Carbon Debye temperature

At very high pressures, above 12 GPa, and temperatures above 1000 K, a transparent,yellowish, ultra-hard material, believed to consist of the remnants of collapsed molecules, is formed. In several cases ultrasonic, scratch, and indentation studies have shown this material to have a bulk modulus and hardness far exceeding that of diamond [123,131,147], although these reports are by no means uncontested [124,148,149]. The material is extremely disordered and probably has a high fraction of sp2 coordinated bonds, but the structure is unknown. There are some similarities with amorphous carbon (ta-C),but differences in Raman spectra and mechanical properties show that the structures differ. The question of bond types is interesting, since sp2 bonds are known to be stronger than sp3 ones. The materials are semiconducting and have Debye temperatures near 1450 K, somewhat lower than that of diamond [150]. 

Below the Debye temperature, only the acoustic modes contribute to heat capacity. It turns out that within a plane there is a quadratic correlation to the temperature, whereas linear behavior is observed for a perpendicular orientation. These assumptions hold for graphite, which indeed exhibits two acoustic modes within its layers and one at right angles to them. In carbon nanotubes, on the other hand, there are four acoustic modes, and they consequently differ from graphite in their thermal properties. StiU at room temperature enough phonon levels are occupied for the specific heat capacity to resemble that of graphite. Only at very low temperatures the quantized phonon structure makes itself felt and a linear correlation of the specific heat capacity to the temperature is observed. This is true up to about 8 K, but above this value, the heat capacity exhibits a faster-than-Unear increase as the first quantized subbands make their contribution in addition to the acoustic modes. 

The ability to observe the ZPL lines even at room temperature is a result of small electron-phonon coupling, which is the manifestation of large Debye temperature due to the rigidity of the diamond lattice and the small carbon mass. 

The first theoretical work providing information on the Debye temperature (Go) of intermetallic clathrates dates back to the year 1999 [33]. Molecular dynamics calculations for the carbon-framework of type-I and type-II clathrates used a Lennard-Jones potential (later on also for Si-based clathrates [34]). 0d for Ci36 [35] and for Siiae [34] were estimated from the calculated elastic constant Cn applying the empirical relation Qd = —11.3964 + 0.3475 x C — 1.6150 x 10 X Cj 1. Moriguchi et al. [36] used an empirical bond-order potential developed by Tersofif for the calculation of several thermodynamic properties, including the heat capacity, for the type-I and type-II Si networks. From the heat capacity data in the temperature range from 0 to 150 K 6d was extracted applying the Debye-model. The heat capacity, Cy, was calculated by the density functional theory (DFT),... 

These carbon films are considered as dirty metals whose temperature dependence of conductivity would depend on the inelastic mean free path 1 T) [76]. Now, when electron-phonon scattering is dominant, the mean free path will follow the relationship of 1, T) T. At low temperatures (for T < where 0 is the Debye temperature of the material) for both electron-electron scattering and electron-phonon scattering. 

For calcium carbonate, which has 15 degrees of freedom, six will be acoustic vibrations with two Debye temperatures and nine degrees of freedom will be optical vibrations, with an Einstein temperature for each one. The partition function (and the resulting internal energy) contains two Debyean terms and nine Einsteinian terms. 

Polytype Hexagonality D Chemical shift (eV) Effective charge q Ratio of silicon and carbon concentrations CJC, Lattice parameters X-ray and practical density Carbon and silicon vacancy concentration Debye- temperature 0D Formation enthalpy A77°298 (kJ/mol) Entropy °298 (J/mol K)... 

An observation of motion of single atoms and single atomic clusters with STEM was reported by Isaacson et al,192 They observed atomic jumps of single uranium atoms on a very thin carbon film of —15 A thickness or less. Coupled motion of two to three atoms could also be seen. As the temperature of the thin film could not be controlled, no Arrhenius plot could be obtained. Instead, the Debye frequency , kTIh, was used to calculate the activation energy of surface diffusion, as is also sometimes done in field ion microscopy. That the atomic jumps were not induced by electron bombardment was checked by observing the atomic hopping frequencies as a function of the electron beam intensity. 

T. It is always much smaller than rD. Furthermore, there is an apparent trend that as the ratio of 0/e increases the deviation from the Debye model becomes more severe (the solvent propylene carbonate [5] at low temperature shows an especially big deviation from t,). This trend is consistent with theories that go beyond the continuum model (see Section II.E). 

Solution Carbon monoxide has a small electric dipole moment (approx 0.1 Debye), which gives the molecules an energetically preferred orientation as T — 0. However, this dipole moment is so small that the preference is not appreciable until very low temperatures, and the random orientation of the molecules (the dipole has equal probability of pointing in one direction or its opposite) remains as the temperature is lowered. For a mole of CO, each molecule can point in either of two directions and there are 2Na configurations that are about equally probable. This model predicts a residual entropy of... 

The approach of research institutes AGLARG [9] was used for an operative estimation of gas sorption capacity for carbon sorbents. According to it micropore volume and the specific surface area have been chosen as determining parameters. To obtain the function approximating dependence of hydrogen sorption capacity on carbon materials from value of a specific surface area (at pressure 0.1 MPa and temperature 77 K), we used our experimental data (Table 1) and an experimental database (Table 2) of group of institutes - Inorganic Chemistry and Catalysis, Debye Institute, Utrecht University [10],... 

The viscosities of many binary liquid systems display minima as functions of composition at constant temperature, so that negative values of D are also possible. Yajnik and his coworkers (265 ) long ago observed that very frequently an extremum in the isothermal vapor pressure-composition curve is accompanied by an extremum of the opposite sense in the viscosity-concentration curve. Data are apparently not available for solutions of very low-molecular-weight paraffins in carbon tetrachloride, but minima are found for the viscosities of solutions of CC14 with ethyl iodide, ethyl acetate and acetone, so that a minimum appears quite probable for mixtures of small aliphatic hydrocarbons with carbon tetrachloride. If this were true, the downward trend of the Meyer-Van der Wyk data on C17—C31 paraffins, earlier discussed in connection with the polyethylene plots of Fig. 14, would be understood. It will be recognized that such a trend is also precisely what is to be expected from the draining effect of the hydrodynamic theories of Debye and Bueche (79), Brinkman (45 ) and Kirkwood and Riseman (139). However, the absence of such a trend in the case of polyethylene... 

In contrast to molar polarisation calculated from optical refractivities, that calculated from relative permittivities observed at lower frequencies is by no means always independent of temperature. Actually, materials tend to fall into one of two classes. Those in one class show a relatively constant molar polarisation in accord with the simple Clausius-Mosotti relation, whilst the members of the other class, which contains materials with high relative permittivities, show a molar polarisation that decreases with increase in temperature. Debye recognised that permanent molecular dipole moments were responsible for the anomalous behaviour. From theories of chemical bonding we know that certain molecules which combine atoms of different electronegativity are partially ionic and consequently have a permanent dipole moment. Thus chlorine is highly electronegative and the carbon-chlorine... 

On the basis of the study of the solvent, temperature, and pressure effects, we show how the NMR rotational correlation times T2k for a heavy water molecule in neat liquid and organic solvents are cotrelated with the strength of solute-solvent interactions, in particular, H bonds. At room temperature (30 C), the correlation time is 2.1 ps in the random H-bond network in heavy water, whereas it is as small as 0.1 ps in such an apolar, hydrophobic solvent as carbon tetrachlmi because of the absence of the H bonds between water molecules. Pressure distorts H bonds and accelerates the orientational motion of water molecules in neat liquid. I%m evidence is collected for the limitations of the Stdces-Einstein-Debye (SED) law in solution. 

Abstract For three liquids, salol, propylene carbonate, and o-terphenyl, we show that the relaxation time or the viscosity at the onset of Arrhenius behavior is a material constant. Thus, while the temperature of this transition can be altered by the application of pressure, the time scale of the dynamics retains a characteristic, pressure-independent value. Since the onset of an Arrhenius temperature-dependence and the related Debye relaxation behavior signify the loss of intermolecular constraints on the dynamics, our result indicates that intermolecular cooperativity effects are governed by the time scale for structural relaxation. 

For complex ions of similar size within a homologous series, it is expected that t//tc remains relatively constant for different solvents at a given temperature, in accordance with the Stokes-Einstein-Debye model. From the slope of the plot 5iso versus y/(Az/f/2)/A av shown in Fig. 16, the correlation time constants of a series of tra 5 -[Co(acac)2XY] complexes were estimated and the results were compared favourably with the Tc obtained from the relaxation measurements of the methene carbons (see Table 5). 

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