Impurities distribution coefficient

The two values differ by the impurity distribution coefficient, dangling bonds are the only deep defects which take up donor or acceptor electrons and holes. No other charged gap states of significant density have been found. 

Here 2k 0 and 3are, respectively, the distribution coefficient of i in Si-i binary and Si-i-j ternary systems. Calculated A values for different impurities in pure Si are shown in Fig. 13.23. Most of the common impurities in pure Si have a positive contribution to the impurity distribution coefficient, i.e., the appearance of secondary impurities will increase the distribution coefficient of the primary impurity in silicon. 

The accumulation of impurities in the interfacial region causes an effective increase in incorporation in the crystalline phase relative to that predicted by Eq. (3.5) alone. J.A. Burton et al. developed an expression that quantitatively relates the effective impurity distribution coefficient, K f/, to the equilibrium distribution coefficient, K... 

The distribution coefficient of penicillin G between a solvent (isoamyl acetate or methyl isobutyl ketone (MIBK)) and an aqueous solution is shown in Figure 5.2.4(b) as a function of aqueous solution pH. In the initial aqueous clarified fermentation broth, there are other impurities from which penicillin htis to be separated. Suggest a pH of the aqueous broth at which solvent extraction should take place. Suggest also the pH of an aqueous solution into which the penicillin is to be back extracted from the solvent extract to purify it further. Assume that the impurity distribution coefficient is independent of pH. 

We will work with the mass fractions u,f and U/s of the impurity in the melt and the solid phase, respectively. The impurity distribution coefficient >4 is given by... 

Information on ionization energies, solubiUties, diffusion coefficients, and soHd—Hquid distribution coefficients is available for many impurities from nearly all columns of the Periodic Table (86). Extrinsic Ge and Si have been used almost exclusively for infrared detector appHcations. Of the impurities,... 

In most cases, the activator impurity must be incorporated during crystal growth. An appropriate amount of impurity element is dissolved in the molten Ge and, as crystal growth proceeds, enters the crystal at a concentration that depends on the magnitude of the distribution coefficient. For volatile impurities, eg, Zn, Cd, and Hg, special precautions must be taken to maintain a constant impurity concentration in the melt. Growth occurs either in a sealed tube to prevent escape of the impurity vapor or in a flow system in which loss caused by vaporization from the melt is replenished from an upstream reservoir. 

Fig. 2. Typical binary phase diagram for host and impurity, showing a constant distribution coefficient if impurity content is low. L = liquid composition after some solidification, a = B and small amount of A, /5 = A and small amount of B, = liquidus, and = solidus.

Fig. 3. Impurity concentration profiles resulting from progressive freezing with different values of distribution coefficient k (from eq. 2).

If the impurity or minor component is completely or partially soluble in the sohd phase of the component being purified, it is convenient to define a distribution coefficient /c, defined by Eq. (22-1) ... 

C, is the concentration of impurity or minor component in the solid phase, and Cf is the impurity concentration in the hquid phase. The distribution coefficient generally varies with composition. The value of k is greater than I when the solute raises the melting point and less than I when the melting point is depressed. In the regions near pure A or B the hquidus and solidus hues become linear i.e., the distribution coefficient becomes constant. This is the basis for the common assumption of constant k in many mathematical treatments of fractional solidification in which ultrapure materials are obtained. 

The distribution-coefficient concept is commonly applied to fractional solidification of eutectic systems in the ultrapure portion of the phase diagram. If the quantity of impurity entrapped in the solid phase for whatever reason is proportional to that contained in the melt, then assumption of a constant k is valid. It should be noted that the theoretical yield of a component exhibiting binary eutectic behavior is fixed by the feed composition and position of the eutectic. Also, in contrast to the case of a solid solution, only one component can be obtained in a pure form. 

Component Separation by Progressive Freezing When the distribution coefficient is less than I, the first solid which ciystaUizes contains less solute than the liquid from which it was formed. As the frac tion which is frozen increases, the concentration of the impurity in the remaining liquid is increased and hence the concentration of impurity in the sohd phase increases (for k < 1). The concentration gradient is reversed for k > 1. Consequently, in the absence of diffusion in the solid phase a concentration gradient is estabhshed in the frozen ingot. 

Fig. 4.5. Schematic of top left corner of the "silicon-impurity" phase diagram. To make things simple, we assume that the liquidus and solidus lines ore straight. The impurity concentration in the solid is then always less than that in the liquid by the factor k (called the distribution coefficient).

The selectivity of a gel, defined by the incremental increase in distribution coefficient for an incremental decrease in solute size, is related to the width of the pore size distribution of the gel. A narrow pore size distribution will typically have a separation range of one decade in solute size, which corresponds to roughly three decades in protein molecular mass (Hagel, 1988). However, the largest selectivity obtainable is the one where the solute of interest is either totally excluded (which is achieved when the solute size is of the same order as the pore size) or totally included (as for a very small solute) and the impurities differ more than a decade in size from the target solute. In this case, a gel of suitable pore size may be found and the separation carried out as a desalting step. This is very favorable from an operational point of view (see later). 

It has been determined that there is a distribution coefficient for the impurities between crystal and melt which favors the melt. We can see how this arises when we reflect that impurities tend to cause formation of intrinsic defects within the crystal and lattice strain as a result of their presence. In the melt, no such restriction applies. Actually, each impurity has its own distribution coefficient. However, one can apply an average value to better approximate the behavior of the majority of impurities. 

When a melt-zone is moved through a long crystal, an impurity concentration builds up in the melt zone due to rejection by the crystal as it resolidifies. We can also say that the distribution coefficient favors a purification process, i.e.- k 1. Another reason (at least where metals are concerned) is that a solid-solution between impurity and host ions exists. It has been observed that the following situation, as shown in the following diagram, occurs ... 

The impurity, x, builds up at the solid- liquid interface as the liquid zone moves and the solid forms. We can write for the distribution coefficient ... 

Here, we show two cases for impurity segregation between melt and crystal as it grows in time. Note that an initial purification occurs in both cases but the distribution coefficient for the case on the right is such that the amount of impurity actually incorporated into the crystal, ki Cq. 

The following diagram, given as 6.8.5. on the next page, illustrates further phenomena regarding zone refining. The same situation seen in 6.8.4. occurs for the case at the bottom right of 6.8.5. except that the distribution coefficient is such that the impurity buildup is slower. Nevertheless, simple solid-solution for impurity systems is rarely the norm. The most prevalent case is that of Case III of 6.8.5. Limited solid solution occurs, and we get a two-phase system. 

In addition, if the apparent pKa of an ionizable compound lies within the pH operating range of the column support, the apparent pKa usually can be determined simultaneously with logP by measuring the log distribution coefficient at several pH values (Table 15.11). The main advantages of the procedure are that it gives rapid results, requires little material, and can tolerate impurities. 

The photometric determination of mixtures of aniline, p-nitroaniline and o-nitroaniline was described. Distribution coefficients and separation efficiency of these compounds by LLE in various solvents were compared517. Substituted nitroanilines such as 2-chloro-4-nitroaniline and 2,4-dinitroaniline are intermediates in the manufacture of the dye D C Red No. 36 and were identified as impurities by RP-LC518. A spectrophotometric method was developed for the determination of aniline and m-nitroaniline in a mixture of aniline and nitroaniline isomers by derivatization with 5,7-dichloro-4,6-dinitrobenzofuroxan (244). The relative error of the determination is <5%519. See also Section IV.D.3.b for similar derivatives. 

---