Fractionated crystallization factors

Warren P. H., Claeys P., and Cedillo-Pardo E. (1996) Megaimpact melt petrology (Chicxulub, Sudbury, and the Moon) effects of scale and other factors on potential for fractional crystallization and development of cumulates. In The Cretaceous-Tertiary Event and Other Catastrophes in Earth History, Spec. Pap. 307 (eds. G. Ryder, D. Fastovsky, and S. Gartner). Geological Society of America, Boulder, CO, pp. 105-124. 

Dimethylnaphthalene concentrate contains significant amounts of 2,6-dimethylnaphthalene bound in a binary eutectic with 2,7-dimethylnaphthalene. This eutectic cannot be broken by distillation or solvent crystallization. A practical method for separating this eutectic mixture of 2,7-dimethylnaphthalene and 2,6-dimethylnaphthalene has been achieved. Selective adsorption of 2,7-dimethylnaphthalene from a dimethylnaphthalene concentrate is obtained with sodium type Y molecular sieves. 2,6-Dimethylnaphthalene then can be crystallized from the unadsorbed raffinate fraction. Separation factors of 6 to 8 are obtained, indicating the high selectivity of these particular molecular sieves for this adsorption. Previous work in this area achieved a separation factor of 2.7. A continuous method has been developed for adsorption and desorption of 2,7-dimethylnaphthalene. Toluene has been selected as the optimum desorbent. This process makes 2,7-dimethylnaphthalene potentially available. 

Theoretical analyses and surveys of the factors affecting the choice of different fractional crystallization schemes have been made by Doerner and Hoskins... 

Several factors can influence the fractionated crystallization behavior. An important parameter that has already been discussed is the thermal history of the sample. CrystaUizable dispersed droplets that were submitted to premelting at higher temperatures or longer times generally display a shift in the heterogeneous... 

In this context, it is interesting to evaluate also the influence of compatibUization on the crystallization behavior of the dispersed phase. Since compatibihzation reduces the droplet size of the minor phase even more drastically, it can be expected that this can lead to a serious shift of the crystallization temperature toward lower temperatures, resulting in more pronounced fractionated crystallization or even in a homogeneous crystallization. However, this issue is more complex due to numerous other factors involved in the nucleation process. Some examples from the literature are listed in Table 3.26. They illustrate how differently the compatibi-lization can influence the crystallization behavior of the dispersed phase. 

Several factors have been reported to influence fractionated crystallization. However, these ones are said to be very influential [92-95] ... 

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

As is well known, the recoil-free fraction of very small crystals differs markedly from that of bulk material. Roth and Horl [236] observed a decrease of the/-factor from 0.61 to 0.57 in going from 1 p,m crystals to microcrystals with a diameter of about 60 A. Two effects will contribute to this decrease (1) the low frequency cutoff, because the longest wavelength must not exceed the dimensions of the crystal, and (2) high frequency cut-off caused by the weaker bonds between surface atoms. 

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