An improved technique for accurate heat capacity measurements on powdered samples using a commercial relaxation calorimeter

We have modified our earlier technique for accurate PPMS heat capacity measurements on powdered samples by means of applying Wakefield grease or small copper strips in the sample preparation instead of using Apiezon N high-vacuum grease. For the Wakefield grease measurements, we put a small amount of Wakefield thermal compound in a copper cup instead of potting with Apiezon N, and the accuracy of measurements on powdered benzoic acid was determined to be ±1% and ±4% in the temperature ranges of 10 K < T < 280 K and 280 K < T < 300 K, respectively. The Wakefield grease was found to improve the accuracy somewhat but overall there was no noticeable improvement in the “grease region” above T = 220 K. To overcome the known shortcomings of using Apiezon N grease above 220 K, we have replaced the Apiezon N grease with small copper strips in the sample preparation to aid thermal conductivity, which results in a less time-intensive two-step technique for the PPMS heat capacity measurement but with an accuracy, based on measurements of benzoic acid, that is ±1% from T = (10 to 300) K and, more importantly, the elimination of the “grease problem”. As an additional test of the new technique, the heat capacity of powdered bulk rutile has been measured twice within the temperature range from (2 to 300) K using the PPMS, and its standard entropy at T = 298.15 K was calculated to be (50.39 ± 0.50) and (50.31 ± 0.50) J · K^?1 · mol^?1, which deviates 0.08% and ?0.08% from the measurement results of our low-temperature adiabatic and semi-adiabatic calorimeters, respectively. We recommend that this technique become the standard for accurate heat capacity measurements on insulating powdered samples using a PPMS system and the corresponding thermodynamic calculations.     

Heat capacity (Cp) and entropy of olivine-type LiFePO4 in the temperature range (2 to 773) K

The heat capacity of olivine-type lithium iron phosphate (LiFePO₄ – LFP) has been measured covering a temperature range from (2 to 773) K. Three different calorimeters were used. The Physical Property Measurement System (PPMS) from Quantum Design was applied in the range between T = (2 and 300) K, a Micro-DSC II from Setaram within the range between T = (283 and 353) K and data between T = (278 and 773) K were measured by means of a Sensys DSC (Setaram) using the Cp-by-step method. Experimental data are given with an error of (1 to 2)% above T = 20 K and up to 8% below 20 K. The data were subdivided into appropriate temperature intervals and fitted using common heat capacity functions. The low temperature results permit the calculation of standard entropies and temperature coefficients of electronic, lattice, as well as magnetic (antiferromagnetic transition at T = 49.2 K) contributions to the heat capacity. The obtained experimental values were compared to results of a recently published first principles phonon study (DFT) and to few available experimental data from the literature.     

Heat capacity of hafnia at low temperature

The low temperature (2 to 300) K heat capacity of monoclinic hafnia (HfO₂) was measured using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). The thermodynamic functions in this temperature range were derived by curve fitting. The standard entropy and enthalpy of hafnia at T = 298.15 K was calculated to be 56.15 ± 0.57 J · mol^?1 · K^?1 and 9.34 ± 0.09 kJ · mol^?1, respectively. The results are in fairly good agreement with old data, which only covered temperatures from (50 to 298) K. Hafnia has a higher heat capacity than zirconia at all temperatures from (2 to 300) K.     

Low temperature heat capacity Study of Fe(PO3)3 and Fe2P2O7

The heat capacities of two iron phosphates, Fe(PO₃)₃ and Fe₂P₂O₇, have been measured over the temperature range from (2 to 300) K using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). A phase transition related to magnetic ordering has been found in the heat capacity at T = 8.76 K for Fe(PO₃)₃ and T = 18.96 K for Fe₂P₂O₇, which are comparable with literature values from magnetic measurements. By fitting the experimental heat capacity values, the thermodynamic functions, magnetic heat capacities, and magnetic entropies have been determined. Additionally, theoretical fits at low temperatures suggest that Fe₂P₂O₇ has an anisotropic antiferromagnetic contribution to the heat capacity and a large linear term likely caused by oxygen vacancies. Further data fitting in a series over widened temperature regions found that this linear term exists only below 15 K and disappears gradually from (15 to 17) K.     

Magneto-structural correlation and low temperature heat capacity of a Mn (III) quadridentate Schiff-base coordination compound

A new Mn (III) Schiff-base coordination compound, [Mn(L)(NCS)]₂ (H₂L = N,N′-bis(5-chlorosalicylidene)-1,2-diaminoethane), has been synthesized and characterized structurally and magnetically. The target compound is a phenoxo-bridged dimeric compound with the isothiocyanate coordinating in a usual bent mode. A magnetic susceptibility study reveals that the target compound exhibits antiferromagnetic intra-dimer coupling between Mn (III) ions. The low temperature heat capacity of the compound over the temperature range (2 to 300) K has been measured using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). The thermodynamic functions in the experimental temperature range have been determined by curve fitting. The standard entropy and enthalpy of the as-prepared compound at T = 298.15 K have been calculated to be (924.52 ± 10.17) J · K⁻¹ · mol⁻¹ and (133.47 ± 1.47) kJ · mol⁻¹, respectively.     

Heat capacities,third-law entropies and thermodynamic functions of the negative thermal expansion material Zn2GeO4 from T=(0 to 400) K

The molar heat capacity of Zn₂GeO₄, a material which exhibits negative thermal expansion below ambient temperatures, has been measured in the temperature range 0.5⩽(T/K)⩽400. At T=298.15 K, the standard molar heat capacity is (131.86 ± 0.26) J · K⁻¹ · mol⁻¹. Thermodynamic functions have been generated from smoothed fits of the experimental results. The standard molar entropy at T=298.15 K is (145.12 ± 0.29) J · K⁻¹ · mol⁻¹. The existence of low-energy modes is supported by the excess heat capacity in Zn₂GeO₄ compared to the sums of the constituent binary oxides.     

Heat capacities,third-law entropies and thermodynamic functions of the geometrically frustrated antiferromagnetic spinels GeCo2O4 and GeNi2O4 from T=(0 to 400) K

The molar heat capacities of GeCo₂O₄ and GeNi₂O₄, two geometrically frustrated spinels, have been measured in the temperature range from T=(0.5 to 400) K. Anomalies associated with magnetic ordering occur in the heat capacities of both compounds. The transition in GeCo₂O₄ occurs at T=20.6 K while two peaks are found in the heat capacity of GeNi₂O₄, both within the narrow temperature range between 11.4<(T/K)<12.2. Thermodynamic functions have been generated from smoothed fits of the experimental results. At T=298.15 K the standard molar heat capacities are (143.44 ± 0.14) J · K⁻¹ · mol⁻¹ for GeCo₂O₄ and (130.76 ± 0.13) J · K⁻¹ · mol⁻¹ for GeNi₂O₄. The standard molar entropies at T=298.15 K for GeCo₂O₄ and GeNi₂O₄ are (149.20 ± 0.60) J · K⁻¹ · mol⁻¹ and (131.80 ± 0.53) J · K⁻¹ · mol⁻¹ respectively. Above 100 K, the heat capacity of the cobalt compound is significantly higher than that of the nickel compound. The excess heat capacity can be reasonably modeled by the assumption of a Schottky contribution arising from the thermal excitation of electronic states associated with the CO²⁺ ion in a cubic crystal field. The splittings obtained, 230 cm⁻¹ for the four-fold-degenerate first excited state and 610 cm⁻¹ for the six-fold degenerate second excited state, are significantly lower than those observed in pure CoO.     

Heat capacity studies of the iron oxyhydroxides akaganéite (β-FeOOH) and lepidocrocite (γ-FeOOH)

The iron oxides and iron oxyhydroxides exist as several different polymorphs, and a thermodynamic understanding of these polymorphs can provide us with an understanding of their relative stability and chemical reactivity. This study provides heat capacity measurements for lepidocrocite (γ-FeOOH) over the temperature range (0.8 to 38) K and akaganéite (β-FeOOH) over the range (0.7 to 302) K. Fits of the heat capacity of the two samples below T = 15 K showed similar behavior to previously published fits of goethite (α-FeOOH), which required a linear term and an anisotropic gap parameter to model accurately the antiferromagnetic spin–wave contributions. The akaganéite measurements were compared to previously reported measurements all of which showed significant disagreement. It is believed that the measurements reported here are the most reliable. Also, the presence of adsorbed water contributes significantly to the heat capacity of akaganéite, and the standard molar entropy at T = 298.15 K of the hydrated form was calculated to be (81.8 ± 2) J · mol^?1 · K^?1.     

Low temperature heat capacity of bulk and nanophase ZnO and Zn1−xCoxO wurtzite phases

The low temperature heat capacity of the ZnO–CoO solid solution system was measured from 2 to 300 K using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). The thermodynamic functions in this temperature range were derived by curve fitting. The standard entropies of bulk ZnO and bulk ZnO–CoO (wurtzite, 18 mol% CoO) at T = 298.15 K were calculated to be (43.1 ± 0.4) J · mol⁻¹ · K⁻¹ and (45.2 ± 0.5) J · mol⁻¹ · K⁻¹, respectively. The surface entropy of ZnO was evaluated to be (0.02 ± 0.01) mJ · K⁻¹ · m⁻², which is essentially zero. No sharp magnetic transitions were observed in the solid solution samples. The nanophase solid solution, 12 mol% CoO, appears to bind H₂O on its surface more strongly than ZnO.     

Heat capacity,third-law entropy,and low-temperature physical behavior of bulk hematite (α-Fe2O3)

The constant pressure heat capacity of a bulk hematite powder was measured using a Quantum Design physical properties measurement system (PPMS). The results of two series showed good precision and agreed well with measurements reported by Westrum and Grønvold. The standard molar entropy at T = 298.15 K was calculated to be (87.32 ± 2) J · mol^?1 · K^?1 for Series 1 and (87.27 ± 2) J · mol^?1 · K^?1 for Series 2, which are in good agreement with the value of (87.40 ± 0.2) J · mol^?1 · K^?1 (originally 20.889 cal · deg^?1 · mole^?1) calculated by Westrum and Grønvold. No anomaly was observed for the Morin transition, and theoretical fits below T = 15 K required a ferromagnetic T^3/2 term.     

High-temperature calorimetry of zirconia: Heat capacity and thermodynamics of the monoclinic–tetragonal phase transition

The high-temperature heat capacity of zirconia was directly measured by differential scanning calorimetry between T = (1050 and 1700) K and derived from the heat content measured by transposed temperature drop calorimetry between T = (970 and 1770) K, including the monoclinic–tetragonal (m–t) phase transition region. The enthalpy and entropy of the m–t phase transition are (5.43 ± 0.31) kJ · mol⁻¹ and (3.69 ± 0.21) J · K⁻¹ · mol⁻¹, respectively. Values of thermodynamic functions are provided from room temperature to 2000 K.     

Density measurements of liquid 2-propanol at temperatures between (280 and 393) K and at pressures up to 10 MPa

Liquid densities for 2-propanol have been measured at T = (280, 300, 325, 350, 375, and 393) K from about atmospheric pressure up to 10 MPa using a vibrating tube densimeter. The period of vibration has been converted into density using the Forced Path Mechanical Calibration method. The R134a has been used as reference fluid for T ? 350 K and water for T > 350 K. The uncertainty of the measurements is lower than ±0.05%. The measured liquid densities have been correlated with a Starling BWR equation with an overall AAD of 0.025%. The same BWR equation agrees within an AAD lower than 0.2% with the experimental values available in the literature over the same temperature and pressure range.     

Thermodynamic study on complex of neodymium with glycine

Neodymium complex with glycine, Nd(Gly)₂Cl₃·3H₂O, was synthesized and characterized by IR spectra. The thermal stability of the complex was tested through TG and DTG and a possible mechanism of thermal decomposition was proposed. The heat capacities of the complex were measured by using an automated adiabatic calorimeter over the temperature range from T = (80 to 380) K, the thermodynamic functions, [H_T − H_298.15] and [S_T − S_298.15], were calculated based on the heat capacity measurements. Two (solid + solid) phase transitions in the ranges of T = (170 to 247) K were observed with the peak temperatures of 184.896 K and 231.217, respectively. The standard molar enthalpy of formation of [Nd(Gly)₂Cl₃·3H₂O] was determined to be (−3081.3 ± 1.1) kJ · mol⁻¹ in terms of an isoperibol solution-reaction calorimeter.     

Measurements of (p, ρ, T) properties for isobutane in the temperature range from 280 K to 440 K at pressures up to 200 MPa

Measurements of (p, ρ, T) properties for isobutane in the compressed liquid phase have been obtained by means of a metal-bellows variable volumometer in the temperature range from 280 K to 440 K at pressures up to 200 MPa. The volume-fraction purity of isobutane used was 0.9999. The expanded uncertainties (k = 2) of temperature, pressure, and density measurements have been estimated to be less than 3 mK, 1.5 kPa (p ⩽ 7 MPa), 0.06% (7 MPa < p ⩽ 50 MPa), 0.1% (50 MPa < p ⩽ 150 MPa), and 0.2% (p > 150 MPa), and 0.11%, respectively. In region more than 100 MPa at 280 K and 440 K, the uncertainty in density measurements rise up to 0.15% and 0.23%, respectively. The differences of the present density values at the same temperature between two series of measurements, in which the sample fillings are different, are within the maximum deviation of 0.09% in density, which is enough lower than the expanded uncertainty in density. Eight (p, ρ, T) measurements at the same temperatures and pressures as the literature values have been conducted for comparison. In addition, vapour pressures were measured at T = (280, 300) K. Moreover, the comparisons of the available equations of state with the present measurements are reported.     

Saturated liquid densities of propane at T = (280 to 365) K

Saturated liquid densities for propane were obtained by means of a metal-bellows variable volumometer at T = (280, 300, 320, 340, 360, and 365) K. The mol-fraction purity of the propane used in the measurements was 0.99997. The expanded uncertainties (k = 2) in temperature, pressure, and density measurements were estimated to be less than ±3 mK, 1.4 kPa (p ≦ 7 MPa), and ±0.09%, respectively. For the determination of the saturation boundary at each temperature for propane, we measured the density data at intervals of about 20 kPa very close to the saturation boundary. After such measurements had been completed, the saturated liquid density data at each temperature were determined as the intersection between the isotherm and our previously determined vapour pressure value. The discrepancies between the three series in the present measurements, in which different sample fillings were used, were also confirmed to be sufficiently lower than the experimental uncertainty. The saturated liquid density correlation was also provided for the systematic comparisons between the present measurements and the literature data.     

Size-dependence of the heat capacity and thermodynamic properties of hematite (α-Fe2O3)

The heat capacity of a 13 nm hematite (α-Fe₂O₃) sample was measured from T = (1.5 to 350) K using a combination of semi-adiabatic and adiabatic calorimetry. The heat capacity was higher than that of the bulk which can be attributed to the presence of water on the surface of the nanoparticles. No anomaly was observed in the heat capacity due to the Morin transition and theoretical fits of the heat capacity below T = 15 K show a small T³ dependence (due to lattice contributions) with no T^3/2 dependence. This suggests that there are no magnetic spin-wave contributions to the heat capacity of 13 nm hematite. The use of a large linear term to fit the heat capacity below T = 15 K is most likely due to superparamagnetic contributions. A small anomaly within the temperature range (4 to 8) K was attributed to the presence of uncompensated surface spins.     

The heat capacities and thermodynamic properties of NiAl2O4 and CoAl2O4 measured by adiabatic calorimetry from T = (4 to 400) K

The low-temperature heat capacity of NiAl₂O₄ and CoAl₂O₄ was measured between T = (4 and 400) K and thermodynamic functions were derived from the results. The measured heat-capacity curves show sharp anomalies peaking at around T = 7.5 K for NiAl₂O₄ and at T = 9 K for CoAl₂O₄. The exact cause of these anomalies is unknown. From our results, we suggest a standard entropy for NiAl₂O₄ at T = 298.15 K of (97.1 ± 0.2) J · mol^?1 · K^?1 and for CoAl₂O₄ of (100.3 ± 0.2) J · mol^?1 · K^?1.     

Thermal properties of [Cr(NH3)6](BF4)3 studied by adiabatic and relaxation calorimetry

Four (solid–solid) phase transitions were detected in the temperature range of (9 to 300) K in polycrystalline [Cr(NH₃)₆](BF₄)₃ at T_C1 = 240.7 K, T_C2 = 108.0 K, T_C3 = 91.9 K, and T_C4 = 61.3 K by adiabatic calorimetry. The measurements by relaxation calorimetry were followed on lowering temperature from 20 K down to 0.35 K under six different external magnetic field values (9, 7, 5, 3, 1 and 0) T. For non-zero values of applied magnetic field well-defined Schottky anomaly appears. Magnetic heat capacity was calculated assuming the zero-field splitting for the decoupled Cr(III) ions. There is no discrepancy between the observed and calculated values. Isothermal magnetization curve recorded up to 5 T was measured at temperature of 1.8 K.     

(p, ρ, T) Properties for n-butane in the temperature range from 280 K to 380 K at pressures up to 200 MPa

The (p, ρ, T) properties for n-butane in the compressed liquid phase were measured by means of a metal-bellows variable volumometer in the temperature range from 280 K to 380 K at pressures up to 200 MPa. The mole fraction purity of the n-butane used in the measurements was 0.9997. The expanded uncertainties (k = 2) in temperature, pressure, and density measurements have been estimated to be less than ±3 mK; 1.4 kPa (p ⩽ 7 MPa), 0.06% (7 MPa < p ⩽ 50 MPa), 0.1% (50 MPa < p ⩽ 150 MPa), and 0.2% (p > 150 MPa); and 0.09%, respectively. In the region above100 MPa at T = 280 K and T = 440 K, the uncertainty in density measurements increases from 0.09% to 0.13% and 0.22%, respectively. Eight (p, ρ, T) measurements at the same temperatures and pressures as the literature values have been conducted for comparisons. In addition, comparisons of the available equations of state with the present measurements are reported.