11 Phase Transitions and Surfaces

11 Phase Transitions and Surfaces - Phase Transitions...

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Sections 6.7-6.10, 7th Ed.; 4.7, 18.7, 18.8 in 8th Ed. Ehrenfest Classification of Phase Transitions Physical Liquid Surface Surface Tension Curved Surfaces Bubbles, cavities and droplets Nucleation Capillary Action Chapter 6 of Atkins, 7th Ed. Chapter 4 and 18, 8th Ed. Last updated Nov. 18, 2009: New slide, 25
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Ehrenfest Classification of Phase Transitions Common phase transitions: Less common phase transitions: Fusion Solid-Solid Vapourization Conducting-Superconducting Fluid-Superfluid Paul Ehrenfest came up with a classification scheme for phase transitions, based on the thermodynamic properties of substances Many phase transitions are accompanied by changes in enthalpy and volume - these changes can alter the chemical potentials on both sides of the phase transition. For example, phase " changing to phase $ : M μ $ M p T M μ " M p T ' V $ ,m V " ,m ' ) trs V M μ $ M T p M μ " M T p S $ ,m % S " ,m ) trs S ) trs H T trs
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Ehrenfest Classification of Phase Transitions ) trs V and ) trs H are nonzero for fusion and vapourization, so slopes of μ as fucntions of p or T on each side of the phase transition are different First order phase transition : first derivative of μ w.r.t. T is discontinuous Second order phase transition : first derivative of μ w.r.t. T is continuous, but second derivative is discontinuous The C p of a substance is the slope of the plot of enthalpy wrt temperature: at the transition, H changes by a finite amount, so at the transition, the heat capacity is infinite : i.e., heat drives the transition instead of raising temperature (a) first order (b) second order
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8 -Transition The 8 -transition is a phase transition that is not first-order, but has infinite heat capacity at the transition - the heat capacity increases well before the transition, and occurs in: # order-disorder transitions in alloys # ferromagnetic materials # fluid-superfluid transition in liquid helium a) Low T phase: orderly arrangement of atoms b) Islands of disorder appear as T increased c) Islands grow and merge at the transition temperature (742 K), where heat capacity increases and drives the transition Order-disorder transition in $ -brass (CuZn) is a 8 - transition
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Second-Order Phase Transition in a Solid Change of symmetry of a crystal structure in a solid is an example of a second-order phase transition At first, the crystal has a unit cell (smallest repeating unit in the crystal) which is tetragonal in symmetry, meaning that one axis of the unit cell is longer than the other two, which are equal As T is increased, the shorter dimensions of the unit cell increase faster than the longer dimension At some point, the sides of the unit cell become equal, and the crystal is said to have cubic symmetry at this point - after which, all sides of the unit cell increase at the same rate This tetragonal-cubic solid-solid phase transition does not involve discontinuity in energy between atoms of the volume they occupy: so it is not a first-order transition
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This note was uploaded on 07/31/2011 for the course CHEM 171 taught by Professor Ednacalderon during the Spring '11 term at Mapúa Institute of Technology.

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11 Phase Transitions and Surfaces - Phase Transitions...

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