Solid Solution Thermodynamic

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02.02.2010 1 Friedrich-Alexander –Universität Erlangen-Nürnberg Thermodynamics of Solid Solution Seminar for Solid State Thermodynamic Dr.Virtanen Student:Mostafa Arghavani 02.02.2010

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Contents Introduction Solid Solution Raoult’s Law and Henry’s Low Activity Gibbs-Duhem Equation The Gibbs Free Energy of Formation of a Solution The Relationship between Henry’s and Raoult’s Law The Method of Tangential Intercepts Proprty Change of Mixing For Ideal and Nonideal solution Nonideal Solution Sammary 02.02.2010 2

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Introduction The misciblity of alloy‘s components depends on the interaction between the atoms: separate phases with limited miscibility . single crystal of a different structure . solid solution 02.02.2010 3

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Solid Solution Types of solid solution: Substitutional solid solution : by substitution of one type of atom in the structure by another. Coupled substitution : by substitutions of two coupled cation to maintain charge balance. Omission solid solution : by omitting cations from cation sites that are normally occupied. Interstitial solid solution : by addition of atoms or ions to sites that are not normally occupied. 02.02.2010 4

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Solid Solution Factors affecting the extent of solid solution: Atomic/ionic size Temperature Structural flexibility Cation charge 02.02.2010 5

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Raoult’s Law and Henry’s Low Case 1:with assumption that magnitudes of the A-A ,B-B and A-B bond energies in the solution be identical PA=XA P°A PB=XB P°B PTotal=PA+PB= XAP°A+ XBP°B 02.02.2010 6

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Raoult’s Law and Henry’s Low Case 2 : If the A-B bond energy is more or less negetive than A-A and B-B bond energies PA ≠ XA P°A PB≠XB P°B so: PA= kA XA PB= kB XB 02.02.2010 7

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Activity The thermodynamic activity of a component in any state at the temperature T is defined as: where: fi=fugacity of component i at the temperature T. f°i= fugacity of pure I at the temperature T (standars state). If the vapor in equilibium with the solution is ideal: fi=pi 02.02.2010 8

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Activity If the component I exhibits Raoultian behaviour: ai = xi If the component I exhibits Henrian behaviour: ai=kixi 02.02.2010 9

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Gibbs-Duhem Equation To obtain the properties of a component from corresponding properties of other components. (If Q is an extensive molar property) We know that: 02.02.2010 10

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Gibbs-Duhem Equation Is the value of per mole of in the solution: Differentiattion: Comparison with the last equation in former slide: Or generally: Gibbs-Duhem or equation 02.02.2010 11

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The Gibbs Free Energy of Formation of a Solution Some definitions: :Molar property of pure component i. :Partial molar property of the component i in a solution. :Molar property change of mixnig of component i in a solution : Example: 02.02.2010 12

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The Gibbs Free Energy of Formation of a Solution In terms of Gibbs free energy (for a binary solution ): 02.02.2010 13

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The Gibbs Free Energy of Formation of a Solution The Results: And 02.02.2010 14

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The Relationship Henry’s and Raoult’s Law Thus : In the range of composition over wich the solute B obeys Henry’s law,the solvent A obeys Raoult’s law. 02.02.2010 15

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The Method of Tangential Intercepts 02.02.2010 16

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The Method of Tangential Intercepts As result: 02.02.2010 17

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Proprty Change of Mixing For Ideal and Nonideal solution 02.02.2010 18 Nonideal Solution Ideal Solution

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Nonideal Solution The activities of the components are not equal to their mole fraction. Ideal Raoultian behaviour. Positive deviation from ideal Raoultian behaviour. Negative deviation from ideal Raoultian behaviour. 02.02.2010 19

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Nonideal Solution 02.02.2010 20 Variation of ai with Xi for negative deviation (Iron-Nickel)

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Nonideal Solution 02.02.2010 21 Variation of ai with Xi for positive deviation (Iron-Copper)

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Nonideal Solution 02.02.2010 22 Variation of with Xi (Iron-Nickel)

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Nonideal Solution 02.02.2010 23 Variation of ith Xi (Iron-Copper)

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Nonideal Solution T 02.02.2010 24

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Nonideal Solution 02.02.2010 25 :An increase in temprature Positive (Endothermic Mixing) :An increase in temprature Negative (Exothermic Mixing)

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Sammary Now we should have some general information about: What is solid solution. Ideal and nonideal solution and relationship with Raoult’s and Henry’s law. Gibbs-Duhem equation and its application. Most important thermodynamic’s properties for solid solution. Proprty Change of formation of solid solutions. 02.02.2010 26

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Refrences Introduction To The Thermodynamics of Materials,David R.Gaskell,New York.London,2003. Introduction To Chemical Engineering Thermodynamics ,J.M.Smith,H.C.Van Ness,M.M.Abbott,U.S.A,1985. University of Cambridge,TLP library, www.doitpoms.ac.uk www.earth.ox.ac.uk 02.02.2010 27

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Thanks For Attention 02.02.2010 29