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

Geiger, Charles A.; Dachs, Edgar

doi:10.1111/jmg.12291

Cited by 13 publications

(12 citation statements)

References 55 publications

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“…As C p below 2 K (−271.15°C) has low absolute values <0.3 J/(mol·K), the entropy increment from 0 to 2 K (−273.15 to −271.15°C) was neglected. As outlined in Ref, standard entropy determinations, based on PPMS‐measured C p data, can be expected to be accurate to within 0.5%. A graphical representation of the data is given in Figures 5 and 6.…”

Section: Experimental Methodsmentioning

confidence: 94%

“…Furthermore details on the PPMS measurements and evaluation procedures can be found, for example, in and will not be repeated here. Experimental uncertainties associated with this method are discussed in Ref …”

Section: Experimental Methodsmentioning

confidence: 99%

“…and will not be repeated here. Experimental uncertainties associated with this method are discussed in Ref 17. Starting chemical compositions (wt%) of the samples…”

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confidence: 99%

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Stability and calorimetric studies of silico‐ferrites of calcium aluminum and magnesium

et al. 2018

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In a systematic study on silico‐ferrites of calcium aluminum and magnesium (SFCA phases) this investigation focuses on synthesis of silicon‐free SFCA‐type compounds with low‐MgO contents (~1.00 apfu—atoms per formula unit). Previous studies revealed the existence of iron‐rich SFCA phases similar to the SFCA‐I structure with the chemical composition Ca3MgAl6Fe10O28 (Metall Mater Trans B. 2017;48:2207). The experimental results in the quaternary Fe2O3‐CaO‐Al2O3‐MgO system confirm large stability fields of 2 silicon‐free ferrites FCAM‐I and FCAM‐III, which are members of the homologous series M14+6nO20+8n (n = 1, 2). Starting with compositions corresponding to Ca3MgAlxFe16‐xO28 (with increasing aluminum content from x = 0‐12 apfu), it was possible to synthesize these phases with an x‐value ≥2 apfu, which corresponds to Al2O3 contents ≥7.14 wt%. Synthesis of pure silicon‐free ferrites with n = 1 (FCAM‐I) and 2 (FCAM‐III) and silicon‐bearing ferrites with n = 0 (SFCA) was possible. Samples were characterized by electron probe microanalysis, powder diffraction, and subsequently studied using relaxation calorimetry measurements in combination with differential scanning calorimetry for determination of the heat capacities and standard entropies S°(298). The corresponding values are S°(298) = 650.3 ± 4.6 J/mol·K for SFCA, S°(298) = 864.5 ± 6.1 J/mol·K for FCAM‐I, and S°(298) = 1206.2 ± 8.4 J/mol·K for FCAM‐III. These thermodynamic data are a step toward a rigorous quantitative thermodynamic modeling of the iron ore sintering process.

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Section: Experimental Methodsmentioning

confidence: 94%

Section: Experimental Methodsmentioning

confidence: 99%

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Stability and calorimetric studies of silico‐ferrites of calcium aluminum and magnesium

et al. 2018

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“…Converting vol.% to mol%, we obtain 6.7 mol% wollastonite and 93.3 mol% andradite, and taking a value of S°= 163.4 J/mol · K for wollastonite (Robie & Hemingway, 1995), we obtain a final corrected S°value of ∼330 J/mol · K ( Table 4). The S(T) behavior for andradite from 0 K to 298 K is given in Geiger & Dachs (2018). It shows that S(T) is underestimated by the Robie et al (1987) results at about T < 13 K and slightly overestimated at roughly T >50 K. Finally, in another early calorimetric investigation, Kiseleva et al (1972) reported S°value of 329.28 ± 5.4 J/mol · K (Table 4).…”

Section: Magnetic Phase Transitionmentioning

confidence: 89%

“…The closer the sample coupling is to 100%, the better the thermal conductance between the sample platform and the sample, which ensures a more robust heat-capacity determination via relaxation calorimetry. Experience indicates that an accuracy of about 0.2 (or even 0.1)% above ∼30 K in C p and the standard entropy, S°, can be achieved for single crystals (Benisek & Dachs, 2008;Dachs & Geiger, 2018). It is between about 0.2% and 0.5% for measurements on powders (weighing about 10-20 mg) contained in thin Al-metal foil.…”

Section: Uv/vis Optical Absorption Single-crystal Spectroscopymentioning

confidence: 98%

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

Geiger¹,

Dachs²,

Vielreicher³

et al. 2018

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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 .

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Garnet EoS: a critical review and synthesis

Angel¹,

Gilio

Mazzucchelli

et al. 2022

Contrib Mineral Petrol

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All available volume and elasticity data for the garnet end-members grossular, pyrope, almandine and spessartine have been re-evaluated for both internal consistency and for consistency with experimentally measured heat capacities. The consistent data were then used to determine the parameters of third-order Birch–Murnaghan EoS to describe the isothermal compression at 298 K and a Mie–Grüneisen–Debye thermal-pressure EoS to describe the PVT behaviour. In a full Mie–Grüneisen–Debye EoS, the variation of the thermal Grüneisen parameter with volume is defined as $$\gamma = {\gamma }_{0}{\left(\frac{V}{{V}_{0}}\right)}^{q}$$ γ = γ 0 V V 0 q . For grossular and pyrope garnets, there is sufficient data to refine q which has a value of q = 0.8(2) for both garnets. For other garnets, the data do not constrain the value of q and we therefore refined a q-compromise version of the Mie–Grüneisen–Debye EoS in which both γ/V and the Debye temperature θ D are held constant at all P and T, leading to $$\left( {{\raise0.7ex\hbox{${\partial C_{{\text{V}}} }$} \!\mathord{\left/ {\vphantom {{\partial C_{{\text{V}}} } {\partial P}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\partial P}$}}} \right)_{{\text{T}}} = 0$$ ∂ C V ∂ P T = 0 , parallel isochors and constant isothermal bulk modulus along an isochor. Final refined parameters for the q-compromise Mie–Grüneisen–Debye EoS are: Pyrope Almandine Spessartine Grossular V0 (cm3/mol)a 113.13 115.25 117.92 125.35 K0T (GPa) 169.3 (3) 174.6 (4) 177.57 (6) 167.0 (2) $$K^{\prime}_{{0{\text{T}}}}$$ K 0 T ′ 4.55 (5) 5.41 (13) 4.6 (3) 5.07 (8) θ D0 771 (28) 862 (22) 860 (35) 750 (13) γ0 1.185 (12) 1.16 (fixed) 1.18 (3) 1.156 (6) for pyrope and grossular, the two versions of the Mie–Grüneisen–Debye EoS predict indistinguishable properties over the metamorphic pressure and temperature range, and the same properties as the EoS based on experimental heat capacities. The biggest change from previously published EoS is for almandine for which the new EoS predicts geologically reasonable entrapment conditions for zircon inclusions in almandine-rich garnets.

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

Cited by 13 publications

References 55 publications

Stability and calorimetric studies of silico‐ferrites of calcium aluminum and magnesium

Stability and calorimetric studies of silico‐ferrites of calcium aluminum and magnesium

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

Garnet EoS: a critical review and synthesis

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