Study on thermodynamic properties of Fe³⁺-substituted yttrium iron garnets

This paper presents the molar heat capacity at constant volume C_{V} and characteristic Debye temperature θ, determination for the garnet system, Y_{3-x}Fe_{5+x}O_{12}, x=0.0, 0.1, 0.3, and 0.5 at 300 K. The θ values determined from Waldron's approach and those calculated using ultrasonic mean sound velocity, V_{mo}, are in agreement. C_{V} values calculated from the Einstein theory are consistent with the reported one and theoretically expected values using the Dulong-Petit law, but Waldron's approach based on the Debye theory and the Debye T³ law fail to estimate consistent C_{V} values. The result has been discussed in the light of key physical differences between the two theories. The applicability of the Kieffer model for molar heat capacity at constant pressure, C_{p}, determination has been tested. Finally, an attempt has been made to estimate electronic contribution and the temperature at which the lattice contribution and electronic contribution to the molar heat capacity become comparable.