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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

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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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