Crystallization distribution coefficient

Partitioning of Elements Between Aqueous Solution and Crystal Distribution coefficient (Kd) is given by... 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

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. 

Atmospheric sensitivity renders the preparation of ultrapure samples difficult. Nevertheless, vacuum distillation ", ultra-high-vacuum reactive distillation " and crystal growth purification methods " are described zone-refining methods have been applied on a limited scale only - , presumably because of the high volatility of the metals and the unfavorable distribution coefficients. 

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 ... 

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. 

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

In qualitative terms, microscopic interactions are caused by differences in crystal chemical properties of trace element and carrier, such as ionic radius, formal charge, or polarizability. This type of reasoning led Onuma et al. (1968) to construct semilogarithmic plots of conventional mass distribution coefficients K of various trace elements in mineral/melt pairs against the ionic radius of the trace element in the appropriate coordination state with the ligands. An example of such diagrams is shown in figure 10.6. 

Bromine has an ionic radius of 1.96 A and thus easily substitutes for chlorine (1.81 A) in the halite crystal lattice as well as in the other chloride salts. The distribution coefficients for bromine in chloride salts deposited from seawater is less than 1 (Warren 2006). 

Aim of the directed crystallization is in most cases to reach a crystal coat of highest possible purity. The most used measure to qualify the purification effect of the crystallization is the effective distribution coefficient k ff. For the case of crystallization processes in which the concentration of the feed remains constant the effective distribution coefficient is defined as the ratio of the impurity concentration in the crystal product C to the impurity concentration in the feed cq ... 

Several investigations (8.9 show, that the effective distribution coefficient can be described as a function of the growth rate. Own experiments show that a model to calculate the purity in dependence of the real growth rate is rather realistic. To considerate irregularities by the calculation of k ff, the effective distribution coefficient is presented as a function of the ideal growth rate of the crystal layer V, 3 and the growth rate deviation dy. ... 

A generally used expression to (quantify the uptake is the distribution coefficient K, which for cadmium as an example is defined as K(Cd) = [Cd ] (crystal)/[Cd ] (solution). ... 

The initial predictive method by Wilcox et al. (1941) was based on distribution coefficients (sometimes called Kvsi values) for hydrates on a water-free basis. With a substantial degree of intuition, Katz determined that hydrates were solid solutions that might be treated similar to an ideal liquid solution. Establishment of the Kvsj value (defined as the component mole fraction ratio in the gas to the hydrate phase) for each of a number of components enabled the user to determine the pressure and temperature of hydrate formation from mixtures. These Kysi value charts were generated in advance of the determination of hydrate crystal structure. The method is discussed in detail in Section 4.2.2. 

Transition metal dopants and impurities are probably incorporated substitutionally for Ti in BaTi03. Emission spectrographic analyses indicate that the distribution coefficients for Mn and Fe dopants are on the order of 1 to 2, i.e., the crystals are slightly enriched relative to the melt. Cr and Ni may have distribution coefficients slightly less than 1. For Co, the measured concentrations in the crystals display considerable scatter we estimate that the distribution coefficient is on the order of 4. Fe is the most prevalent transition metal impurity and is typically present at a concentration of 10-15 ppm by weight. Si, Al, Mg, and Cu are also typically present at 5-50 ppmw. Fe and Cr impurities have also been observed by EPR spectroscopy, although Cr could not be detected by emission spectroscopy, with a detection limit of 10 ppmw. 

The octahedral site preference energy parameter listed in table 6.3, applied originally to spinel crystal chemistry, has had a profound influence in transition metal geochemistry following its introduction into earth science literature in 1964 (Bums and Fyfe, 1964 Curtis, 1964). The use of such site preference energies to explain distribution coefficients of transition metal ions in coexisting minerals and phenocryst/melt systems are described in 7.6, 7.8 and 8.5.3. 

One of the most successful applications of crystal field theory to transition metal chemistry, and the one that heralded the re-discovery of the theory by Orgel in 1952, has been the rationalization of observed thermodynamic properties of transition metal ions. Examples include explanations of trends in heats of hydration and lattice energies of transition metal compounds. These and other thermodynamic properties which are influenced by crystal field stabilization energies, including ideal solid-solution behaviour and distribution coefficients of transition metals between coexisting phases, are described in this chapter. 

Figure 7.8 Relationship between the octahedral site preference energy and distribution coefficient of divalent transition metal ions partitioned between olivine or pyroxene crystals and the basaltic groundmass (modified from Henderson Dale, 1969 Henderson, 1982, p. 147).

A relationship between octahedral site preference energies (table 6.3) and distribution coefficients has been demonstrated for transition metal ions partitioned between olivine or pyroxene crystals and the groundmass of oceanic basalts, which is assumed to represent the composition of the magma from which the ferromagnesian silicates crystallized (Henderson and Dale, 1969 Dale and Henderson, 1972). Plots of In D against OSPE, such as those illustrated in fig. 7.8, show linear trends between the two parameters. 

Ionic radius. The wide variation of metal-oxygen distances within individual coordination sites and between different sites in crystal structures of silicate minerals warns against too literal use of the radius of a cation, derived from interatomic distances in simple structures. Relationships between cation radius and phenocryst/glass distribution coefficients for trace elements are often anomalous for transition metal ions (Cr3+, V3+, Ni2+), which may be attributed to the influence of crystal field stabilization energies. 

Thomas, B. R., et al.. Distribution coefficients of protein impurities in ferritin and lysozyme crystals - Self-purification in microgravity. J. Cryst. Growth 2000,... 

---