Radius, effective

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Let us consider the calculation of sensitivity threshold in the case when the cracks are revealing by PT method. Constant distance H between crack s walls along the whole defect s depth is assumed for the simplicity. The calculation procedure depends on the dispersity of dry developer s powder [1]. Simple formula has to be used in the case when developer s effective radius of pores IC, which depends mainly on average particle s size, is smaller than crack s width H. One can use formula (1) when Re is small enough being less than the value corresponding maximum sensitivity (0,25 - 1 pm). For example. Re = 0,25 pm in the case when fine-dispersed magnesia oxide powder is used as the developer. In this case minimum crack s width H that can be detected at prescribed depth lo is calculated as... 

Calculate the vapor pressure of water when present in a capillary of 0.1 m radius (assume zero contact angle). Express your result as percent change from the normal value at 25°C. Suppose now that the effective radius of the capillary is reduced because of the presence of an adsorbed film of water 100 A thick. Show what the percent reduction in vapor pressure should now be. 

Hydration and solvation have also been studied by conductivity measurements these measurements give rise to an effective radius for the ion, from which a hydration number can be calculated. These effective radii are reviewed in the next section. 

Figure 9.10 Schematic relationship between the radius Rq of an unsolvated sphere and the effective radius R of a solvated sphere or of a spherical volume excluded by an ellipsoidal particle rotating through all directions.

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). 

Ri = effective radius of miter bend, defined as the shortest distance from the pipe centerhne to the intersection of the planes of adjacent miter joints 0 = angle of miter cut, °... 

Similarly, the assumption that the contact area is small enough that the particle can be represented by an elastic half space allows the radii of the two contacting particles to be combined into a single effective radius that represents how the contacting shapes interact. 

This allows for the equivalence between crossed cylinders and the particle on a plane problem. Likewise, the mechanics of two spheres can be described by an equivalently radiused particle-on-a-plane problem. The combination of moduli and the use of an effective radius greatly simplifies the computational representation and allows all the cases to be represented by the same formula. On the other hand, it opens the possibility of factors of two errors if the formula are used without realizing that such combinations have been made. Readers are cautioned to be aware of these issues in the formulae that follow. 

The effective radius of H in II2 is 0.375 A. In other compounds, however, a lower value is operative from the hydrogen halides and other compounds this is found to be 0.29 A, as given in Table VI. 

Other Covalent Radii. In Cu20 and Ag20 each metal atom is equidistant from two nearest oxygen atoms, the interatomic distances corresponding to the radius values 1.18 and 1.39 A for Cu1 and Agl with coordination number two. In KAg(GN)2, in which each silver atom is similarly attached to two cyanide groups1), the effective radius of Agl is 1.36 A. It has been pointed out to us by Dr. Hoard that the work of Braekken2) indicates the presence of strings —Ag—G=N—Ag—G... 

The general geometrical problem of the packing of spheres has not been solved. An example of closest packing of atoms with some variation in effective radius is the icosahedral packing found (13) in the intermetallic compound Mg3B(Al,Zn) (Fig. 1). The successive layers in this structure contain 1, 12, 32, and 117 spheres. These numbers are reproduced (to within 1) by the empirical equation (12)... 

Rough quantitative calculations of the energy of interaction of the electron pairs and the phonon can be made with use of the force constants for the bonds19 and the changes in the position of the minimum in the potential functions for a bond, as given by the foregoing values of the change in effective radius. 

The foregoing discussion leads to the conclusion that static deformations as well as phonons should be stabilized for superconducting metals by the change in effective radius associated with unsynchronized resonance of electron-pair bonds. Deformation from cubic to tetragonal symmetry, presumably the result of this interaction, has been reported for VsSi at temperatures below 21 K26- 27 and for Nb2Sn at temperatures below 43°K.28... 

Among the tetraborides, UB4 has the smallest volume and hence the smallest effective radius. Thus an actinide element having a metallic radius of 1.59 A (Pu) or smaller forms a diboride, while those having larger radii do not. As in the rare-earth series, the actinides able to form MB4, MBg and MB,2 borides form also MB2 diborides (Table 1). 

Here, is the average effective radius of pore, is surface tension between liquid and vapor, 0 is the contact angle, rj is the dynamic viscosity of the electrolyte, and h is the height elevation of the electrolyte within pore at time r. In the experiment, the amount of electrol he wetted within the anode electrode, m, expressed as h = m/pAP, was measured instead of the height, h. Integrated Eq. (l)for t becomes Eq. (2). 

Here, A is the contacting surface area of anode electrode facing with electrolyte and P is the porosity of anode electrode. The average effective radius of pore,, could be calculated from the results of the capillary rise method using ethanol, which shows a contact angle of 0° with the anode electrode. And then, the contact angle 0 could be acquired as the slope from the plot of m versus... 

Unlike solid electrodes, the shape of the ITIES can be varied by application of an external pressure to the pipette. The shape of the meniscus formed at the pipette tip was studied in situ by video microscopy under controlled pressure [19]. When a negative pressure was applied, the ITIES shape was concave. As expected from the theory [25a], the diffusion current to a recessed ITIES was lower than in absence of negative external pressure. When a positive pressure was applied to the pipette, the solution meniscus became convex, and the diffusion current increased. The diffusion-limiting current increased with increasing height of the spherical segment (up to the complete sphere), as the theory predicts [25b]. Importantly, with no external pressure applied to the pipette, the micro-ITIES was found to be essentially flat. This observation was corroborated by numerous experiments performed with different concentrations of dissolved species and different pipette radii [19]. The measured diffusion current to such an interface agrees quantitatively with Eq. (6) if the outer pipette wall is silanized (see next section). The effective radius of a pipette can be calculated from Eq. (6) and compared to the value found microscopically [19]. 

The radii of both orifices can be either on a micrometer or a submicrometer scale. If the device is micrometer-sized, it can be characterized by optical microscopy. The purposes of electrochemical characterization of a dual pipette are to determine the effective radii and to check that each of two barrels can be independently polarized. The radius of each orifice can be evaluated from an IT voltammogram obtained at one pipette while the second one is disconnected. After the outer surface of glass is silanized, the diffusion-limiting current to each water-filled barrel follows Eq. (1). The effective radius values calculated from that equation for both halves of the d-pipette must be close to the values found from optical microscopy. 

Bismuth forms both 3+ and 5+ cations, although the former are by far the more common in nature. The ionic radius of Bi is even closer to that of La, than Ac, so again La is taken as the proxy. As noted above, Bi has the same electronic configuration as Pb, with a lone pair. It is unlikely therefore that the Shannon (1976) radius for Bi is universally applicable. Unfortunately, there is too little known about the magmatic geochemistry of Bi, to use its partitioning behavior to validate the proxy relationship, or propose a revised effective radius for Bi. The values of DWD u derived here should be viewed in the light of this uncertainty. 

The ionic atmosphere can thus be replaced by the charge at a distance of Lu = k 1 from the central ion. The quantity LD is usually termed the effective radius of the ionic atmosphere or the Debye length. The parameter k is directly related to the ionic strength I... 

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