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What is Chemical Potential Diagram?

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This program is to construct the generalized chemical potential diagram.

  1. What is the chemical potential diagram?
  2. What is the generalization?
      The current CHD program constructs diagrams using the generalized construction method. In what follows, a comparison will be made between the conventional and generalized method in constructing strategy and in utilization with an emphasis on the features of generalization.

    1. The conventional chemical potential diagram:
      • Selection of specified element：
        This is based on the selection of one redox element and then shows the chemical forms of this element in various chemical environment as functions of chemical potentials. This can be regarded as the stability diagram for the selected element.
        • For example, in the Fe-O-H-e- system, the Pourbaix diagram can be set up by using pH and the electric potential as coordinates for presenting the stability fields of the Iron-containing species/compounds.
        • For example in the Fe-S-O-H system, the high-temperature chemical potential diagram can be set up by using log p(O2) vs. log p(S2) as the environmentally regulable chemical potential.
      • Coordinates as Environmentally controllable variable:
        Implicitly, the coordinate variable is selected given chemical potentials which can control the chemical feature of the environment.
      • Meaning of Borderlines：
        Borderlines in the diagram show the change in the chemical form of the selected redox element. This borderline can be represented by one chemical reaction.
      • Chemical Reactions from the constructing strategy
        To construct one diagram, many chemical reactions are written down and the most important chemical reactions for one species are selected. It is thus common to write down the chemical reactions containing H+ or electrons to construct the Pourbaix diagram.
      • Redox element：
        It will be convenient to see systematically the redox reaction as well as the acid-base reaction concerning the selected element. Thus, this selected element is often called the redox element.
      • Limitation in applying to Multicomponent systems:
        The conventional approach has demerits in difficulties of representing the complicated equilibrium relation for alloys or double oxide systems.
      • Relation to Mass Transfer：
        The conventional approach is based on the idea that the mass transfer associated with changes in the environmental variables is quite fast, and therefore the chemical reactions can be emphasized. For example, mass transfer associated with the change in the chemical state from FeS to FeO will not be paid attention.

    2. Generalization:
      • No selection of elements is made for particular purposes in the construction strategy. In the n-dimensional chemical potential space, the thermodynamic relations among compounds will be examined. This makes it possible to treat alloy and non-alloy elements without any difference. Furthermore, temperature and pressure are also included as one of the dimensions constructing space. Similarly, the charge can be treated in a similar way to element. Thus, the characteristic features in comparison with the conventional one can be pointed out as follows: This means that some important differences will appear, such that the borderlines in diagrams do not necessarily indicate chemical reactions, but sometimes indicate phase boundaries, like in the compositional phase diagram. In this sense, these new generalized chemical potential diagrams can be well compared with phase diagrams.
        1. No difference in treatment of elements. This makes it possible to treat alloys and double oxides easily.
        2. The generalized way of selecting coordinate variables. It is possible to adopt the environmentally related chemical potentials and also to adopt more generalized chemical potential variables. Thus, it is erasonable to adopt the diffusion potential defined as the differences between two elemental chemical potentials; this is very convenient to consider the diffusion properties across the interfaces bewteen disimilar materials.
        3. The same algorithm can be applied to the Pourbaix diagram and the high temperature chemical potential diagram, so that it becomes easy to convert the phase relations in the Pourbaix diagram to the high temperature chemical potential diagram. Thus, it is possible to compare the phase relations in the aqueous system with those in the wet system or the dry system.
        4. Temperature and pressure can be selected as coordinate variables. This makes it possible to construct the popular diagram in high-temperature chemistry, such as the Ellingham diagram or Alrenius plot.
      • There is no requirement in the constructing strategy to construct the three-dimensional chemical potential diagram, and the calculation time is not long, so that it becomes possible to construct more complicated diagrams than those that the conventional diagram can be set up. Even so, it is quite difficult to obtain all the features of the three-dimensional diagrams. This leads to new requirements in handling the diagrams with complicated but newly appearing features.
        1. Touch diagram mode：
          Since one point in the diagram always corresponds to one point in the original thermodynamic chemical potential space. This information can be displayed in response to the movement of the mouse.
        2. Dissections：
          It is not easy to see inside the three-dimensional polyhedron. The dissection by a selected (arbitrary) chemical potential value can be set up as an additional diagram.
        3. Profile diagram：
          The dissection of the two-dimentional diagram will lead to the profile diagram, which shows changes in the partial pressure of gaseous species or the activity of aqueous species along the dissected line.
        4. Transparent：
          The three dimensional chemical potential diagram consists of several polyhedrons corresponding to respective compounds. When some of the compound polyhedrons can be transparent to make other polyhefrons visible. This also makes it possible to touch on one polygon of a non-transparent compound polyhedron and show the thermodynamic information of that point.
        5. Swing：
          By swinging the chemical potential value of the dissection, it is easily examined how the dissection diagram or the profile diagram will change in features on swing.
        6. Rotation：
          It is possible to rotate the three-dimensional diagram with or without transparent polyhedrons.
      • The following treatment is adopted to make consistent treatment with the conventional diagram.
        1. Specification of elements in some aspects:
          As described above, it is possible to make transparent for the selected compounds. In addition to this function, a new treatment is introduced to make systematic treatment of transparency by specification of elements for several purposes, such as transparency. In particular, the Pourbaix diagram for the multielemts sytems can be set up in a simmilar manner. For example, in the Fe-S-O-H-e- system, Fe is selected as the redox element in the conventional one. In the present situation, this means exactly that S is selected to be transparent. When the transparency of S compounds is relaxed, the normal three-dimensional Pourbaix diagram will be constructed.
      • New interesting features:
        1. Diffusion and Reactions:
          The chemical potential difference that controls diffusion is called the diffusion potential. As described in the conventional diagram, the chemical potential is also the key property in understanding chemical reactions of the condensed materials in the various chemical media. By combining these ideas, it is reasonable to consider that the chemical potential diagram is a very convenient tool for examining diffusion and chemical reactions simultaneously. This is particularly important in the interface chemistry for solid-solid interfaces. Thus, it is highly suggested to draw the reaction diffusion path on the chemical potential diagram with the thermodynamic information along such path.
        2. Cooperation with Phase diagram calculation or chemical equilibrium calculations
          The generalized chemical potential diagrams have essentially the same thermodynamic information as the phase diagram. Furthermore, it well corresponds to the chemical equilibrium calculations, which are convenient for calculating the complicated equilibriums by the Gibbs minimization method. In the MALT system, gem is such software to calculate the complicated chemical equilibria. It is therefore quite encouraging to be able to apply such major thermodynamic software by using the same thermodynamic data. This will make the quality of the thermodynamic considerations quite high in many industrial fields.

    For further understanding of the generalized chemical potential diagrams, see the following