Diagram Example : Non-Chemical Potential Variable (1b)

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The chemical potential diagram for the Mn-O system.

1. The three dimensional diagram in the μ(Mn)-μ(O)-1/T plot.
   
   
   
   
2. Description of Diagram Example : Non-Chemical Potential Variable (1b)
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   • In the Mn-O systems, Mn metal, MnO, Mn₃O₄, Mn₂O₃, MO₂ exist as stable phases. In the diagram, O₂(g), Mn(g) are also included as stable gas phases.
     
   • The intersect line between the O₂(g) plane and the frame plane at μ(Mn)/RT=-300 shows that μ(O)/RT decreases with increasing temperature (or with decreasing inverse temperature, 1/T). Similarly, decrease of μ(Mn)/RT is plotted in the frame plane of μ(O)/RT.
     
   • The chemical potential divided by RT is expressed in terms of enthalpy and entropy as follows;
     
     μ(O)/RT = (h/R)(1/T) - s/R
     
   • In the diagram, the enthalpy term, h/R, is expressed as a slope of the tangent plane, whereas the entropy term is expressed as intersect at 1/T=0. The values of h and s are always positive for elements so that μ(O)/RT is always going down with increasing temperature.
     
   • The borderline between Mn and Mn(g) indicates the vaporization temperature.
     
     Mn = Mn(g)
     
   • The three phase point among MnO₂, Mn₂O₃, and O₂(g) indicates that MnO₂ is reduced into Mn₂O₃. This corresponds to the following chemical reaction.
     
     MnO₂ = 0.5 Mn₂O₃ + 0.25 O₂(g)
     
   • The plane of MnO₂ has a negative slope for the 1/T axis. This corresponds to the negative enthalpy change for formation of MnO₂.
     
     
3. Detailed procedure for reproducing Diagram Example Non-Chemical Potential Variable(1b)
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   1. [System] MALT

      Search Compounds

   Selection of <Mn,O> system

   2. Project > Chemical System

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

   4. Project > Specify Diagram

   5. [Diagram Specification]Dialog Main part
      
      • (1) Dimension SelectionPage
        
        • Temperature
          
          o Fixed
          x Not Fixed
          
        • Pressure
          
          x Fixed at 1 atm
          o Not Fixed
          

   6. Run > Calculation

   7. Diagram > Rotation

   8. [Rotation of 3D diagram] Dialog
      • X-axis
        
        Horizontal 100 => 40
        Vertical 0 => -15
        
      • Z-axis
        
        Horizontal -50 => -100
        Vertical 0 => -15
        
      • As a result, the following matrix values are obtained
        
        0.4 0.0 -1.0
        -0.15 1.0 -0.2
        

   9. Diagram > Display Mode > Move Location