PD-OneComp - Phase Transitions and Phase Diagrams...

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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei Phase Transitions and Phase Diagrams One-component systems Enthalpy and entropy dependence on P and T Gibbs free energy dependence on P and T Clapeyron equation Understanding phase diagrams for one-component systems Polymorphic phase transitions Driving force for a phase transition First order and second-order phase transitions Reading: 1.2 of Porter and Easterling Chapter 7.1 7.4 of Gaskell
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PVT Surface of a Pure Substance http://www.eng.usf.edu/~campbell/ThermoI/ThermoI_mod.html
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei A pure substance is heated at constant pressure T T b V P
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei H and S as function of T at constant P In a closed one-component system equilibrium, at temperature T and pressure P, corresponds to the state with minimum Gibbs free energy G. Therefore, in order to predict what phases are stable under different conditions we have to examine the dependence of G on T and P. Let s use thermodynamic relations to predict the temperature dependence of H, S, and G at constant P. For H(T) we have ± ² ³ ´ T 298 P 298 dT C H T H P P C T H ¸ ¹ · ¨ © § w w For S(T) we have ± ² ³ T 0 P dT T C T S T C T S P P ¸ ¹ · ¨ © § w w 0 0 0 C P H S T, K T, K T, K 298 Slope = C P Slope = C P /T
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei G as function of T at constant P For G = H TS we have dG = -SdT +VdP and for P = const S T G P µ ¸ ¹ · ¨ © § w w for the slope T c T S T G P P P 2 2 µ ¸ ¹ · ¨ © § w w µ ¸ ¸ ¹ · ¨ ¨ © § w w for the curvature 0 H T, K TS Slope = C P Slope = -S G G(T) for a single phase at P = const
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei G as function of T at constant P for liquid and solid phases At all temperatures the liquid has a higher internal energy U and enthalpy H as compared to the solid. Therefore G l > G s at low T. The liquid phase, however, has a higher entropy S than the solid phase at all T. Therefore G l decreases more rapidly with T as compared to G s . At T m G l (T) crosses G s (T) and both liquid and solid phases can co-exist in equilibrium (G l = G s ) 0 H l T, K T m G l At T m the heat supplied to the system will not rise its temperature but will be used to supply the latent heat of melting ' H m that is required to convert solid into liquid. At T m the heat capacity C p = ( w H/ w T) P is infinite addition of heat does not increase T.
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