Edgar Dachs

Precision and accuracy of the heat-pulse calorimetric technique: low-temperature heat capacities of milligram-sized synthetic mineral samples

Low-temperature heat capacities (cp) for milligram(mg)-sized samples of corundum, fayalite and sanidine were measured with a recently available commercial calorimeter (the heat capacity option of the Physical Properties Measurement System (PPMS), produced by Quantum Design®, which operates on the basis of a heat-pulse technique. The measurements were performed between 5 and 300 K on synthetic single-crystals and powders. Since cp-data for the above minerals are known from low-temperature adiabatic calorimetry (low-TAC) these data were used to constrain the accuracy of the PPMS-calorimeter in measuring their cp on mg-sized samples. A relative uncertainty (100*σcp/cp), as a measure of precision, of ~0.3% for T > 50 K, increasing to ~0.5% for T 100 K, 2-3% at T < 100 K for 10-20 mg powders, and ~ 5% for 5 mg powders). The accuracy was highest for cp measurements on single-crystals and sintered-powder. For these, PPMS heat capacities were in excellent agreement with comparable low-TAC data (deviating from these by a maximum of 0.5 ± 0.8% in the temperature range 100–300 K). Heat capacity measurements on sealed powders did not achieve such a high degree of accuracy, but were systematically lower than low-TAC data by 1-2%. Reference entropies were reproduced with a relative error of ≤ 0.5% using single-crystal and sintered-powder samples, and were 1-2% too low for sealed-powder samples. Our measurements demonstrate that the PPMS-calorimeter is a promising new tool for obtaining low-temperature cp-data and calorimetrically determined standard entropies for mg-sized mineralogical samples which are only available in limited amounts.

Heat capacities and entropies of mixing of pyrope-grossular (Mg3Al2Si3O12-Ca3Al2Si3O12) garnet solid solutions: A low-temperature calorimetric and a thermodynamic investigation

Abstract The low-temperature heat capacities for a series of synthetic garnets along the pyrope-grossular (Py-Gr) join were measured with the heat capacity option of the Physical Properties Measurement System (PPMS) produced by Quantum Design. The measurements were performed between 5 and 300 K on milligram-sized polycrystalline garnets that have been well characterized in previous studies. The CP measurements indicate positive excess heat capacities (ΔCPxs) for all solid-solution compositions at temperatures <50 K with a maximum value of 2.31 ± 0.18 J/(mol·K) for the composition Py50Gr50 at about 35 K. Pyrope-rich garnets (i.e., Py90Gr10 and Py75Gr25) have no or slightly positive ΔCPxs at higher temperatures, whereas grossular-rich garnets (i.e., Py10Gr90 and Py25Gr75) show negative ΔCPxs values in the temperature range between 50 and 150 K. At T > 150 K, ΔCPxs values scatter around zero for all compositions and the experimental error is too large to permit a clear determination of whether ΔCP xs is different from zero within 2σ uncertainty. Excess entropies (ΔSxs) at 298.15 K, calculated from the CP data of the various solid-solution members, are asymmetric in nature with the largest positive deviations in pyrope-rich compositions. An asymmetric Margules mixing model was found to be inappropriate for modeling the ΔSxs-X data and, thus, a two-parameter Redlich-Kister model was used to describe the excess entropy-composition relationships. Using this macroscopic mixing model for the excess entropy, a T-X diagram for Py-Gr garnets was calculated using different published values for the excess enthalpies of mixing. The effect of short range Ca-Mg order in the solid solution also was considered in the calculations. The calculations give a solvus for the pyrope-grossular join with a higher critical temperature in the range 850-1330 °C at XGr = 0.35 compared to previous thermodynamic models (Tcrit < 600 °C) that use symmetric mixing models to describe the excess entropy. Unmixing of garnets in nature, as documented from occurrences in ultramafic diatremes may, therefore, have occurred at higher temperatures than previously thought. The atomistic and lattice-dynamic properties of Py-Gr garnets are reviewed and compared to the macroscopic CP data. Published IR and Raman spectra are consistent with the occurrence of positive ΔCPxs values at low temperatures.

A Mössbauer and X-ray diffraction study of annites synthesized at different oxygen fugacities and crystal chemical implications

A refined set of Mössbauer parameters (isomer shifts, quadrupole splittings, Fe2+/Fe3+ ratios) and lattice parameters were obtained from annites synthesized hydrothermally at pressures between 3 and 5 kbars, temperatures ranging from 250 to 780° C and oxygen fugacities controlled by solid state buffers (NNO, QMF, IM, IQF). Mössbauer spectra showed Fe2+ and Fe3+ on both the M1 and the M2 site. A linear relationship between Fe3+ content and oxygen fugacity was observed. Towards low Fe3+ values this linear relationship ends at ≈10% of total iron showing that the Fe3+ content cannot be reduced further even if more reducing conditions are used. This indicates that in annite at least 10% Fe2+ are substituted by Fe3+ in order to match the larger octahedral layer to the smaller tetrahedral layer. IR spectra indicate that formation of octahedral vacancies plays an important role for charge balance through the substitution 3 Fe2+ → 2 Fe3+ + ▪(oct).

Relics of high-pressure metamorphism from the Grossglockner region, Hohe Tauern, Austria: Paragenetic evolution and PT-paths of retrogressed eclogites

Retrogressed eclogites occur embedded in mostly calcareous micaschists and greenschists of the Upper Schieferhulle in the Grossglockner region of the central Tauern Window, east of the Eclogite Zone. A four-stage meta-morphic evolution has been derived from textural and mineral chemical observations: Relics of early pre-eclogitefacies events (stage I: chlorite, actinolite, plagioclase and glaucophane, paragonite, clinozoisite) are preserved mainly in the cores of gamets. The peak-metamorphic paragenesis (stage II) of garnet, omphacite, paragonite, glaucophane, (clino)zoisite, quartz and rutile ± phengite and dolomite records conditions of around 17 kbar and 570°C, slightly below those reported from the Eclogite Zone (around 600°C, 20 kbar). In several instances, growth of coarse-grained barroisitic to actinolitic amphibole occurred during uplift, apparently still within the eclogite facies (stage III). As it is impossible to reconcile the observed amphibole growth textures at the expense of omphacite, glaucophane, garnet, paragonite and quartz with a closed-system reaction, metasomatic interaction must have played a role in the formation of these rocks. The final emplacement in the present tectonic setting and co-metamorphism with the surrounding metasediments (stage IV) occurred under conditions of about 5-6 kbar and 500-530°C. It caused severe hydration and retrograde alteration (symplectite formation), transformed most of the eclogite bodies into garnet amphibolites and even green-schists, with a new, strong stage-IV foliation parallel to that of the country rocks, and erased most evidence of the earlier PT-path. Evidence of eclogite-facies metamorphism of the country rocks has been found only in the westernmost eclogite occurrence. Since the lower tectonic units, the gneiss domes and the Lower Schieferhulle, have not yet produced any evidence of Alpine eclogite-facies metamorphism either, we prefer the interpretation that one major tectonic slice -the Eclogite Zone—and several minor ones -those found within the Upper Schieferhulle nappes today—have been tectonically injected into the evolving Penninic nappe stack during underthrusting of the Penninic units underneath the Austroalpine.

Excess heat capacity and entropy of mixing in high structural state plagioclase

Abstract Low- and high-temperature heat capacities for a series of synthetic high structural state plagioclase crystals (Ab-An) were measured using both a relaxation calorimeter and a differential scanning calorimeter. The measurements were performed at temperatures between 5 and 800 K on milligram-sized polycrystalline samples that had been characterized in a previous study. The data show positive excess heat capacities of mixing at temperatures below 300 K with a maximum value of ~2 J/(mol·K). Below ~70 K, the excess heat capacities exceed two standard deviations and are thus significant. Above 300 K, the measurements indicate negative excess heat capacities with a maximum of ca. -1.5 J/(mol·K) at about 400 K, and do not exceed two standard deviations. The excess vibrational entropies of mixing are positive with an asymmetric variation. At T = 298.15 K, the largest deviation from ideal behavior occurs at Ab20An80 amounting to ΔSexvib = 2.8 ± 2.4 J/(mol·K). An asymmetric Margules mixing model was found to adequately describe the vibrational entropy-composition behavior, yielding WSvibAbAn = 16.4 J/(mol·K) and = WSvibAnAb 4.7 J/(mol·K).

Mssbauer spectroscopic and x-ray powder diffraction studies of synthetic micas on the join annite KFe3AlSi3O10(OH)2-phlogopite KMg3AlSi3O10(OH)2

Micas of the composition K(Fe3−xMgx)AlSi3 O10(OH)2 (x=0.6, 1.2, 1.8, 2.4 and 3.0, corresponding to ann80phl20, ann60phl40, ann40phl60, ann20phl80 and ann0phl100) were synthesized hydrothermally under controlled oxygen fugacity conditions. Lattice parameters a0 and b0 show a distinct linear decrease with increasing Mg content. With increasing ferric iron content a deviation from this linear trend is observed especially within iron rich samples. The tetrahedral rotation angle α increases smoothly from 0° in annite to 9.1° in phlogopite. Mössbauer spectra show Fe2+ and Fe3+ on the octahedral M1 and M2 sites and partially also Fe3+ on the tetrahedral site. There is a smooth increase of the quadrupole splitting on both the M1 and the M2 site going from annite to phlogopite, probably due to changes in the lattice contribution to the electric field gradient, assuming a positive correlation between quadrupole splitting and distortion. Fe3+ contents, as determined by Mössbauer spectroscopy, versus oxygen fugacity shows that, depending on the composition of the micas, minimum amounts of Fe3+ are present. For ann80phl20 this minimum amount of Fe3+ is about 8% decreasing to about 1–2% Fe3+ for ann20phl80.The molar volume of each solid solution member has been estimated from the determined relations of the molar volume versus % Fe3+ contents, extrapolated back to 0% Fe3+. Plotting these volumes as a function of Xphl shows that negative excess volume occur in the annitephlogopite join, with the maximum deviation from ideality around Xphl=0.3. Margules volume parameters have been constrained as: Wv, AnnPhl=0.018±0.016 J/(bar.mol) and Wv, PhlAnn=-0.391±0.025 J(bar.mol) (three site basis).

Excess heat capacity and entropy of mixing in ternary series of high-structural-state feldspars

Low- and high-temperature heat capacities were measured for ternary series of synthetic, high structural state feldspars in the NaAlSi 3 O 8 –KAlSi 3 O 8 –CaAl 2 Si 2 O 8 system that had been characterised by X-ray diffraction and transmission light microscopy. The compositions of the phases lie in the NaAlSi 3 O 8 -rich part of the system where the stability is less limited by the ternary miscibility gap than in other compositional fields. The heat capacities of the end-members had been measured in previous studies using the same calorimeters as in this study (relaxation calorimeter and differential scanning calorimeter). Below 300 K, all samples showed strong positive excess heat capacities of mixing giving rise to excess entropies of mixing up to Δ S ex = 5.8 ± 1.6 J mol −1 K −1 at T = 298.15 K. Above 300 K, further contributions to the excess entropies of mixing do not appear to be significant. The non-ideal entropic mixing behaviour was described by a ternary asymmetric Margules model, resulting in the ternary interaction parameter W AbOrAn S = 93.9 J mol −1 K −1 .

Almandine: Lattice and non-lattice heat capacity behavior and standard thermodynamic properties

Abstract The heat capacity of three synthetic polycrystalline almandine garnets (ideal formula Fe3Al2Si3O12) and one natural almandine-rich single crystal was measured. The samples were characterized by optical microscopy, electron microprobe analysis, X-ray powder diffraction, and Mössbauer spectroscopy. Measurements were performed in the temperature range 3 to 300 K using relaxation calorimetry and between 282 and 764 K using DSC methods. All garnets show a prominent λ-type heat-capacity anomaly at low temperatures resulting from a paramagnetic-antiferromagnetic phase transition. For two Fe3+-free or nearly Fe3+-free synthetic almandines, the phase transition is sharp and occurs at 9.2 K. Almandine samples that have ~3% Fe3+ show a λ-type peak that is less sharp and that occurs at 8.0 ± 0.2 K. The low-T CP data were adjusted slightly using the DSC results to improve the experimental accuracy. Integration of the low-T CP data yields calorimetric standard entropy, S°, values between 336.7 ± 0.8 and 337.8 ± 0.8 J/(mol·K). The smaller value is recommended as the best S° for end-member stoichiometric almandine, because it derives from the “best” Fe3+-free synthetic sample. The lattice (vibrational) heat capacity of almandine was calculated using the single-parameter phonon dispersion model of Komada and Westrum (1997), which allows the non-lattice heat capacity (Cex) behavior to be modeled. An analysis shows the presence of an electronic heat-capacity contribution (Cel, Schottky anomaly) superimposed on a larger magnetic heat-capacity effect (Cmag) around 17 K. The calculated lattice entropy at 298.15 K is Svib = 303.3 J/(mol·K) and it contributes about 90% to the total standard entropy at 298 K. The non-lattice entropy is Sex = 33.4 J/(mol·K) and consists of Smag = 32.1 J/(mol·K) and Sel = 1.3 J/(mol·K) contributions. The CP behavior for almandine above 298 K is given by the polynomial [in J/(mol·K)]: CP = 649.06(±4) - 3837.57(±122)⋅T-0.5 - 1.44682(±0.06)·107·T-2 + 1.94834(±0.09)·109·T-3 which is calculated using the measured DSC data together with one published heat-content datum determined by transposed-drop calorimetry along with a new determination in this work that gives H1181K - H302K = 415.0 ± 3.2 kJ/mol. Using our S° value and the CP polynomial for almandine, we derived the enthalpy of formation, ΔH°f, from an analysis of experimental phase equilibrium results on the reactions almandine + 3rutile = 3ilmenite + sillimanite + 2quartz and 2ilmenite = 2Fe + 2rutile + O2. A ΔH°f = -5269.63 kJ/mol was obtained.

Heat-pulse calorimetry measurements on natural chlorite-group minerals

Abstract Low- and high-temperature heat capacities of five natural chlorite-group samples were measured using the heat-capacity option of the Physical Properties Measurement System (Quantum Design), which is based on the principles of heat-pulse calorimetry, and by differential scanning calorimetry. Comprehensive chemical analyses were performed on these samples by electron microprobe analysis, by inductively coupled plasma mass spectrometry, and by Karl-Fischer titration (for H2O). The natural chlorites span a range in XFe from 0.052 to 0.885 with increasing Al-content due to the Tschermak substitution with increasing XFe. The measured heat capacities were extrapolated to the end-member compositions of chamosite and clinochlore. Integration of heat-capacity data yields the calorimetric standard entropies of chamosite (Fe5Al)[Si3AlO10](OH)8 and clinochlore (Mg5Al)[Si3AlO10](OH)8, with values of 572.0 ± 0.2 and 425.6 ± 0.4 J/(mol·K), respectively. The CP-polynomial for end-member chamosite is CP = 1151.7 - 8.4564 × 103·T-0.5 -13.206 × 106·T-2 + 15.233 × 108·T-3 [J/(mol·K)], valid in the temperature range of 298.15.900 K, and that for end-member clinochlore is CP = 1160.5 - 9.9819 × 103·T-0.5 . 5.9534 × 106·T-2 + 3.8677 × 108·T-3 [J/(mol·K)], valid in the temperature range of 298.15-1000 K. The Fe-rich chlorites exhibit an asymmetric distribution of the excess heat capacity in a plot of CexP vs. T, with a maximum at about 52 K. By analogy to annite, we interpret this peak to represent the magnetic ordering temperature. Based on our standard entropy value for chamosite, the enthalpy of formation of berthierine (Fe2.5Al0.5)[Si1.5Al0.5O5](OH)4 was estimated as -3570.30 kJ/mol using a reported onset temperature of 70 °C at 16 MPa for the berthierine-chamosite polymorphic transition.

Grossular: A crystal-chemical, calorimetric, and thermodynamic study

Abstract In spite of the amount of research that has been done on grossular, Ca3Al2Si3O12, there is still uncertainty regarding its exact thermodynamic properties. Because of insufficient sample characterization in the various published calorimetric studies, it is difficult to analyze conflicting CP and S○ results. To resolve the discrepancies, a detailed and systematic multi‑method investigation was undertaken. Three synthetic grossular samples and four natural grossular‑rich garnets were characterized by optical microscopy, electron microprobe analysis, IR, and MAS 29Si and 27Al NMR spectroscopy, and X-ray powder diffraction methods. Two of the natural grossulars, crystallized at relatively low temperatures, are optically anisotropic and two from the higher temperature amphibolite faces are isotropic. The natural garnets have between 94 and 97 mol% grossular with minor fractions of other garnet components, as well as small amounts of OH in solid solution. 29Si and 27Al MAS NMR spectra indicate that synthetic grossular crystallized at high‑P and high‑T conditions is ordered with respect to Al and Si. Heat-capacity measurements between 5 and 300 K were made using relaxation calorimetry and between 282 and 764 K using DSC methods. For the three synthetic grossulars, the CP data yield an average S○ value of 260.23 ± 2.10 J/(mol·K). The S○ values for the four natural grossular‑rich garnets, adjusted to end‑member grossular composition, range between 253.0 ± 1.2 and 255.2 ± 1.2 J/(mol·K). The results of this work thus confirm earlier low‑temperature adiabatic calorimetric studies that show small, but experimentally significant, differences in S° between natural and synthetic grossular samples. The difference in terms of heat-capacity behavior between synthetic and natural samples is that the latter have lower CP values at temperatures between 20 and 100 K by up to about 20%. Above 298 K, CP for grossular is given by CP J/(mol·K) = 556.18(±12) - 1289.97(±394)⋅T-0.5 - 2.44014(±0.24)⋅107⋅T-2 + 3.30386(±0.39)⋅109⋅T-3. Applying mathematical programming, published high‑P‑T results on the reaction 3anorthite = grossular + 2kyanite + quartz were analyzed thermodynamically. The calculations yield best‑fit values of ΔfH○ = -6627.0 kJ/mol and S○ = 258.8 J/(mol·K) for grossular. It is concluded that S○ ≈ 260 J/ (mol·K) is the best value for end‑member grossular. Variations in structural state and composition in natural samples, as well as assumptions used in correcting for solid‑solution and OH groups, appear to be the most important factors that could account for the smaller S○ values of 253-257 J/(mol·K).