Heat capacity and entropy behavior of andradite: a multi-sample and −methodological investigation

Andradite, ideal end-member formula Ca3Fe23+Si3O12, is one of the common rock-forming garnets found in the Earth's crust. There are several outstanding questions regarding andradite's thermodynamic and physical property behavior. Three issues are: i) Could there be differences in the thermodynamic properties, namely heat capacity, c, between synthetic and natural andradite crystals, as observed in the Ca-garnet grossular, Ca3Al2Si3O12? ii) What is the thermal nature of the low-temperature magnetic-phasetransition behavior of andradite? and iii) How quantitative are older published calorimetric (i.e., adiabatic and DSC) heat-capacity results? In this work, four natural nearly end-member single crystals and two synthetic polycrystalline andradite samples were carefully characterized by optical microscope examination, X-ray powder diffraction, microprobe analysis, and IR and UVNIS single-crystal spectroscopy. The IR spectra of the different samples commonly show a main intense OH- stretching band located at 3563 cm(-1), but other OH- bands can sometimes be observed as well. Structural OH- concentrations, calculated from the IR spectra, vary from about 0.006 to 0.240 wt% H2O. The UV/VIS spectra indicate that there can be slight, but not fully understood, differences in the electronic state between synthetic and natural andradite crystals. The C-p behavior was determined by relaxation calorimetry between 2 and 300 K and by differential scanning calorimetry (DSC) methods between 150/300 and 700/950 K, employing the same andradite samples that were used for the other characterization measurements. The low-temperature C-p results show a magnetic phase transition with a Neel temperature of 11.3 +/- 0.2 K, which could be slightly affected by the precise electronic state of Fe2+/3+ in the crystals. The published adiabatic calorimetry results on andradite do not provide a full and correct thermal description of this magnetic transition. The calorimetric C-p measurements give a best estimate for the standard third-law entropy at 298.15 K for andradite of S degrees approximate to 324 +/- 2 J/mol . K vs. the value of 316.4 +/- 2.0 J/mol . K, as given in an early adiabatic investigation. Both natural and synthetic crystals give similar S degrees values within experimental uncertainty of about 1.0%, but one natural andradite, richer in OH, may have a very slightly higher value around S degrees approximate to 326 J/mol . K. Low-temperature DSC measurements made below 298 K agree excellently with those from relaxation calorimetry. The DSC measurements above 298 K show a similarity in C-p behavior among natural and synthetic andradites. A C-p polynomial for use above room temperature to approximately 1000 K was calculated from the data on synthetic andradite giving: C-p (J/mol . K) = 599.09 (+/- 14) - 2709.5 (+/- 480) . T-0.5 - 1.3866 (+/- 0.26) . 10(7) . T-2 + 1.6052 (+/- 0.42) . 10(9) . T-3.