Diagram Example : Fixation of Chemical Potential 3a

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Fixation of Oxygen Potential :The chemical potential diagram for the La - Mn - Zr - O system at 1273 K.

1. Diagram : The three dimensional diagram in the μ(La)-μ(Mn)-μ(Zr) plot.
   
   
   
   
2. Description of Diagram Example : Fixation of Chemical Potential (3a)
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   • This is the La-Mn-O-Zr quaternary system at a constant temperature.
     
   • By fixing the oxygen partial pressure at 1 atm, the diagram is constructed as a normal three dimensional diagram. Since the oxygen potential is fixed, three chemical potentials μ(La)/RT, μ(Mn)/RT, μ(Zr)/RT, are selected as diagram axes.
     
   • In a ZrO₂ plane, the thermodynamic activity of ZrO₂ is equal to unity; that is, the chemical potential is constant. Since the oxygen potential is fixed, the chemical potential of Zr, μ(Zr)/RT, becomes constant. Thus, the plane of ZrO₂ is perpendicular to the axis of μ(Zr)/RT. Similarly, the slope of respective planes is determined the stoichiometry of other elements than oxygen.
     
   • Double oxides, La₂Zr₂O₇ and LaMnO₃, appear between the respective constituent oxides.
     
   • A reaction between ZrO₂ and LaMnO₃ can be checked as follows;
     
   • This reaction can be written as
     
     ZrO₂ + LaMnO₃ = 0.5 La₂Zr₂O₇ + 1/3 Mn₃O₄ + 1/12 O₂(g)
     
   • The stability region of ZrO₂ is contacted directly with that of LaMnO₃, whereas the stability regions of products, La₂Zr₂O₇ and Mn₃O₄ are separated from each other. This means that the Gibbs energy change for the above reaction is positive.
     
     
3. Detailed procedure for reproducing Diagram Example Fixation of Chemical Potential (3a)
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   1. [System] MALT

      Search Compounds

   Selection of <La,Mn,Zr,O> system

   2. Project > Chemical System

   3. [Chemical System] dialog
      
      • [Select Compound] page
        
        Selection by Default
        
        x Condensed phases
        o Respective Gaseous Species
        o Gaseous mixture
        

   4. Project > Specify Diagram

   5. [Diagram Specification]Dialog Main part
      
      • (1) Dimension SelectionPage
        
        Temperature
        
        x Fixed at 1273 K
        o Not Fixed
        
        Pressure
        
        x Fixed at 1 atm
        o Not Fixed
        
      • (2) Fixation page
        
        Add
        
        [Select Fixation] dialog
        
        Select "O2(g)" Species
        
        [Coefficient] dialog
        
        Select ReEnter 1.0
        
      • (3) Diagram Selection page
        
        {Diagram Selection}
        
        3D surface
        
        Coordinates
        
        (La)
        (Mn)
        (Zr)
        

   6. Run > Calculation

   7. Diagram > Color Details

   8. [Diagram Action Form]
      
      (3) Polygon Color
      
      (1)Tricolors based on the Coordinates
      
      X-Axis red
      Y-Axis yellow
      Z-axis Blue