Extinction Symbol

The eombination of the information on the Laue group with the analysis of the systematieally absent reflections allows the determination of the so-called Extinction symbol fES). In the International Tables for Crystallography the list of extinetion symbols is given per erystal system. There are 14 ES for the... 

Table 7.1 Some extinction symbols and the eorresponding compatible space groups.

The ES does not unambiguously define the space group. Table 7.1 shows some extinction symbols and the corresponding compatible space groups. 

This is based on the evaluation of the joint probability /7(Egr P), where Egj-denotes the extinction symbol, and P = (A, G... /n) are the correlated reflection intensities obtained from the linear least-squares Pawley refinement, when the most general extinction group of the crystal system under consideration is adopted. From Bayes s theorem ... 

The prior probability distribution (Egi-) is constant because all the extinction symbols are assumed to be equally probable / (P) is also constant because data do not change by varying the extinction group. Accordingly ... 

The algorithm provides a probability value for each extinction symbol compatible with the lattice symmetry established by the indexing procedure. 

Luzzati, V., Vargas, R., Gulik, A., Mariani, P., Seddon, J. M. Rivas, E. (1992). Lipid polymorphism a correction. The structure of the cubic phase of extinction symbol Fd— consists of two types of disjointed reverse micelles embedded in a three-dimensional hydrocarbon matrix. Biochemistry, 31(1), 279-85. 

Throughout this manual the term extinction (symbol E) is employed. The extinction is defined as log 1 1 where and 1 are incident and transmitted light intensities, respectively. Spectrophotometers are calibrated directly in extinction units (also called optical density or absorbency). If the absorptiometer employed reads percentage transmission, T, calculate E as logio(100/r). The use of transmission values in absorptiometry is to be discouraged as they are rarely if ever simply related to the concentration of substance being measured. 

This is the fundamental equation of colorimetry and spectrophotometry, and is often spoken of as the Beer-Lambert Law. The value of a will clearly depend upon the method of expression of the concentration. If c is expressed in mole h 1 and / in centimetres then a is given the symbol and is called the molar absorption coefficient or molar absorptivity (formerly the molar extinction coefficient). 

Experimental (symbols) and computed (lines) extinction stretch rates of w-decane/02/N2 mixtures with T, = 400 K. The molar ratio of N2/ (Nj + O2) is 0.84. 

Profile comparison of temperature, velocity, major species (CH, Oj, CO, COj, and HjO), and minor species (H, O, and OH) at the extinction state using different outer-flow conditions, for counterflow twin-stoichiometric methane/air flames. For clarity, the symbols do not represent the actual grid distribution employed in the calculation. 

The right part of equation [4], E = e c d, represents Lambert-Beer s law. E is called the extinction, c is the substance concentration, and d is the thickness of the sample. The E values span from 0 (this is the case when all light is transmitted and no absorption takes place, i.e., 1 = Iq) to inhnity, °o (this is the case of maximal extinction when no incident light is transmitted, i.e., 1 = 0). Realistic E values that can be correctly measured by normal spectrometers range between 0 and 2. Instead of using the E expression for extinction, A for absorbance is often used. E and A are dimensionless values, i.e., numbers without units. Nevertheless, OD, the symbol for optical density, is often added to E and A in order to clarify their meanings. 

Early studies of Mg isotope ratios in geological materials used the notation A Mg to mean per mil deviations from a standard as expressed in Equation (1) above, a convention that persists today (e.g., Elsu et al. 2000). The values assigned to A "Mg in those studies represent the level of mass-dependent isotopic fractionation relative to the standard. The same convention defined fi Mg as the per mil deviation from the standard after correction for the mass fractionation evidenced by A "Mg. In this system of nomenclature, A values refer to mass dependentfractionations while 5 values refer to deviations from mass-dependent fractionation (i.e., the S Mg defines excesses in Mg relative to mass fractionation attributable to decay of the extinct nuclide Al). In some cases A "Mg has been replaced by the symbol Fn,g (Kennedy et al. 1997) where the F refers to fractionation. ... 

The fifth letter in the Greek alphabet hence, used to denote the fifth in a series (for example, the fifth methylene carbon in a fatty acid). 2. Symbol for molar absorption coefficient or extinction coefficient. 3. Symbol for permittivity (cq refers to permittivity of a vacuum refers to relative permittivity). 4. s, Symbol for degree of activation (lUB (1982) Eur. J. Biochem. 128, 281). 5. 8i, Symbol for degree of inhibition. 6. Symbol for efficiency. 7. Symbol for linear strain. 8. Symbol for emit-tance. 

A fundamental unit in spectroscopy (synonymous with molar extinction coefficient) and symbolized by e. It is equal to the absorbanee of light per unit path length and per unit eoncentration. See Absorption Spectroscopy Beer-Lambert Law... 

Figure 9. Stoichiometry between mal-ondialdehyde formation and Os uptake. The data from Figure 8 was used to construct this curve, by converting ml of Os taken up into moles by the perfect gas volume at 25°C (24 l/mole) and by converting the TEA reactant value into malondialde-hyde formed by using an extinction coefficient of 155 mM cm (23). Different symbols refer to separate experiments.

Fig. 3.8. Extinction angles % vs. reduced shear rate for solutions of a high density polyethylene fraction (Dow Chem. Corp.) in transdecalin at 160° C (75). The concentrations are indicated near the curves in g/100 cm. Open and closed symbols indicate repeat measurements. The dotted line gives the extinction angle vs. at zero concentration, as obtained by linear extrapolation at several...

When concentration is expressed in g/100 ml, k is described as the specific absorbance and given the symbol A cm or A(l%, 1 cm), defined as The absorbance of a 1% w/v solution in a cell of 1 cm path-length . It is usually written in the shortened form Ai and is widely used in analytical chemistry. It was formerly known as the specific extinction coefficient , symbol or E (1%, 1 cm). American convention recognises the constant k as absorptivity (a, litre/g/cm) defined as the absorbance of a 1 g/litre solution in a cell of 1 cm path-length . These terms for absorptivity can be readily inter-converted, as follows... 

Figure 1 Phanerozoic carbon isotope record. Mass extinction intervals are shaded in gray (widths do not correspond to durations of inserts) (a) global marine carbonate record (after Veizer et al, 1999) (b) marine carbonate record from the Late Ordovician of the Baltic States (after Brenchley et al, 1994) (c) Late Devonian marine organic carbon record from New York State (after Murphy et al, 2000) (d) Late Permian marine carbonate record from China (after Bowring etal, 1998) (e) Late Triassic marine organic carbon record from Canada (after Ward etal, 2001) (f)Late Cretaceous-early Tertiary record of the carbon isotopic difference between fine fraction and benthic carbonate (left panel), between shallow dwelling planktonic and benthic foraminifera (open symbols, right panel) and between more deeper dwelling planktonic and benthic foraminifera (filled symbols, right panel) from the south Atlantic...

All the probabilities of the symmetry operators are combined to provide the probability of the extinction group. For example, in the orthorhombic system, the probability of the extinetion symbol P— is given by ... 

We have used the symbols and terminology recommended by the journal Analytical Chemistry. Other terms— such as optical density (OD) in place of absorbance, and extinction coefficient in place of absorptivity—may appear, especially in the older literature, but their use is not now recommended. Table 16.4 lists some of the older nomenclature. 

The quantity Bf23Q3 can be written as A and is known as the decadic absorbance, or simply as the absorbance. This is the term recommended in the SI (see Appendix A). However the terms decadic extinction and optical density are still commonly used, and the student should be familiar with them. The quantity h/2.303 (i.e., the absorbance divided by the light path) is called the linear decadic absorption coefficient and usually is given the symbol a. Thus equation (2.9) can be written as... 

Since the molecular extinction coefficient s cannot be independently determined, we have two equations for the three unkno vns s, a, and K. It is therefore necessaiy to combine the results for at least two solutions to determine K. We denote quantities relating to two experiments by primed and unprimed symbols. We farther use the abbreviations... 

Fig. 9.5 (a) Bifurcation diagram for depensation growth for a = 0.1 and D = r =. Solid lines correspond to stable branches and the dotted lines to unstable branches. Symbols depict numerical results. Vertical dashed lines separate the extinction, relative extinction/survival, tind survival regions, (b) Plot of the critical initial density vs the patch size for the relative extinction/survival region... 

In this model, the symbols have the following meaning. ( )R(a3) ao(l)HD(a3) is the optical rotation produced by the vapour and depends on the number of absorption lengths ao and on the lineshape function D(o)) which takes the form of a Doppler-broadened dispersion curve for magnetic and electric field induced rotation ( )r will depend on the strength of the field and D(oa) on the direction and type of field (see table 2). The transmitted intensity 1 - Ij exp[-aoG(o))] where the lineshape function G(o)) for a single spectral component can usually be accurately described by a Doppler-broadened Lorentzian curve. Finally the terms B and C in equation (53) represent respectively the finite extinction ratio of the polarisers and a laser independent... 

From Eq. (1.14), we can see that the real parts of the wavenumber and the refractive index, k and n, respectively, determine the phase velocity of the wave in the medium, whereas the imaginary parts, k and k, determine the attenuation of the electromagnetic field along the direction of propagation of the wave. By virtue of this, the imaginary part of the refractive index, k, is called the extinction coefficient or absorption index. Note that the symbol k is used to designate the wavenumber and the extinction coefficient. To distinguish between them, we label the wavenumber with a hat, as k. 

Figure 10.12 Comparison of the axial profiles of (a) propane mass fraction, (b) wall and bulk gas temperature and (c) Nusselt number obtained from CFD simulations (symbols), pseudo-2D model with Nu/Sh fits (solid lines) and pseudo-2D model with constant Nu/Sh (dashed lines) near extinction, i.e. with ks = 20W/m K ...

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