Cell constants

Figure C2.3.3. Molecular packing of SDS monohydrate viewed as projected on the ac plane. This polymoriDh crystallizes in a triclinic cell with unit cell constants a, b and c of 10.423 A, 5.662 A and 28.913 A, respectively, and with a = 86.70°, (3 = 93.44°, y = 89.55°. There are four molecules per unit cell. Adapted from figure 2 of [18].

The values of conductivity k are corrected for the conductivity of the water used. The cell constant 0 of a conductivity cell can be obtained from the equation... 

Conductivity. The standard unit of conductance is electrolytic conductivity (formerly called specific conductance) k, which is defined as the reciprocal of the resistance of a 1-m cube of liquid at a specified temperature m— ]. See Table 8.33 and the definition of the cell constant. 

Physical Properties. The absorption of x-rays by iodine has been studied and the iodine crystal stmcture deterrnined (12,13). Iodine crystallizes in the orthorhombic system and has a unit cell of eight atoms arranged as a symmetrical bipyramid. The cell constants at 18°C (14) are given in Table 1, along with other physical properties. Prom the interatomic distances of many iodine compounds, the calculated effective radius of the covalently bound iodine atom is 184 pm (15). 

C), (cmVohm geqmv) K = Ci/R = specific conductance, (ohm cm) h C = solution concentration, (gequiv/ ) Ot = conductance cell constant (measured), (cm ) R = solution electrical resistance, which is measured (ohm) and/(C) = a complicated function of concentration. The resulting equation of the electrolyte diffusivity is... 

Finally, the use of the constant pressure minimization algorithm allows searching for phenomena that can be considered as precursors of pressure-induced transitions. For example, the predicted behaviour of the anatase cell constants as a function of pressure shows that the a(P) and c(P) plots are only linear for P<4 GPa, the value that is close to both the theoretical and experimental transition pressures. At higher pressures the a constant starts to grow under compression, indicating inherent structural instability. In the case of ratile there is a different precursor effect, nami y at 11 GPa the distances between the titanium atom and the two different oxygens, axial and equatorial, become equal. Once again, the pressure corresponds closely to the phase transition point. 

Resistivity. Control of the resistivity of the mud and mud filtrate while drilling may be desirable to permit better evaluation of formation characteristics from electric logs. The determination of resistivity is essentially the measurement of the resistance to electrical current flow through a known sample configuration. Measured resistance is converted to resistivity by use of a cell constant. The cell constant is fixed by the configuration of the sample in the cell and is determined by calibration with standard solutions of known resistivity. The resistivity is expressed in ohm-meters. 

To measure the conductivity of a solution it is placed in a cell carrying a pair of platinum electrodes which are firmly fixed in position. It is usually very difficult to measure precisely the area of the electrodes and their distance apart, and so if accurate conductivity values are to be determined, the cell constant must be evaluated by calibration with a solution of accurately known conductivity,... 

Ion chromatography (see Section 7.4). Conductivity cells can be coupled to ion chromatographic systems to provide a sensitive method for measuring ionic concentrations in the eluate. To achieve this end, special micro-conductivity cells have been developed of a flow-through pattern and placed in a thermostatted enclosure a typical cell may contain a volume of about 1.5 /iL and have a cell constant of approximately 15 cm-1. It is claimed15 that sensitivity is improved by use of a bipolar square-wave pulsed current which reduces polarisation and capacitance effects, and the changes in conductivity caused by the heating effect of the current (see Refs 16, 17). 

Because of anomalous scattering by H the results for the as-precipitated Ni(OH)2 could not be refined. Nevertheless, cell constants and the O-H bond distance could be determined. The results showed that the as-precipitated material was different from the well-crystallized material. The unit cell dimensions were aQ =3.119 and c0 =4.686 A. Also the... 

Changes in the reference electrode junction potential result from differences in the composition of die sample and standard solutions (e.g., upon switching from whole blood samples to aqueous calibrants). One approach to alleviate this problem is to use an intermediate salt bridge, with a solution (in the bridge) of ions of nearly equal mobility (e.g., concentrated KC1). Standard solutions with an electrolyte composition similar to that of the sample are also desirable. These precautions, however, will not eliminate the problem completely. Other approaches to address this and other changes in the cell constant have been reviewed (13). 

The crystal structures of Hf 2 (OH) 2 (S0O 3 (H2O) i, (14) and Ce2(0H)2(S0i,)3 (H20)it (14) also have been determined and found to be isomorphous to the zirconium compound. The cell constants for this series of four isomorphous compounds reflect the effect of the ionic radii on the dimensions of the unit cell. The values for these cell constants are in Table II. Thus, the cell constants for the zirconium and hafnium compounds are nearly identical and smaller than the cell constants for the cerium and plutonium compounds which are also nearly identical. This trend is exactly that followed by the ionic radii of these elements. 

Cell constants, cesium and hafnium. .53, 55/ Cell coupled with absorption spectrophotometry, electrochemical... 

Analysis of the lanthanide-induced crystalline arrays by negative staining (Fig. 5) or freeze-fracture electron microscopy reveals obliquely oriented rows of particles, corresponding to individual Ca -ATPase molecules [119]. The unit cell dimensions for the gadolinium-induced Ca -ATPase crystals are a = 6. l A, b = 54.4 A and y = 111°. Similar cell constants were obtained for the crystals induced by lanthanum, praseodymium and calcium. The unit cell dimensions of the Ei crystals are consistent with a single Ca -ATPase monomer per unit cell. The space group of the Eptype crystals is PI [119], while that of the E2 crystals is P2 [88,90]. 

In fact, one can construct conductance cells with accurately known values of l and A in which the conductivity of standard electrolytes can be calibrated however, in analytical practice cells with less restricted shape requirements are applied as their cell constants can be adequately established by measurements on a standard electrolyte (generally KC1) of known conductivity (see Fig. 2.3). Suppliers of commercial cells usually give the cell constants. 

Fichtner-Schmittler, H., Lohse, U., Engelhardt, G. et al. (1984) Unit-cell constants of zeolites stabilized by dealumination - determination of al-content from lattice-parameters, Cryst. Res. Technol., 19, Kl. 

Higuchi [11] determined a cell constant, L(cell), using compounds with known diffusion coefficients according to the equation... 

Values for G(unknown) were experimentally determined by using the previously calibrated cells, and these data were used to calculate values for D(unknown) using the cell constants. The overall average value of D(unknown) was 1.11 x 1(T5, which compares well with a reported value of 1.1 X 10 5. The coefficient of variation associated with the diffusion coefficient was 2.7% for one cell and 1.7% for a second cell. This calibration procedure thus provided information about the accuracy and precision of the method as well as the effect of temperature and concentration on the determination of the diffusion coefficient. 

Flow in stirred vessels was also investigated by Holmes et al. (H5), who simulated mass transfer in a diaphragm diffusion cell stirred by magnetic stirrer bars. This is a good example of a simple model study with a direct practical purpose. A minimum stirring speed in such cells is necessary to avoid appreciable errors in the cell constant. The experiment permits this stirring speed to be related to the solution properties. 

The two structurally similar polymorphs of (R,S)-ethambutol dihydrochloride have been shown to bear an enantiotropic relationship, and can reversibly interconvert in a single crystal transformation mode [27]. It was reported that despite the identity in space group type and similarity in unit cell constants, the two forms could be distinguished on the basis of their X-ray powder diffraction and solid-state nuclear magnetic resonance properties. Interestingly, while the (polymorphic forms, the (R,S)-diastereomer was only obtained in two different polymorphs. 

The table 1 shows that the asymmetric stretching vibration, va linearly decreases with increasing amount of silver exchanged. This shift in IR frequency as a function of silver exchange is explained on the basis of cell constant. The silver halide sodalites have a... 

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