A calorimetric investigation of spessartine: Vibrational and magnetic heat capacity

Dachs, Edgar; Geiger, Charles A.; Withers, A. C.; Essene, Eric J.

doi:10.1016/j.gca.2009.03.011

“…Through the comparison of magnetic susceptibility and specific-heat measurements, here we show that for this case the structural glass exhibits signs of greater magnetic frustration than the crystalline phase. Comparison of the specific heats of crystalline Ca 3 Al 2 Si 3 O 12 and Mn 3 Al 2 Si 3 O 12 shows that the previously observed anomalous extra contribution to the specific heat in the Mn compound is consistent with either an order-disorder transition of the Mn 2+ ions, [14][15][16] in our analysis occurring over a temperature range of 30-300 K, or the shift of one of the phonon modes of the Mn in spessartine to approximately one third the energy seen for the Ca in grossular.…”

Section: Introductionmentioning

confidence: 53%

“…The existence of excess entropy in spessartine is a well-known issue in geochemistry and the observed heat capacity has been fit to various models. 10,[14][15][16] The current data, by directly characterizing the difference in low-temperature thermodynamic behavior between Mn 3 Al 2 Si 3 O 12 and Ca 3 Al 2 Si 3 O 12 , provides further insight into this issue.…”

Section: As Shown Inmentioning

confidence: 95%

“…The low-temperature change is that of the magnetic ordering transition at 7 K. The entropy sum for this part is within experimental uncertainty of R ln 6, the ideal expected for the full ordering of spin 5/2 moments, in agreement with previous studies. 15 The second part, the entropy under the broad peak near 90 K, integrates to approximately R ln 4. If this is due to the presence of a freezing transition of the Mn into off center positions in its cage ͑i.e., a disorder to order transition 14,16 ͒ occurring over a wide range of temperatures, about 300-30 K from our data, and assuming that the Ca ions are frozen in their positions at high temperatures, then the integrated entropy is expected to be R ln n, where n is the number of Mn positions within the cage.…”

Section: As Shown Inmentioning

confidence: 99%

See 1 more Smart Citation

Magnetic properties of the garnet and glass forms ofMn3Al2Si3O12

Lau

¹

,

Klimczuk

²

,

Ronning

³

et al. 2009

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The magnetic susceptibilities and specific heats of the crystalline garnet and glass forms of Mn 3 Al 2 Si 3 O 12 are reported. This allows a direct comparison of the degree of magnetic frustration of the triangle-based garnet lattice and the structurally disordered solid at the same composition for isotropic spin 5 / 2 Mn 2+ ͑3d 5 ͒. The results show that the glass phase shows more pronounced signs of magnetic frustration than the crystalline phase. Through comparison of the specific heats of Ca

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“…The composition of the natural andradite platelets was determined using a JEOL microprobe at Kiel University, Germany, and WDS methods were applied under conditions of 15 kV and 15 nA with a focused beam size of 1 mm as done in other studies on garnet (e.g., Dachs et al, 2012a, b). Due to the generally small sizes (less than roughly 40 mm) of most crystals and difficulties in obtaining quantitative microprobe results on synthetic garnets (Dachs et al, 2009;Fournelle & Geiger, 2010), the synthetic andradites were not measured. The standards used for analysis were corundum for Al, wollastonite for Ca and Si, and a natural fayalite-rich olivine for Fe, V metal for V, chromite for Cr, tephroite for Mn, rutile for Ti, and forsterite for Mg.…”

Section: Microprobe Analysismentioning

confidence: 99%

“…Here, it must be noted that lowtemperature adiabatic calorimetry C p measurements are/were often not made below about 8 K. This is the case for andradite (Robie et al, 1987) as well as other transition-metal-bearing garnets. They show cooperative magnetic transitions whose thermal signatures extend below 8 K and approach 0 K (Klemme et al, 2005;Dachs et al, 2009;Dachs et al, 2012b), and iii) Improvements in power-compensated DSC methods allow more precise determinations of C p (T) from roughly 150 or 300 K to 900-1000 K compared to data obtained using first-generation devices and measurements made from the 1970s through the 1980s (see discussion in, e.g., Bosenick et al, 1996, for the case of grossular).…”

Section: Introductionmentioning

confidence: 99%

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

Geiger¹,

Dachs²,

Vielreicher³

et al. 2018

ejm

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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

²

,

Mazzucchelli

³

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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A calorimetric investigation of spessartine: Vibrational and magnetic heat capacity

Cited by 24 publications

References 36 publications

Magnetic properties of the garnet and glass forms ofMn3Al2Si3O12

Magnetic properties of the garnet and glass forms ofMn3Al2Si3O12

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

Garnet EoS: a critical review and synthesis

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