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

Slide 2:

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

Slide 3:

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

Slide 4:

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

Slide 5:

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

Slide 6:

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

Slide 7:

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

Slide 8:

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

Slide 9:

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

Slide 10:

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

Slide 11:

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

Slide 12:

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

Slide 13:

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

Slide 14:

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

Slide 15:

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

Slide 16:

The Method of Tangential Intercepts 02.02.2010 16

Slide 17:

The Method of Tangential Intercepts As result: 02.02.2010 17

Slide 18:

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

Slide 19:

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

Slide 20:

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

Slide 21:

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

Slide 22:

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

Slide 23:

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

Slide 24:

Nonideal Solution T 02.02.2010 24

Slide 25:

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

Slide 26:

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

Slide 27:

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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02.02.2010 28

Slide 29:

Thanks For Attention 02.02.2010 29

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