Ellingham diagram

The Ellingham Diagram

Bapin Kumar Rout

Technical presentation

Research and Development, Steelmaking and Casting Research Group

Before we start: Thermodynamic terminologies

Gibb’s Free Energy ( G ): Energy of the system available to do work


G= H-T*. S

∆H: Measure of the actual energy that is liberated when the reaction occurs ∆S: Measure of the change in the possibilities for disorder in the products compared to the reactants

Enthalpy term Entropy term

Spontaneity of the Reaction ( G<0)

Free Energy and Equilibrium


Under non-standard conditions, we need to use G instead of G°.

1. If G is negative, the forward reaction is spontaneous.

2. If G is 0, the system is at equilibrium.

3. If G is positive, the reaction is spontaneous in the reverse direction.

Standard state free energy ( G0=):



1Ellingham H. J. T., “Reducibility of Oxides and sulfides in Metallurgical Processes , J Soc Chem Ind (London) 63 125 (1944)

Ellingham1 plotted experimentally determined standard free energy of formation (∆G0) of various oxides (and sulfides) using one mole of oxygen with temperature

Ellingham Found that, the standard enthalpy and entropy of formation of a compound don’t change significantly with temperature as long as there is no change of state

Thus, ∆G0-T relationship is approximated to straight lines:

Y= mx+C Intercept Slope



Oxide stable Metal stable

The Ellingham Diagrams


Two intersecting lines


T<TE A and BO2 are most stable T>TE B and AO are most stable At T=TE A,B,AO,BO2 are in equilibrium

A as a reducing agent to reduce BO2 to form B and AO- T> TE

Additional scales on Ellingham diagram


Y=-mX

Reading pO2 from Ellingham diagram


• In to avoid calculating the equilibrium partial pressure for each value of ΔG°, Richardson2 added a nomographic scale to the Ellingham diagram

• For a metal oxidation reaction ,

2M (s) + O2 (g) = 2MO (s)

The equilibrium constant has the form

K=1/pO2

∆G= RT ln(pO2)

2 F.D. Richardson and J.H.E. Jeffes, "The Thermodynamics of Substances of Interest in Iron and Steel Making from 0°C to 2400°C: I-Oxides," J. Iron and Steel Inst. (1948), 160 261.

Reading pO2 from Ellingham diagram


1. Identify a point corresponding to a selected temperature on the line for: Fe + O FeO, above M

2. Using this point, and the point O in the top left corner, draw a line across the diagram

3. Read the partial pressure of O2 from the right hand axis

At any oxygen pressure higher than~10-8.5, the iron will be oxidised at thetemperature of 1600°C

Other gas mixtures


• The oxygen required to cause oxidation in the gas phase need not to come from oxygen gas. Consider the following reaction:

2CO (g) + O2 (g) = 2CO2 (g)

• For this reaction,

• We see that pO2 is equivalent to a ratio: pco/ pco2

• Similarly for the reaction 2H2+O2=2H2O pO2 is equivalent to a ratio: pH2O/ pH2

• Thus two nomographic scale may be added to the diagram, with a new origin, C and H respectively for pco/ pco2 and pH2O/ pH2

CO-CO2 gas mixture as reducing agent (374)


MO2+2CO=M+2CO2

At T>Ts CO-CO2 mixture is reducing w.r.t MO2 at pCO/pCO2=1At T<Ts CO-CO2 mixture is oxidisingw.r.t MO2 at pCO/pCO2=1

If CO-CO2 mixture to be made reducing at T<Ts the pCO/pCO2(>1) must be increasingAt T=Tu pCO/pCO2 should be increased from 1to 10 to maintain reaction equillibrium

Limitation


References


1. D.R. Gaskell, "Introduction to the Thermodynamics of Materials“2. http://www.doitpoms.ac.uk/tlplib/ellingham_diagrams/

Thank you

http://www.doitpoms.ac.uk/tlplib/ellingham_diagrams/



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Ellingham diagram

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