Diagram Example : Visualization of DFT results (Li-Fe-P-O system)

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(1)Utilization of DFT calculations in Materials Science

Recently, there is increasing interest in obtaining the Energetics of target materials systems by making first pronciple calculations (DFT), whereas the number of calorimateres in materials science is not inceased in the high temperature chemical thermocyanmics. Thus, it should be quite important to use such calculational results in a regorous manner. Here, an attempt will be made to construct the potential diagram by directly using the DFT results. In Example 9b, similar diagrams are constructed using the MALT data.

(2)Conversion of DFT results to the *.abs file

Literature
• Ong, SP., Wang, L., Kang, B., Ceder, G., Li-Fe-P-O2 Phase Diagram from First Princeple Calculations, Chem. Mater. 20, 1798-1807, 2008. doi:10.1149/1.3362896

• Since DFT results provide the energy value at 0 K for respective substances, those data are transfered into the *.abs file. This file is for construction of diagrams consisting of a number of planes which are characterized by the following equation.
  a x + b y +c z = d
  Here, x, y, z is the dimension variables in a considered space, whereas a, b, c are coefficients of linear equations and d is constant which are given for respetive planes. Coefficients give slope of plane and constant give the distance from the origin. In the thermodynamic space, these are correspond to the stoichiometric numbers, and the energy.
  
• DFT results As an example, data given in the above literature are used. The content of the lifepo.abs file is given in the end of this page and also can be found in the given in the folder of users > DATA together with other examples of *.abs files.

1. Diagram
     Fig. 1   Fig. 2   Fig. 3   Fig. 3a    
   (1)The three dimensional Diagram for the Li-Fe-P-O system
   
   
   
   Fig. 1 The Diagram with apparent axes of Fe-P-O:Compare with F09b
   
   • Three dimensional diagram corresponds to the Fe-P-O system where ternary compounds among Fe, P, O can be seen in the diagram.
   • In the table 1 of the literature,�@P4O18 is listed.�@ In the right-hand end of the diagram, this compound appears as stable phase.�@�@ It must be mis-typed or misprinted. This phase will not damage otherphase relations, we will ignore this phase in the following discussion.
   • In the Fe-O system, FeO appears as stable phase, whereas this phase is recognized as high temperature stable phase.
   • In the Fe-P-O system, there are many ternary compounds whose features in the chemicla potential diagram can be characterized as the fact that a series of compounds having the same Fe valence state appearsin parallel.
   • In the Fe2O3-P2O5 subsystem, 46 Fe(PO3)3, 41 FePO4,and 44 Fe4(P2O7)3 appear.
   • in the FeO-P2O5 susbsystem, 47 FeP4O11, 45 Fe2P4O12, 40 Fe2PO7, 38 Fe3(PO4)2, and 36 Fe4(PO4)2O appear as stable phase.
   • Between the two series of subsystems, several mixed valence compounds appear. That is, 43 Fe3(P2O7)2 and 39 Fe7(PO4)6.
   
   (2)The three dimensional Diagram for the Li-Fe-P-O system
   
   
   
   Fig. 2 The Diagram with axes of Li-Fe-O: Compare with 9b
   • In the Li-Fe-O system, three ternary compounds appear in the diagram.
   • In the Fe2O3-P2O5 subsystem, 30 Li5FeO4 and 29 LiFeO2 appear. In addition, 28 Li3Fe5O8 appears between 29 LiFeO2 and 7 Fe2O3.
   • In the legend, the stable compounds are listed. Note that three quaternary compounds are presented as stable one. These are 48 LiFePO4 (c), 49 Li3Fe2(PO4)3 (c), and 50 LiFeP2O7 (c). However, 51 LiFeP3O9 (c) and 52 Li9Fe3(P2O7)3(PO4)2 (c) will not appear.
   • Some other compounds are also unstable. These are 12 FeP (c), 13 FeP2 (c), 19 P4O7 (c), 20 P4O6 (c), 22 LiP5 (c), 26 LiFeP (c), 27 LiFe5O8 (c), 34 Fe9(PO4)O8 (c), 35 Fe3(PO4)O3 (c), 37 Fe2PO4O (c), 42 Fe7(P2O7)4 (c),
   
   (3)The three dimensional Diagram for the Li-Fe-P-O system
   
   
   
   Fig. 3a The Diagram with axes of U(O2)-U(Li)-{U(P)-U(Fe)}: Compare with 9b
   
   • the U(O2) axis, the U(Li) axis and the U(P)-U(Fe) axis are adopted. In this plot, the phase relations among the Li-P-O system appear in the front side, whereas those for the Li-Fe-O sytems are in the rear side.
   • In the Li2O-P2O5 subsystem, three double oxides are stable. Those are 31 Li3PO4, 32 Li4P2O7 and 33 LiPO3.
   • In the Li-P subsystem, 21 LiP7, 23 LiP, 24 Li3P7, 25 Li3P are stable.
   
   
   Fig. 3b The Diagram with axes of U(O2)-U(Li)-{U(P)-U(Fe)}:enlarged.
   
   • In order to look at the phase relations among the Li-Fe phosphates and the related compounds, several compounds are made to be transparent. Those are 4 Li, 5 Li2O, 6 Li2O2, 31 Li3PO4, 32 Li4P2O7, 33LiPO3.
   • Three quaternary compounds are stable. 48 LiFePO4, 49 Li3Fe2(PO4)3 and 50 LiFeP2O7.
   
   
2. Description
   
     To Top   Diagram   Details   Data source file
   
   1. Requirements in the thermochemical net-work consistency
      • The total number of compounds whose DFT values are given is 48, whereas 38 compounds are pesent as stable phase in the diagram.
      • Among the five quaternary compounds, only three are regarded as stable.
      • This is partly because the highly precise data are required to reproduce the available phase relations. For a given composition, quite a narrow range of energies are permitted to exist as the stable phase. With increasing the number of composing elements, this range becomes narrower. This requires accurate and also precise values.
        
   2. Electrode related phase relations
      Unfortunately, it is not easy to see the graphical relations among the electrode materials. Compare with the corresponding diagrams in Example 9b.
      
      
   3. Details
        To Top   Diagram   Description   Details   Data source file
      
      • Start CHD under the MALT environment.

        File > Open File

      • Move to the right folder, that is,
        
        if your directory is located at MALT, then
        ..\users\Data
        is the right location where the lifepo.abs file is located.
      • Select the fourth category "test data" as the file kind.
      • Select "lifepo.abs" and click OK button.
      • Confirm the data read from the file.

        View > Compound List

      Table Plane list for the lifepo.abs
      
      This is the last part of list.
      
      
      • Select the compounds to be included in construction procedure

        Project > Chemical System

      • Click Reselection button.
      • Click on the compound of O2(g) and remove it.
      
      
      • Select the Diagram specification (construction conditions)

        Project > Specify Diagram

      • For *.abs file, only the fixation and the diagram type pages appear, whereas the dimension page will not appear becuase there is no need to define.
      • In Diagram type Page
        • Change the axes from D:O, D:P, D:Fe, and D:Li to D:O, D:Fe, D:Li, and D:P.
          This is because the first focus will be paid to the Li-Fe-O subsystem.
      
      
      • Run
        
      • Change the range to be shown

        Diagram > Range

      
      
      • Change the axes

        Project > Specify Diagram

      • In Diagram type Page
        • Change the axes from dimension variable to the compound type.
          This is because one axis is set as the difference between tow dimensions.

   Data source file
     To Top   Diagram   Description   Details
   Source text of lifepo.abs file

   1. The first line gives the number of dimensions of space. This system is 4. The name of respective dimensions can be given as string variable.
   2. From 2 to 13 lines, the fundamental information of the four dimensions are given in the same manner as other compound imformaion.
   3. The first line of respective compounds is the name of the compound.
   4. The second line of respective compound is the stoichiometric numbers for four dimensions.
   5. The third line of respective compound is the energy value given as the DFT calculation in the unit of eV.
   
   File:lifepo.abs
   4, O, P, Fe, Li
   O2 (gs)
   2, 0, 0, 0,
   0
   P (cs)
   0, 1, 0, 0,
   0
   Fe (cs)
   0, 0, 1, 0,
   0
   Li (cs)
   0, 0, 0, 1,
   0
   Li2O (c)
   1, 0, 0, 2,
   -6.2
   Li2O2 (c)
   2, 0, 0, 2,
   -7.04
   FeO (c)
   1, 0, 1, 0,
   -4.095
   Fe2O3 (c)
   3, 0, 2, 0,
   -11.25
   Fe3O4 (c)
   4, 0, 3, 0,
   -15.682
   Fe3P (c)
   0, 1, 3, 0,
   -1.114
   Fe2P (c)
   0, 1, 2, 0,
   -0.876
   FeP (c)
   0, 1, 1, 0,
   -0.339
   FeP2 (c)
   0, 2, 1, 0,
   -0.601
   FeP4 (c)
   0, 4, 1, 0,
   -1.265
   P4O18 (c)
   18, 4, 0, 0,
   -32.042
   P2O5 (c)
   5, 2, 0, 0,
   -17.343
   P4O9 (c)
   9, 4, 0, 0,
   -31.265
   (P4O6)O2 (c)
   8, 4, 0, 0,
   -27.792
   P4O7 (c)
   7, 4, 0, 0,
   -24.028
   P4O6 (c)
   6, 4, 0, 0,
   -20.173
   LiP7 (c)
   0, 7, 0, 1,
   -2.261
   LiP5 (c)
   0, 5, 0, 1,
   -1.873
   LiP (c)
   0, 1, 0, 1,
   -1.193
   Li3P7 (c)
   0, 7, 0, 3,
   -4.619
   Li3P (c)
   0, 1, 0, 3,
   -2.944
   LiFeP (c)
   0, 1, 1, 1,
   -1.238
   LiFe5O8 (c)
   8, 0, 5, 1,
   -30.65
   Li3Fe5O8 (c)
   8, 0, 5, 3,
   -35.668
   LiFeO2 (c)
   2, 0, 1, 1,
   -9.156
   Li5FeO4 (c)
   4, 0, 1, 5,
   -21.883
   Li3PO4 (c)
   4, 1, 0, 3,
   -22.189
   Li4P2O7 (c)
   7, 2, 0, 4,
   -36.022
   LiPO3 (c)
   3, 1, 0, 1,
   -13.685
   Fe9(PO4)O8 (c)
   12, 1, 9, 0,
   -47.628
   Fe3(PO4)O3 (c)
   7, 1, 3, 0,
   -26.078
   Fe4(PO4)2O (c)
   9, 2, 4, 0,
   -38.36
   Fe2PO4O (c)
   5, 1, 2, 0,
   -20.143
   Fe3(PO4)2 (c)
   8, 2, 3, 0,
   -34.187
   Fe7(PO4)6 (c)
   24, 6, 7, 0,
   -95.984
   Fe2P2O7 (c)
   7, 2, 2, 0,
   -29.097
   FePO4 (c)
   4, 1, 1, 0,
   -15.309
   Fe7(P2O7)4 (c)
   28, 8, 7, 0,
   -113.022
   Fe3(P2O7)2 (c)
   14, 4, 3, 0,
   -55.034
   Fe4(P2O7)3 (c)
   21, 6, 4, 0,
   -80.173
   Fe2P4O12 (c)
   12, 4, 2, 0,
   -47.801
   Fe(PO3)3 (c)
   9, 3, 1, 0,
   -33.953
   FeP4O11 (c)
   11, 4, 1, 0,
   -41.533
   LiFePO4 (c)
   4, 1, 1, 1,
   -18.853
   Li3Fe2(PO4)3 (c)
   12, 3, 2, 3,
   -53.192
   LiFeP2O7 (c)
   7, 2, 1, 1,
   -29.376
   LiFeP3O9 (c)
   9, 3, 1, 1,
   -37.523
   Li9Fe3(P2O7)3(PO4)2 (c)
   29, 8, 3, 9,
   -132.471