Molar Heat Capacity of Potassium Alum KAl(SO₄)₂ ·12H₂O at Low Temperatures: Revisited with Determination of the Debye Temperature

Two earlier published experimental data [C. H. Shomate, J. Am. Chem. Soc. 67, 765 (1945); D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] of the molar heat capacity C_p of potassium alum, KAl(SO₄)₂·12H₂O, are revisited. From analysis of the temperature dependence of C_p [D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] below 20 K by using the experimental values of C_p represented as a plot of C_p/T = γ+AT², the Sommerfeld parameter γ (electronic heat capacity coefficient) and the slope A (lattice heat capacity coefficient) are estimated as γ = 0 JK ⁻²mol ⁻¹ and A = 3.35×10 ⁻³ JK ⁻⁴mol ⁻¹, respectively. This indicates that only acoustic phonons contribute to the heat capacity below 4 K. The Debye T³-law is found to hold good to 4 K, i.e., to T < θ_D/20, where θ_D is the calorimetric Debye temperature calculated as θ_D = 83.4 K, indicative of the strength of the chemical bonding in the system.