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Unformatted text preview: 1 GLY 421 El-Shazly, A. K., 2004 Crystallization of Magmas: Crystal liquid equilibria a- Equilibrium and the phase rule Definitions: Equilibrium: A system is said to be in equilibrium if there is no observed change within it over time. At equilibrium, the system has a minimum internal energy, and all processes taking place within it have to be reversible. Types : Equilibrium can be one of three types: stable, metastable or unstable. A stable equilibrium is one that will not change unless the variables of the system (e.g. P, T, composition) are changed. A metastable equilibrium is one that appears without change over time, but the system under such conditions will not have the minimum energy. In addition to these three types, there is the local or partial equilibrium, where only part of the system is in equilibrium. Phase: Is that part of the system with distinct chemical and physical properties, and which can be separated from the system physically. System Components : Smallest number of chemical constituents needed to make up all phases in the system (i.e. to define the system). Variance (also known as the degrees of freedom " f "): Is the maximum number of intensive properties (i.e. properties that are independent of the mass of the system; e.g. P & T) that can be changed independently within a system without causing the appearance or disappearance of any phase in this system. The phase rule: The phase rule was formulated by J. Willard Gibbs (1874), and is used to determine the variance or degrees of freedom of a system ( f ). The variance of a system can be expressed as the total variables of this system minus the "fixed variables". For any system of " c " components and containing " p " phases, the total number of variables is c.p + 2 , where the latter term represents the two variables P and T. The fixed variables are represented by those variables defined by what is already in the system, or more appropriately, the number of equations needed to fully define the composition of the system, and are given by: c(p-1) + p . Accordingly, the degrees of freedom will be given by: f = cp + 2 - [cp - c + p] f = c - p + 2 The phase rule therefore allows us to determine the minimum number of variables that must be defined in order to perfectly define a particular condition of the system from a knowledge of the number of system components and phases. Note that this "number of 2 GLY 421 El-Shazly, A. K., 2004 variables" cannot be negative (i.e. f 0). The phase rule also allows us to determine the maximum number of phases that can coexist stably in equilibrium; e.g. if a system has 20 components, according to the phase rule, the maximum number of phases in equilibrium will be 22 (when f = 0). Accordingly, if the number of phases present exceeds that calculated by the phase rule (after the number of components has been correctly identified), then these phases are not in equilibrium! Note that in the case of metastable equilibrium, the phase rule may be obeyed, but will be violated over time!metastable equilibrium, the phase rule may be obeyed, but will be violated over time!...
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