Combined correction term

Although the errors introduced by the atomic-sphere approximation are unimportant for many applications, e.g. self-consistency procedures, there are cases where energy bands of high accuracy are needed, and where one should include the perturbation (6.2) in some form. Below, we derive an expression which accounts to first order for the differences between the sphere, atomic or muffin tin, and the atomic polyhedron, re-establishes the correct kinetic energy in the region between the sphere and the polyhedron, and corrects for the neglect of higher partial waves. The extra terms added to the LMTO matrices which accomplish these corrections are called the combined correction terms [6.2]. 

With the combined correction term included in an LMTO calculation, one... 

The basic output from STR is the canonical structure constants used in CANON and LMTO to calculate band structures. In addition, STR produces a file with real and reciprocal space vectors which is used by the combined correction term programme COR. This file may also be read by STR next time the same crystal structure is encountered, thus saving the time used to generate these vectors. 

Here, the wavelength of the laser light is A, and is a correction term due to the wavelength dependence of the refractive index of the etalon material ( = 0.034 at 514.5 nm when fused silica etalons are used to achieve the necessary delay, or = 0 when a lens combination is used). The optical correction term Av/v results from the change in refractive index of the window material with shock stress (Barker and Hollenbach, 1970). If the measure-... 

For recording of the emission spectrum, the emitted radiation is focussed on the slit of a monochromator and intensities measured attach wavelength. Since sensitivities of photocells or photomultipliers are wavelength dependent, a standardization of the detector-monochromator combination is necessary for obtaining true emission spectrum This can be done by using a standard lamp of known colour temperature whose emission characteristics is obtained from Planck s radiation law. The correction term is applied to the instrumental readings at each wavelength. Very often substances whose emission spectra have been accurately determined in the units of relative quanta per unit wavenumber intervals are... 

It is a remarkable fact that, until 1965, no direct check of the described theory could be given with the aid of flow birefringence. A discussion of possible reasons for such a failure seems worthwile. For this purpose, flow birefringence is expressed in terms of the dimensionless parameter /3. Omitting the correction term A n0 for the solvent, the following expression can be derived by combining eqs. (3.44b) and (3.42) ... 

Nitroglycerin (correctly termed glyceryl trinitrate) is the most successful analogue of organic nitrates (Fig. 10.2). The compound is a triester formed by the nitration of glycerol (1,2,3-propanetriol), and was discovered by Sobrero in 1847 [14]. In pure form, nitroglycerin is an explosive, as was discovered by Alfred Nobel, but when combined with an inert carrier (such as lactose) it is stable enough to be... 

A combination of heat of mixing data and the state parameters of the pure components can be used with Eq. (21) to obtain the interaction term Xjj. It should be noted that is obtained rather than Xj2 as the heat of mixing does not also depend on the entropy correction term, Qj. ... 

Stokes equation is usually considered valid for Reynolds numbers less than 0.25 and the correction term is neglected. Combining equations (6.5) and (6.8) and applying the condition that Re 0.25 gives the upper size limit (upper critical diameter D ). 

Lauritzen (1995) and Lauritzen and Lundberg (1999) have proposed a speleothem delta function . Using the expression for the calcite-water fractionation constant (equation 9) combined with the known exponential dependence of the fractionation constant, acw, on temperature and adding some correction terms the following was obtained. 

Finally, Heithmar et al. [110] combined this concentration procedure with a coupled ICP/MS-technique to overcome matrix-caused interferences in the ICP/MS when environmental samples are investigated. These could be both of spectral nature [111] and of a physical-chemical nature [112]. While the former may be mathematically eliminated by introducing respective correction terms in the calibration function, physical-chemical interferences are best be removed by the above-described separation of the heavy metals to be analyzed from interfering alkali and alkaline-earth metal salts. 

In a subsequent paper, Munn [98] showed that the frequency-dependent local-field tensors accounted for the shift of the poles of the linear and nonlinear susceptibilities from the isolated molecular excitation frequencies to the exciton frequencies. The treatment also described the Davydov splitting of the exciton frequencies for situations where there is more than one molecule per unit cell as weU as the band character or wave-vector dependence of these collective excitations. In particular, the direct and cascading contributions to x contained terms with poles at the molecular excitation energies, but they canceled exactly. Combining both terms is therefore a prerequisite to obtaining the correct pole structure of the macroscopic third-order susceptibility. Munn also demonstrated that this local field approach can be combined with the properties of the effective or dressed molecule and can be extended to electric quadrupole and magnetic dipole nonlinear responses [96]. 

Fig. 9. Correction term for combining diffusional resistances. Courtesy of A. I. Ch. E. Journal (H4).

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