Divalent impurity concentrations

Asay and Gupta [25] measure elastic precursor amplitudes as functions of propagation distance for two different divalent impurity concentrations in <100)-loaded LiF. It is shown that not only does the presence of divalent ions affect the precursor amplitude, but also that the state of the dispersion plays an important part. It is concluded that, for a given concentration of defects, the rate of precursor attenuation is reduced if the defects are clustered. 

The serial sectioning technique was used to investigate the simultaneous diffusion of 85 Sr and Co into single crystals with a divalent impurity concentration of about 5 x 10 2/cm. The data for 600 to 750C could be described by ... 

As mentioned above alkali halide crystals are strongly hardened by small additions of divalent impurities. Data are available for 12 cases, the host crystals NaCl, NaBr, KC1, and KBr with additions of Ca2+, Sr2+, and Ba2+ (Chin, et al., 1973). It was found that the hardness increases depend only on the concentrations of the additions and not on the divalent specie (Ca, Sr, or Ba). However, a dependence on the valence (1, 2, or 3) is observed. It was also found that hardness increment is proportional to the square root of the concentration, (C1/2). 

The effect of atomic motion in the solid state on nuclear resonance line width is illustrated by the behavior of Na resonance from NaCl as a function of temperature 97). In Fig. 9 is shown the variation of the Na line width with temperature for pure NaCl and NaCl doped with an atomic fraction concentration of 6 X 10 of CdCU. As discussed in Section II,A,2 the low-temperature, rigid-lattice line width will narrow when the frequency of motion of the nuclei under observation equals the line width expressed in sec.-. The number of vacancies present should be equal to the concentration of divalent impurities and the jump frequency of Na+ is the product of the atomic vacancy concentration and the vacancy jump frequency... 

Several isovalent ions form solid solutions with KTP (Table II), showing that this structure is relatively tolerant, with respect to isovalent impurities, as are the traditional nonlinear optical oxide crystal structures. But due to the relatively limited range of nonstoichiometry in KTP, aliovalent impurities, such as divalent Ba, Sr and Ca introduced through ion exchange in nitrate melts, which substitute on the K site, are incorporated at concentrations less than one mole percent.(36) Typical impurity concentrations present in flux and hydrothermally grown KTP are shown in Table ID. 

At this point let us briefly consider the formation of associates. The formation of associates between cation vacancies and divalent impurities in alkali halides has already been given as an example. Such reactions are homogeneous solid state reactions, and so the relaxation time for the formation of associates can be calculated in a completely analogous manner to the calculation of the relaxation time for the equilibration of Frenkel defects. The result of such calculations is precisely the same as the result given in eq. (6-5). It is only necessary, in the case of association, to replace the concentration c (eq) = in the denominator by the nearly constant concentration of the corresponding majority defect. In general, in the case of the formation of defect associates, we can conclude that the equilibrium concentration is attained rapidly compared to the time required by defect reactions which occur at sites of repeatable growth. 

As seen from equation (27) the surface concentration of impurity ions depends critically on the difference in binding at the surface from the bulk. The space charge concentration of divalent ions on the other hand depends mainly on the sign of the surface electrostatic potential. Thus, various impurity concentration profiles are possible i.e., enriched/depleted surface monolayers combined with enriched/depleted space charge regions. As discussed later experimental surface analytical techniques have difficulty in distinguishing these possibilities. 

The potential for the formation of ionic crosslinks with Vamac terpolymers precludes the use of fillers that may contain soluble divalent metal ions. Metal stearates, metal stearate-coated fillers, clays, and precipitated silicas are not recommended for use in Vamac terpolymers. Precipitated fillers can contain impurities, which can lead to ionic bonding. Another potential source of soluble divalent metal ions is the pigment used to color mineral-filled compounds. Ionic bonds can significantly increase the viscosity of the uncured stock and increase the compression set of vulcanizates. The effect of metal ions and ionic bonds on stock and vulcanizate properties can vary considerably from batch to batch and is dependent on the impurity concentration in the lot of filler as well as the mixing/processing procedures. 

In this section we are concerned with the properties of intrinsic Schottky and Frenkel disorder in pure ionic conducting crystals and with the same systems doped with aliovalent cations. As already remarked in Section I, the properties of uni-univalent crystals, e.g. sodium choride and silver bromide which contain Schottky and cationic Frenkel disorder respectively, doped with divalent cation impurities are of particular interest. At low concentrations the impurity is incorporated substitutionally together with an additional cation vacancy to preserve electrical neutrality. At sufficiently low temperatures the concentration of intrinsic defects in a doped crystal is negligible compared with the concentration of added defects. We shall first mention briefly the theoretical methods used for such systems and then review the use of the cluster formalism. 

Ionic conduction may dominate the electrical behavior of materials with small electronic conductivity, and its study is useful in the investigation of lattice defects and decomposition mechanisms. In order to establish that conduction takes place by the motion of ions and not of electrons or holes, one can compare the transport of charge with the transport of mass plated out on electrodes in contact with the sample. In practice, this approach is not always feasible because of the very low conductivities associated with ionic motion. When ionic conductivity is suspected one usually attempts to vary the concentration of defects by introducing impurities. For example, for cation conduction in monovalent ionic compounds, addition of divalent cations should enhance the conductivity, since the vacancies produced (in order to ensure charge compensation) lead to enhanced diffusion of the monovalent cation. (The diffusion of a vacancy in one direction is equivalent to the diffusion of an ion in the opposite direction). 

By supersonic expansion of mixed vapours, Kappes and coworkers [28] have obtained clusters containing a small amount of impurity atoms. In particular, we concentrate here on a series of clusters with the formula A B, that is, the cluster contains N atoms of type A (alkali element) and a single impurity of type B (monovalent or divalent). The systems studied are listed in Table 2, along with the experimental abundance maxima in the small-size range. The order chosen for the list in the Table is that of increasing values of dn+ = n +(B) — n (A),... 

Concentration-dependent diffusion coefficients for Sr + in ion-exchanged NaCl were determined by using a sectioning method. Isothermal diffusion annealing was performed at 448 to 683C. The saturation diffusion coefficients, enthalpies and entropies of impurity-vacancy associations were calculated by using the common-ion model for the simultaneous diffusion of divalent ions in alkali halides. The saturation diffusion data could be described by ... 

There are two solutions for the problem of changes in selectivity and retention times caused by carbonate impurities when working with hydroxide eluents, especially in the lowest millimole/Liter concentration range. A very simple and inexpensive solution is provided by adding divalent, electroinac-tive cations such as Ca(II), Sr(II), or Ba(II) to the mobile phase, which improves peak symmetry for sugar alcohols and, therefore, chromatographic efficiency [219-221]. Moreover, the addition of Ba(II) in the form of barium... 

Accordingly, we have a potential difference A0 = 0 — across the interface as illustrated in Figure 3.1. According to Eqs. (3.29) and (3.30), the potential difference A0 between the metal electrode and the electrolyte is also expected to vary by 30 mV when the concentration of the divalent metal ions is changed by one decade. This has been verified experimentally over a lai e concentration range. At lower metal ion concentrations, however, such a measurement can be influenced by other factors. Then a potential drop across the electrode-electrolyte interface is mainly determined by the interaction between the electrode and electrolyte, as will be discussed in detail in Chapter 5, or by impurities such as a redox system or oxygen. 

Shinoda and co-workers [33-35] varied the counterion concentration and found that usually only about half of the expected amount of the counterion was adsorbed at the surface. Recently, An et al. [27] examined the surface excess of perfluorooctanoate counterions with neutron reflection and surface tension measurements. The authors found that a prefactor less than 2 in the Gibbs equation [Eq. (9)1 is an artifact caused by the presence of a divalent cation impurity. Once the impurity, usually calcium, is removed, neutron reflection results are in agreement with surface tension results using a Gibbs prefactor of 2. 

Assume that a compound MX consists of divalent M and X atoms (e.g., ZnS) and the lattice contains a fixed concentration of a singly ionized impurity (e.g., Ag). If the pressure of M vapor is sufficiently high to maintain an excess of X vacancies, we have... 

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