Rebecca Stevens

Heat capacities and thermodynamic functions of TiO2 anatase and rutile: Analysis of phase stability

Abstract At high temperature, coarse-grained (bulk) rutile is well established as the stable phase of TiO2, and nanophase anatase, thermodynamically stable relative to nanophase rutile, transforms irreversibly to rutile as it coarsens. The lack of experimental heat-capacity data for bulk anatase below 52 K lends uncertainty to its standard entropy and leaves open a slight possibility that anatase may have a thermodynamic stability field at low temperature, as suggested by some theoretical calculations. In the present study, the molar heat capacities of rutile and anatase were measured from 0.5 K to about 380 K. These data were combined with previously measured high-temperature heat capacities, and fits of the resulting data set were used to generate CP°,m, Δ0TSm°, Δ0THm°, and Δ0TGm° values at smoothed temperatures between 0.5 and 1300 K for anatase and 0.5 and 1800 K for rutile. Using these new data and the enthalpy of transformation between anatase and rutile at 298 K, the change in Gibbs free energy for the transition between anatase and rutile from 0 to 1300 K was calculated. These calculations reveal that the transformation from bulk anatase to bulk rutile is thermodynamically favorable at all temperatures between 0 and 1300 K, confirming that bulk anatase does not have a thermodynamic stability field. Implications for the natural occurrence of these two minerals in terrestrial, lunar, and planetary settings are discussed. In particular, anatase requires low-temperature aqueous conditions for its formation and may be a reliable indicator of such conditions in both terrestrial and extraterrestrial settings.

Thermodynamics of Fe oxides: Part I. Entropy at standard temperature and pressure and heat capacity of goethite (α-FeOOH), lepidocrocite (γ-FeOOH), and maghemite (γ-Fe2O3)

Abstract The heat capacities (CP) of goethite (goe, α-FeOOH), lepidocrocite (lep, γ-FeOOH), and maghemite (mag, γ-Fe2O3) were measured from below liquid helium temperature up to their decomposition temperatures by a combination of adiabatic, semi-adiabatic, and differential scanning calorimetry. All three phases were synthetic, with <160 ppm of Al. Chlorine content in goe (32 ppm) and lep (202 ppm) is too low to affect the calorimetric results of this study. Phase purity was verified by Rietveld refinement of the powder X-ray diffraction (XRD) patterns; we determined lattice parameters, atomic positions, crystallite size, and microstrain for all three samples. The Brunauer-Emmet-Teller (BET) surface area is 21 (goe), 23 (lep), and 18 (mag) m2/g. No amorphous impurity was found in the goethite sample by extraction of the oxalate soluble fraction. The excess water, determined from weight loss after firing at 1200 K overnight, is 0.083 ± 0.010 (goe), 0.087 ± 0.005 (lep), 0.042 ± 0.003 (mag) moles of water per mole of FeOOH or Fe2O3. The entropy at standard temperature and pressure (STP) was calculated from subambient CP data and corrected for the excess water content using a Debye-Einstein representation of the CP of hexagonal ice. The entropy at STP is 59.7 ± 0.2 (goe), 65.1 ± 0.2 (lep), and 93.0 ± 0.2 (mag) J/(K·mol). The XRD pattern of maghemite lacks superstructure peaks, and complete disorder of the vacancies leads to configurational entropy Sconf = 2.0 J/K·mol. Because very weak superstructure peaks can be overlooked, or the vacancies may be short-range ordered, this calculated Sconf represents only an upper limit. The heat capacity above 273 K was fitted to a Maier-Kelley polynomial CP [J/(K·mol), T in K] = a + bT + cT-2. The CP polynomial coefficients are a = 1.246, b = 0.2332, c = 313900 (goe, valid in temperature range 273-375 K), a = 59.76, b = 0.06052, c = -772900 (lep, 273-390 K), and a = 106.8, b = 0.06509, c = -1886000 (mag, 273-760 K).

Heat capacities, third-law entropies and thermodynamic functions of the negative thermal expansion materials, cubic α-ZrW2O8 and cubic ZrMo2O8, from K

Abstract The molar heat capacities of crystalline cubic α-ZrW2O8 and cubic ZrMo2O8 have been measured at temperatures from (0.6 to 400) K. At T=298.15 K , the standard molar heat capacities are (207.01±0.21) J · K −1 · mol −1 for the tungstate and (210.06±0.42) J · K −1 · mol −1 for the molybdate. Thermodynamic functions have been generated from smoothed fits of the experimental results. The standard molar entropies for the tungstate and molybdate are (257.96±0.50) J · K −1 · mol −1 and (254.3±1) J · K −1 · mol −1 , respectively. The uncertainty of the entropy of the cubic ZrMo2O8 is larger due to the presence of small chemical and phase impurities whose effects cannot be corrected for at this time. The heat capacities of the negative thermal expansion materials have been compared to the weighted sums of their constituent binary oxides. Both negative thermal expansion materials have heat capacities which are significantly greater than the sum of the binary oxides over the entire temperature region.

Heat capacity calorimetry

Experimental heat capacity measurements of α-ZrW2O8, and zeolitic polymorphs of SiO2, BEA and MFI, have been made from 0.6 to 400 K. Measurements on β-ZrMo2O8 have been made from 8 to 400 K. Analysis of the results yields evidence for very low frequency modes in all four materials. These modes are responsible for negative thermal expansion behavior in α-ZrW2O8 and β-ZrMo2O8. Negative thermal expansion has been observed in some pure SiO2 zeolites, but no studies have been made to look for it in BEA and MFI. The appearance of low frequency modes in these two zeolites suggests that temperature dependent structural investigations would be worthwhile. These modes are lower in energy than the Boson peak in vitreous silica.

Thermochemistry of Hf-Zirconolite, CaHf Ti 2 O 7

The formation enthalpy, - 3752.3 ± 4.7 kJ·mol −1 , of Hf-zirconolite, CaHfTi 2 O 7 , was obtained using high temperature oxide-melt solution calorimetry. Combined with heat capacity data obtained using low temperature adiabatic calorimetry we report the heat capacity (Cp) and the standard molar formation energetics (ΔH° f. elements , Δ S° T , and ΔG° f. elements )for Hf-zirconolite from T = 298.15 K to T = 1500 K. Comparison of Hf-zirconolite with Zr-zirconolite is made.