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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
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
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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
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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.
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Solid Solution
Factors affecting the extent of solid solution:
• Atomic/ionic size
• Temperature • Structural flexibility
• Cation charge
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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
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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
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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
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Activity
If the component I exhibits Raoultian behaviour:
ai = xi
If the component I exhibits Henrian behaviour:
ai=kixi
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Gibbs-Duhem EquationTo obtain the properties of a component from corresponding properties of other components. (If Q is an extensive molar property)
We know that:
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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
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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:
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The Gibbs Free Energy of Formation of a Solution
In terms of Gibbs free energy (for a binary solution ):
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The Gibbs Free Energy of Formation of a Solution
The Results:
And
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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.
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The Method of Tangential Intercepts
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The Method of Tangential Intercepts
As result:
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Proprty Change of Mixing For Ideal and Nonideal solution
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Nonideal Solution Ideal Solution
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.
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Nonideal Solution
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Variation of ai with Xi for negative deviation (Iron-Nickel)
Nonideal Solution
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Variation of ai with Xi for positive deviation (Iron-Copper)
Nonideal Solution
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Variation of with Xi (Iron-Nickel)
Nonideal Solution
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Variation of ith Xi (Iron-Copper)
Nonideal Solution
T02.02.2010 24
Nonideal Solution
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:An increase in temprature Positive (Endothermic Mixing)
:An increase in temprature Negative (Exothermic Mixing)
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.
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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
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Thanks For Attention
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