Melt crystallization solid solutions

Iron always contains carbon. A part of the phase diagram of the iron/carbon system is shown in Figure 10.5. The carbon has different solubilities in the different iron modifications, which form mixed crystals (solid solutions). In a-iron the solubility is only 0.04% (ferrite) and in 5-iron the solubility is 0.36%. In the y-modification with its fee struemre, carbon and iron form an intercalation lattice as a solid solution called austenite with the maximum solubility of 2.06% carbon at 1147 °C. Iron with more carbon is called cast iron. Iron with less than 2.06% carbon is called steel. During slow cooling of a melt (above 1147 °C) iron solidifies either as austenite (carbon content of the melt <4.3%) or as cementite (FcjC, carbon content of the melt > 4.3%). At 1147 °C the melt solidifies in a eutectic mixture of both these phases called ledeburite. 

System in which the two components form a continuous series of solid solutions. In all the preceding examples the individual components (A or B or A By) form separate crystals when solidifying from the melt. There are, however, a number of examples of the separation of a homogeneous solid solution of A and B (or A and A By, etc.). 

Purification of a chemical species by solidification from a liquid mixture can be termed either solution crystallization or ciystallization from the melt. The distinction between these two operations is somewhat subtle. The term melt crystallization has been defined as the separation of components of a binaiy mixture without addition of solvent, but this definition is somewhat restrictive. In solution crystallization a diluent solvent is added to the mixture the solution is then directly or indirec tly cooled, and/or solvent is evaporated to effect ciystallization. The solid phase is formed and maintained somewhat below its pure-component freezing-point temperature. In melt ciystallization no diluent solvent is added to the reaction mixture, and the solid phase is formed by cooling of the melt. Product is frequently maintained near or above its pure-component freezing point in the refining sec tion of the apparatus. 

Preparation of the Methyl Bromide To the acetone solution of the free base was added an acetone solution, containing an excess of methyl bromide. Within a few minutes the methobromide started to crystallize. The mixture was allowed to stand for several hours. The crystallized solid was filtered, and additional product was obtained by evaporation of the filtrate. The yield was nearly quantitative. After recrystallization from acetone, the product melted at 329°C. 

The relations apply also to the case of a liquid mixture of two substances which is solidifying to a homogeneous solid which contains the two substances in proportions depending on the composition of the melt—a so-called solid solution or mixed crystal ( 138). 

If the phases present can be unambiguously identified, microscopy can be used to determine the geometry of interface initiation and advance, and to provide information about particle sizes of components of mixed reactants in a powder. Problems of interpretation arise where materials are poorly crystallized and where crystallites are small, opaque, porous or form solid solutions. With the hot-stage microscope, the progress of reactions can be followed in some instances and the occurrence of sintering and/or melting detected. 

Elements dissolved in boron influence its crystal structure. Dissolved impurities also influenee the physical and chemical properties of boron, especially the electrical properties, because boron is a semiconductor. Preparation of solid solutions in jS-rh boron requires a careful choice of crucible material. To avoid contamination, boron nitride or a cold, coinage-metal crucible should be used or the levitation or floating-zone melting techniques applied. 

The materials for solid solutions of transition elements in -rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by crystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (VT ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, Co, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V, . Boron is a brittle material, indicating the accommodation of transition-element atoms in the /3-rh boron structure is associated with an increase in the cohesion energy of the solid. 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

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 dominant mechanism of purification for column crystallization of solid-solution systems is recrystallization. The rate of mass transfer resulting from recrystallization is related to the concentrations of the solid phase and free liquid which are in intimate contact. A model based on height-of-transfer-unit (HTU) concepts representing the composition profile in the purification section for the high-melting component of a binary solid-solution system has been reported by Powers et al. (in Zief and Wilcox, op. cit., p. 363) for total-reflux operation. Typical data for the purification of a solid-solution system, azobenzene-stilbene, are shown in Fig. 20-10. The column crystallizer was operated at total reflux. The solid line through the data was com-putecfby Powers et al. (op. cit., p. 364) by using an experimental HTU value of 3.3 cm. 

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

Heat of fusion This value, normally reported inkcal/mol, is also referred to as the heat of melting. For solids, the heat of fusion is required to estimate the solubility of the solute to account for crystal lattice interactions. The theoretical basis for introducing this value into the estimation of aqueous solubility of organic solids is explained by Irmann(1965) and Yalkowsky and Valvani (1979). Heat of fusion data is available in many texts including Dean (1987), Weast (1986), and CHRIS (1984). Experimentally determined data were reported by Plato and Glasgow (1969) and Hickley et al. (1990). 

Capobianco, C.H., Hervig, R.L., Drake, M. 1994. Experiments on crystal/liquid partitioning of Ru, Rh and Pd for magnetite and hematite solid solutions crystallised from silicate melt. Chemical Geology, 113, 23-43. 

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