Juliana Boerio-Goates

Critical examination of heat capacity measurements made on a Quantum Design physical property measurement system

Abstract We examine the operation and performance of an automated heat-capacity measurement system manufactured by Quantum Design (QD). QD’s physical properties measurement system (PPMS) employs a thermal-relaxation calorimeter that operates in the temperature range of 1.8–395 K. The accuracy of the PPMS specific-heat data is determined here by comparing data measured on copper and synthetic sapphire samples with standard literature values. The system exhibits an overall accuracy of better than 1% for temperatures between 100 and 300 K, while the accuracy diminishes at lower temperatures. These data confirm that the system operates within the ±5% accuracy specified by QD. Measurements on gold samples with masses of 4.5 and 88 mg indicate that accuracy of ±3% or better can be achieved below 4 K by using samples with heat capacities that are half or greater than the calorimeter addenda heat capacity. The ability of a PPMS calorimeter to accurately measure sharp features in Cp(T) near phase transitions is determined by measuring the specific heat in the vicinity of the first-order antiferromagnetic transition in Sm2IrIn8 (T0=14 K) and the second-order hidden order (HO) transition in URu2Si2 (TN=17 K). While the PPMS measures Cp(T) near the second-order transition accurately, it is unable to do so in the vicinity of the first-order transition. We show that the specific heat near a first-order transition can be determined from the PPMS-measured decay curves by using an alternate analytical approach. This correction is required because the latent heat liberated/absorbed at the transition results in temperature–decay curves that cannot be described by a single relaxation time constant. Lastly, we test the ability of the PPMS to measure the specific heat of Mg11B2, a superconductor of current interest to many research groups, that has an unusually strong field-dependent specific heat in the mixed state. At the critical temperature the discontinuity in the specific heat is nearly 15% lower than measurements made on the same sample using a semi-adiabatic calorimeter at Lawrence Berkeley National Laboratory.

Evidence of linear lattice expansion and covalency enhancement in rutile TiO2 nanocrystals

Lattice variations and bonding characteristics in rutile TiO2 nanocrystals were examined by x-ray diffraction and x-ray photoelectron spectroscopy. With a reduction in the physical dimensions, rutile TiO2 nanocrystals show a linear lattice expansion and an anomalous covalency enhancement in apparent contradiction to the ionicity increase in BaTiO3 and CuO nanocrystals as reported recently by S. Tsunekawa et al. [Phys. Rev. Lett. 2000, 85, 3440] and V. R. Palkar et al. [Phys. Rev. B 1996, 53, 2167]. A surface defect dipole model is proposed to explain these physical phenomena in terms of the strong interactions among the surface dipoles that produce an increased negative pressure. The covalency enhancement is interpreted according to the critical properties of the increased TiO bond lengths in the expanded lattice.

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.

Chemical Thermodynamics: Principles and Applications

Preface to the Two-Volume Series. Preface to the First Volume. Introduction. The First and Second Laws of Thermodynamics. Thermodynamic Relationships and Applications. The Third Law and Absolute Entropy Measurements. The Chemical Potential and Equilibrium. Fugacity, Activity, and Standard States. The Thermodynamic Properties of Solutions. The Equilibrium Condition Applied to Phase Equilibria. The Equilibrium Condition Applied to Chemical Processes. Statistical Thermodynamics. APPENDIX 1: Mathematics for Thermodynamics. APPENDIX 2: The International Temperature Scale of 1990. APPENDIX 3: Equations of States for Gases. APPENDIX 4: Calculations from Statistical Thermodynamics.

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).

Grain-growth kinetics of rutile TiO 2 nanocrystals under hydrothermal conditions

Rutile nanocrystals were directly prepared under hydrothermal conditions using TiCl 4 as the starting material. The formation reactions proceeded by suppressing the crystallization of the other TiO 2 polymorphs using a fixed concentration of 0.62 M [Ti 4 + ]. With increasing reaction temperatures from 140 to 220 °C, rutile nanocrystals were found to grow from 5.4 to 26.4 nm in size, and by varying the reaction time from 2 to 120 h at 200 °C the particle size increased from 17 to 40 nm. The grain-growth kinetics of rutile TiO 2 nanocrystals under hydrothermal conditions was found to follow the equation, D n = k 0 x t x e ( - E a / R T ) with a grain-growth exponent n = 5 and an activation energy of E a = 170.8 kJ mol - 1 . The nanocrystals thus obtained consist of an interior rutile lattice and a surface hydration layer. With decreasing particle size, the hydration effects at the surface increase, while the rutile structure shows a lattice expansion and covalency enhancement in the Ti-O bonding.

Heat-capacity measurements and thermodynamic functions of crystalline α-D-glucose at temperatures from 10 K to 340 K

The heat capacity of crystalline α-D-glucose has been measured at temperatures from 7 K to 347 K with an adiabatic calorimeter. Heat capacity, entropy, enthalpy increments, and values of (TΔT0Som − ΔT298.15 K Hom)/RT are reported at smoother temperatures from 10 K to 340 K. Comparisons are made with previously reported values for the heat capacity of crystalline glucose; the agreement is generally within ±2 per cent. Our value for the standard molar entropy at 298.15 K is (209.2±0.4) J·K−1·mol−1; the only other value in the literature is 211.3 J·K−1·mol−1.

Inelastic Neutron Scattering Study of Confined Surface Water on Rutile Nanoparticles

The vibrational density of states (VDOS) for water confined on the surface of rutile-TiO(2) nanoparticles has been extracted from low temperature inelastic neutron scattering spectra. Two rutile-TiO(2) nanoparticle samples that differ in their respective levels of hydration, namely TiO(2) x 0.37 H(2)O (1) and TiO(2) x 0.22 H(2)O (2) have been studied. The temperature dependency of the heat capacities for the two samples has been quantified from the VDOS. The results from this study are compared with previously reported data for water confined on anatase-TiO(2) nanoparticles.

Heat capacity measurements from 10 to 300 K and derived thermodynamic functions of lyophilized cells of Saccharomyces cerevisiae including the absolute entropy and the entropy of formation at 298.15 K

Abstract Heat capacity measurements using an adiabatic calorimeter have been made from 7 to 310 K on a carefully prepared specimen of lyophilized cells of Saccharomyces cerevisiae (yeast). From these measurements, a value of 1.304 J K−1 g−1 has been obtained for the absolute entropy of yeast cells at 298.15 K, based on third-law calculations. Chemical analysis of the cells yielded an empirical chemical formula for the cellular stoichiometry, which has been expressed as an ion-containing carbon mole, (ICC-mol). A value of 34.167 J K−1·ICC-mol−1 for the absolute entropy of this mass of cells and of −151.46 J K−1·ICC-mol−1 for the entropy of formation has been calculated. The absolute entropy/g of the yeast cells falls within the range of those for simple biological molecules like sugars and amino acids and more complex biopolymers like proteins. We conclude that the thermodynamic effect of cellular organization in the dried cells is negligible.

Thermochemistry of hydrotalcite-like phases in the MgO-Al2O3-CO2-H2O system: A determination of enthalpy, entropy, and free energy

Abstract Interest in hydrotalcite-like compounds has grown due to their role in controlling the mobility of aqueous metals in the environment as well as their use as catalysts, catalyst precursors, and specialty chemicals. Although these materials have been studied in a number of contexts, little is known of their thermodynamic properties. Here we present a complete thermochemical study of hydrotalcite- like compounds of the MgO-Al2O3-CO2-H2O system. Using high-temperature oxide-melt solution calorimetry, we determined the enthalpies of formation at 298 K from the elements (Afor the compounds: Mg0.69Al0.31(OH)2.013(C03)0.15·0.30H20, Mg0.74Al0.26(OH)2(CO3)0.13·0.39H2O, Mg0.67Al0.33 (OH)2(CO3)0.16·0.69H2O, and Mg0.66Al0.34(OH)2(CO3)0.17-0.70H2O to be -1171.55 ± 1.81, -1165.98 ± 2.06, -1284.65 ± 1.97, and -1292.07 ± 2.05 kJ/mol, respectively. We also present the heats of formation of these materials from the single-cation hydroxides [Mg(OH)2 and Al(OH)3] and carbonates (MgCO3) and water (ΔHfscc); they are energetically stable by 10-20 kJ/mol. Using low-temperature adiabatic heat-capacity measurements we determined the third-law entropy (S°) for the compound Mg0.74Al0.26 (OH)2(CO3)0.13-0.39H2O [85.58 ± 0.17 J/(mol-K)], neglecting any configurational contributions. From our experimental data for Mg0.74Al0.26(OH)2(CO3)0.43·0.39H20, we calculated the free energy at 298 K (ΔG0f= -1043.08 ± 2.07 kJ/mol). Our thermodynamic studies also provide insight into the state of the interlayer water in hydrotalcite, namely the water of hydration appears to exist in a state intermediate in thermodynamic properties between that of ice and liquid water.