Subject solid sphere model

Scientists commonly interpret a theory in terms of a model, a simplified version of the object of study. Like hypotheses, theories and models must be subjected to experiment and revised if experimental results do not support them. For example, our current model of the atom has gone through many formulations and progressive revisions, starting from Dalton s vision of an atom as an uncut-table solid sphere to our current much more detailed model, which is described in Chapter 1. One of the main goals of this text is to show you how to build models, turn them into a testable form, and then refine them in the light of additional evidence. 

The solid-fluid transition in the hard-sphere system has been the subject of great interest for about 50 years now. Although it was originally only a computer model, researchers in colloid science have come close to a complete experimental realization of the hard-sphere model [2,3]. The hard-sphere system is one with an intermolecular potential of the form... 

The indirect transformation technique models the r -multiplied autocorrelation function r (y(r)) , = r y(r) = p r) as a superposition of equidistant B-splines (up to a cutoff maximum particle size that needs to be given in advance) that are Fourier transformed, subjected to any applicable collimation effects (the method was originally developed for a Kratky slit collimation), and then least-squares fitted to the experimental intensity distribution, so that p r] can be computed using the fit coefficients and the untransformed B-splines. The shape of p(r) is known for many standard particles including solid spheres, core-shell hollow spheres, and rods. 

Although most of the studies of this model have focused on the fluid phase in connection with the theory of electrolyte solutions, its solid-fluid phase behavior has been the subject of two recent computer simulation studies in addition to theoretical studies. Smit et al. [272] and Vega et al. [142] have made MC simulation studies to determine the solid-fluid and solid-solid equilibria in this model. Two solid phases are encountered. At low temperature the substitutionally ordered CsCl structure is stable due to the influence of the coulombic interactions under these conditions. At high temperatures where packing of equal-sized hard spheres determines the stability a substitutionally disordered fee structure is stable. There is a triple point where the fluid and two solid phases coexist in addition to a vapor-liquid-solid triple point. This behavior can be qualitatively described by using the cell theory for the solid phase and perturbation theory for the fluid phase [142]. Predictions from density functional theory [273] are less accurate for this system. 

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