Continuous variation

While the phase rule requires tliree components for an unsymmetrical tricritical point, theory can reduce this requirement to two components with a continuous variation of the interaction parameters. Lindli et al (1984) calculated a phase diagram from the van der Waals equation for binary mixtures and found (in accord with figure A2.5.13 that a tricritical point occurred at sufficiently large values of the parameter (a measure of the difference between the two components). 

Yamada T, Ogaki K, Okubo S and itaya K 1996 Continuous variation of iodine adiattices on Ag(111) eiectrodes In situ STM and ex situ LEED studies 1996 Surf. Sc/. 369 321-35... 

A wavelength selector that uses a diffraction grating or prism, and that allows for a continuous variation of the nominal wavelength. 

Of the three methods, the method of continuous variations, also called Job s method, is the most popular. In this method a series of solutions is prepared such that the total moles of metal and ligand, tot> in each solution is the same. Thus, if ( m)( and ( l)( are, respectively, the moles of metal and ligand in the i-th solution, then... 

In essence, the corrected absorbance gives the change in absorbance due to the formation of the metal-ligand complex. An example of the application of the method of continuous variations is shown in Example 10.7. 

Both the method of continuous variations and the mole-ratio method rely on an extrapolation of absorbance data collected under conditions in which a linear relationship exists between absorbance and the relative amounts of metal and ligand. When a metal-ligand complex is very weak, a plot of absorbance versus Ay or n-J m may be curved, making it impossible to determine the stoichiometry by extrapolation. In this case the slope ratio may be used. 

Bruneau, E. Lavabre, D. Levy, G. et al. Quantitative Analysis of Continuous-Variation Plots with a Comparison of Several Methods, /. Chem. Educ. 1992, 69, 833-837. 

In this experiment the method of continuous variations is used to determine the stoichiometry and equilibrium constant for the organic complex of 3-aminopyridine with picric acid in CHCI3, and the inorganic complex of Fe +with salicylic acid. 

Data from the spectrophotometric titrations of Fe + with SCN , and of Cu + with EDTA are used to determine the stoichiometry of the resulting complexes using the method of continuous variations. 

This experiment describes the use of FIA for determining the stoichiometry of the Fe +-o-phenanthroline complex using the method of continuous variations and the mole-ratio method. Directions are also provided for determining the stoichiometry of the oxidation of ascorbic acid by dichromate and for determining the rate constant for the reaction at different pH levels and different concentration ratios of the reactants. 

Extmsion accounts for about 30% of nylon produced and is used in various processes (24). Nylons can be extmded on conventional equipment having the following characteristics. The extmder drive should be capable of continuous variation over a range of screw speeds. Nylon often requires a high torque at low screw speeds typical power requirements would be a 7.5-kW motor for a 30-mm machine or 25-kW for 60-mm. A nylon screw is necessary and should not be cooled. Recommended compression ratios ate between 3.5 1 and 4 1 for nylon-6,6 and nylon-6 between 3 1 and 3.5 1 for nylon-11 and nylon-12. The length-to-diameter ratio, T/D should be greater than 15 1 at least 20 1 is recommended for nylon-6,6, and 25 1 for nylon-12. 

It has been established, that both DN and Ibp form complex compounds with ions Eu(III), Sm(III), Tb(III) and Dy(III), possessing luminescent properties. The most intensive luminescence is observed for complex compounds with ion Tb(III). It has been shown, that complexation has place in low acidic and neutral water solutions at pH 6,4-7,0. From the data of luminescence intensity for the complex the ratio of component Tb Fig was established equal to 1 2 by the continuous variations method. Presence at a solution of organic bases 2,2 -bipyridil, (Bipy) and 1,10-phenanthroline (Phen) causes the analytical signal amplification up to 250 (75) times as a result of the Bipy (Phen) inclusion in inner coordination sphere and formation of different ligands complexes with component ratio Tb Fig Bipy (Phen) = 1 2 1. 

It is worth noting that in exactly the same way, a material subjected to a continuous variation of strain may have its stress at any time predicted by... 

In general, the number of boosters determines the operational flexibility of the unit with respect to the refrigeration load. A single booster unit operates continuously, regardless of load. A two booster unit can operate at 50% load by shutting off one unit at lower load levels it uses a pressure controller on the steam actuated by the condenser pressure. Because jets are not usually very flexible with respect to steam consumption and vacuum, load control may be in increments as compared to continuous variation. If a 100-ton unit is expected to operate an appreciable portion of the time at 25% of load, it may prove economical to install a four-booster unit and to operate only one for this period. Auxiliary ejectors remove uncondensed water vapor and air from the main condenser. 

If static capacitors are employed this can be achieved by using several capacitors arranged in units (banks) which can be switched in or out as required. This variation can only be carried out in discrete steps. In the case of the A.C. machine (the synchronous condenser), it is possible to obtain a continuous variation. The switching of the equipment can be carried out by an operator or automatically in response to the output from a power factor-sensing instrument. 

Except for zones below the level of permanent ground water where the environment is water-saturated, and for zones of dry surface sand, continual variation may be expected to occur in the water content of soils. This is usually dependent on rainfall, snow, flooding and such climatic influences, though irrigation practices in many agricultural areas influence water content and hence the corrosion rates. 

The Hull cell cathode has a continuous variation of current density along its length, and there are equations which give the primary current density at any point not too near the end. If the local thickness is measured at two points for which P is known, Tcan be calculated. The real current distribution is a function of cathode and anode polarisation as well as of the resistance of the electrolyte. The metal distribution ratio will be... 

Continuous variation mixing experiments in aqueous media have shown that A12 and Poly U form a complex with a 1 1 stoichiometry in bases, and T12 and... 

The alternating component of the applied voltage causes a continuous variation in the efficiency of the x-ray excitation (Step II) during each cycle of operation. A polychromatic x-ray beam has a different total absorption coefficient and a different ratio of photoelectric to scattering absorption coefficient for each wavelength (Step V). It is very difficult to take account of these factors exactly. Fortunately, reasonable estimates will suffice in the making of the calculations for Table 4-4 and Figure 4-15. The efficiency has been taken as that for the root-mean-... 

We shall return to this topic in Chapter 9. Remember that the unequal distribution of electrons within bonds results in a continuous variation from covalent to ionic bonding. 

Within the framework of the present chapter the domain G -f F of continuous variation of an argument (point) is replaced by some discrete set of points (nodes) known as a grid. 

The transverse magnetization and the applied radiofrequency field will therefore periodically come in phase with one another, and then go out of phase. This causes a continuous variation of the magnetic field, which induces an alternating current in the receiver. Furthermore, the intensity of the signals does not remain constant but diminishes due to T and T2 relaxation effects. The detector therefore records both the exponential decay of the signal with time and the interference effects as the magnetization vectors and the applied radiofrequency alternately dephase and re-... 

The wavelet interval-tree of scale is constructed fi om log 2 N distinct representations, where N is the number of points in the record of measured data. This is a far more efficient representation than that of scale-space filtering with continuous variation of Gaussian a. 

In this procedure, the length coordinate of the system is divided into N finite-difference elements or segments, each of length AZ, where N times AZ is equal to the total length or distance. It is assumed that within each element, any variation, with respect to distance, is relatively small. The conditions at the midpoint of the element can therefore be taken to represent the conditions of the element as a whole. This is shown, in Fig 4.1, where the average concentration of any element n, is identified by the midpoint concentration C . The actual continuous variation in concentration with respect to length is therefore approximated by a series of discontinuous variations. 

In a second-order phase transition, volume and entropy experience a continuous variation, but at least one of the second derivatives of G exhibits a discontinuity ... 

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