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

Abstract

Andradite, ideal end-member formula Ca 3 Fe 3þ 2 Si 3 O 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 3 Al 2 Si 3 O 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 À stretching band located at 3563 cm À1 , but other OH À bands can sometimes be observed as well. Structural OH À concentrations, calculated from the IR spectra, vary from about 0.006 to 0.240 wt% H 2 O. 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 2þ/3þ 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 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) À 2709.5 (±480) · T À0.5 À 1.3866 (±0.26) · 10 7 · T À2 þ 1.6052 (±0.42) · 10 9 · T À3 .

Recent developments and the future of low‐T calorimetric investigations in the Earth sciences: Consequences for thermodynamic calculations and databases

“…First, relaxation measurements can be made relatively easily and routinely down to 2 K and this is critical when, for example, low‐ T phenomena such as cooperative magnetic transitions occur with associated Nèel temperatures ( T N ) of ~10 K and one has C p = C vib + C mag and S total = S vib + S mag . Indeed, andradite shows a paramagnetic to antiferromagnetic transition with T N = 11.3 ± 0.2 K (Figure —modified from Geiger et al., in press). It is related to an ordering of the electronic spins of the d‐electrons of Fe 3+ .…”

“…The data from Geiger et al. (in press, sample SD 23) are shown as red circles and those of Robie et al. () as blue circles.…”

“…It has been considered for years to be the calorimetric method par excellence for studying low‐ T thermophysical properties and in obtaining S °. There can be, though, experimental issues, in some cases, as shown by the newer commercial relaxation calorimetric method (Lashley et al., ) and careful differential scanning calorimetry (DSC) measurements (made on both synthetic and natural andradite samples (Geiger, Dachs, Vielreicher, & Rossman, in press).…”

“…(). The red circles are from relaxation calorimetry measurements (Geiger et al., in press, sample SD 23)…”

“…Geiger et al. (in press) measured the C p behaviour of andradite between 100 and 300 K using both relaxation and DSC methods. The agreement in C p ( T ) using both devices was excellent.…”