A hypothetical arsenic chalcogenide glass

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Lattice dynamics and thermal properties of solids

Solid State Physics, Ch Solids without a lattice: glasses and quasicrystals

Problem

A hypothetical arsenic chalcogenide glass, of mass density ρm=3.2 g cm−3\rho_m = 3.2\,\mathrm{g\,cm^{-3}}, has a low-temperature heat capacity written as C(T)/T=c1+c3T2C(T)/T = c_1 + c_3 T^2, the standard form for a glass below 1 K1\,\mathrm{K} (a linear term from two-level systems plus the Debye T3T^3 term). Two measurements give C/T=1.20 μJ g−1 K−2 at T=0.20 K,C/T=1.35 μJ g−1 K−2 at T=0.50 K.\begin{aligned} C/T &= 1.20\,\mu\mathrm{J\,g^{-1}\,K^{-2}} \text{ at } T=0.20\,\mathrm{K}, \\ C/T &= 1.35\,\mu\mathrm{J\,g^{-1}\,K^{-2}} \text{ at } T=0.50\,\mathrm{K}. \end{aligned} ((a)) Find c1c_1 and c3c_3 from these two points. ((b)) Convert c1c_1 to a heat capacity coefficient per unit volume, and use CTLS=π26kB2PˉTC_{\rm TLS} = \dfrac{\pi^2}{6}k_B^2\bar P T to extract the flat density of two-level splittings Pˉ\bar P (per unit energy per unit volume).

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