Heat capacity and thermal expansion of icosahedral lutetium boride LuB66

The experimental values of heat capacity and thermal expansion for lutetium boride LuB₆₆ in the temperature range of 2–300 K were analysed in the Debye–Einstein approximation. It was found that the vibration of the boron sub-lattice can be considered within the Debye model with high characteristic temperatures; low-frequency vibration of weakly connected metal atoms is described by the Einstein model.     

Heat capacity of poly(vinyl methyl ether)

The heat capacity of poly(vinyl methyl ether) (PVME) has been measured using adiabatic calorimetry and temperature‐modulated differential scanning calorimetry (TMDSC). The heat capacity of the solid and liquid states of amorphous PVME is reported from 5 to 360 K. The amorphous PVME has a glass transition at 248 K (?25 °C). Below the glass transition, the low‐temperature, experimental heat capacity of solid PVME is linked to the vibrational molecular motion. It can be approximated by a group vibration spectrum and a skeletal vibration spectrum. The skeletal vibrations were described by a general Tarasov equation with three Debye temperatures Θ₁ = 647 K, Θ₂ = Θ₃ = 70 K, and nine skeletal modes. The calculated and experimental heat capacities agree to better than ±1.8% in the temperature range from 5 to 200 K. The experimental heat capacity of the liquid rubbery state of PVME is represented by C_p(liquid) = 72.36 + 0.136 T in J K^?1 mol^?1 and compared to estimated results from contributions of the same constituent groups of other polymers using the Advanced Thermal AnalysiS (ATHAS) Data Bank. The calculated solid and liquid heat capacities serve as baselines for the quantitative thermal analysis of amorphous PVME with different thermal histories. Also, knowing C_p of the solid and liquid, the integral thermodynamic functions of enthalpy, entropy, and free enthalpy of glassy and amorphous PVME are calculated with help of estimated parameters for the crystal. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2141–2153, 2005     

Heat capacity measurements of SnSe and SnSe2

The heat capacities of SnSe and SnSe₂ were measured in the temperature range 230–580 K using a computer interfaced differential scanning calorimeter. From these measurements, the Debye temperatures of SnSe and SnSe₂ were calculated as a function of temperature. An estimated Debye temperature of 220 K for SnSe was used to calculate the absolute entropy of SnSe at 298 K to be 85.2 ± 6.0 J K^?1 mole^?1. In the light of other work, the suitability of Debye temperatures for estimating low temperature heat capacities of SnSe₂ is questioned.     

Structure and Specific Heat of Disordered and Ordered Titanium Monoxide TiOy

The structure of disordered and ordered titanium monoxide containing structural vacancies in both sublattices was studied by Xray diffraction. The symmetry of the monoclinic Ti₅O₅ superstructure (space group C2/m) was analyzed. The type and channel of the TiO_y–Ti₅O₅ disorder–order transition was determined. The distribution functions of Ti and O atoms in the metal and nonmetal sublattices of titanium monoxide were calculated. The specific heats of TiO_y titanium monoxides (0.8< y< 1.27) were measured by differential scanning calorimetry for the disordered and ordered states in the range from 340 to 600 K. The dependences of the specific heat, enthalpy, and entropy on the composition and structure of TiO_y were found for the first time. A notable effect of the structural state on the specific heat was detected. In the indicated temperature range, the C _p (T) dependence is adequately described by a function that accounts for the Debye effect and the electronic specific heat.     

Analysis of the contribution of skeletal vibrations to the heat capacity of linear macromolecules in the solid state

Automatic computer programs are developed to calculate one- two-, and three-dimensional Debye functions. Prior tables of these functions are critically reviewed. Also, strategies are derived to calculate Debye temperatures from heat capacities. Both, simple three-dimensional Debye analyses and Tarasov analyses were carried out on 35 linear macromolecules. The experimental heat capacities for these analyses were collected in the ATHAS data bank. It is shown that the skeletal heat capacity of linear macromolecules is often best represented by only two vibrations per chain atom. For most of the all-carbon chain macromolecules the intramolecular skeletal heat capacity can be given by C_vs=D₁[520 (28/MW)^1/2] whereMW is the molecular mass andD ₁ represents the one-dimensional Debye function. Polyoxides show a higher intramolecular theta temperature, but a lower intermolecular theta temperature. Double bonds and phenylene groups in the chain increase the intramolecular theta temperature.Dedicated to Prof. Dr. F. H. Müller.On leave from the Lumumba Peoples' Friendship University, Moscow, USSR.     

Thermal Expansion Behaviors of Li3AsW7O25: A Case Study for Comparative Debye Temperature for a Large Polyatomic Unit Cell

The thermal expansion behavior of Li₃AsW₇O₂₅ has been studied. The temperature‐dependent development of crystal structural parameters was obtained from Rietveld refinement using neutron time of flight powder diffraction data. Modeling of the lattice thermal expansion was carried out using a Grüneisen first‐order approximation for the zero‐pressure equation of state, where the temperature‐dependent vibrational energy was calculated taking the Debye‐Einstein‐Anharmonicity approach. Temperature‐dependent Raman spectra shed light on some selective modes with unusual anharmonicity. Debye temperatures were calculated using three different theoretical approaches, namely, thermal expansion, mean‐squared isotropic atomic displacement parameter and heat capacity. Similarities as well as discrepancies between the numerical values obtained from different theoretical approaches are discussed.     

Heat-Induced Gelation of Globular Protein Mixtures

Heat-induced conformational changes and heat-induced gels of whey and egg white albumen, and their major components were studied under physicochemical conditions that favour protein-protein interactions. We used differential scanning calorimetry (DSC) to compare their conformational heat stability, through the characteristic temperature (Θ_max) corresponding to the maximal heat flow and the overall calorimetric heat of reaction (Δ_r H _cal). Times needed to observe sol-gel state transitions at various temperatures were determined by a tilting test and the corresponding time-temperature experimental points were best fitted to two successive Arrhenius plots intersecting at Θ～Θ_max corresponding to the major protein component for whey proteins and to a minor protein component for egg white albumen. Observations of gel-networks by scanning electron microscopy indicated a wide range of stuctural patterns, depending on the composition of protein solutions. The results are discussed in terms of the temperature of maximal rate of heat-induced conformational changes and of sol-gel state transitions of protein molecules.     

Application of Neumann–Kopp rule for the estimation of heat capacity of mixed oxides

The empirical Neumann–Kopp rule (NKR) for the estimation of temperature dependence of heat capacity of mixed oxide is analyzed. NKR gives a reasonable estimate of C_pm for most mixed oxides around room temperature, but at both low and high temperatures the accuracy of the estimate is substantially lowered. At very low temperatures, the validity of NKR is shown to be predominantly determined by the relation between the characteristic Debye and Einstein temperatures of a mixed oxide and its constituents. At high temperatures, the correlation between their molar volumes, volume expansion coefficients and compressibilities takes the dominance. In cases where the formation of a mixed oxide is not accompanied by any volume change, the difference between dilatation contributions to heat capacity of a mixed oxide and its constituents is exclusively negative. It turns out that in the high-temperature range, where the contribution of harmonic lattice vibrations approached the 3NR limit, Δ_oxC_p assumes negative values. For more complex oxides whose heat capacity has contributions from terms such as magnetic ordering, electronic excitations, the applicability of NKR is only restricted to lattice and dilatation terms.     

Relationship between oxygen self-diffusion and debye temperature in the polycrystalline magnesium aluminum ferrite series,MgAl2−xFexO4

Self-diffusion coefficients of oxygen in a spinel solid solution system, MgAl_2−xFe_xO₄, have been measured by a gas-solid isotope-exchange technique using¹⁸O as a tracer. Mo¨ssbauer spectra of the same spinel solid solution have been studied over the temperature range where the materials were paramagnetic. The line broadening characteristic of Mo¨ssbauer spectra of these materials was interpreted in terms of distribution of the electric field gradient at⁵⁷Fe nuclei. Debye temperatures were calculated from the temperature dependence of the absorption intensity of their Mo¨ssbauer spectra. The compositional dependence of the Debye temperature from the Mo¨ssbauer effect followed that of the activation energy of diffusion. A linear relationship between the activation energy and the square of the Debye temperature exists.     

Low temperature and high pressure thermoelastic and crystallographic properties of SrZrO3 perovskite in the Pbnm phase

The thermoelastic and structural properties of SrZrO₃ perovskite in the Pnma (Pbnm) phase have been studied using neutron powder diffraction at 82 temperatures between 11 K and 406 K at ambient pressure, and at sixteen pressures between 0.07 and 6.7 GPa at ambient temperature. The bulk modulus, derived by fitting the equation of state to a second order Birch-Murnaghan equation-of-state, 157(5) GPa, is in excellent agreement with that deduced in a recent resonant ultrasound investigation. Experimental axial compressional moduli are in agreement with those calculated from the elastic stiffness coefficients derived by ab-initio calculation, although the experimental bulk modulus is significantly softer than that calculated. Following low temperature saturation for temperatures less than 40 K, the unit cell monotonically increases with a predicted high temperature limit in the volume expansivity of ∼2.65 × 10⁻⁵ K⁻¹. Axial linear thermal expansion coefficients are found to be in the order α_b < α_c < α_a for all temperatures greater than 20 K with the b axis indicating a weak, low temperature negative expansion coefficient at low temperatures. The thermoelastic properties of SrZrO₃ can be approximated by a two-term Debye model for the phonon density of states with Debye temperatures of 238(4) K and 713(6) K derived in a self-consistent manner by simultaneously fitting the isochoric heat capacity and the unit cell volume. Atomic displacement parameters have been fitted to a modified Debye model in which the zero-point term is an additional refinable variable and shows the cations and anions have well separated Debye temperatures, mirroring the need for two Debye-like distributions in the vibrational density of states. The temperature dependence of the crystal structure is presented in terms of the amplitudes of the seven symmetry-adapted basis vectors of the aristotype phase that are consistent with space group Pbnm, thus permitting a direct measure of the order parameter evolution in SrZrO₃. The temperature variation of the in-phase tilt, which is lost at the phase transition at 973 K, is consistent with tricritical behaviour, in agreement with published results based on high temperature crystallographic data.     

Heat capacity of poly(butylene terephthalate)

The low‐temperature heat capacity of poly(butylene terephthalate) (PBT) was measured from 5 to 330 K. The experimental heat capacity of solid PBT, below the glass transition, was linked to its approximate group and skeletal vibrational spectrum. The 21 skeletal vibrations were estimated with a general Tarasov equation with the parameters Θ₁ = 530 K and Θ₂ = Θ₃ = 55 K. The calculated and experimental heat capacities of solid PBT agreed within better than ±3% between 5 and 200 K. The newly calculated vibrational heat capacity of the solid from this study and the liquid heat capacity from the ATHAS Data Bank were applied as reference values for a quantitative thermal analysis of the apparent heat capacity of semicrystalline PBT between the glass and melting transitions as obtained by differential scanning calorimetry. From these results, the integral thermodynamic functions (enthalpy, entropy, and Gibbs function) of crystalline and amorphous PBT were calculated. Finally, the changes in the crystallinity with the temperature were analyzed. With the crystallinity, a baseline was constructed that separated the thermodynamic heat capacity from cold crystallization, reorganization, annealing, and melting effects contained in the apparent heat capacity. For semicrystalline PBT samples, the mobile‐amorphous and rigid‐amorphous fractions were estimated to complete the thermal analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4401–4411, 2004     

Low-temperature specific heat of polystyrene and related polymers (1.6° to 4°K)

The specific heat of polystyrenes of different origin and molecular weight, of α-substituted and ortho-substituted polystyrenes, and of polystyrenes crosslinked with different amounts of divinylbenzene have been measured between 1.6 and 4°K. The specific heat of all samples shows a temperature dependence that can not be explained by assuming a Debye frequency spectrum for the vibrational modes in these polymers. Good agreement is obtained by fitting the data to a superposition of a Debye T³ term and an Einstein specific heat with a characteristic temperature of 15–18°K. This localized frequency mode may have its origin in the one-dimensional nature of the polymer chain. A simple calculation of the length of a polystyrene chain necessary to obtain these characteristic temperatures shows reasonable agreement with the number of Einstein oscillators observed in the samples.     

Low-temperature thermal properties of Pb2P2Se6 and Pb1.424Sn0.576P2Se6

The heat capacities of Pb₂P₂Se₆ and Pb_1.424Sn_0.576P₂Se₆ were measured at temperatures between 10 and 320 K for the former and between 10 and 330 K for the latter. The heat capacities values were analyzed by harmonic approximation using the Debye and Einstein functions. They were calculated using 3 Debye and 7, 7, 7, 6 Einstein sets. The calculated heat capacities were in good agreement with the observed ones.     

The use of crystallography for the studies of semiconductor materials

The effect of sublattices on the electronic structure of Zn₂SiO₄ crystals is ab initio studied from the first principles calculations at the density functional theory level. Based on the analysis of band spectra and sublattices the different role of Zn and Si cations in the formation of the valence band structure is determined, which is due to the crystal structure and atomic interactions in SiO₄ and ZnO₄ cationic tetrahedra.     

Conformational contribution to the heat capacity of the starch and water system

The heat capacities of starch and starch—water have been measured with adiabatic calorimetry and standard differential scanning calorimetry and are reported from 8 to 490 K. The amorphous starch containing 11–26 wt % (53–76 mol %) water shows a partial glass transition decreasing from 372 to 270 K, respectively. Even the dry amorphous starch gradually increases in heat capacity above 270 K beyond that set by the vibrational density of states. This gradual increase in the heat capacity is identified as part of the glass transition of dry starch that is, however, not completed at the decomposition temperature. The heat capacities of the glassy, dry starch are linked to an approximate group vibrational spectrum with 44 degrees of freedom. The Tarasov equation is used to estimate the heat capacity contribution due to skeletal vibrations with the parameters Θ₁ = 795.5 K, Θ₂ = 159 K, and Θ₃ = 58 K for 19 degrees of freedom. The calculated and experimental heat capacities agree better than ±3% between 8 and 250 K. Similarly, the vibrational heat capacity has been estimated for glassy water by being linked to an approximate group vibrational spectrum and the Tarasov equation (Θ₁ = 1105.5 K and Θ₃ = 72.4 K, with 6 degrees of freedom). Below the glass transition, the heat capacity of the solid starch—water system has been estimated from the appropriate sum of its components and also from a direct fitting to skeletal vibrations. Above the glass transition, the differences are interpreted as contributions of different conformational heat capacities from chains of the carbohydrates interacting with water. The conformational parts are estimated from the experimental heat capacities of dry starch and starch—water, decreased by the vibrational and external contributions to the heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3038–3054, 2001     

The thermodynamic functions of 4f metal dichlorides in the condensed state

The temperature dependences of heat capacity were obtained for solid 4f metal dichlorides LnCl₂ (Ln = La, …, Lu) in the quasi-harmonic approximation over the temperature range from 0 K to the melting point T _m . The correction for systematic underestimation of the lattice heat capacity component in this approximation was determined from high-temperature EuCl₂ heat capacity measurements. The literature data were analyzed to select the temperatures and enthalpies of phase transitions and estimate the heat capacities of the substances in the liquid state. The thermodynamic functions of LnCl₂ in the condensed state were calculated over the temperature range 298.15–2000 K. The calculations were performed taking into account excited electronic states whose energies did not exceed 10000 cm^?1.     

Theory of paramagnetic spin-lattice relaxation in solids. Part I

A method is proposed for calculating T₁ for an isotropic solid described by the Debye model; the formulas reduce the computations of T₁ to determination of the form of the spin-lattice hamiltonian, which is governed by the spin of the paramagnetic particle and by the atomic coordinates. This provides an explanation of the behavior of T₁ over the entire temperature range from a single point of view.The Kronig-van Vleck theory disagrees with experiment at low temperatures; the causes of this are demonstrated, together with the changes in the formulas that are needed to eliminate it. The T₁ for radicals with appreciable anisotropy in g is calculated to illustrate the argument.     

Dependence of the pure quadrupole resonance frequency on temperature for KBrO3

The pure quadrupole resonance frequency of KBrO₃ in the temperature range 4.17–300.16 K was determined experimentally and compared with the model developed by Stahl which contains three adjustable constants. Excellent agreement between the experimental data and the model was obtained when considering only the temperature range 4.17–52 K. As a result of the comparison, the following values are suggested for KBrO₃: the resonance frequency at 0 K is 179.50373 MHz, the Debye temperature, Θ_d, is 108 K, and the rotational energy, Iω_l², of each of the first two modes of oscillation of the BrO₃ group is 1.707 × 10^?18 kg m². Here I is the moment of inertia and ω_l is the lattice vibration frequency. Comparison of model and experimental data over the entire temperature range from 4.17 to 300.16 K shows that the suggested theory reflects very well the general trend of the experimental data but lacks in some detail. Copyright © 2003 John Wiley & Sons, Ltd.     

Ab initio Predictions of Structural and Thermodynamic Properties of Zr2AlC Under High Pressure and High Temperature

The structural and thermodynamic properties of Zr₂AlC at high pressure and high temperature are investigated by first principles density functional theory method. The calculated lattice parameters of Zr₂AlC are in good agreement with the available theoretical data. The pressure dependences of the elastic constants, bulk modulus, shear modulus, Young's modulus, and Vickers hardness of Zr₂AlC are successfully obtained. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. By using the quasiharmonic Debye model, the thermodynamic properties including the Debye temperature, heat capacity, volume thermal expansion coefficient, and Grüneisen parameter at high pressure and temperature are predicted for the first time.