Solution phase models interstitial solutions

Equation (S.21) is normally used in metallic systems for substitutional phases such as liquid, b.c.c., f.c.c., etc. It can also be used to a limited extent for ceramic systems and useful predictions can be found in the case of quasi-binary and quasi-temary oxide systems (Kaufman and Nesor 1978). However, for phases such as interstitial solutions, ordered intermetallics, ceramic compounds, slags, ionic liquids and aqueous solutions, simple substitutional models are generally not adequate and more appropriate models will be discussed in Sections 5.4 and 5.5. 

The use of the sublattice model, developed by Hillert and Staffansson [70Hil] based on Temkin s model for ionic solutions [45Tem] and extended by Sundman and Agren [81Sun], allows a variety of solution phases to be treated, for example interstitial solutions, intermediate phases, carbides etc. All of these represent an ordering of the constituents on different sublattices. 

The sub-lattice model is now the predominant model used in most CALPHAD calculations, whether it be to model an interstitial solid solution, an intermetallic compound such as 7-TiAl or an ionic solution. Numerous early papers, often centred around Fe-X-C systems, showed how the Hillert-Staffansson sub-lattice formalism (Hillert and Staffansson 1970) could be applied (see for example Lundberg et al. (1977) on Fe-Cr-C (Fig. 10.8) and Chatfteld and Hillert (1977) on Fe-Mo-C (Fig. 10.9)). Later work on systems such as Cr-Fe (Andersson and Sundman 1987) (Fig. 10.10) showed how a more generalised sub-lattice treatment developed by Sundman and Agren (1981) could be applied to multi-sub-lattice phases such as a. 

The following assumptions were made in formulating this model 1) there is no solute adsorption to the stationary phase, 2) the porous particles which form the stationary phase are of uniform size and contain pores of identical size, 3) there are no interactions between solute molecules, 4) the mobile phase is treated as a continuous phase, 5) the intrapore diffusivity, the dispersion coefficient and the equilibrium partition coefficient are independent of concentration. The mobile phase concentration. Cm, is defined as the mass (or moles) per interstitial volume and is a function of the axial coordinate z and the angular coordinate 0. The stationary phase concentration, Cs, is defined as the mass per pore volume and depends on z, 6 and the radial coordinate, r, of a spherical coordinate system whose origin is at the center of one of the particles. 

The linear approximation is also able to describe creep and stress relaxation experiments in suspended cells (e.g., leukocytes) and several types of anchorage-dependent cells [Koay, 2003 Sato, 1990]. Taking the continuum theory to another level of complexity, the cytoplasm may be considered to consist of both solid polymeric contents and interstitial fluid. Then it will be appropriate to treat the two phases separately as in the biphasic model [Humphrey, 2001], This model has been widely used to study musculoskeletal cell mechanics, especially single chondrocytes and their interaction with the extracellular cartilage matrix [Shieh, 2002 Shieh, 2003], However, the biphasic theory and irregular geometry often render analytical solution too challenging [Shieh, 2003]. 

Exercise E.3.6 Define the solvation process as the process of transferring a simple solute from a fixed position in an ideal gas phase to a specific hole in the interstitial model. Calculate AG, A5, and AH for this process. Examine the effect of changing the molecular parameters on these quantities and on the entropy-enthalpy compensation. 

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