Advantages to Conversion of Lattice Heat Capacity to Cv in the Resolution of Excess Properties The Ln2S3's as an example

This paper represents a fitting (modeling) of the temperature dependence of the Komada-Westrum characteristic temperature for those γ-, δ- and ε-phase lanthanide sesquisulfides for which the total heat capacities, including internal degrees of freedom (e.g., Schottky and magnetic contributions), were connected to the residue of only lattice vibrations yielding lattice heat-capacity contributions. These characteristic temperatures (θ_KW) at 298.15 K are seen to behave smoothly (nearly linearly) as a function of (cationic) atomic number within the region of stability of each phase as does the density. The trends between the phases also show some consistency but not predictability of one from the other. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermophysics of alkali and related azides II. Heat capacities of potassium,rubidium, cesium,and thallium azides from 5 to 350 K

The heat capacities of potassium, rubidium, cesium, and thallium azides were determined from 5 to 350 K by adiabatic calorimetry. Although the alkali-metal azides studied in this work exhibited no thermal anomalies over the temperature range studied, thallium azide has a bifurcated anomaly with two maxima at (233.0±0.1) K and (242.04±0.02) K. The associated excess entropy was 0.90 cal_th K^?1 mol^?1. The thermal properties of the azides and the corresponding structurally similar hydrogen difluorides are nearly identical. Both have linear symmetrical anions. However, thallium azide shows a solid-solid phase transition not exhibited by thallium hydrogen difluoride. At 298.15 K the values of C_p^o, S^o, and $\text{?{G}{}^{\mathrm{o}}\text{(T)?H}{}^{\mathrm{o}}\text{(0)}}\text{T}$, respectively, are 18.38, 24.86, and 12.676 cal_th K^?1 mol^?1 for potassium azide; 19.09, 28.78, and 15.58 cal_th K^?1 mol^?1 for rubidium azide; 19.89, 32.11, and 18.17 cal_th K^?1 mol^?1 for cesium azide; and 19.26, 32.09, and 18.69 cal_th K^?1 mol^?1 for thallium azide. Heat capacities at constant volume for KN₃ were deduced from infrared and Raman data.     

Modeling Sub- and Super-ambient Heat Capacities of the Group Iva Compounds Despite the Lanthanide Contraction

This paper is concerned with the estimation of heat capacities in the IVA 3d-transition element compounds using especially Zr and Hf compounds as examples. Most prediction schemes routinely tacitly assume that volumes and masses trend in parallel. However, the lanthanide contraction here ensures for ZrX/HfX systems — and generally elsewhere — that this is not so in this portion of the periodic table. Available methods such as Latimer's, Volumetric Priority, Komada-Westrum, Grimvall's, and Sommers' are compared on IVA elements and compounds. Only the Sommers approach has volumetric input. It provides the best prediction.This revised version was published online in November 2005 with corrections to the Cover Date.     

Thermodynamics of the lanthanide halides I. Heat capacities and Schottky anomalies of LaCl3, PrCl3, and NdCl3 from 5 to 350 K

The heat capacities of LaCl₃, PrCl₃, and NdCl₃ have been measured from 5 to 350 K by adiabatic calorimetry. No co-operative thermal anomalies were seen in the temperature range investigated but substantial magnetic heat-capacity contributions of the non-cooperative (Schottky) type were found. Subtraction of the heat capacity of the diamagnetic and isostructural LaCl₃ from those of the paramagnetic members yields experimental Schottky heat-capacity contributions which are compared with heat capacities derived from spectroscopically determined energy levels. Small discrepancies between the calculated and experimental contributions are probably due to differences in lattice heat capacities between LaCl₃ and the others. The values of {(S^o(298.15 K) ? S^o(0)}/cal_th K^?1 mol^?1 are for LaCl₃ and NdCl₃, 32.88 and 36.67. Due to the possibility of a low-temperature phase transition, the entropy of PrCl₃ covers only the experimental range of this research and that of Colwell, Mangum, and Utton. {S^o(298.15 K) ? S^o(0.294 K)} for PrCl₃ is 36.64 cal_th K^?1 mol^?1.     

Heat capacity and other thermodynamic properties of CoTe2 from 5 to 1 030 K and of CoTe2.315 from 300 to 1 040 K

The heat capacity of orthorhombic (marcasite-type structure) cobalt ditelluride has been measured from 5 to 1 030 K by adiabatic-shield calorimetry with alternate energy inputs and equilibrations. Above 900 K a marked increase in heat capacity occurs which probably signals a change in the composition of the CoTe₂-phase towards higher tellurium content. Values at 298.15 and 1 000 K in J K^–1 mol^–1 of the heat capacity (C _p,m), entropy [S _m ^° (T)–S _m ^° (0)], andGibbs energy function – [G _m ^° (T)–H _m ^° (0)]T ^–1 are 75.23, 114.5, 49.93, and 132.4, 216.2, 139.17, respectively. Consistent with the metallic behavior of CoTe₂, deviation of the heat capacity from theDebye T ³-law was found at low temperatures. Comparison with the heat capacity of FeTe₂ shows aSchottky-like deviation with a maximum of 7.3 J K^–1 mol^–1 at 80 K and evidences the influence of the additional 3 d-electron in cobalt compared to iron. Heat capacity measurements were made on CoTe_2.33 to ascertain the existence range of the CoTe_2+x -phase and the entropy of the associated structural disorder.The portion of this research done at Ann Arbor was supported in part by the Structural Chemistry and Chemical Thermodynamics Program of the Division of Chemistry of the National Science Foundation under Grant No. CHE-7710049.     

Measurement of the charged pion electromagnetic form factor

Separated longitudinal and transverse structure functions for the reaction 1H(e,e(')pi(+))n were measured in the momentum transfer region Q2 = 0.6--1.6 (GeV/c)(2) at a value of the invariant mass W = 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q2 elastic data.     

Thermophysical Properties of CeB6 and PrB6 at subambient temperatures

Equilibrium adiabatic heat-capacity measurements have been made on zone refined samples of CeB₆ and PrB₆. Companion measurements made on LaB₆, NdB₆, and GdB₆ have been reported elsewhere. These show cooperative lambda-type anomalies associated with antiferro-magnetic ordering. Except for lanthanum hexaboride, Schottky internal crystal field levels result in significant contributions to the thermodynamic functions. The gross thermodynamic properties at 298.15 K heat capacity (C_p/R), entropy increment (Δ^T _0,m S ⁰/R), and Gibbs energy function are correlated with the nature of the lanthanide. For LaB₆, CeB₆, PrB₆, NdB₆, and GdB₆ the three properties are, respectively: {11.654, 12.014, 11.997, 11.916, 11.695} Cp/R; {10.001, 11.803, 12.430, 12.558, 13.982} S⁰/R, and finally {4.379, 5.912, 6.232, 6.451, 7.905}Φ⁰ _m/R. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermodynamics,handmaiden to science and technology

Generally, the only items of reference data with real economic impact are—except in a few instances—the basic values from which the standard enthalpy increment of reactions and the Gibbs energy of formation of the substances involved in the reaction. The energetic requirements of chemical processing mandate exact values here as well as for rather precise Gibbs energies needed for evaluation of equilibrium constants. Even here the contribution may lie less in the intrinsic value of that accuracy than in the implicit reliability and ready availability of the tables. CODATA's endeavors and scientific task groups dealing with fundamental constants, key values for thermodynamics, internationalization and systematization of thermodynamic tables to assist chemical industry are noted.     

Neutron scattering study of the phase transitions in a doped polycrystalline Fe3O4: Zn0.005Fe2.995O4

Temperature dependent neutron elastic scattering and resistivity measurements have been made on a polycrystalline sample of Zn_0.005Fe_2.995O₄, which displayed a well-separated, bifurcated, heat-capacity anomaly. The lower-temperature anomaly (near 110 K) was found to be associated with a lattice distortion, but no change in neutron intensity was observed at the higher-temperature anomaly (near 119 K). The electrical resistivity of this sample also exhibited an abrupt change only at the lower-temperature anomaly. The downward shift of the lower-temperature, λ-type anomaly as a result of the very low Zn impurity is, however, confirmed by the neutron scattering results and demonstrates the extreme sensitivity of the structural transition to impurities.     

Schottky contributions in chemical thermodynamics

Cryogenic heat-capacity determinations provide a useful tool for the determination of the energetic spectrum of condensed phases and also reveal information on their discrete electronic level structures as well. We have been interested in applying these techniques to actinide elements and have in recent months been working up the techniques to unravel the corresponding data for the lanthanide compounds—where opposite trends in cationic masses and molar volumes provide an opportunity to test theories useful for the resolution of excess heat capacity from lattice contributions.As an important aspect of heat capacities—especially of compounds withd andf electrons—the Schottky contribution deserves to be much better known—by chemists, by physicists, and by students of thermodynamics. These remarks are designed to further that goal.

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Zusammenfassung Bestimmungen der kryogenen Wärmekapazität sind nützlich zur Bestimmung des energetischen Spektrums kondensierter Phasen und liefern zugleich Informationen über deren diskrete Elektronenniveaustrukturen. Wir waren an der Anwendung dieser Techniken auf Actinidenelemente interessiert und haben in den letzten Monaten Methoden zur Ordnung der entsprechenden Daten für die Lanthaniden-Verbindungen ausgearbeitet — wo entgegengesetzte Trends von Kationenmasse und molarem Volumen die Möglichkeit bieten, Theorien zu prüfen, die nützlich für die Absonderung der Überschußwärmekapazität von Gitterbeiträgen sind. Als ein wichtiger Aspekt von Wärmekapazitäten, besonders von Verbindungen mit d- und f-Elektronen, sollte der Schottky-Beitrag von Chemikern, Physikern und Studenten der Thermodynamik besser verstanden werden. Diese Bemerkungen sollen diesem Zwecke dienen.

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