Excess contribution

In Fig. 12.16, the metallized wafer, in contrast to the non-metallized one, shows a large excess contribution in the heat capacity. The excess heat capacity cannot be attributed to the term CM of eq. (12.11), since the material of the two wafers is the same, and they were produced in the same run of neutron irradiation. Instead, this excess is to be attributed to the metallization process. 

These contributions, in order to be deductible, must be paid by the last day of your taxable year, December 31 in most cases. For taxable years beginning after 1976, this requirement has been changed so that contributions may be made not later than the 45th day after the end of the taxable year and still be deductible for that taxable year. In addition these contributions must be in cash they may not be in property. There are times when an individual, by the last day authorized for making such contributions, does not have a complete picture of his total earnings for that year. Therefore, it is possible that he may contribute in excess of 15% of his earned income. If that were to occur, the individual would be able, prior to the due date of his return, to get back such excess contributions, plus interest on such excess, and thereby avoid a 6% excise tax penalty on the excess that was made. However, if the contributions are not returned, the employee is subject to the 6% excise tax penalty. 

In order for the contributions to be deductible, payments for both cash and accrual basis taxpayer may be made no later than the due date of the income tax return. If a contribution is made in excess of the 15% or 7500 limitations, the excess is subject to a yearly 6% excise tax penalty until such excess contribution is fully utilized. Distributions under a Keogh Plan may not commence before an individual reaches age 59%, except for reasons of disability or death. Like the individual retirement account, distributions must commence no later than the taxable year in which the individual attains age 70%. 

The intercept term C Ar/ Ar)o, which accounts for igneous, metamorphic, or atmospheric sources, is regarded as the excess contribution present at time = 0, whereas the second term is the radiogenic component accumulating in the various minerals of the isochron by decay of If all the minerals used to construct the isochron underwent the same geologic history and the same sort of contamination by excess " Ar, the slope of equation 11.100 would have a precise chronological... 

The excess contribution is due to the distribution of the valence electrons over the energy levels, and includes the splitting of the ground term by the crystalline electric field (Stark effect) and is called the Schottky heat capacity or Schottky anomaly. It can be calculated from... 

The data shown in fig. 10 are not the values reported by Gorbunov et al. (1986) and Tolmach et al. (1987, 1990a, 1990b, 1990c), because they did not extrapolate their measurements to 0 K in all cases. To derive S° (298.15 K) we have assumed that the heat capacity of L11CI3 represents the lattice component, and Am at the lower temperature limit is derived from the results for this compound. The excess contribution at this temperature is calculated from the crystal field energies (see table 5) derived from spectroscopic studies of the ions in transparent host crystals (Dieke et al., 1968 Morrison and Leavitt, 1982 ... 

In analogy with the approach that has been described in the section on the low-temperature heat capacity, the high-temperature heat capacity of the LnXj compounds can be described as the sum of the lattice and excess contributions (eq. (1)). However, whereas at low temperature the lattice heat capacity mainly arises from harmonic vibrations, at high temperatures the effects of anharmonicity of the vibrations, of thermal dilation of the lattice and of thermally... 

The heat capacities for the other compounds were derived using the estimation procedure described for the trichlorides, i.e., from the lattice and excess contributions. The former was derived from the enthalpy measurements, the latter from the crystal field energies. As the crystal energies of the tribromides and triiodides are poorly known, we have used the values for the trichlorides to approximate Cexs- The results thus obtained are listed in tables 10 and 11. The calculated data for TmG agree within 2% with the DSC results of Gardner and Preston (1991). 

The recommended enthalpies of formation of the gaseous trichlorides derived from the selected enthalpies of sublimation are shown in table 22. The mean bond energies derived from these values is shown in fig. 40, which reveals the same pattern as for the trifluorides, which should be explained by a f°-f7-f14 linear base variation and an excess contribution which is related to the changes in the electronic nature of the lanthanide(III) ions. 

The variation in the heat capacity and entropy of the solid lanthanide trihalides can be described by a lattice contribution that linearly varies with atomic number within each crystallographic class of compounds, and an excess contribution that depends on the electronic configuration (crystal field) of the lanthanide ions. A distinct difference is observed between... 

More restrictive, but perhaps more convenient, one can separate out ideal gas and excess contributions ... 

Analogously we have to proceed if we are measuring in the orthogonal direction the results will be completely different (space charge profile, core effects). Even though the overall effect can be obtained more precisely by a superposition of bulk values and interfacial excess contributions, it is more convenient for large space... 

The quantity of primary interest in our thermodynamic construction is the partial molar Gihhs free energy or chemical potential of the solute in solution. This chemical potential depends on the solution conditions the temperature, pressure, and solution composition. A standard thermodynamic analysis of equilibrium concludes that the chemical potential in a local region of a system is independent of spatial position. The ideal and excess contributions to the chemical potential determine the driving forces for chemical equilibrium, solute partitioning, and conformational equilibrium. This section introduces results that will be the object of the following portions of the chapter, and gives an initial discussion of those expected results. 

Similar reasoning can be applied to the situation after Immersion. Then also an adsorbate is present, of which the enthalpy is also written as the sum of two ideal terms and an excess contribution. The result Is... 

When analyzing thermodynamic properties of polymer solutions it is sufficient to consider only one of the components, which for reasons of simplicity normally is the solvent. It is convenient to separate Eq. (3.88) for solvent (i = 1) into ideal and nonideal (or excess) contributions by defining... 

Comparison of these two equations shows that for dilute polymer solutions, Flory-Huggins theory predicts the excess contribution to be... 

The interfacial free energy is then defined as the excess contribution of a system such as that considered in fig. 35a, containing one interface, and a homogeneous system where 4> z) = 4>a everywhere. Denoting the surface area of the interface by A, we thus obtain the interfacial tension fml [eq, (4)] as... 

It has proven to be useful to decompose the Helmholtz free energy functional A[p(N)], where p(N) is the N-body particle density, into an ideal contribution from non-interacting particles and an excess contribution,... 

Obviously, the problem posed by Eqs. (1), (2) is very difficult and an exact analytic solution does not exist. So Flory and Huggins and others [1,2,13-22] resorted to drastic approximations. Rather than presenting the mathematical details of their calculations, we shall only discuss the physical content of their final result here. Their excess contribution to the free energy of mixing becomes... 

But the right-hand term in (17-16) is identical to the second term on the right-hand side of (17-13). Thus, the change in excess enthalpy is equal to the excess contribution to the minimum rate of work. Consequently, the rate of heat transfer is equal to only the ideal contribution to the minimum rate of work. 

The important conclusion is that all of the deviations from ideal gas behaviour are due to the presence of interactions between the atoms in the system, as calculated using the potential energy function. This energy function is dependent only upon the positions of the atoms and not their momenta, and so a Monte Carlo simulation is able to calculate the excess contributions that give rise to deviations from ideal gas behaviour. 

The relationship between CTA and A " ", Eq. 25, has been tested on a collection of bonds and molecules. Linear function (A R) vs CTA was confirmed [60], and included even the hydrides never properly accounted for by the Pauling method. However, the non-zero intercept for a group of considerably ionic halides indicated, that CTA and A " " may differ by some additive excess contribution [60]. Further study is needed in order to disclose the hidden beauty of the Pauling scale. 

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