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Unformatted text preview: last modified 10/30/2009 M. S. Shell 2009 1/20 Solids ChE210A General properties of solids The term solids denotes materials with the following properties: Atoms are in a condensed, closely packed state. Atoms vibrate around a fixed equilibrium position. That is, they are largely fixed near a specific location in space, as their diffusion is very slow relative to the time scales of ob- servation. The bulk material has an elastic modulus . In other words, straining the material pro- duces an opposing stress that tends to return the material to its original state after straining. This contrasts with viscous behavior, in which the strain results in continuous, permanent deformation, i.e., flow. Generally speaking, there are two main classes of solids: crystalline solids These are equilibrium states of matter in which the microscopic structure is ordered and has a well-defined geometric pattern, i.e., a crystalline lattice. amorphous solids In contrast to crystals, these are microscopically disordered, mean- ing that there is no crystalline lattice structure that can be used to describe the positions of the atoms. Glasses and many plastics and polymeric materials are amorphous. Fre- quently these systems are not at equilibrium, but rather, are metastable with respect to a crystalline phase. However, typically the time scale for relaxation to equilibrium is so long that for all practical purposes the amorphous state appears stable. Thus, in an em- pirical sense, we can often treat such systems as if they were equilibrium systems. In the discussions thus far, we have sought expressions for gG, for the systems we ex- amined, since these provide a fundamental starting point for deriving other thermodynamic properties of the system. These functions were derived from simple microscopic models of gases and liquids. We will derive the properties of a simple model of crystals later in this lecture, but the resulting expression for the chemical potential will not be as simple and hence physically informative as those determined thus far. Instead for solids, we can first make several broad generalizations that will enable us to solve problems involving them without yet invoking a microscopic model: last modified 10/30/2009 M. S. Shell 2009 2/20 The thermodynamics of solids can often be modeled in simple ways by consider- ing the physical behavior of the chemical potential derivatives: 1) g G G Thus, we can calculate changes in the chemical potential with temperature using the molar enthalpy of the solid. Moreover, we have that g G G , so we can compute the change in enthalpy with temperature using the heat capacity. In the simplest approximation, the heat capacity is constant....
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