New Developments in Relaxation Micro-Calorimetry and Cp Measurements: A Thermodynamic Study of Andradite-Grossular Garnet Solid Solutions

Abstract:

Heat capacity, C_p, is a fundamental thermodynamic property. There have been recent technical developments in the area of relaxation calorimetry. The Physical Properties Measuring System from Quantum Design is a new relaxation calorimetric technique that allows for C_p measurements on samples weighing just milligrams. This enables a number of phases, for example those synthesized at high pressures or occurring in nature in small amounts, to be studied for the first time.

Much of our research is concentrating on the thermodynamic mixing properties (C_p and Entropy) of binary garnet solid solutions synthesized at high pressures. The vibrational part of the third-law entropy, S^o, of a substance at 298.15 K can be determined via: , where ΔS_trans is any entropy change resulting from a phase transition and S_r is the residual entropy incorporating all quenchable contributions such as frozen-in structural disorder (often referred to as configurational entropy). The C_p integral is generally the most important contribution to the entropy and it is accessible for measurement (combined with ΔS_trans,) and may be termed the calorimetric entropy S^cal_298.15.

Two important aspects of our C_p measurements on garnet solid solutions are in investigating the nature of low-temperature magnetic contributions to C_p and vibrational ΔS^mix behavior. Following this, C_p of a series of well-characterized synthetic grossular-andradite garnets [(Ca₃(Al, Fe³⁺)₂Si₃O₁₂] was measured between 3 and 300 K using relaxation calorimetry and between 300 and 900 K using DSC methods. The garnets show a λ-type anomaly at low temperatures (< 10 K) resulting from a paramagnetic-antiferromagnetic phase transition. A first analysis of the C_p data indicates nearly or nearly ideal thermodynamic mixing behavior.