055 × 10 - 34 J s m = 9.110 × 10 - 31 kg μ 0 = 4 π × 10 - 7 H m - 1 μ B = 9.274 × 10 - 24 A m 2 k B = 1.381 × 10 - 23 J K - 1 ε 0 = 8.854 × 10 - 12 F m - 1 N A = 6.022 × 10 23 mol - 1 1. Calculate the Debye temperature Dθand angular frequency Dωand maximum density of phonon states for a solid with atomic number density n= 330 nm-3and sound velocity 0v1.96 km s-1. 2. Copper has an fccstructure with lattice constant a= 0.361 nm and an elastic wave speed of 3.38 km s-1. Find its (i) atomic number density atn, (ii) Debye temperature = 3. Chromium Cr has a bccstructure with lattice constant a= 0.288 nm. Its Debye temperature Dθis 630 K. Determine its atomic number density and estimate its eleastic wave speed. 4. Derive an expression for the temperature at which the zero point energy is equal to the thermal lattice energy of a Debye solid in which the speed of sound is 0v. Calculate this for (i) copper Cu and (ii) sodium Na.

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