Anharmonic effects in the specific heat of aluminum

The specific heat at constant pressure, C _p , of aluminum has been measured by Leadbetter between 300 and 772 K and by Brooks and Bingham between 330 and 893 K. Both sets of data are converted to the specific heat at constant 0 K volume, C _v0, by the Slater-Overton method, based on the equation of state and not the Debye type of theory. Corrections to the work of Overton are given. Our analysis shows that the C _v0 obtained from Leadbetter's data remains below 3R up to 750 K, whereas it becomes >3R for the Brooks and Bingham data in the temperature range 650–850 K. Calculations of C _v0 (harmonic + anharmonic) from three pseudopotentials are reported for (a) Harrison modified point ion potential with Hubbard exchange and correlation factor in the dielectric function, (q); (b) Ashcroft pseudopotential with the same (q) as in (a); and (c) Dagens-Rasolt-Taylor (DRT) M2 pseudopotential with Geldart-Taylor (q). The shape of the C _v0 curve is found to be similar for all three potentials. For DRT potential, C _v0 reaches 3R at 700 K, whereas the other two barely approach 3R about 900 K. The anharmonic contribution to C _v0 is a factor of two larger for the Dagens et al. compared to the other two potentials. There is a marked difference between the C _v0 curve from the analysis of the Brooks and Bingham data and the theoretical curves. It appears that the experimental points are too high from about 500 K up. The C _v0 curve from Leadbetter's data is very similar to the three theoretical curves, but the results appear to be too low. A remeasurement of the specific heat from 500 K to the melting point is needed.     

Electronic structure of boron-doped diamond with B–H complex and B pair

The electronic structure of boron–hydrogen complex and boron pair in diamond are studied by first-principles density-functional calculations with supercell models. The electronic structure calculated for the B–H complexes with C_2v or C_3v symmetry and the nearest-neighbor B pair is used to interpret recent experimental results such as B 1s x-ray photoemission spectroscopy, ¹¹B nuclear quadruple resonance and B K-edge x-ray absorption spectroscopy, which cannot be explained solely by the isolated substitutional boron.     

Molar Heat Capacity at Constant Volume of Trifluoromethane (R23) from the Triple-Point Temperature to 342 K at Pressures to 33 MPa

Molar heat capacities at constant volume (C _v) of trifluoromethane (R23) have been measured with an adiabatic calorimeter. Temperatures ranged from the triple point to 342 K, and pressures up to 33.5 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid and gaseous samples. The samples were of high purity, as verified by chemical analysis. Calorimetric quantities are reported for the two-phase (C ⁽²⁾ _v), saturated-liquid (C or C_x), and single-phase (C _v) molar heat capacities. The C ⁽²⁾ _v data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the two-phase internal energy U ⁽²⁾ and the temperature derivatives of the vapor pressure. The triple-point temperature and the enthalpy of fusion were also measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) is estimated to be 0.7% for C _v, 0.5% for C ⁽²⁾ _v, and 0.7% for C .     

Electronic structure of boron-doped diamond with B–H complex and B pair

Abstract

The electronic structure of boron–hydrogen complex and boron pair in diamond are studied by first-principles density-functional calculations with supercell models. The electronic structure calculated for the B–H complexes with C_2v or C_3v symmetry and the nearest-neighbor B pair is used to interpret recent experimental results such as B 1s x-ray photoemission spectroscopy, ¹¹B nuclear quadruple resonance and B K-edge x-ray absorption spectroscopy, which cannot be explained solely by the isolated substitutional boron.     

Molar Heat Capacity at Constant Volume of 1,1-Difluoroethane (R152a) and 1,1,1-Trifluoroethane (R143a) from the Triple-Point Temperature to 345 K at Pressures to 35 MPa

Molar heat capacities at constant volume (C _v) of 1,1-difluoroethane (R152a) and 1,1,1-trifluoroethane (R143a) have been measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase ((C _v ⁽²⁾ ), saturated-liquid (C or C _x ^' ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 105 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature and the enthalpy of fusion were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) for C _v is estimated to be 0.7%, for C _v ⁽²⁾ it is 0.5%, and for C it is 0.7%.     

Optical and Electrical Properties of Star-Like Fullerene-Containing Polymers

Abstract

Polystyrene and polyethyleneoxide films both containing fullerene, C₆₀, designated as FPS and FPEO were investigated by the ellipsometry, photoluminescence spectra and electrical dc conductivity methods. The FPS and FPEO films display complex refractive index of 1.7 ? 10.05 and 1.45 ? 10.0 respectively. The photoluminescence maximum attributed to C₆₀ shifted to higher photon energies proportionally to with the increase of the number of the polymer rays attached. The shift can be described by the linear relationship ΔE=004N, where ΔE is the shift in eV and N is the number of polymer rays attached. The magnitude of dc conductivity exhibited by the FPS films varied directl proportionally to molar concentration of C₆₀     

Isochoric Heat Capacity Measurements for 2,2-Dichloro-1,1,1-Trifluoroethane (R123) at Temperatures from 167 to 341 K and 1-Chloro-1,2,2,2-Tetrafluoroethane (R124) from 94 to 341 K at Pressures to 35 MPa

Molar heat capacities at a constant volume (C _v) of 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) were measured with an adiabatic calorimeter. Temperatures ranged from 167 K for R123 and from 94 K for R124 to 341 K, and pressures were up to 33 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C ⁽²⁾ _v), saturated liquid (C or C _x ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. Due to the tendency of both R123 and R124 to subcool, the triple-point temperature (T _tr) and the enthalpy of fusion ( _fus H) could not be measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (at the 2 level) for C _v is estimated to be 0.7%, for C ⁽²⁾ _v it is 0.5%, and for C it is 0.7%.     

Molar Heat Capacity (Cv) for Saturated and Compressed Liquid and Vapor Nitrogen from 65 to 300 K at Pressures to 35 MPa

Molar heat capacities at constant volume (C_v,) for nitrogen have been measured with an automated adiabatic calorimeter. The temperatures ranged from 65 to 300 K, while pressures were as high as 35 MPa. Calorimetric data were obtained for a total of 276 state conditions on 14 isochores. Extensive results which were obtained in the saturated liquid region (C_v⁽²⁾ and C_σ) demonstrate the internal consistency of the C_v (ρ,T) data and also show satisfactory agreement with published heat capacity data. The overall uncertainty of the C_v values ranges from 2% in the vapor to 0.5% in the liquid.     

Molar heat capacity at constant volume of difluoromethane (R32) and pentafluoroethane (R125) from the triple-point temperature to 345 K at pressures to 35 MPa

Molar heat capacities at constant volume (C _v) of dill uoromethane (R32) and pentalluoroethane (R125) were measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C _v ⁽²⁾ ), saturated liquid (C orC _x ), and singlephase (C _v) molar heat capacities. TheC data were used to estimate vapor pressures for values less than 0.3 MPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature (T _tr) and the enthalpy of fusion (_fus H) were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-ofvolume work adjustment. The expanded uncertainty (at the two-sigma level) forC _v is estimated to be 0.7%, forC _v ⁽²⁾ it is 0.5%, and forC it is 0.7%.     

Sc2O@C78: Calculations of the yield ratio for two observed isomers

The very recently observed production ratio 3:1 between Sc₂O@C₇₈(C_2v/3) and Sc₂O@C₇₈(D_3h/5) endohedrals can be reproduced in quantum-chemical calculations though only after a transition from the DFT to MP2 approach. It is concluded that the C_2v/3-cage-based species should be lower in the potential energy by about 1.5 kcal/mol.     

Molecular structures of the open-shell IPR isomers of fullerene C90

Fifteen open-shell isomers off the forty six IPR isomers of fullerene C₉₀ were found and investigated: 5 (C_s), 7 (C₁), 9 (C₁), 10 (C_s), 11 (C₁), 20 (C₁), 21 (C₁), 22 (C₁), 23 (C₂), 24 (C₁), 25 (C_2v), 41 (C₂), 42 (C₂), 43 (C₂), and 44 (C₂). According to developed by us approach the positions of single, double, and delocalized π-bonds in the molecules of these isomers are shown for the first time. The obtained results of electronic and geometrical structures are fully supported by DFT method with the B3LYP functional at the 6-31G and 6-31G* levels. Molecules of these open-shell isomers contain different radical substructures (mainly the phenalenyl-radical substructures), they should be unstable and could not be obtained as empty molecules. Nevertheless, there is a possibility of obtaining them in polymeric forms or as endohedral or exohedral derivatives.     

Ideal gas relations for the description of the real gas isentropic changes

Using the best available relations describing the thermal and caloric behaviour of the media H₂O, air, NH₃ and of the refrigerants R12 and R22, numerous isentropic expansions starting at different initial points, have been computed. The results obtained were approximated by explicit relations having mathematical forms similar to those of the ideal gas but with different constants and exponents. The obtained accuracy is remarkable, being for the most cases better than 0.5% and in any case better than 3%. In this way the isentropic change, of the above mentioned media, can be computed by simple explicit relations having as independent variable the Mach number. Considering all the above media, the following general rules can be traced. The specific volume, reduced by the corresponding value of the stagnation point, up to a Mach number of less than 0.7, follows a parabolic law common to all gases considered. The reduced pressure, in the transonic region 0.7≦M≦1.3, has a nearly linear decrease, having a slope, common to all media, and equal to about ?0.605. The reduced nozzle cross-sectional area, for M≦1,2 has a common form given by the relation F^*/F=?0.034+M(2.04?M). The values of the constants and exponents used in the relations cannot be derived from the k _id =C_p/C_v values since they are all the three different isentropic exponents k_p,v, k_T,v and k_p,T involved and further since the true sound velocity α is given by the relation α=(zk_p,v RT)^1/2 and is not approximated by the ideal gas sound velocityα _id=(k _id RT)^1/2.     

Infrared Studies in the 1- to 15-Micron Region to 30,000 Atmospheres

A pressure cell was constructed using a pair of type II diamonds for study of infrared spectra of solids in the 1- to 15-micron region. Using commercial infrared equipment, spectra can be studied routinely to calculated pressures as high as 30,000 atmospheres. Under pressure, bands generally shift to higher frequencies and decrease in intensity. The magnitude of both changes depends on the mode of vibration. Occasionally major changes in spectra occur. In calcite the carbon-oxygen symmetric stretching, mode v₁, becomes active at elevated pressures while the doubly degenerate v₃, stretching, and v₄, bending, frequencies split. From the shift in frequency of v₁ with pressure the “compressibility”, [(−1/R_o) (dR/dp)], of the C—O bond length, R, is calculated to be 2.8×10⁻⁷/atmosphere. Major spectral changes are not observed in the same pressure ranges in other carbonates having the calcite or aragonite structures. The results for calcite may be explained by a shift of the CO3= ion from the trigonal axis under pressure.     

Isochoric heat capacity and coexistence curve of methyl alcohol in the neighborhood of the critical point

A high-temperature adiabatic calorimeter is used to experimentally measure the isochoric heat capacity C _υ of methyl alcohol in the temperature range from 474.39 to 531.63 K along 22 isochores which cover the density range from 136.1 to 750.1 kg/m³. The data on C _υ are used to determine the curve of liquid-vapor phase equilibrium for methyl alcohol. The thus obtained data are described by scaling equations. Comparison is made with results of other researchers.     

Exploitation of symmetry in graphs with applications to finite and boundary elements analysis

We present explicit and parametric forms of transformation matrices for three well‐known and widely used symmetry groups: S₂, C_2v and C_4v. Group representation theory is the most powerful method for exploiting symmetry. We propose an efficient algorithm for systematic generation of reducible representations that can be combined linearly to obtain the projection operators. The exact column spaces of these projection operators are calculated and integrated through special orderings, leading to exact explicit and parametric forms of transformation matrices. The transformation matrices could be used directly for block diagonalization of single‐variable scalar field problems. Another algorithm is proposed to extend the application of the method to nonscalar and multivariable field problems. Finally, the generality and efficiency of the proposed method in relation to computation times and the accuracy of results are illustrated through examples from spectral decomposition, free vibration, buckling of FEMs and boundary element analysis of a symmetric field. Copyright © 2012 John Wiley & Sons, Ltd.     

Wetting and reactivity in Ni–Si/C system: experiments versus model predictions

Wetting of vitreous carbon C_v by NiSi alloys is studied in high vacuum using the sessile drop and dispensed drop techniques. The role of reactions between NiSi and C_v (simple dissolution or SiC formation) on wetting, adhesion and mechanical behaviour of the interface is determined and discussed. The experimental results on reactive wetting are compared with the predictions of two different approaches proposed recently in order to explain the thermodynamics and kinetics of this type of wetting.     

Determination of the pressurising period for stored cryogenic fluids

It is a normal operating condition for a lot of cryogenic storage vessels that no boil-off gas is vented over long periods, which leads to a simultaneous pressure increase of the stored fluid. One main reason therefore is to avoid product losses during transport or between withdrawals. At transport conditions the mixing of the fluid can be assumed to be ideally, which results in a maximum reachable pressurising period. At stationary conditions the pressurising period is expected to be shorter, because a stratification is rising up, so that the heat capacity of the stored fluid cannot be used completely.In a thermodynamic view, an isochore change of state takes place and the heat flux into the vessel rises the internal energy of the fluid. For the representation of the isochore change of state a new developed Δu/v-v-diagram with the 1 × 10⁵ Pa reference as a basis line is introduced. The basis line is linear for the filling rate and functionally connected with the specific volume.For the fluids He and H₂ e.g., Δu/v-v-diagrams are pointed out, using the u- and v-values on the saturation lines for the two phase region and those of some isobar lines for the region above the critical pressure.     

The determination of equations of state for nitrogen and oxygen

Methods of developing accurate thermodynamic equations of state for oxygen and nitrogen using least squares fitting to experimental data from the literature are presented and evaluated. A discussion of the critical evaluation and selection of experimental data is included. The selection of an appropriate functional form for the equation of state, weighting of the data points for least squares fitting, and the simultaneous fitting of various thermodynamic data including PVT data, isochoric heat capacity measurements, and saturation density values are presented. The resulting equation accurately represents all the data, and exhibits correct functional behaviour for the PVT surface and the derivatives used in the calculation of derived properties. Techniques of constraining the equation of state to be consistent with measured critical point parameters and with a vapour pressure equation determined from separate measurements of saturation properties are discussed. The equations developed in the work described here conform to the Maxwell criterion and may be used for the calculation of properties by continuous integration along isotherms through the two-phase region. Comparisons of the selected property values calculated from the equations of state with experimental PVT, C_p, and C_v data used in the development of equations are included. The calculations of the liquid properties by continuous integration along the isotherms and by use of the Clapeyron equation are compared.     

Experimentally determined key curves for fracture specimens

Crack extension during fracture toughness tests of ferritic structural steels cannot be determined from measurements of unloading compliance or electric potential change when the specimen is dynamically tested. Measurements of crack extension in fracture toughness tests are also very difficult when the test temperature is high or the test environment is aggressive. To circumvent this limitation, researchers for years have been developing key curve and normalization function methods to estimate crack extension in standard elastic-plastic fracture toughness test geometries. In the key curve method (Ernst et al., 1979; Joyce et al., 1980) a load-displacement curve is measured for a so-called `source' specimen that is sub size or has a blunt notch so that the crack will not initiate during elastic-plastic loading. The load and displacement are then converted to normalized stress-strain units to obtain a key curve that can be used to predict crack extension in geometrically similar `target' specimens of same material loaded at similar loading rates and tested under similar environmental conditions. More recently Landes and coworkers (Herrera and Landes, 1990; Landes et al., 1991) proposed the normalization data reduction technique – Annex A15 of ASTM 1820 specification – that presents an alternative to the standard E1820 unloading compliance procedure. Although the normalization method works well in many cases, it has serious drawbacks: the load, displacement and crack length at the end of the test must be measured; the prescribed functional form that is fitted to the initial and final data may not be accurate for all materials; and the iterative method of inferring crack length from the combination of the data and the normalization function is complex. The compliance ratio (CR) method developed in this paper determines key curves for predicting crack extension as follows. First, a statically loaded source specimen with the unloading compliance procedure specified in ASTM 1820. Second, the so-called CR load-displacement curve is calculated for the source specimen, which is the load-displacement record that would have been obtained if the crack had not extended. Third, non-dimensionalizing the CR load by the maximum load and the displacement by the elastic displacement at the maximum load, P ^* _i/P _max and v _i/v _{el max} from the source specimen yields the adjusted key curve. Analysis of extensive data shows that the key curve is independent of notch type, initial crack length and temperature. But it is dependent on specimen size and steel type. Assuming that the key curves of the source and target specimens are one and the same, the compliance of the target specimens are calculated with a reverse application of the compliance ratio method, and the crack length is obtained using the equations in ASTM E1820. The CR Method is found to be much simpler than the normalization method described in the Annex A15 of ASTM 1820. With the compliance ratio method, Joyce et al. (2001) successfully predicted crack extension in dynamically loaded specimens using a key curve of a statically loaded specimen.     

The three isentropic exponents of dry steam

The isentropic change of an ideal gas is described by the well known relations pv^k=const, Tv^(k−1) =const and p^(1−k)T^k=const, where the exponent k is defined as the ratio of the constant pressure to the constant volume specific heat, k=c_p/c_v. The same relations are also used for real gases if small or differential isentropic changes are considered. A better examination of the differential isentropic change shows that for p, v, T systems, there are three different isentropic exponents corresponding to each pair formed out of the variables p, v, T. These three exponents noted k_T,p, k_T,v, k_p,v after the corresponding pair of variables used, are interconnected by one relation, and accordingly only two out of the three are independent. The analysis of the present paper leads to the conclusion that calculations encountered in real gas isentropic change, with the exponent k taken as the ratio of the local specific heat values may lead to incorrect results. The numerical values of these exponents for steam, have been calculated and are presented. It can be seen that the deviations obtained, in comparison to the use of conventional k=c_p/c_v values are considerable.