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

Abstract

Andradite, ideal end-member formula Ca_3 Fe^(3+)_2Si_3O_(12), 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_p , between synthetic and natural andradite crystals, as observed in the Ca-garnet grossular, Ca_3Al_2Si_3O_(12)? 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 UV/VIS 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% H_2O. 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 Néel temperature of 11.3 ± 0.2 K, which could be slightly affected by the precise electronic state of Fe^(2+/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 Cp measurements give a best estimate for the standard third-law entropy at 298.15 K for andradite of S^o ≈ 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 o values within experimental uncertainty of about 1.0%, but one natural andradite, richer in OH, may have a very slightly higher value around S^o≈ 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.

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