Chapter 1 Introduction

This chapter describes how to use this user’s manual; outline of the CHD forWindows system will be given in the following sequence;
1. What can be done with CHD?
2. Commands
3. Menus
4. How to Use this manual

1.1 What can be done with CHD for Windows?
This program is for constructing the chemical potential diagram.
By the chemical potential diagram, the following diagrams are included;
1) Conventional diagrams such as the Pourbaix diagram
2) Generalized chemical potential diagrams
Detailed description on chemical potential diagram will be given in Chapter 2.
To draw a diagram, the following procedures should be adopted;
1) retrieve the thermodynamic data from the MALT database or read thethermodynamic data from a file;2) change the specification of chemical system, if necessary;3) define the diagram type, the diagram coordinates, and the fixation of chemical
potential, if necessary.
4) calculate to construct the diagram.
To manipulate the diagram, the following functions are available;
1) change the location of the diagram in the display panel;2) touch the point on the diagram to know the detailed thermodynamic
information;3) draw a continuous line by manually clicking;4) change the location of the diagram and the text string or change rectangularshape;
5) zoom up or down;6) rotate the three dimensional diagram;
7) make dissections of the diagram;8) change colors or Fonts.
-1-

To transfer the diagram to other software or hardware, the following ways areprepared;1) save the diagram as a file of bitmap, jpeg, or metafile;2) copy the diagram to clipboard as metafile.

1.2 Commands
Commands in CHD for Windows will be made by selecting one of menus.
Even so, typical commands can be listed below in relation with the given
menus.
Read Data From Files (menu “File”)
Specify the Chemical System (menu “Project / Chemical System”)
Define the Diagram Type (menu “Project / Specify Diagram”)
Calculate (menu “Run / Calculate”)
Save Diagram to File (menu “File / Save Diagram to File”)
Copy Diagram to Clipboard (menu “Edit / Copy Diagram to Clipboard”)
Manipulate the Diagram (menu “Diagram”)
Diagram Display mode (menu “Diagram / Diagram Display mode”)

1.3 Menus
CHD menus are organized as follows;
File
Open file
ReopenMALT Direct
Open Default File
Save Diagram to File
Save Screen
Printer Set Up
Print
Exit

Edit
Copy Diagram
to ClipBoard
Copy Table to
ClipBoard
Copy List to
Clipboard

View
Project Status
Compound List
Graph Inspector
Chemical Potential Table
Points List
Language
Message Font
ToolbarMain Diagram

TableList
Display mode
Zoom
LoglistAdd String

-2-

Run
Calculation
One Dissection
One Dissection Swing
Many Dissection

Diagram
Range
Rotation
ChangeCoordinates
Display Mode
Diagram Size
Diagram Color
Diagram Font
Additional Lines
Options

NormalTouch Diagram
Draw Line
Move Location
Maximize
Standard
Arbitrary
Diagram Stay on
Diagram Resize
Default Color
Default Black andWhite

Window
HiddenF

Help
CHD Contents
Version Info

1.4 How to Use This Manual

List of Points
Space Value
Coordinates Values
Display Points
Specieslog(Activities)
Species concentration
Coefficients of Space
Selection of Columns
Exit

CHD for Windows provides facilities for constructing generalized chemical
potential diagrams.
This manual has been prepared by assuming that users are able to do thefollowings without any problems;
1. With adequate knowledge about Windows and related software to start
Windows;
2. to have ability of writing computer programs in more than two computer
languages;
3. to have proper knowledge about the thermodynamics to convert their own
materials problems to thermodynamic problems.

-3-Even so, the Chapter 3 is prepared for beginners in both applying
thermodynamics and handling personal computers.
This manual consists of the following chapters;
chapter 1 : introduction
chapter 2 : Generalized chemical potentials diagrams
To use this CHD for Windows, it is essential to know the materials
thermodynamics properly. In this chapter, a brief explanation will be given forgeneralized chemical potentials diagrams. Users are highly recommended toread review articles to know the whole features of the generalized chemical
potentials diagram.
The followings are articles which give rather detailed description ofgeneralized chemical potential diagrams,
1) H. Yokokawa, “Generalized Chemical Potential Diagram and its
Applications to Chemical Reactions at Interfaces between Dissimilar
Materials,” J. Phase Equilibria. 20(3), 258-287 (1999).
2) H. Yokokawa, “Fundamental and Applications of the Generalized
Chemical Potential Diagram (in Japanese),” Materia (Journal of Metal.
Society Japan) 35, 1025-1030, 1133-1139 , 1250-1255 , 1345-1351 (1996).

chapter 3 : Instruction Let's run CHD for Windows
This chapter describes the most fundamental way of using CHD for Windows
in an appropriate sequence. Please run MALT for Windows according to the
instruction given in chapter 3 of the Manual for MALT for Windows. Then,try to touch CHD for Windows to draw different kinds of diagrams. This will
give you interestingly interactive time with generalized chemical potentials
diagrams.
chapter 4 : For full use of CHD for Windows functions
This chapter describes details of CHD for Windows menus and functions
including those which are not described in chapter 3.

-4-Chapter 2 Generalized Chemical Potential
Diagrams

In this chapter, the generalized chemical potential diagram will be described in
the following aspects:
1) Conventional vs. Generalized chemical potential diagram
2) Characteristic features of chemical potential diagram
3) A New Algorithm for Further Generalization
4) Applications of generalized chemical potential diagram

2.1 Conventional vs. Generalized chemical potential diagrams
2.1.1 Conventional chemical potential diagram
The conventional chemical potential diagram is a kind of stability diagram inwhich the redox element is selected and the stability area of its compounds are
displayed as functions of chemical potentials that represent the chemical
properties of environments. In Fig. 1, the chemical potential diagram for the
Fe-O-S system at 800K is displayed. A typical chemical reaction for
representing such a diagram is given as
2FeSO4 = Fe2O3 +S2 + 2.5O2[2.1]

The left hand side of this fundamental equation is always one compound of theselected redox element, whereas the right hand side consists of anothercompound of the redox element and species adopted for coordinates. Thus,
two-phase-coexistence relation between FeSO4 and Fe2O3 is given as areaction with S2 and O2. This makes it possible to give the following relation
to representing the phase boundary in the chemical potential diagram.
2µ(FeSO4) = µ(Fe2O3) + µ(S2) + 2.5µ(O2)

-5-

[2.2]

log {p(S2)/atm}

5
0

S

-10

FeS2
Fe0.877S
FeS

FeSO4

Fe2(SO4)3
-20

-30

Fe

-30

SO3
Fe3O4

Fe2O3

-10

-20

0

log {p(O2)/atm}
Fig. 2.1 Conventional chemical potential
diagram for the Fe-O-S system at 800 K.

The coefficients of 1 and 2.5 for µ(S2) and µ(O2) provides a slope of the phaseboundary in the chemical potential diagram.
The main features of such conventional chemical potential diagram can besummarized as follows;
1) In any cases, the redox element has to be determined.
2) The coordinate variables are selected from the chemical potential
values which can characterize the chemical environments. For
example, log {p(O2)/atm}, log {p(S2)/atm}, log {p(CO2)/atm}, log{p(Na)/atm} are usually used .
In many cases, the coordinate variable can be regulated by an appropriate
experimental way. This makes this diagram valuable as the stability diagramor the predominant area diagram. This provides useful tools to understand thethermodynamic stability of materials in various chemical environments.
On the other hand, there are several demerits in the conventional chemical
potential diagrams. These are1) When there are several candidates for redox elements, it becomes difficult
to select properly one redox element. This makes it difficult to apply the-6-conventional diagrams to those systems containing alloys or doubleoxides;2) From a similar reason, it is difficult to extend to the multi-component
systems. When the appropriate environmental coordinates could beselected, the stability diagram could be extended to the multi component
systems. However, it is not easy to find out appropriate coordinates in
actual material systems without difficulties;3) The interface stability among different materials cannot be examined
properly, just because more than two elements are always to be consideredsimultaneously.
2.1.2 Generalization
The above demerits are originated from the selection of the redox element andthe coordinates corresponding to the environmental variables.
To overcome such demerits, it is essential to have the more generalized
fundamental reaction to construct the chemical potential diagram. This can begiven in the following relation:
2La + 2 Zr + 7O = La2Zr2O72µ(La)+2µ(Zr)+7µ(O)=∆fGº(La2Zr2O7)[2.3]

Here, the Gibbs energy for formation of La2Zr2O7 is correlated with thechemical potentials of elements La, Zr and O.
Strictly speaking, the above reaction should be corrected for the reference
state for the elemental chemical potential. In the convention for thereference state adopted in the JANAF table, the reference state is selected at
respective temperatures. In such a case, the above equation should be
rewritten as follows;
2{µ(La)-µº(La)}+2{µ(Zr)-µº(Zr)}+7{µ(O)-µº(O)} = ∆fGº(La2Zr2O7)
where µº(La) is the chemical potential value at the reference state at atemperature. In another convention adopted in data book by Barin-Knacke,
the reference state is defined only at 298.15 K. In such a case,2{µ(La)-µºLa}+2{µ(Zr)-µºZr}+7{µ(O)-µºO} = ∆f’Gº(La2Zr2O7)
where µºLa is the reference chemical potential of La at 298.15 K and∆f’Gº(La2Zr2O7) is the Gibbs energy change referred to the standard-7-

µ(La)/RT
La2O3

LaCoO3La2Zr2O7

CoOµ(Co)/RT

ZrO2µ(Zr)/RT
Fig. 2.2 Generalized chemical potential diagram for the
La-Co-Zr-O system at 1273 K under p(O2) = 1 atm.

temperature. The difference between ∆fGº(La2Zr2O7) and ∆f’Gº(La2Zr2O7)
is described in details in the Manual of MALT for Windows.
In Eq. [2.3]. the references states are adopted as µºLa=µºZr=µºO=0.0 andGº=∆f’Gº.
The equation [2.3] is a linear equation in theµ(La)- µ(Co)- µ(Zr)-µ(O) four dimensional space. When the phase relations
under the condition of p(O2) = 1 atm are considered, the above equation has
two variables in the µ(La)- µ(Co)- µ(Zr) space. Geometrically, this indicatesthe plane in the µ(La)- µ(Co)- µ(Zr) space that has a slope of (2,0,2) as shownin Fig. 2.2. When another compound, LaCoO3, having the different
stoichiometric numbers is considered, this phase corresponds to a plane having
a different slope so that two compounds have a common edge. Furthermore,
Gº in Eq.[2.3] determines the relative location of the plane to the origin,
namely, the reference states of elements. Thus, the thermodynamic
information of compounds all well appears as the geometrical features of theplane. By using Eq. [2.3] as the fundamental reaction for constructing thechemical potential diagram, the generalized chemical potential diagrams canbe thus constructed without selecting any redox element or specifying theenvironmental chemical potentials.

-8-

Table 2.1 Comparison between conventional and generalized chemical
potential diagrams.
Chemical potential diagrams
Conventional
Generalized
Selection of one Redox Element
Free to Select Metals/Nonmetals
As functions ofAs functions of
any chemical potentials
chemical potentials
for representing
for representing the state
Environmentsof elements(pH, log p(O2) etc)
inside solid substances.
(µ(M)/RT)
Difficult to apply to Alloys or
Simultaneous considerations
Complex oxides
on Chemical Reactions
and Diffusion
Solid/gas, solid/solid interfaces

As shown in Fig. 2.2, three-phase coexistence can be represented as a corner ofthree planes. This corner represents a point in the chemical potential space sothat the thermodynamic functions are uniquely determined as suggested fromthe Gibbs phase rule.
All stable compounds form a polyhedron consisting of planes having negative
slopes. That is, this polyhedron is open to the negatively infinite directions.
This corresponds to the fact that the stoichiometric number is always positive.
Comparison between the conventional and the generalized chemical potential
diagrams is given in Table 2.1.
Since there is no need to select any redox element, it is possible to treat twoelements in an equivalent way. This generalization makes it possible toexamine the interface stability between two materials. In Fig. 2.2, the chemical
stability between LaCoO3 and ZrO2 can be identified as unstable against theformation of La2Zr2O7 and CoO. This corresponds to the following chemical
reaction:
LaCoO3 + ZrO2 = 0.5 La2Zr2O7 + CO + 0.25 O2(g)

-9-

[2.4]

O2(g)
LaCoO3CoO

La2Zr2O7

ZrO2

J(La3+)
J(Zr4+)
J(Co2+)

Fig. 2.3 Reactive diffusion path for interface reaction between LaCoO3 andZrO2The Gibbs energy change for this reaction can be found to be negative at 1273
K.
In solid involved reactions, diffusion plays important roles. Unlike gaseous
reactions, homogeneous reaction cannot proceed in the solid-solid reactions.
Since the driving force for diffusions is provided as the chemical potential
difference, reaction diffusion path can be well represented in the chemical
potential diagram. In other words, coordinates for the generalized chemical
potential diagrams indicate the thermodynamic state inside solid materials
which can be correlated with the reactive diffusion. In this sense, thegeneralized chemical potential diagram provides not only the stability of thesubstance but also the driving force for diffusion and resulting reactive
diffusion path. For example, the chemical reaction between LaCoO3 and ZrO2
proceeds through diffusion shown in Fig. 2.3. The reaction products, CoO and
La2Zr2O7, form a layered structure; the sequence is given as
LaCoO3/CoO/La2Zr2O7/ZrO2. A key point is in that CoO appears just next to
the LaCoO3 not in between La2Zr2O7 and ZrO2. Since the oxygen potential isnearly constant throughout the reaction zone, this sequence is reasonable fromthe chemical potential point of view. That is, the chemical potential of Co
should be maximum in CoO. This does not allow for Co ions to migrate toform CoO. Instead, CoO is formed as a result of diffusion of La ions in
LaCoO3 to migrate beyond the CoO phase. In such a case, La ions can diffuse
through along the La chemical potential gradient. On the formation of CoO
phase, the valence of Co ions changes so that oxygen may be evolved aroundthe LaCoO3 and CoO interface. On the other hand, Zr ions diffuse through
La2Zr2O7 phase. The La and Co ions meet at the CoO and La2Zr2O7 interface.
These features in diffusion associated with solid-solid interface reactions canbe represented as the reactive diffusion path in the chemical potential diagram- 10 -

(a)

n(A)

AC

(b)

A

AB

AC

AB
n(C)

B

C

n(B)

(c)

(d)

µ(A)

AB
B

AC
C

µ(C)

µ(A) - µ(B)

A
A

AB

AC

B

C

µ(C) -µ(B)µ(B)

Fig. 2. 4 Type 1 diagram for the A-B-C system. (a) three dimensional molar
space, A1-xB1-yCx+y. Compound AB and AC are represented by lines whichstart from the origin and the slope corresponding to the stoichiometricnumbers; (b) Composition diagram, (c) three dimensional chemical
potential diagram, (d) two dimensional chemical potential diagram using
two variables in the chemical potential difference type.

as shown in Fig 2.2. This is one of the characteristic features of generalizedchemical potential diagram.

2.2 Characteristic features of generalized chemical potential
diagrams
The generalization can be realized in many aspects.
Conventional chemical potential diagrams can be constructed from thepolyhedron in the chemical potential space. For example, Fig. 2.1 wasconstructed from the same procedure as the generalized chemical potential- 11 -

(a)

(b)

n(A)

AC 2

AC
AB

AC 2

AB 2

AC
n(C)

ABC
n(B)

A

(c)

AB

AB 2

(d)

µ (C)

AC 2

AC 2

ABC

µ(C)

ABC
AC

AC

AB 2
AB
A

AB 2

µ (B)

A

µ (A)

AB

µ (B)

Fig 2.5. Type 2 diagram for the A-B-C system. (a) Molar space and systemrepresentation as ABnCm. (b) Compositional diagram where n and m in
ABnCm are adopted as coordinates, (c) three dimensional chemical potential
diagram, (d) two dimensional diagram with coordinates of elemental
chemical potentials.

diagram. In Fig. 2.1, the thermodynamically inaccessible areas are displayed
as a gray area. In this area, any sulfur – oxygen compounds arethermodynamically unstable and decomposed into S or SO3. From thegeneralized diagram point of view, this corresponds to the fact that only on thesurface of the convex polyhedron, thermodynamically meaning states are
realized. In other words, spaces above the polyhedron are thermodynamicallyunstable. This space is displayed as gray in Fig. 2.1.
2.2.1 Three types of two dimensional chemical potential diagrams
To construct the two dimensional diagram, two chemical potentials should
be selected as coordinate variables. This is a kind of the projection ofpolyhedron to a plane which is defined by the two coordinates. Here, one
problem arises due to the convex nature of polyhedron; that is, in some cases,
projected phase relations are doubly folded on the coordinate plane. To avoid- 12 -

(a)

n(A)

AC

(b) A

AC

A2B
A 2C
AB2C3

n(C)
AB2C3
n(B)

B

BC

BC

(d)
µ(A)

A
AC

A
AC

A2B

AB2C3
B

µ(C)

BC

µ(A) - µ(B)

(c)

A2B
AB2C
B

µ(B)

BC

µ(C)

Fig. 2.6 Type 3 diagram for the A-B-C system. (a) Molar space for thesystem represented by A1-xBxCn. (b) Compositional diagram for A1-xBxCn
system, (c) three dimensional chemical potential, (d) two dimensional
diagram with coordinates of elemental chemical potential and chemical
potential difference.

this overlapping, there can be several ways of selecting the coordinate
variables. For three component systems, the following diagrams can beconstructed:(1) Type 1 is for the three component system where the three components areequivalently treated as shown in Fig. 2.4. In the molar space, this system isrepresented as A1-xB1-yCx+y. In the compositional space, a triangle diagram
is appropriate for representing this system. This is frequently used for
ternary alloys and ternary oxides systems. For the two dimensional
chemical potential diagram, two chemical potential differences, µ(A)-µ(B)and µ(C)-µ(B), are used as coordinates. Use of the chemical potential
difference is a key point in representing phase relations in the twodimensional plane. A sum of elemental chemical potentials, µ(A)+µ(B), is- 13 -

inappropriate as coordinate, because phase relations are always folded andoverlapped.
(2) Type 2 is for the three component system where the element A and theelements B and C can be treated differently; for example, A is the metallic
element and B and C are the non-metallic elements. For the twodimensional diagram, two elemental chemical potentials, µ(B) and µ(C),are used as coordinates. Since µ(A) is not used as coordinates, it is thesame as the conventional diagram.
(3) Type 3 is for the three component system where the elements A and B andthe element C are different. For example, A and B are metallic and C is
non-metallic. For the two dimensional diagram, the elemental chemical
potential difference, µ(A)- µ(B), and the elemental chemical potential,µ(C), are used.
Note that in any cases, the three dimensional chemical potential diagram shows
properly the phase relations in the three-component system without further
treatment. In this sense, the generalization of the three dimensional chemical
potential diagram is extremely high.
Figs. 2.4 to 2.6 were constructed by using the test data which are stored as
ABC1.abs, ABC2.abs, and ABC3.abs; see 4.3 Menu “File” and Fig.4.4.

2.2.3 Some features of two dimensional diagram
The geometrical features of the generalized two-dimensional diagrams are
explained by using the type-3 two dimensional diagram for the La-V-O systemand the Sr-V-O system shown in Fig. 2.7 and 2.8.
1) The phase relations in the La-V-O system are shown in the twodimensional diagram with coordinates of log [p(O2)/atm] and log[a(V)/a(La)].
2) The phase relations in the V-O sub-binary system are shown in the upper
part, those in the La-O sub-binary system being in the lower part. Phaseboundaries of such systems are represented by vertical lines. The La-V
sub-binary system is shown in the left hand side of the diagram. Here, no
La-V intermetallic compounds are presented in the absence of their
thermodynamic data. Phase boundaries in the La-V system are given as
the horizontal lines.

- 14 -

Fig. 2.7 Two dimensional diagram for the La-V-O system at 1273 withcoordinates of log [p(O2)/atm] and log [a(V)/a(La)].

Fig. 2.8 Two dimensional diagram for the Sr-V-O system at 1273 withcoordinates of log [p(O2)/atm] and log [a(V)/a(Sr)].

3) Ternary compounds appear in the middle of the diagram. In the
La2O3-V2O5 pseudo binary system, ternary compounds appear in parallel.
Their borderlines have the slope of –1/2. Similarly, in the La2O3-V2O3
pseudo binary system, LaVO3 appears with borderlines having the slope ofzero.
4) Generally speaking, the slope of two adjacent phases is determined by theirstoichiometric numbers.
5) Compounds belonging to a pseudo binary system appear in parallel having
the same slope for borderlines. For example, the followings are in the samebinary systems:
La2O3/LaVO3/V2O3 (Fig. 2.7)
- 15 -

La2O3/La3VO7/La1.42V.58O3.5/V2O5 (Fig 2.7)
SrO/Sr2VO4/SrVO3 (Fig. 2.8)
SrO/Sr3V2O7/Sr2V2O7/SrV2O6/V2O5 (Fig. 2.8)
This is true even when the same valence number is not realized in a
sub-binary system. For example,
VO/SrVO3/Sr3V2O8/SrO2 (Fig. 2.8)
From the stoichiometric number point of view, these compounds belong tothe VO-SrO2 subsystem and appear in parallel, although the valence
number of V ions changed from +2 to +6.
6) An interruption of a series of the compounds in parallel indicates that acompound in the pseudo-binary system decomposes into other compounds
in the true ternary systems. For example, in the following reaction,
SrVO3 + VO2 = Sr2V2O7 + V2O3
[2.5]
the vanadium tetravalent ions disproportionate into the trivalent ions andthe double oxide of penta-valent V ions.
Many two-phase boundaries meet with other boundaries to form thethree-phase coexistent points.
2.2.4 Extension to multi-component systems
Adopting the fundamental equation [2.3] for constructing a diagram makes it
possible to extend to the multi-component systems.
Instead of three dimensional chemical potential space, the n-component
chemical potential space can be setup for the n-component chemical systems.
In such a space, the n-phase coexistence determines the chemical potentials
uniquely, corresponding to a point in the space. The (n-1)-phase coexistence
gives lines. In other words, any compounds can be represented by super planesin the space.
To represent such phase relations in a diagram, however, special means will beneeded to reduce the dimensionality such as fixation of selected chemical
potential; make a dissection; make some parts of diagram transparent.
Fixation of chemical potential
When the system has n (>3) components, the chemical potential diagram canbe set up by fixing the (n-3) chemical potentials.

- 16 -

Fig. 2.9 Chemical potential diagram for multicomponent systems.
La-Zr-Co-O system at 1273 K and under a condition of p(O2) = 1 atm.

The

Fig 2.9 shows the chemical potential diagram for the La-Zr-Co-O system at1273 K. Since the component number is four, one fixation of chemical
potential makes it possible to draw the chemical potential diagram. In Fig. 2.9,
the oxygen partial pressure is fixed at 1 atm. As coordinates, the threeelemental chemical potentials are adopted. Geometrical features of thisdiagram is essentially the same as those in the three dimensional surface
diagram for the three component systems. For example, binary oxides, insteadof elements, appear as the planes perpendicular to the corresponding
coordinates; that is, La2O3, ZrO2, CoO are perpendicular to axes of µ(La),µ(Zr), µ(Co). Double oxides appear between the binary oxides in a similarmanner.
This diagram should be compared with the triangle compositional diagram at
p(O2)= 1 atm. In pseudo ternary ceramic systems, phase relations provide thefundamental basis of understanding the chemical reactions and related phasebehavior. Similarly, the chemical potential diagram like Fig.2.9 can provide
the basis for chemical reaction among the ceramic materials. Particularly, Fig.
2.9 shows that LaCoO3 and ZrO2 can react to form La2Zr2O7 and CoO as
already given in Eq.[2.4].
Selection of chemical potential to be fixed is arbitrary. It is therefore very
important to select the appropriate fixation of chemical potential in order toextract useful thermodynamic information. Fig. 2.10 compares the two three
dimensional surface diagrams; (a) is for the La-Co-O system at 1273 K and (b)- 17 -

(a)(b)

Fig. 2.10 Chemical potential diagram for multicomponent systems. The
La-Zr-Co-O system at 1273 K and under a condition of a(ZrO2) = 1 (b) iscompared with the La-Co-O system at 1273 K (a).

is for the La-Zr-Co-O system at 1273 K under the condition of a(ZrO2)=1.
Since the zirconium oxide is used in fixation, it is natural to use other threeelemental chemical potentials. This makes it possible to compare two
diagrams directly. The condition of a(ZrO2)=1 means that zirconia oxide isalways present in an excess amount. In such a condition, La2O3 is no longer
stable against the reaction with ZrO2 to form La2Zr2O7. The presence of
La2Zr2O7 in addition to ZrO2 indicates that the chemical potential of the La2O3
component is lowered. In Fig. 2.10, the stability polygon for La2Zr2O7 appears
so as to cut off the stability polygons of La2CoO4 and La4Co3O10. This meansthat these compounds are completely unstable against the reaction with ZrO2.
La2CoO4 + 2ZrO2 = La2Zr2O7 + CoO
La4Co3O10 + 4ZrO2 = 2La2Zr2O7 + 3CoO + 0.5 O2(g)

[2.6]
[2.7]

There remains the stability region of LaCoO3 although the area is narrowed by
the presence of La2Zr2O7. This suggests that the formation of La2Zr2O7 and
CoO from LaCoO3 and ZrO2 is governed by the oxygen potential, and only inthe high oxygen potential region, LaCoO3 is stable against reaction with ZrO2.
Construction of three dimensional diagram with a function of dissection
For the ternary system, two dimensional diagram can be set up. This implies
that a three dimensional diagram can be set up for the quaternary systems. Fig.
2. 11 shows one example for the Li-Fe-C-O system at 923 K. In the three
dimensional chemical potential diagrams, the stable compounds are- 18 -

Fig. 2.11 Three dimensional chemical potential diagram for multicomponent
systems. The Li-Fe-C-O system at 923 K. The stability polyhedrons of carbon
and Li2CO3 are made transparent.

represented by polyhedrons instead of polygons in the three dimensionalsurface diagram. In this sense, it becomes difficult to display thesepolyhedrons in a visually understandable way.
One way to see the geometrical features of those polyhedrons is to make somepolyhedrons transparent. In Fig. 2. 10, the polygon of carbon and thepolyhedron of Li2CO3 are made transparent.
Another way is to make dissections for the three dimensional diagram to givethe two dimensional diagram. Dissection is defined in a similar manner to thefixation; that is, selection of species chemical potential and their fixed value.
This dissection diagram can be changed by adjusting the location of dissection
plane in terms of the fixed value.

2.3 A New Algorithm for Further Generalization
CHD for Windows adopts a new algorithm of constructing a polyhedroncorresponding to a chemical potential diagram. This algorithm is named asconvex polyhedron method and is briefly explained here.

- 19 -

New features in chemical potential diagrams
The new algorithm is based on the polyhedron approach which proves newfeatures of the chemical potentials as follows:(1) Further generalization of coordinate axis.
The fundamental coordinates are based on the elemental chemical
potentials. In principle, this can be easily extended to other intensive
thermodynamic variables. Particularly, temperature and pressure are themost important intensive variables. In the present version of CHD, thefollowing axes:
Temperature
Inverse Temperature
Pressure
logarithmic Pressure
are adopted.
Since the temperature dependence of chemical potential is not linear, thisextension has to include the treatment for non-flat planes.
(2) Treatment for mixture phase
Initially, CHD was coded for treating only the stoichiometric compounds.
However, treatment for mixtures is highly required particular whenapplications to practically important materials problems are concerned.
As the simplest mixture, the ideal association model is adopted.
Algorithm for Constructing Chemical Potential Diagrams
Some twenty years ago, Linkson and coworkers summarized the computer
methods for construction of the Pourbaix diagrams and categorized into threemethods; that is, Point-by-Point method, Line elimination method and Convex
polygon method.
P. B. Linkson, B. D. Phillips, and C. D. Rowles, “Computer Methods for the
Generation of Eh-pH Diagrams,” Minerals Sci. Engng., 14(2), 65-79(1979).

Since the convex polygon method is the most advanced and elegant algorithm,
almost all recent methods are based on the convex polygon method.
Old CHD program for constructing the generalized chemical potential
diagrams is also based on the polygon method. More generalization, however,has been achieved in our previous algorithm, that is, adoption of the formation
reaction as basic equation, no need of selecting one redox element, generalized
selection of coordinate axes and so on.

- 20 -B
B

C

C

BeneathA

BeyondCreation of Skelton Frame

Polyhedron
Next Plane()

Determination of Intersection
between Polyhedron andsuperplane

New Polyhedron

Fig. 2.12 Convex polyhedron approach to constructing the chemical
potential diagram.

The present new method aims at extending this method to more flexible one
and making applicable to multicomponent systems. Since the algorithm isbased on the three dimensional polyhedron, this can be called as “Convex
Polyhedron Approach.”
The main point of the convex polyhedron approach is to obtain theintersection between a previously obtained polyhedron and a new plane. Theintersection is obtained as follows;
1) a polyhedron consists of facets, edges and vertices.
2) For respective vertices, judgment will be made on whether the vertex isbeneath or beyond the plane.

- 21 -

4) Between the beneath vertex and the beyond vertex, a new vertex point
can be obtained as the intersection point of the edge and the new plane.
5) New vertices can be connected with each other to form new edges and afacet. This facet forms the intersection.
6) The beyond vertices can be deleted to form a new polyhedron having the
new facet in it.

Merits of Convex Polyhedron Approach
The present polyhedron approach has many merits as a computer algorithm.
This can be briefly explained below.
Computer geometrical considerations are the basis of constructing chemical
potential diagrams. This makes it possible to divide complicated procedures
into two independent procedures:(1) Geometrical procedures based on the features of vertices, edges and facets
are common to any kind of diagrams. This is based on the geometricalfeatures alone and does not need any numerical calculations.
The geometrical judgment is made by using the convexity of the twoplanes. As shown in Fig 2.13, the thermodynamic relations given in the
Gibbs energy(chemical potential) vs. composition plot can be re-plotted in
the chemical potential-chemical potential plot. In the Gibbs energy vs.
composition plot, the stable phases are represented as lines which locatedat the lowest part, and those sable phases form convex relations in the
downward direction. The same relations plotted in the chemical
potential-chemical potential plot have the similar features; that is, thestable phase is represented by a line which dissects the lowest parts and thestable phases form the convex polygon.
This makes it possible to extend easily to multi component systems. The
basic relations to be used in the geometrical considerations are theconvexity of the intersected planes. When the n-component system isconsidered, the super plane is given by one equation and the intersection of
the super planes is determined by two equations.
This is also makes it possible and easy to include the temperature orpressure as coordinate axes. As shown in Fig. 2.13, the same convexity canbe applied to the temperature dependent phase. Here, the chemical
potential can be given as a function of temperature. In a unary system, the- 22 -

chemical potential is equal to the Gibbs energy. In the chemical potential
vs. temperature plot, the stable phase is always the lowest value at thegiven temperature. When the stable phase is changed, the convexity
appears in this plot. The same geometrical features can be obtained in thechemical potential divided by RT vs. inverse temperature as given in Fig. 2.
13.
(2) Numerical Calculations
Several judgments are made by numerical calculations independently of
the geometrical consideration. For example, the following procedures
require the numerical calculations.
(a) Beneath-beyond criterion for a plane against respective points(Vertices) This is quite important judgment. Whenever one plane isconsidered in a geometrical convex polyhedron, this judgment is required.
(b) Derive an Intersection between An Edge and A Plane
This is the most frequently appearing procedure. This intersection point
usually becomes a new vertex.
(c) Derive An Edge between Two Vertices
When all phases involved are stoichiometric compounds, this procedure isquite simple; this is the connection of two points by a straight line.
These features make it possible to treat mixture phases in a simple way. The
above three calculations can be easily extended to include mixture phases.
For treatment of temperature dependent phase relations
Generalization can be made to extend to include the axes corresponding
temperature and pressure by using the same geometrical considerations; that is,convexity and beyond – beneath criterion.
First, we check the equation for chemical potential. Here we have to recognizethat there are two ways of adopting the reference state in representing Gibbs
energy. First one is the following;l (µ(A) - µ°(A))+ m (µ(B) - µ°(B)) + n (µ(C) - µ°(C)) = ∆fG°(AlBmCn)[2.8]- 23 -

(b)

B
µ (A)
1

A

A3B

µ (B)

AB

µ (A)

3

{µ (A),µ (B)}1µ(A)

G, µ(A),µ(B)

(a)

2

µ (B)
2

A

1

{µ (A),µ (B)}
2

A3B

2

AB
{µ (A),µ (B)}
3

3

µ (A)
3

B
µ (B)
1

A
(c)

xB
µ(Α) = hº(T) - T sº(T)

µ(Β)

B

(d) µ(Α)/RT = hº(T)/RT - sº(T)/Rµ(Α)/RTµ(Α)µ(Β)/RT

µ

µ/RT

µ(Β)

T

1/T

Fig. 2.13 Convexity in (a) Gibbs energy vs. composition space; (b)chemical potential space and (c,d) in the chemical potential – temperature
space.

In this representation that the JANAF thermochemical table and other major
data books adopt, the reference state is defined for each temperature; this canbe expressed as µ°(A). Second way isl (µ(A) - µ°A)+ m (µ(B) - µ°B) + n (µ(C) - µ°C) = G°(AlBmCn)[2.9]

Here, the reference state is defined only at the standard temperature, 298. 15 K.
This is adopted for example in the data book by I. Barin. To describe the phaserelations as a function of temperature, the second method is appropriate. Note

- 24 -

that in this representation, the element in the reference state has no longer zero
Gibbs energy.
In the chemical potential diagram, usually the value of the chemical potential
divided by RT is used. Correspondingly, the inverse temperature can be
adopted to be consistent with the treatment of chemical potentials:{- h°(AlBmCn) /R} {1/T}+{l}{(µ(A) - µ°A)/RT}+{m} {(µ(B) - µ°B) /RT}+{n}{(µ(C) - µ°C) /RT} = - s°(AlBmCn) /R[2.10]Here,
G°(AlBmCn) = h°(AlBmCn) - s°(AlBmCn) T[2.11]

where h°(AlBmCn) and s°(AlBmCn) are the enthalpy and the entropy of thecompound AlBmCn.
In Fig. 2.13, the convexity is compared in various spaces; in the G-x plot (a),the convexity appears in the downward, whereas in the µ(A) - µ(B) plot, it
appears in the right-upper direction. In the µ - T plot (c), it appears in the samemanner as (b). In the last µ/RT- 1/T plot (d), it appears in the left – upperdirection.
In Fig. 2.14, an example of the generalized chemical potential diagram
including the inverse temperature as axis is shown for the Mn-O system.
Oxygen gas is also included in this case. Its chemical potential divided by RT
decreases increasing temperature; the same behavior can be seen for
manganese. From the equation [2.10], it is easily understood that a slope inµ/RT- 1/T plot means minus enthalpy and the intersection at 1/T=0 indicatesminus entropy value. Always, entropy of elements increase with increasing
temperature.
Binary oxides in the µ(Mn)/RT-µ(O)/RT- 1/T plot appear in a different manner.
At a constant temperature, the chemical potential diagram behaves like in Fig.
2.13(b). In Fig. 2.14, this can be seen as the dissection at the lowest
temperature. With increasing temperature (decreasing inverse temperature),
the chemical potential values change with a positive slope in the plot. This
corresponds to the fact that the enthalpy change for formation of compounds is
usually negative.

- 25 -

1.0

50

kK/T
2.0

3.0

O2(g)
MnO2
Mn2O3

0

µ(O)/RT

Mn3O4
-50
MnO
-100

-150

-250

Mn

-200

-200

0

-150
-100
-50 µ(Mn)/RT

50

Fig. 2.14 Generalized chemical potential with inverse temperature for
Mn-O system.

Along the boundaries with p(O2)=1 atm, the manganese chemical potential
decreases with lowering temperature. This is completely opposite behavior
against the manganese chemical potential in Mn metal.
The decomposition of binary oxides can be represented by the geometricalfeature that the stability region of one compound disappears at the higher
temperatures. For example, in Fig. 2.14, the three phase point of
MnO2/Mn2O3/O2(g) indicates that MnO2 decomposes into Mn2O3 as follows;
MnO2 = 0.5 Mn2O3 + 0.25 O2(g)[2.12]

Similarly, the decompositions of Mn2O3, Mn3O4, MnO can be seen in Fig.
2.14.

- 26 -

kK/T
1.0µ(Mn)/RT

-100

3.0

MnO
Mn3O4
Mn2O3

0

-50

2.0

LaMnO3MnO2

La2O3
La2Zr2O7

-150

-400
-300
-200µ(La)/RT
-100

-200

0

Fig. 2.15 Generalized chemical potential with inverse temperature for
La-Mn-Zr-O system under the conditions of p(O2)=1 atm a(ZrO2)=1.
From the chemical potential point of view, there is an interesting feature in Fig.
2.14; that is, µ/RT-can be lowered with decreasing temperature in binaryoxides, although this kind of behavior could not be seen in elements.
In Fig. 2.15, another example is shown for the generalized chemical potential
diagram with inverse temperature. Since the La-Zr-Mn-O system has 5
freedom in the chemical potential – temperature space, two chemical potential
values should be fixed to obtain the three dimensional surface chemical
potential diagram. In Fig.2.15, oxygen partial pressure is fixed at 1 atm andalso the activity of zirconium oxide is fixed at unity. This condition isconvenient to see the reactivity of ZrO2 with LaMnO3.
In this figure, there are several points to b e noted :1) µ(Mn)/RT in the manganese oxides decreases with decreasing temperature.
This corresponds to the fact described above on the behavior along the
MnOn-O2(g) boundaries.
2) La2Zr2O7 phase appears instead of La2O3 because ZrO2 is always available
to form the zirconate.
3) the stability area of LaMnO3 appears between manganese oxides and
La2Zr2O7. This means that in this region, LaMnO3 can stably coexist with- 27 -

log {a(Mn2O3)/a(La2O3)}

20
10
0

MnO2

Mn3O4 Mn
Mn
O
2O23 3MnO

0.01

0.001 0.0001

d=0.05

-10

0.1

0.02

0.2

0.01

La1-xMn1-yO3-d
Perovskite

-20

La2O3

La2O3

-30
-40

y=0.01
x=0.2
0.1

1.0

2.0

3.0

kK/T

Fig. 2.16 Generalized chemical potential with inverse temperature for
La-Mn-O system under the conditions of p(O2)=1 atm with additionallines for constant substoichiometric values for La, Mn and O
stoichiometry.
ZrO2. Note that this area is limited at both high and low temperatures. Thiscan be written down as follows;
LaMnO3 + ZrO2 + 0.25 O2(g) = 0.5 La2Zr2O7 + MnO2
LaMnO3 + ZrO2 = 0.5 La2Zr2O7 + MnO + 0.25 O2(g)[2.13][2.14]

It is interesting to note that both reactions are related with oxidation or
reduction of manganese ions.
Framework and Points in the stability region
The generalized chemical potential diagram consists of frames which gives theborders among the stable phases. This gives the information of phaseequilibria and related chemical reactions.
On the other hands, each point inside stability polygons exhibits one
thermodynamic state that should be characterized in terms of defects. Relation
between defect concentration and the chemical potentials is not trivial so that it
will be needed to have a simple model to correlate the defect properties and thechemical potentials. In such a case, it will be straight-fold that the diffusion
properties will be discussed in the chemical potential space.
Fig.2.16 shows the chemical potential diagram for the La-Mn-O system inwhich the perovskite phase is treated with an ideal association model to- 28 -

represent the La, Mn, and oxygen nonstoichiometries. Each point inside thestable field of LaMnO3 phase has the different stoichiometric numbers. It will
give some information how those cations and anions have the vacancies andexhibit the diffusivities.

2.4 Applications of generalized chemical potential diagrams
Use as stability diagram, predominance area diagram
This is one of the conventional ways of utilization of chemical potential
diagram. One element is selected; this is frequently called “redox element.”
The diagram shows the stable chemical forms of these elements as functions ofenvironmental chemical potential values. By “environmental” valuables, itmeans that these values are controllable. This implicitly assumes that thechemical species which represents the environmental conditions can easilyinteract with those substances which contain the redox element.
Fig. 2.17 indicates that the stability diagram or the predominance area diagram
is based implicitly on the situation that the diffusion of oxygen gas and its
interaction with the solid materials is sufficiently fast so that any gradient ofoxygen chemical potential will appear in the system.

MO2 = MO + 1/4 O2(g)O2(g)
Fig. 2.17 Phase equilibria and environmental chemical potential. Oxygen gas
can freely penetrate into any parts of the system to realize phase equilibria.

- 29 -

Fig. 2.18 Interface reaction and associated with reactive diffusion path in thecompositional diagram and in the chemical potential diagram.

Use as Compatibility diagram or Reactive diffusion path plotter
The generalized chemical potential diagram can treat alloys or complex oxides
as well. That is, the stability of such materials can be easily examined asfunctions of environmental valuables. In addition, this can be applied to
examine the chemical compatibility of different materials. When twomaterials are in equilibrium with each other, their stability regions should be
adjacent in the chemical potential space. It is a quite simple criterion.
When two materials are not in equilibrium, there appears driving force forchemical reactions and/or interdiffusion across the interface of two materials.

- 30 -

Chemical reaction and associated interdiffusion will provide a microstructureof a developed reaction zone as shown in Fig. 2.18. To examine how thechemical reaction and interdiffusion proceed at the interface, it becomes
common to plot the reactive diffusion path in the compositional phase diagram
particularly in the alloy systems. As shown in Fig. 2. 18, such reactive
diffusion path exhibits quite complicated features in the compositional
diagram. In some cases, elements diffuse against the compositional gradient.
This is called up-hill diffusion and is expressed by the path having the
backward direction.
In the chemical potential diagram, the reactive diffusion path can be drawn as
well. Since the diffusion is driven from the chemical potential difference, it isreasonably understood that the reactive diffusion path in the chemical potential
diagram becomes very simple as shown in Fig. 2. 18. Although there had been
discussed many conventional points on how to represent the reactive diffusion
path in the compositional diagram, it is essentially no need to set theconventions in the chemical potential diagram.

- 31 -

Chapter 3 Instruction
Let's Use CHD for Windows

In Chapter 3, the fundamental methods of running CHD for Windows will be
described.
This chapter consists of the followings;
1. MALT/CHD Interface
2. Set up a Typical Diagram
3. Fixation of Chemical Potentials
4. Three Dimensional (Polyhedron) Diagram for Multicomponent System
5. Non-Chemical Potential Variables

3.1 MALT/CHD Interface
In order to utilize CHD for Windows, it is essential to be familiar with MALT
for Windows. Almost all thermodynamic data to be used in CHD for Windows
will be supplied from the MALT database and its facility for treating data.
This data set is called a “compound system.” In this section, the essential part
given in the manual for MALT for Windows will be reproduced.
MALT for Windows provides the computer programs, CHD for constructing
chemical potential diagrams and gem for calculating complicated chemical
equilibria. Compared with chemical equilibrium calculations, utilization ofchemical potential diagrams is not popular. Even so, chemical potential
diagrams are quite convenient for materials thermodynamics.
Here,
explanation will be made only on how to construct the chemical potential
diagram by using the thermodynamic data stored in MALT.
1) prepare the thermodynamic data for a selected chemical system;2) run the computer program, CHD;
3) specify the conditions to construct the chemical potential diagram for theselected system;- 32 -

4) do calculation based on the polyhedron approach for constructing thegeneralized chemical potential diagrams;5) display the obtained diagram;6) manipulate the diagram upon some requirements for dissection, touch etc.
3.1.1 Preparation of the compound system in MALT for Windows
As an example to construct the chemical potential diagram, we will use the
Ca-O-C system. To retrieve the thermodynamic data, you can do the sameprocedure given as Section 3.3 in the MALT user’s manual; that is, select the“Get a Compound System” menu with the option of “Selection by Elements.”
Ca, O, C should be selected together with the mode of “compounds consistingof combination of elements.” This retrieval mode is very convenient for theconstruction of chemical potential diagrams.
3.1.2 Run the computer program, CHD
Here, it is ready to run the CHD program. The easiest way of running “CHD”
is the selection of the “CHD” command in the “Tools” main menu. This
command is to execute the following command“CHDWin.exe /md”
The meaning of the switch “/md” is that the command “MALT Direct” will bemade after the initialization procedure.
Another way to run the CHD is to use the short cut. In the link field in the“property” dialog for short cut, the name of “CHDWin.exe” is usually given.
In this field, “/md” can be added. In such a case, whenever CHDWin starts, thefirst command “MALT Direct” is performed. When it is succeeded, thethermodynamic data of the current compound system is transferred. When it isfailed, the message of “MALT is not running” appears.
Fig. 3.1 shows the resulting “CHD” main form after executing the MALT
Direct” command.

- 33 -

Fig. 3.1 CHD Main form after selecting “CHD” in the “Tools” menu.

In the title line of the Main Form, it is indicated that data are obtained by
MALT Direct for the Ca-O-C system,
The next line is the menu bar, whereas the second line indicates the tool
buttons for selected commands given in the menus. The status line is located in
the bottom of the Main form.
The main menu consists of Files, Edit, Project, View, Run, Diagram, Windows

Fig. 3.2 Chemical System Form with the page for Selection of Compound.
- 34 -

and Help.

3.2 Set up a Typical Diagram
3.2.1 Specification of Chemical System
In order to construct a chemical potential diagram, many parameters should be
defined. In the “CHD” program, such parameters are given as default values inmany cases.
In the situation given in Fig. 3.1, the CHD is ready to construct a diagram byusing default values given for this system. Even so, users may have some idea
what kinds of diagrams they want to construct. This is made in the “Chemicalsystem” submenu and the “Specify diagram” submenu in the “Project” main
menu .
MALT Direct provides the chemical system that has already organized as asystem consisting of the gaseous mixture, aqueous solution and condensed

Fig. 3.3 Select Compound for “Selection by User” for compounds to be
included in construction of diagrams.

- 35 -

phases. Usually, the chemical potential diagram is constructed for condensed
phases. In what follows, we accept this default setting for chemical system.
Even so, there are some needs to include gaseous mixture or respective
gaseous species. This can be made in the page of “Selection of Compound” inthe “Chemical System” Form as shown in Fig. 3.2.
Selection can be made between “Default” treatment or “Selection by User."
When “Default” is selected, compounds to be included can be selected from 1)
Condensed phases, 2) respective aqueous species, 3) and gaseous mixture.
When some compounds are to be excluded or included, “Selection by User”
can be selected. Clicking the “Reselection” button leads to the appearance of
the Select Compound Form as shown in Fig.3.3.
This setting for the Default selection will be stored in “CHDWin.ini” file.

3.2.2 Specification of calculation conditions
When the “Specify Diagram” submenu in the “Project” menu is selected, theFig. 3.4 Diagram Specification for giving the selected values for temperatureand pressure.
- 36 -

“Diagram Specification” Dialog will appear as shown in Fig. 3.4.
In the upper part of Fig. 3.4, the information of the current system is given to
make a proper selection of the parameters. The current Ca-O-C system is the 5component (dimension) system including temperature and pressure. For asystem which has more than 5 dimensions, default setting of the fixation ismade to fix temperature and pressure. Usually, pressure is set as 1 atm,
whereas temperature is set at 298.15 K.
In Fig. 3.4, there are 3 tabsheets for specification of conditions.
The first tabsheet of “Dimension” is for determination of temperature andpressure. Since default temperature is 298.15 K, this value is changed to 1000
K in Fig. 3.4.
In the second tabsheet of “Fixation” is for further fixation of component(dimension) properties. In the current system, we have three free dimensions
that is the appropriate number for constructing the chemical potential diagram
for the Ca-O-C system. We do not need to specify in this tabsheet for thecurrent system.

Fig. 3.5 Diagram Specification for giving the selected values for Diagram
selection.
- 37 -

Fig. 3.6 Three dimensional surface diagram for the Ca-O-C system at 1000 K.
This is the default type diagram.

The tabsheet of “Diagram Selection” is to specify the diagram type to beconstructed. The default diagram type for the current system is the 3D surface
diagram.
3.2.3 Calculation
By selecting the “Calc” submenu in the “Run” main menu, calculation starts
and then a diagram will be shown, if calculation will be done successfully.
Fig. 3.6 shows the three dimensional surface diagram for the Ca-O-C system.
“Three dimensional” indicates that there are three dimensions which can bechanged. In this case, three dimensions mean the elemental chemical
potentials of Ca, O and C. By “surface”, it means that the three chemical
potentials have one relation likeµ(Ca) + µ(C) + 3µ(O) = µº(CaCO3)[3.1]

for CaCO3. This indicates that each stable compound has its own plane having
the slope corresponding to its stoichiometry. Such planes form one polyhedron
as shown in Fig. 3. 3. Surface in this polyhedron indicates the thermodynamic
stable states. Inside polyhedron is thermodynamically inaccessible.
- 38 -

3.2.4 Diagram Rotation
For the three dimensional surface diagram, it is important to determine how todraw the three dimensional information on the two dimensional plane. This is
made by adopting the conversion parameters as follows:
U = a11 x + a12 y + a13 z
V = a21 x + a22 y + a23 z

[3.2]
[3.3]

Where U and V are the coordinates of a new two dimensional display panel andx, y, z are the coordinates of the three dimensional surface diagram. This
conversion is a part of the conversion from a three dimensional space toanother three dimensional space. The invisible third coordinate can be called“Depth, w.”
W = a31 x + a32 y + a33 z[3.4]

Rotation of the three dimensional surface diagram is realized by changing
these coefficients. This is made in the “Rotation of 3D Diagram.”
Fig. 3.7 shows the “Rotation of 3D Diagram” dialog, where the conversion
coefficients are given in the upper part.

Fig. 3.7 Rotation of 3D Diagram- 39 -

The coefficients can be changed by two different ways: the first is to change
directly the coefficients in the upper part. When one of matrix cells is clicked,
the corresponding edit field is focused among given spin edit fields. This field
can be directly edited by inputting numerical keys or by clicking the upward or
the downward arrow buttons. The second is to use scroll bars prepared forrespective axes. Furthermore, scroll bas are prepared for rotations aroundrespective axes.
Here, we change the coefficients as follows;
X-axisHorizontal 100 => 40
Vertical
0 => -15
Z-axisHorizontal -50 => -50
Vertical-20 => -80
3.2.5 Diagram Color
The diagram can be draw in black/white mode or in color mode. In color
mode, several ways can be adopted to give colors for respective polygons.
These are1) Tricolors based on the coordinates;
2) Tricolors based on the coefficients of space dimensions;
3) Colors based on Given 15 colors: Sequential
4) Colors based on Given 15 colors: Preselection.
Fig. 3.8 shows how to define the color in the diagram, where “Tricolor basedon the coefficients of space dimensions” is adopted; In this particular diagram,the dimensions of µ(O), µ(C), µ(Ca) are used and the colors of “white”, “blue”
and “yellow” are attributed. By this attribution, respective polygons can begiven according to their stoichiometric numbers. These colors can be shownby clicking the “Show Compound” button in the Form.
3.2.6 Summary of procedures[Compound System]
Selection of <Ca,C,O> system- 40 -

Fig. 3.8 Diagram Action Form / Page for Polygon Color

Here, the same Ca-C-O system is used.
[Project / Chemical System]<Chemical System> Dialog{Selection of Compounds} Page
Selection by Default
x Condensed phaseso Respective Gaseous Species
o Gaseous mixture[Project / Specify Diagram ]<Diagram Specification> Dialog{Dimension Selection} Page
Temperaturex Fixedat 1000 K
o Not Fixed
Pressurex Fixedat 1 atm- 41 -

Fig. 3.9 Three Dimension Surface Diagram for the Ca-C-O system at 1000K
after correction for Diagram Rotation.

o Not Fixed[Run / Calc][Diagram / Rotate]<Rotation of 3D diagram> Dialog
X-axis Horizontal 100 => 40
Vertical
0 => -15
Z-axisHorizontal -50 => -50
Vertical-20 => -80
As a result, the following matrix values are obtained
0.4
0.0
-0.5
-0.15 1.0
-0.8
[Diagram/Options]<Diagram Action Form>{Polygon Colors} Page
Tricolors based on the coefficients of space dimensions- 42 -

“white” O“blue” C“yellow” Ca
3.2.7 Diagram for the La-Mn-O system
This is given in Diagrams examples in CHD manual.

3.3 Fixation of Chemical Potentials
One of the merits of the generalized chemical potential diagram is that this canbe applied to multicomponent systems with fixation of an appropriate numberof chemical potentials. Here, we construct the chemical potential diagram for
the La-Mn-Zr-O system at a constant temperature.
3.3.1 Obtain the thermodynamic data for the La-Mn-Zr-O system
In MALT for Windows, the chemical system of the La-Mn-Zr-O system isselected.
The thermodynamic data for the system is transferred into CHD by using“MALT Direct.”
3.3.2 Specification of chemical system
No further specification will be made in the calculation.
3.3.3 Fixation for Diagram construction
Temperature is fixed at 1273 K and pressure is fixed at 1 atm in the“Dimension Selection” page.
Then, “Fixation” page is selected. In Fig. 3.10, the appearance of “Fixation”
page is shown. There are “List of Fixed values” box in the top and “Dissection
to be created” box in the bottom. In the “List of Fixed Values box”, buttons for“Add”, “Change”, “Delete” and “Cancel” are available.
When “Add” button is selected, “Select Fixed” Dialog will appear like given in
Fig. 3.10. First, selection is made among the “type of fixation.” Here, the- 43 -

Fig. 3.10 Fixation of chemical potential is made by the following
sequence:(1) click “Add” button;(2) Select the Fixation Type andcorresponding dimension of species by double clicking (3) Determine thecoefficient.

partial pressure of oxygen gas is to be fixed at one atmosphere. For thispurpose, the “compound type” is first selected. After clicking the compoundtype , then, list of compounds is given. Fixed type can be selected among the
given list. Usually, log(activity) is selected as default and there is no need tochange it.
“O2 g” can be selected by moving the cursor with arrow keys and double
clicking or hitting the “cr” key. The next dialog “Coefficient Form” appears asgiven in Fig. 3.10. Selection should be made among “Reenter” and “Remove”.
This is for editing the linear combination of chemical potentials. Fixation canbe made using the following linear equation:a µ(X) + b µ(Y) + c µ(Z) + … = A[3.5]

Here, X, Y, Z are the compound and a b c are the coefficients to be determined
for respective chemical potentials. The value, A, should be determined at thebottom of in the “Select Fixed Value” dialog.

- 44 -

Fig. 3.11 The chemical potential diagram for the La-Mn-Zr-O system at 1273
K and under p(O2) = 1 atm.

“Remove” in the “Coefficient Form” is given for the purpose to remove thealready selected compound and its coefficient from the given linear
combination.
“Reneter” means to define the coefficient for the selected compound.
Here, “Reenter” and “coefficient”=1.0 are selected.
After selection is made, this “Coefficient Form” disappears and the selectedfunction of linear combination appears instead of the “Not determined yet”
message. The default value for the “Fixed Value” is set as 0.0. This means thatthe logarithmic activity of selected compound is zero, that is, the activity isequal to unity.
“Diagram Selection” page can be then selected to define the diagram
coordinates. The present system is the four-component system and already one
chemical potential is fixed so that the normal three dimensional surface
diagram can be constructed. Here, the default diagram type is selected,
namely, the three dimensional surface diagram. The coordinates of thisdiagram can be selected. Candidates for selecting the coordinates are given as
list. Since the oxygen gas is selected to fix the chemical potential, the element- 45 -

“O” is already removed from the list. As a result, La, Mn and Zr can beselected as coordinates.
3.3.4 Run
The diagram can be constructed by clicking “Run.” The resulting diagram isgiven in Fig. 3.11.
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 asa 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 chemical potential of ZrO2 is equal to unity. Since theoxygen 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 in terms of 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;
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 areseparated from each other. This means that the Gibbs energy change for theabove reaction is positive.
3.3.5 Change ColorIn Fig. 3.12, Tricolors based on the diagram coordinates is selected. In thisoption, the colors should be selected for the X-, Y-, Z- axes. By clicking on the
X-, Y- or Z-axis field, the focus is moved to the field. By hitting the “Change”
button, the dialog for selecting color appears. The same dialog can be also
given by double clicking on the selected field.
Each flat polygon can be characterized as the coefficients of linear equation
representing the flat plane;- 46 -

Fig. 3.12 Diagram Action Form-Polygon Color page. The colors forrespective polygons can be selected by choosing one mode.

a X + bY + c Z = 1[3.6]

Color attributed from the coefficients of coordinates can be seen as triangle
diagram in the left of the page.
3.3.6 Summary of procedures[System]
Selection of <La,Mn,Zr,O> system in MALT
[Project / Chemical System] ]<Chemical System> Dialog{Selection of Compounds} Page
Selection by Default
x Condensed phaseso Respective Gaseous Species
o Gaseous mixture[Project / Specify Diagram ]Diagram Specification> Dialog{Dimension Selection} Page

- 47 -

Temperaturex Fixedat 1273 K
o Not Fixed
Pressurex Fixedat 1 atmo Not Fixed{Fixation} Page
Add
<Select Fixed Value>Dialog
Select O2(g) Species<Coefficient Form> Dialog
Select ReEnter 1.0{Diagram Selection}Page
3D surface
Coordinates
(La)
(Mn)
(Zr)
[Run / Calc][Diagram / Options]<Diagram Action Form> Dialog{Polygon Color} Page
(1)Tricolors based on the Coordinates
X-Axis red
Y-Axis yellow
Z-axis Blue

3.3.6 Fixation of activity of compound
There are many ways to fix the chemical potential in the multi component
systems. The resulting diagram correspondingly provides the different
features depending on the fixed condition. In the above section, the partialpressure of oxygen is fixed. Here, the activity of the compound is fixed.

- 48 -

Fig. 3.13 The chemical potential diagram for the La-Mn-Zr-O system at 1273
K and under the condition of a(ZrO2) = 1.

Procedures to retrieve the thermodynamic data for the La-Mn-Zr-O system andto select temperature and pressure are the same as the above section.
Fixation of the activity of ZrO2 will be made in a similar way to the previous
example. The compound type is selected in the fixation type of the “SelectFixed Value” diagram.
Construction of diagram can be made after selecting “Run” command. Fig.
3.13 shows resulting diagram.
Comparison is made with (2b) where the chemical potential diagram for
La-Mn-O system is given.
The stability region of La2O3 is replaced by that of La2Zr2O7.
corresponds to the following reaction;This

La2O3 + 2ZrO2 = La2Zr2O7
Since the activity of ZrO2 is equal to unity in the present diagram, theactivity of La2O3 is fixed at a certain value in the La2Zr2O7 stability region.
This change in the activity of La2O3 compared with (2b) make a shift of thelocation of the La2O3 plane to the La2Zr2O7. As a result, the three phase
point of MnO, LaMnO3 and La2Zr2O7 is located at a point which has alower La2O3 activity value. This point can be written down as- 49 -

LaMnO3 + ZrO2 = 0.5 La2Zr2O7 + MnO + 1/4 O2(g)Among the five chemical species involved in the reaction, three are shown as
the stable phase plane, one is given as a species whose chemical potential isfixed and one is given as one of species which are used as axes of diagram.
The three phase point of MnO2, LaMnO3 and La2Zr2O7 shows the following
reaction;
LaMnO3 + ZrO2 + 1/4 O2(g) = 0.5 La2Zr2O7 + MnO2

3.4 Three Dimensional
Multicomponent System(Polyhedron)

Diagramfor

The generalized chemical potential diagram makes it possible to construct thethree dimensional diagram for the multicomponent system. Here, theLa-Mn-Zr-O system is considered.
3.4.1 Construction of three dimensional diagram
When the four component system is considered, the chemical potential

Fig. 3.14 The three dimensional chemical potential diagram for the
La-Mn-Zr-O system at 1273 K. Note that other phases than Mn, La, Zr metals
are not seen.
- 50 -

diagram can be displayed in the three dimensional manner.
The first example is the three dimension diagram with elemental chemical
potential coordinates.
Here, the four elemental chemical potentials areavailable. Out of four elements, three elements should be made. Since the
La-Mn-Zr-O system consists of three metallic elements and oxygen, three
metallic elements are selected as coordinates.
Fig. 3. 14 shows the three dimensional diagram for the La-Mn-Zr-O system at1273 K. Only elements of Mn, La, Zr are visible. In any compounds, theactivities of elements are lower than unity except for the cases where suchcompounds are in equilibrium with elements.

Fig. 3.15 The three dimensional chemical potential diagram for the
La-Mn-Zr-O system at 1273 K under the option of Graph inspector which
provides to make the phase polyhedron transparent.
- 51 -

3.4.2 Non-visualization of phases
Since the three dimensional diagram consists of many polyhedrons for stablecompounds, many compounds cannot be seen in the presence of other phases.
Thus, the function of making the stable polyhedron transparent is necessary.
First, the “Graph inspector” dialog is selected in the “View” menu. The“compound” page is selected. The list of compounds appears with theindication of respective colors. Double clicking on the compound is switch formaking the compound transparent or visible. In Fig. 3.15, Zr, La and ZrO2 aredouble clicked and are turned to be transparent.
What are visible in Fig. 3.15 are the compounds which can stably exist in thepresence of ZrO2(in other words, a(ZrO2)=1). Those compounds can becompared with those compounds presented in Fig. 3.13 which was obtained
under the condition of a(ZrO2) = 1.

3.5 Non-chemical potential variables

Fig. 3.16 Selection of the three dimensional surface chemical potential
diagram for the Cr system with coordinates of inverse temperature and withlogarithmic pressure.
- 52 -

To select the non-chemical-potential coordinates, it is needed to selecttemperature and pressure as non-fixed dimension. This is made in the“Dimension selection” page in the “Chemical System” Form.
Fig. 3.16 shows the “Dimension selection” page for the Cr system. In thedefault setting of the system definition, temperature and pressure are fixed at298.15 K and 1 atm. After clicking the “Non Fixed” radio buttons fortemperature and pressure, the default diagram type changes to “ 3D surface
diagram” in the top of the Form.
Since the Cr system contains only one condensed phase, the normal diagram
contains only plane for condensed Cr phase. This diagram does not give any
useful thermodynamic information. To avoid this, the Cr vapor is also
included in the present construction. For this purpose, the Chemical Systemmenu is selected and “Respective Gaseous Species” radio button should bechecked in the default compound option.
Fig. 3.17 shows three dimensional surface diagram for the Cr system in theµ(Cr)-1/T-ln (P/atm) plot. In the present chemical potential diagram, there
appear two stable species, namely, Cr metal (condensed phase) and Cr Vapor.
The stability region of Cr vapor is located below the stability region of Cr

Fig. 3.17 The three dimensional chemical potential diagram for the Cr systemwith coordinates of inverse temperature and with logarithmic pressure.
- 53 -

metal.
The borderline between two stability regions indicates theequilibrium vapor pressure of Cr vapor over Cr metal. In this sense, thisdiagram can be regarded as the generalized Arrhenius plot for theequilibrium vapor pressure. Generalization is realized in the point that thechemical potential of chromium is given for respective equilibrium point.

Next example is the Mn-O binary system. For this system, the three dimension
surface diagram can be set up by adopting the inverse temperature as one
coordinate and the fixed total pressure at 1 atm.
Fig. 3.18 shows the three dimensional surface diagram for the Mn-O system inthe µ(Mn)-m (O)-1/T- plot
In the Mn-O systems, Mn metal, MnO, Mn3O4, Mn2O3, MnO2 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 atµ(Mn)/RT=-300 shows that µ(O)/RT decreases with increasing temperature(or with decreasing inverse temperature, 1/T). Similarly, decrease ofµ(Mn)/RT is plotted in the frame plane of µ(O)/RT.
The chemical potential divided by RT is expressed in terms of enthalpy andentropy 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)- 54 -

Fig. 3.18 The three dimensional chemical potential diagram for the Mn-O
system with coordinate of inverse temperature.

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.

- 55 -

Chapter 4. For Full Use of CHD

4.1 CHD Environments
CHD for windows uses “CHDWin.ini” for reading and saving the CHD
environmental parameters.
When CHDWin.ini file is not available in the same directory as the
CHDWin.exe file, a new CHDWin.ini file is created and will save the current
setting of the parameters. If no apparent parameters were set during thesession, the default setting values will be saved in the CHDWin.ini file.
Command Parameter
CHD will check the command line to examine whether “/md” parameter is
included. If so, the “MALT Direct” command will be executed first.

4.2 Main Form
The CHD Main Form contains the followings:
1) Title bar2) menu bar3) tool bars4) main display panel5) status bar6) Dock panels at the right-hand side and at the bottom partFig. 4.1 shows the main form in which the three dimensional diagram for the
La-Co-Zr-O system at 1273 K is displayed. In addition, one dissection is cut
and displayed in another display panel which is docked in the left docking
panel.
Size of Form

- 56 -

Title bar

Menu

Tool

Cool barRightdockingpanel

Swing form

Main

display

Status bar

Bottomdocking panelAdditional
display panel
for dissection

Fig. 4.1. MALT main form.

The Size of the Main Form can be changed by moving one of corners or one ofedges by mouse.
Title bar
“CHD Win” is the short title. When the thermodynamic data are successfully
read from the MALT database or from the file, the title for the chemical system
will be added to the short title.
Menu bar
Main menus are given in Table 4.1. Menu bar is contained in the cool bar. But,
this menu bar cannot be floated from the cool bar.

- 57 -

Table 4-1 Items in the main menu and their functions
Items
FunctionsFile(F)
Open File for thermodynamic data or save Chemical
Potential Diagram
Edit(E)
Copy Diagram, Table items.
Project(P)Define the chemical system and the conditions forconstructing diagrams.
View(V)
Provides detailed data associated with the chemical
potential diagram.
Run(R)Create a polyhedron, cut dissections of the obtained
polyhedron.
Diagram(D)Provides the functions of manipulating diagram(coordinate range, polyhedron rotation, Select the display
mode, size, Font, color )Windows(W)Display hidden forms.
Help(H)
Manual, version information
Tool bars
The main cool bar is a container for toolbars.
The toolbars to be displayed in this cool bar can be selected in the [View /Toolbar ] menu or by right clicking on the Main Cool bar.
Although the menu bar cannot be floated, other toolbars can be floated. By
dragging at the left side of each tool bar, the tool bar will be floated.
Display panel
This is for displaying a diagram which is constructed under the specified
conditions. The Display Zoom factor can be changed by "Zoom" buttons; thelocation of Diagram in the Panel can be change by using the Horizontal Scroll
bar or the Vertical Scroll bar.
Responsible Diagrams to Menus and tool buttons
Only in the main form, there are menus and tool buttons. Those menus andtool buttons are valid even for the diagram displayed in other display panels.
The active form responsible to menus and buttons is indicated as red square
mark shown in the top-right corner. In Fig. 4.1, the main panel is responsible.

- 58 -

Fig. 4.2. Message for not running MLAT.

4.3 Menu “File”
Read Data from File
The following files can be read from the present CHD version:1) MALT compound data file (*.mcd)
2) MALT Version 1. data file(*.sc)
3) CHD User Compound Data file (*.dat)
4) Test data (*.abs)
Even when the thermodynamic data will be read from the files, it isneeded to run the mother MALT program. When the MALT system is
not running, the message appears as given in Fig. 4.2.
When the menu “Open File” is selected, the “Open File” Dialog appears asshown in Fig. 4.3. This is the Windows supplied dialog so that the message ofthis dialog is given in the Widows message language; note that Fig. 4.3 wasgiven by Japanese windows.
The selection of File type is important because the subsequent procedure will
be made according to the selected type. When the file name selected and thefile type selected are not consistent, reading the thermodynamic data will fail.
Format of Respective Files
The format of respective files is determined as follows:
1) MALT compound data file- 59 -

Fig. 4.3. Open file dialog for reading thermodynamic data. This isWindow’s dialog so that the message language is the same as OS’s
languageThis file is created and managed within the MALT for windows system. This
file is edited in the Menu “Tools” / “Data Format Conversion” and saved in thesame menu items of the MALT for Windows.
2) MALT version 1. compound file (*.sc)
This option is prepared to keep the consistency with the earlier versions of
MALT.
All data are given as ASCII text and the comma "," is used as delimiter. The
first line is a comment line with the title of the file. This is necessary forproperly reading data but will not be used in the present CHD.
Thermodynamic data for respective compounds are followed sequentially.
Data for one compound consists of 4 different lines;(0)
Comment line which starts with "*";
(1)
Compound title line (one line) containing 6items;(2)
Stoichiometry(7lines) consisting two items;(3)
High Temperature Data No. 1(4)High Temperature Data No. 2
Data lines (3) and (4) are repeated for respective high temperature phases
Table 4.2 Example of MALT version 1 compound file:* 87/08/12 [87/08/12]
malt1.0,La,La,g,g, 1
La, 1
0, 0
0, 0
- 60 -

0, 0
0, 0
0, 0
0, 0
138.905 , 431 , 393.59 , 182.268 , 22.753 , 1$,g, 298 , 2500 , 0 ,$,32.372 , .282 ,-28.21 , 0 , 5.869 ,-15.8248 ,-.193013 , 11,malt1.0,La,La,cs,sl, 4
La, 1
0, 0
0, 0
0, 0
0, 0
0, 0
0, 0
138.905 , 0 , 0 , 56.9 , 0 , 1$,c1, 298 , 550 , .364 ,tp,
27.07 , 1.34 ,-.33 , 0 , 0 ,-8.24116 ,-.154819 , 5,$,c2, 550 , 1134 , 3.121 ,tp,
17.66 , 15.02 , 3.93 , 0 , 0 ,-3.99622 ,-.101601 , 5,$,c3, 1134 , 1193 , 6.197 ,mp,39.54 , 0 , 0 , 0 , 0 ,-16.3762 ,-.235862 , 5,$,l, 1193 , 3730 , 0 ,bp,
34.31 , 0 , 0 , 0 , 0 ,-3.93978 ,-.193617 , 5,3) CHD User Compound Data file
This data file is based on the Gibbs energy representation.
1) All data are given in a proper sequence and in the formatted style forrespective lines.
2) Comment line; all lines which start with the asterisk (*) are defined ascomment lines and will be just read.
3) Lines without any string(that is, blank line) will be also read through.
4) All data lines are read and separated into several words using space as
separator.
System Data lines consist of
System Information
Component(Element) Names
Component(Element) atomic mass : This will not be used in CHD
Gibbs energy Expression Information
Additional Information
This will not be used in CHD- 61 -

Main Data Lines consist ofName of Mixture/Stoichiometric Compounds
Type of Mixture
ThermoData For respective compounds, which consists ofName of compound
Data type, Number of phases, stoichiometric numbers
Table 4.3 Example of User Compound Data File
* Data File to be created by user
2
1
5
3
O
Co
15.99940
58.93320
6
1
2
3
4
5
6
1
1
GAS
IDMX
O
4 1
1.00000.00002.5000000E+03 2.4328149E+05 -2.1885825E+01 -2.0845000E+01 8.5000000E-06
0.0000000E+00 -4.8550000E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
O2 4
12.00000.00002.5000000E+03 -1.4231317E+04 3.0877261E+01 -3.4350000E+01 -9.6000000E-04
0.0000000E+00 9.2250000E+05 -6.7666667E+07 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
O3 4
1
3.00000.00002.5000000E+03 1.1552677E+05 1.6258143E+02 -5.7780000E+01 -3.5500000E-04
0.0000000E+00 2.1245000E+06 -1.2850000E+08 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
Co 4
10.00001.00002.5000000E+03 4.1556568E+05 2.1115903E+00 -2.6819000E+01 3.1500000E-05
0.0000000E+00 1.7010000E+05 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
CoO
4 1
1.00001.00004.0000000E+03 2.8028824E+05 1.4209312E+01 -3.6490000E+01 -2.6000000E-04
0.0000000E+00 2.6970000E+05 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
Co
4 4
0.00001.00007.0000000E+02 -6.7380728E+03 1.1042648E+02 -2.0280000E+01 -7.7800000E-03
0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
1.3940000E+03 -1.2804053E+04 2.6397436E+02 -4.5270000E+01 2.3620000E-02-6.4300000E-06 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
1.7680000E+03 2.6707448E+05 -1.0849677E+03 1.2803000E+02 -3.2700000E-02
0.0000000E+00 -7.8695000E+07 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
3.2010000E+03 -1.5016034E+03 2.4415313E+02 -4.0500000E+01 0.0000000E+00
0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
CoO
4 2
1.00001.00002.0780000E+03 -2.5477621E+05 3.1589943E+02 -5.5100000E+01 2.3000000E-03-9.9000000E-07 8.3500000E+04 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.02.5000000E+03 -2.0404540E+05 3.3456010E+02 -6.0670000E+01 0.0000000E+00
0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0
Co3O4
4 1
4.00003.00001.2200000E+03 -9.4106306E+05 8.3592218E+02 -1.3665000E+02 -1.3765000E-02-7.9216667E-06 1.1445000E+06 0.0000000E+00 0.0000000E+00 0.0000000E+00-2.0 0.0
0.0- 62 -

4 ) Test Data file
This file is provided to construct a polygon in a normal (not thermodynamic)
space. Respective planes in this space is represented by the following
equation;la + mb + nc = const[4.1]

Here, the dimensional number is 3. The variables, a, b ,c, form the space. The
coefficients, l, m, n, determine the slope of the plane, and the const determines
the location of the plane.
The first line of the data file gives the dimensional number.
The data for respective planes consist of three lines;
1) Name of the plane2) The data for the coefficients
3) The data for the constant value
Table 4.4 Example of test data file3A
1, 0, 00B0, 1, 00C0, 0, 10AB
1, 1, 0-10
AC
1, 0, 1
-20

Fig.4.4 shows a three-dimensional diagram corresponding to the test data
given in the above file. This system consists of five planes, A, B, C, AB andAC.
Reopen the previously used files- 63 -

Fig. 4.4. Three Dimensional surface diagram corresponding to the test
data given above.

The previously used files are stored with their data type. It is therefore notneeded to specify the file type explicitly. These file names are always renewed
so that old files will disappear.
When the file was moved from the previous directory after the previous use,such a file cannot be read again. In such a case, the menu item for the file
reopen is changed to “not enable”.
MALT Direct
This consists of two procedures;
1) ask MALT to send the current retrieved data to CHD;
2) receive the thermodynamic data and prepare for utilization of CHD.
To use this function, the MALT has to be run. When MALT is not available,
the message given in Fig. 4.2 will appear.
Open Default File
One file can be specified as the default file. This is made in the “Project / Set as
Default File” menu. This file is read in this menu.
Save File- 64 -

Fig. 4.5. Dialog for save the diagram. The file type can be selectedfrom Window metafile, bitmap and jpeg.

When the thermodynamic data are supplied from the MALT for Windows by
the MALT Direct, those data can be saved as the compound data file. This filecan be only read but cannot be edited.
Save Diagram
The diagram in the CHD display panel can be saved in the following forms:
1) window meta file2) bitmap file3) jpeg fileFig. 4.5 shows the dialog for save the diagram. Here, jpeg type is selected. As
a result, available files having the “.jpg” are displayed in the current folder.
Note that Fig. 4.5 is the Window’s providing dialog to that the message
language is controlled by Windows.
Save Screen
The current screen will be save in a bitmap file or a jpeg file in a similar
procedure to “Save Diagram.”
Printer Set Up ; Print
Exit- 65 -

Fig. 4.6. The Chemical System Dialog with a page of Data Source
Name

CHD will be ended.

4.4 Menu “Edit”
Diagram in the display panel and table contents in the lists can be copied toclipboard
Copy Diagram to Clipboard
The format of the diagram is in the window metafile. If other graphic formats
such as bitmap or jpeg files are preferred, the menu “Save Diagram” should beselected.
When there are many displayed panels, the diagram on the panel with red
square mark on the top left corner will be copied.
Copy Table to Clipboard
Table contents in the Graph Inspector and other tables can be copied toclipboard. Such data are easily transferred to other software such as Microsoft
Excel or Origin.

- 66 -

Copy List to Clipboard
CHD provides a list of text strings during its processes particularly in thefollowings:
1) reading data from file: data are read from file and stored in a list. Whenreading data was failed such a list will be given.
2) Creating a graph and constructing a diagram is also recorded for eachprocess.
These lists can be shown by clicking the “List” tool button. Such list can becopied to clipboard.

4.5 Menu “Project”
Chemical System
The specification of the chemical system can be made in the “Project/Chemical
System” as follows;

Fig. 4.7. The Chemical System Dialog with a page of Selection ofCompound..
- 67 -

Fig. 4.8 Select Compound Form

1) Data Source Name
Name and Type of Data source will be displayed as Fig. 4.6.
2) Selection of Compound
Among chemical species, selection can be made for species to be examinedin the construction of chemical potential diagram. Selection is made bychoosing one option from the following two options;i)
Default
ii)
Selection by user
As shown in Fig. 4.7, for default selection, the following items should bechecked or unchecked:
Condensed phases
Respective gaseous species
Gas Mixture
In “Respective gaseous species,” each species in the standard pressure willbe treated as one flat plane in diagrams, whereas in “Gas Mixture”, one
phase under a given pressure is expresses as a curved plane.

- 68 -

In the initialization of the current project, only condensed phases are taken
for this purpose. After selection is made in this menu, however, theselection will be stored in the CHDWin.ini file and applied to any systems
which will be read afterward.
When “selection by user” is selected, the Select Compound Form (Fig. 4.
8) will appear. The currently selected compounds are indicated by blue
color. By double clicking on the selected compound, the selection can bechanged between “selected” and “unselected” states.
Specification of Diagram
CHD can create different types of diagrams. This depends on the total numberof components and the number of fixed variables in the system. Thesefundamental information on the current chemical system is given in the upper
part of the Diagram Specification Form (Fig. 4.9).
As an example, the La-Zr-Mn-O system is retrieved through “MALT Direct.”
This is the four-element system. By adding the temperature and pressure, total
number of the components becomes 6. During the initialization of project,temperature is fixed at 298.15 K and pressure is fixed at 1 atm (101,325 Pa).
In the upper table of the form, the initial terms and the current terms are

Fig. 4.9 Diagram Specification Form

- 69 -

compared. The initial terms are set when this form is opened. Whenever
specification will be changed during the current setting, new specification isshown in the current terms.
Whenever the current terms are changed, the default type of diagram willchange according to the followings:
Table 4.5 Examples of diagram which can be constructed in various types;
diagram with underline is the default type.
Total
Number possible types Examples
dimension of fixed
numbervariables
3
0
2D,
3D Cr
surface4
1
2D,
Mn-O at constant Pres.
3Dsurface
Ca-C-O at constant Pres. and Temp.
52
2D,
La-Mn-O at constant Pres. and Temp.
3Dsurface
6
3
2D,
La-Mn-Zr-O at p(O2)=1 atm
3Dsurface
6
2
3D
Pages
1. Dimension Selection
The thermodynamic intensive variables can be divided into two
categories; that is, the chemical potentials and others such astemperature and pressure. Here, non-chemical potential variables
can be specified about whether those variables are fixed at selectedvalues or not.
Method:To fix at a value, check "fixed" and edit the field in the righthand side. To cancel the fixation, check "not fixed". Then, thetext value in the edit field will disappear.
(1) Temperature : Default = Fixed at 298.15 K.
(2) Pressure: Default = Fixed at 1 atm.
2. Fixation
The current list of “Fixed Values” is given in the Fixation page.

- 70 -

Fig. 4.10 Fixation of chemical potentials with dialog for Select Fixed
Value.

Name : The specified species, a combination of
species;
Type : Fixed Type.
Modification for the current setting can be made by clicking the
buttons for “Add,” “Change,” “Delete,” and “Cancel.”
Add :"Select Fixed Value" Dialog appears as shown in Fig.
4.10. Fixation cam be selected from the Dimension
variables, the Compound type.
When the Dimension variables are selected, only one
dimension can be selected for one fixation.
When the Compound type is selected, a linear
combination of chemical potentials of compounds canbe selected. For this purpose, after selecting one
chemical species, the Coefficient Form will appear andprompt to input a coefficient for a linear equation.
After inputting the coefficient, the current linear
equation will be given below the candidate species.
A fixed value is input at the bottom of the form.
Change : First, select the line in the list of the Fixed values to bechanged. Then click the change button.
Delete : First, select the line to be deleted. Then click the delete
button.

- 71 -

Fig. 4.11 Selection of Diagram.

Cancel : The currently modified fixed values are all canceled
and the old values become valid.
On every change in fixation, the information of the current setting isrenewed at the upper part of the “Diagram Specification” dialog.
Dissection to be created
If you want, the pages for dissections can be added in this [Diagram
Type].
No dissection (default):
One Dissection:
Many Dissections:
To cancel "One Dissection" or "Many dissections", select No
dissection.
It is highly suggested to specify the dissection condition after the
Diagram selection is made first.
3. Diagram Selection
Diagram type and coordinates can be selected.

- 72 -

The chemical potential diagram type can be selected among theavailable types which are given in the combobox. A typical image
is given for the selected diagram type.
Coordinates selection can be made by changing the default
coordinates. Whenever the default diagram type is set, default
coordinates are selected at the same time. The first coordinate is for
the X axis and the second and the third are for the Y and the Z axis,
respectively. Note that three coordinates are needed even for thetwo-dimensional diagrams. This is because the third coordinate isneeded to determine the front and rear surfaces of the polygons.
Change will be made by clicking one of the following buttons:
ChangeDefault
Cancel
Downward or upward arrows make exchange the selected line andthe lower or the upper line, respectively.

Fig. 4.12 Project Status- 73 -

Fig. 4.13 Compound Lists

One Dissection, Many Dissections, Additional Lines
These will be explained elsewhere (see 4.7).
Set as Default File
The current thermodynamic data can be defined as default file which can beread by selection of the menu “default file.”

4.6 Menu “View”
Project Status
The present status of the project will be displayed in the dialog as shown in Fig.
4. 12. The fundamental selections for constructing diagrams are listed.
Compound List
The list of compounds and other properties related to the construction of thechemical potential diagram is given in this section. As given in Fig. 4.13, theCompound List Form has several pages for displaying the numerical data forthe compounds. The first page of “Compounds” shows- 74 -

Name
Name of species
G(T)/RT
Gibbs energy value at previously selected
temperature
DH298
Enthalpy change for formation at 298.15 K
DG298
Gibbs energy change for formation at 298.15 K
S298
Entropy at 298.15 K
N
Number of high temperature phases
Const
Coef1 to Coef5
For data obtained by MALT direct, the thermodynamic data at 298.15 K are
not displayed.
Constant and coefficients are values for the following equation;- s/R = (-∆H/R) 1/T – log P + l µ(A)/RT + m µ(B)/RT+ n µ(C)/RT[4.1]

Here, - s/R is constant and -∆H/R is the coef 1. Note that these values are forpreviously selected temperature. Coef 2 is 1 for gaseous species and zero forthe condensed phase. Coef 3 and others are the stoichiometric numbers.

Fig. 4.14 Information of compound and Dimensions- 75 -

Fig. 4.15 Thermodynamic Table as a function of temperature

Pages for “A Compound” and “Dimensions” give the information on
respective compounds and dimensions as shown in Fig. 4.14. This is used in
the construction of diagrams. Target compound or target dimension can beselected by changing the number of compounds or dimensions.
Page for “Thermo Table” gives the Gibbs energy and constant and coefficientsin equation 4.1 as a function of temperature. Target compound can be selected
in terms of number in the compound list.
Font of those lists can be changed by changing font in the “Message Font
“ Menu, which is described below in this section.
Graph Inspector
Construction of any diagram is based on the graph in the chemical potential
space. Graph is characterized in terms of vertices, edges, and facets. In
addition, the information of planes (compounds) is also given.
Vertices can be characterized in terms of planes which form respective vertices
and the chemical potential values which are determined uniquely.

- 76 -

Fig. 4.16 Graph Inspector/ Vertices together with the chemical potential table
and Vertex List Form.

Fig. 4.16 shows the list of vertices which give the name of compounds
involved. By double clicking on the line, more detailed information appears in
the “Vertex List” Form and the “Chemical Potential” Table like in Fig. 4. 16.
The “Vertex List” Form gives the properties of respective compounds, whereas
the “Chemical potential” Table gives the numerical values as will be explained
below.
Those lines with asterisk (*) are artificial vertices which contain hypotheticalplanes like the lowest limits of the space.
“Edge” list is given in Fig. 4.17. By double clicking on the line selected, thepoint list form gives the list of the chemical potential values as shown in Fig.
4.17. By double clicking on the line in the “Points List” Form, the informationof the vertex will be shown in the “Chemical Potential” Table and the “Vertex
List” Form in the same manner as the above case.

- 77 -

Fig. 4.17 Graph Inspector/ Edges together with the Points List Form

“Facets” page in Graph Inspector provides lists of facets. Since the facets are
painted with colors which are attributed for respective polygons, such colors
are also given in the list. By clicking on the line of facets, the facts in thetarget diagram will be transparent. When another facet is clicked, that facet
becomes transparent and the previous facet is colored again. When the
diagram is repainted, such specification for transparency will be cancelled andall facets are painted properly.
Compounds in Graph Inspector give the list of compounds which are displayedin the diagram. For respective compounds, color is attributed. By clicking on
the compound in the list, the whole area associated with the compounds
becomes transparent except for the framework for the graph, that is, edge parts.
In the three dimensional diagram, this function becomes powerful in inspecting
the geometrical features of the polyhedrons in the diagram. This specification
for transparency will hold for the rest of displaying diagram. In a typical
procedure in inspecting the three dimensional diagram, this option as well as
rotation can be used simultaneously to see geometrical features deep inside thediagram.

- 78 -

Fig. 4.18 Graph Inspector/ Facets docked at the Main Form

Fig. 4.19 Graph Inspector / Compounds docked in the Main Form.

- 79 -

Fig. 4.20 Chemical potential table with selection of columns option /the Selectcompound Form.

Chemical Potential Table; Points List Form
The Chemical Potential Table can be called from the touch diagram mode ofdisplaying diagram and also from the selection in the Graph Inspector.
The listing items of the chemical potential table can be selected by two ways;
one is checking among the following groups;
Space values
Coordinates values
Display Points
Species log(activity)
Species concentration
Coefficients of space;the other being the selection of columns. When selection is made on thisoption, the Select Compound Form will appear like in Fig. 4.20. The currently
selected items are shown as blue lines.
The “Points List” Form has about the same function as the “Chemical
Potential” Table except that the Points list form can display several points atthe same time. The way of selection of display items is the same. When the- 80 -

selection is made in the chemical potential table, this is sent to the Points List
Form
Language
Message language can be selected as Japanese or English. After change
language option, please restart CHD.
Message Font
Windows dialog for font will appear for message font. This font will be used
for Font in the main form and other forms having lists etc. Font used in
drawing diagrams can be changed in “Diagram Font” submenu (see 4.8).
Toolbar
Options for tool bars are the followings:
1) Include or exclude the tool bars in the cool bar.
2) Add strings to tool buttons or exclude strings.

4.7 Menu “Run”
Calculation
In many cases, the default setting is made just after reading the thermodynamic
data in the chemical system so that “Calculation” can be made without further
specification.
When calculation was made with success, a graph is created and the graphinspector becomes available. Here, by graph, it means the geometrical andnumerical information on vertices, edges and facets. When a diagram can be
drawn, the diagram will be displayed after the calculation. When any diagram
cannot be drawn, just new graph is available. Further procedures associatedwith diagram cannot be available. This is particularly for those systems
consisting more than 4elements. For full use of the functions of CHD, it ishighly recommended to decrease the freedom by making further fixation so as
to be able to draw a diagram.
One Dissection
Dissection is available only when a diagram is available.

- 81 -

Fig. 4.21 One dissection for three-dimensional surface diagram.

By specifying another chemical potential at a selected value, one dissection
diagram can be cut off from the original diagram. This specification ofchemical potential decreases one dimension of the chemical potential diagram.
Fig. 4.21 shows the one dimension page in the Diagram Specification Form.
This consists of two parts; the left side is for determination of the dissections.
Editing dissections can be made by clicking the buttons of “Add”, “Change”,“Delete” and “Cancel.”
The way of determining a dissection is similar to that of determining fixation.
That is, the determination is made by selecting dimension variable orcompound type. For dimension variable, only one dimension can be select.
For compound type, the linear combination can be selected. In addition,
constant value should be selected.
The results of dissection can be drawn in two different ways;
1) A specified dissection is displayed on the target diagram.
2) An additional diagram is created in an additional panel.
purpose, the “profile diagram” should be checked.

- 82 -For thisFig. 4.22 Select of Swinging value for dissection and related form for changing
range limits.
Fig. 4.23 One dissection for three dimensional diagram.

The dissected line can be drawn only on the three dimensional surface
diagram. When “Dissection swing” checkbox is checked, a small form forchanging the value of dissection will appear.
The value for dissection can be changed by moving the scroll bar in the
Dissection Swing Form. This scroll bar can be changed in the given range
maximum and minimum. These Maximum and minimum values can bechanged by right clicking on the Dissection Swing Form.
Profile diagram
Additional diagram for three dimensional surface diagram can be called as“Profile Diagram.” This provides the change of chemical potentials as afunction of chemical potential. As “X” axis, one of the chemical potentials canbe selected. Selection is made in the “Select” button. Alternatively, thedistance in the chemical potential space can be selected. In this case, distance
is automatically calculated and there is no need to specify further.

- 83 -

Fig. 4.24 Many dissections for three dimensional diagram.

For “Y” axis, several values can be selected and plotted against the X axis.
Selection can be made by clicking the “select” button to show the following
popup menu:
Space value
Coordinates values
Display Point
Species log (Activity)
Species concentration
Coefficients of Space
Selection of Column
Exit
This is the same popup menu for the Chemical Potential Table. When some of
the above menu items are clicked, candidate properties are renewed. The
target properties are shown as blue lines. This can be changed by double
clicking on the target line.
Dissection Diagram- 84 -

When the target diagram is the three-dimensional diagram, the dissection
diagram can be constructed instead of the profile diagram. As shown in Fig.
4.23, the dissection 2D diagram or the dissection 3D diagram can be used.
As coordinates, any coordinate can be selected as in the target diagram. Evenso, it is recommended to select one of the shown coordinates in the list in theright-hand side. For such a case, no anomalous appearance will be given.
One Dissection Swing
The Dissection Swing Form will appear and then the dissection value can bechanged.
Many Dissections
A number of dissection diagrams can be setup. The dissection values are
specified in terms of the minimum and the maximum values with a step value.
Resulting diagrams are displayed in respective Forms. These Forms can bedocked with each other or on the main form.
To delete these forms for dissection diagrams, the target dissection in the list
can be deleted by clicking the “delete” button.

4.8 Menu “Diagram”
Range
In the normal procedure, range is automatically given so as to show all vertices
calculated in a proper range. Such range can be edited by using “Range” menu.
Fig. 4.25 shows the Range Dialog. “Max value” and “Min value” arecalculated from the obtained vertices. Min limit, Max limit, step value anddisplay factor are to be edited for respective axes. The display factor is
automatically determined so as to display diagram in an appropriate ratio
among axes.

- 85 -

(a)(b)

Fig. 4.25 Range Dialog (a) with Option off, (b) with Option on.

In bottom of the dialog, “Option On/off” button is available. When the“Option on” button is clicked, the options are displayed as shown in Fig.
4.25(b). Two options are available. One is about the range limits, the otherbeing the display factor. When these options are clicked, this option becomesvalid in the subsequent construction of diagrams. Otherwise, the range limits
and the display factor will be automatically determined and renewed.
Rotation
The three dimensional diagram is plotted on the display panel by using theconversion matrix from the diagram coordinates[u, v, w] to the screen
coordinates[X,Y];u  X   a11 a 21 a31   
 v
Y  = 
 
12
22
32
a
a
a
  
  w 

The default matrix values are- 86 -[4.2]

Fig. 4.26 Rotation Dialog

 1 0 − 0.5  0 1 − 0.2 [4.3]

Rotation of the diagram can be made by changing this matrix values. As
shown in Fig. 4.26. the matrix values are shown in the top of the dialog andalso in the two spin edit field for respective axis. This spin edit value can bealso changed by scroll bar in the right hand side. On every action for changing
value, the information is transferred to the current display panel and the target
diagram is repainted.
In the “Rotation” page, rotation along the X, Y, or Z axis will be made on thepresently displayed diagram.
The “previous” button resets the values to the previously restored values.
The “default” button resets the values to the default values given in Eq. [4.3]
Change Coordinates
The “Diagram Selection” page in the “Diagram Specification” Form willappear and the coordinates can be changed.
Display Mode
When a diagram is displayed in a display panel, there are several display- 87 -

Fig. 4.27 Additional lines page in the Diagram Specification Form.

modes available.
The normal mode is to inform only the cursor position in the status line.
The “Touch Diagram” mode is to give the chemical potential table associatedwith the touched point on the diagram. This is only valid inside the visible
facets. The space values are given in the status line and other more detailed
properties are given in the chemical potential table.
The “Draw Line” mode is to draw a line on the three dimensional surface
diagram. Each point is collected and can be shown as profile diagram. Single
clicking on the surface adds a new point and double clicking ends the line. The
profile diagram is shown after ending the lining. Collected points are shown in
the points list form. To delete drawn lines, the “One dissection” menu isselected and items in the list can be deleted by clicking the “delete” button.
The “Move Location” mode is to move the location of the diagram itself or thestring text associated with the diagram. After selecting this mode, cursor canbe moved to the target diagram or text string. For the case of the diagram, ablue box appears along the diagram frame. On the top bar of the box, thecursor shape changes to finger and dragging can be made by left click andmove mouse. By double clicking on the top bar, the diagram is maximized.

- 88 -

On double clicking on the maximized diagram, the previous size is recalled.
On the corners, the shape of the box can be changed. For text string, only thechange of location can be made. Instead, size of text string can be changed in“Diagram Font.”
Diagram Size
Diagram size relative to the display size is selected among maximize, standard
and arbitrary.
“Maximize” makes full use of display panel in whatever shape.
“Standard” is based on a typical ratio between height and width.
“Arbitrary” starts the display mode of “Move location”.
Diagram Stayon / resize
Diagram size responsible to the resize of the display panel is selected between
stay on or resize.
In “Resize,” the diagram size is always resized on change of the display panel
size. For example, when diagram size is selected as standard, the diagram sizeis always resize to have the standard size for new display panel. On the other
hand, In “Stay on,” no scaling will be made and the diagram size stayunchanged even on the change of the display panel. As a result, some parts ofdiagram can be masked by the frame. In such a case, scroll bar in thehorizontal and vertical sides can be used to look the masked parts.
Diagram Zoom
In the normal procedure, the size is determined relative to the display panel
size. This can be defined as the size having the factor of 100. The display
factor can be changed in different ways;
1) Zoom down : Select the zoom down mode by clicking the Zoom down tool
button, or select the “Zoom down” menu first and then clicking on the
diagram gives rise to contraction to half size. The second click gives rise toanother contraction. To stop it, the Zoom down tool button should beclicked again.
2) Zoom up : This mode gives rise to double size.
3) Zoom Plus Minus: After clicking this tool button, the display factor can bechanged by manipulating the scroll bar for display factor which is preparedin the main tool bar. On clicking on the diagram, the center of the display- 89 -

Fig. 4.28 Ca-O-C system with iso-partial pressure lines of CO2

area moves to that clicked point. To zoom up in the vicinity of some point,
first click that point. This leads to making the point at the center. Then
manipulating the scroll bar gives rise to the zoom up and down at the point.
4) In the “Zoom” tool bar, the combobox for display factor is available. By
selecting one of the listed factors, the diagram size can be changed.
5) To recover from undesired treatments on the zooming, there are two tool
buttons are available. One is the initial tool button, the other being the“Default” tool button. Whenever the display mode is adopted among
Zoom Down, Zoom up or Zoom plus minus, the initial position and size ofthe diagram is stored. The “Initial” tool button recalls the stored data.
Note that this position and size are always renewed when Zoom mode isquitted. The “Default” tool button is to recall the normal position andsize.
Diagram Color
Basically, the polygons in the diagram are colored in two ways: one is color,the other being in black and white. This is selected in the Diagram Colormenu.
Diagram Font
Window’s dialog for Font appears for the diagram font. The selected font iscommon for all diagrams and will be saved in CHDWin.ini.

- 90 -

Additional Lines
When the two dimensional diagram or the three dimensional surface diagram
are displayed, additional lines can be added on such diagrams. Fig. 4.27 showsthe “Additional lines” page in the Diagram Specification Form.
When the “Add” button is clicked, the Select Additional Lines Form appears.
This is essentially the same as the Many Dissections Form. Specification cam
be made by using the elemental chemical potential or a linear combination ofchemical potentials of compounds. When target chemical potential is selected,
the default values for maximum, minimum, and step value are given. These
values can be edited by users.
Additional lines are displayed all over the diagram. However, when mixture
phases are included in the system, the additional lines can be limited in a
selected mixture phase or drawn for whole system. This can be selected in theright hand side of the page.
Options
At present, options are available for painting mode of polygons. As shown in
Fig. 4.29, there are five modes:
1) tricolors based on the coordinates values2) tricolors based on the coefficients of space dimensions
3) color based on given 15 colors : sequential
4) color based on given 15 colors : preselected,5) black and white
Tricolors are determined by pre-selected three colors and three coefficientsassociated with polygon. For Tricolors based on the coordinates values, theslope of the polygon plane in the coordinates is used. For tricolors based on thecoefficients of space dimensions, the stoichiometric numbers of associatedcompounds are used instead. In this mode, the compound is displayed always
in the same color
Change color can be made by double clicking on the color to be revised, or byclicking the “Change Color” button.
Brightness of colors can be adjusted by changing “brightness” index between 0
to 255.

- 91 -

Fig. 4.29 The Diagram Options Form for determining polygon colors. No.1,
Tricolors based on the coordinates values.

When the second mode is selected, each compound can have the same color
throughout the series of construction. As shown in Fig. 4.30, “Show
Compounds” button is used to show the present color for respective
compounds in the left part.
Given 15 colors can be prepared by users. Its default values are determinedfrom the following colors ;clGreen, clBlue, clRed, clYellow, clAqua,
clFuchsia, clLime, clMaroon, clNavy, clOlive, clPurple, clSilver, clTeal,
clMoneyGreen, clSkyBlue, clCream.
User’s determined colors are saved in CHDWin.ini file.
The “Sequential” mode is to give colors for list of polygons step by step. Thismode does not check what compound is related to the polygon.
When you want to give a selected color for respective compounds, it is better toadopt the “Preselected” mode. In this mode, two buttons are available. The“Default Given colors” button gives the given 15 colors for compounds in thesystem sequentially.

- 92 -

(a)

(b)

(c)

Fig. 4.30 The Diagram Options Form for determining polygon colors. (a) No.2,
Tricolors based on the coefficients of space dimensions, (b) No. 3 Given 15
colors : Sequential, (c) Given 15 colors : Pre-Selected.

The “Preselected” mode is useful when you want to paint the special
compound with a selected color.

4.9 Menu “Window”- 93 -

Hidden forms
CHDWin uses several forms. Some of these forms will be hidden by otherforms, particularly by the main form. By clicking the “Hidden Forms” menu,
the list of the forms appear as menu items. On clicking the menu item, thehidden form will be shown on other forms. When the form was docked to otherplace, the form will be undocked.

4.10 Menu “Help”
CHD Help
Help system for the CHD for Windows consists of three ways:
1) start the CHD Help from the main menu;
2) click the help button on respective forms;
3) click the F1 key.
Version Info
Version information will be displayed.

4.11 Popup Menu
Popup menus are available for several cases;
1) When the display mode is normal, the popup menus for diagram cam beused after right clicking.
2) On the selection of compounds, popup menus for the following items canbe selected;
Space Value
Coordinates Values
Display Points
Species log(Activities)
Species Concentration
Coefficients Of Space
Selection Of Column
Exit- 94 -

3) On right clicking on the coolbar in the main from, the popup menus fortoolbars will appear.
4) When clicking the downward arrow in the right side of file open tool
button, the popup menus for reopen files will appear.

- 95 -

Appendix For Setup Pourbaix Diagrams

A.1Pourbaix diagrams and MALT/CHD
At present, the thermodynamic database MALT does not contain any aqueous
species in its main database. Even so, the thermodynamic data for someaqueous species are available at 298.15 K and those data can be utilized inconstructing the Pourbaix diagram. On the other hand, the present CHD for
windows can provide a basis of constructing such Pourbaix diagrams, although
this has been developed originally for constructing high temperature chemical
potential diagrams.
Here, a method of constructing Pourbaix diagrams will be explained by using
the user’s data file, “FeSAqueous.txt” which store the thermodynamic data for
aqueous species in the Fe-S-H-O system. This appendix is based on thefollowing paper:
H. Yokokawa, N. Sakai, T. Kawada, and M. Dokiya, “GeneralizedElectrochemical Potential Diagrams for Complex Aqueous (M-X-H-O-e-)
Systems,” J. Electrochem. Soc. 137(2), 388 (1990).
Another example is the Li-Mn-O-H system which appears as the importantsystem for the positive electrode for lithium batteries. This will be based on
the user’s data file, “LiMnOHAqueous.txt.”
User’s DataBase: FeSAqueous.udb
In this appendix, the compounds and aqueous species listed in Table A. 1 areused in constructing Pourbaix diagrams. The condensed compounds are thoseretrieved from the thermodynamic database MALT. Data source “udb” means
the FeSAqous.udb which are compiled from the user data file
“FeSAqueous.txt.” The data source of the aqueous species are the NBS
thermodynamic properties published in 1982 which are the main parts of the
MALT database so that the consistency of the data in the FeSAqueous.udb
with the Main Database is obvious.

- 96 -

In the NBS tables, some data are lack in the absence of the experimental
data. For the construction of chemical potential diagram, only the Gibbs
energy data are used. On the other hand, the Gibbs energy in MALT
Direct is calculated from the enthalpy data and the entropy data. Whenenthalpy and entropy are lack but Gibbs energy is available in the NBS
table, the NBS data could not be used directly. In such a case, user data
are treated as follows as a convenient method although this has no
physical meaning, that is, the enthalpy value is assumed to be the same as
the Gibbs energy and the entropy is calculated to reproduce the Gibbs
energy value from thus assumed enthalpy.
In addition, the heat capacity of all aqueous species is assumed to be zero.
Apparently, this is not correct.
Thus, please note that the present data set of the aqueous species are notvalid at temperatures other than 298.15 K.
Table A.1 Gibbs energy change for formation of compounds and theirdata sources
Compoundstate∆fGº/RT
sourceH2S
g-13.53MALT
SO2
g-121.14
MALT
Fe2+
ao
-31.84
udb
3+
Fe
ao
-1.90
udb
HFeO2ao-176.82
udb
S2ao
34.63
udb
SO42ao-300.49
udb
HSao
4.87
udb
HSO4ao-305.11
udb
FeSO4ao-311.91udb
H2S
ao-11.24udb
H2O
l-95.72MALT
H2O2
l-48.69MALT
H2SO4*6.5H2O
l-922.66
MALT
Fe
c
0.00
MALT
Fe2O3
c
-299.55
MALT
Fe3O4
c
-409.85
MALT
FeS
c-40.52MALT
FeS2
c-67.36MALT
FeSO4
c-331.31MALT
Fe2(SO4)3c-909.78
MALT
FeSO4*7H2O
c-1012.99
MALT- 97 -

What are Pourbaix Diagrams
Usually, the Pourbaix diagrams can be used for different types of diagrams.
One is the predominance area diagram, in which the dominant aqueous species
will be given as a function of pH and pE, where pH means –log a(H+) and pE isthe corresponding variable for electrical potential. Resulting area of eachaqueous species can be expressed in terms of convex polygons.
The second, important diagram is the normal diagram in which the equilibria
between the aqueous species and the condensed phases are shown as chemical
potential diagrams.
Here, these two types of diagrams will be reproduced using the CHD forWindows.
Fe-O-H-e- system
In the MALT for Windows, the thermodynamic data should be retrieved in thefollowing manner.
1) User data file, FeSAqueous.txt, should be selected and compiled (menuTool/User data/compile user data text file).
2) In the menu of Tool/MALT options, check should be made on the option
for including aqueous species in the options in searching.
3) In the menu of “Get compounds by elements”, “Compounds consisting of
combinations of elements” should be selected as the mode of searchingcompounds. When the element sets of O,H, Fe will be selected, thecompounds and aqueous species in the Fe-O-H-e- system will be retrieved.
In CHD for Windows, these thermodynamic data will be transferred fromMALT by means of MALT Direct.
Note again here that the present thermodynamic data for aqueous species
stored in the user database: FeSAqeous.udb does not include the hightemperature heat capacity data. Calculation at temperatures other than298.15 K leads to serious errors so that this should never be attempted.

- 98 -

Fig. A1.1 Selection of Species to be included in the chemical potential
diagram.

Chemical System
The first diagram to be constructed is the Pourbaix diagram for the Fe-O-H-esystem. Species to be included are determined as followed:
1) Menu Chemical System is selected:
Selection of compounds is made by “selection by Default” with checking
on the “Condensed phases” and “Aqueous species.”
2) Then, “Reselection” button is clicked.
3) Among the listed species, the following species are excluded.
O2(a), O3(a), H2O2(a)Fig. A1.1 shows the resulting form for selecting compounds. The focused
species and compounds are to be included in the diagram construction.

- 99 -

Diagram Specification
Dimension Selection :No further specification is needed; that is, 298.15 K is selected.
Fixation
Since the Pourbaix diagram is constructed under the condition of a(H2O) =1. For this purpose, the following is made:1) Select the species, H2O a, in the list of species and compounds.
2) Select the coefficient of 1.
Diagram Selection
Here, the three dimension surface diagram is selected as diagram type.
As Coordinates, the followings are listed:(D:O)(D:Fe)(D:pE)
Here, (D:pE) is the coordinate corresponding to the electric charge. In thepresent treatment of CHD, the charge is treated as pseudo element. As a result,working variable for the electrical potential is defined as follows,
pE = φ / 2.303 kT(A1.1)

where φ is the electrical potential. This is well related with the pH defined as
pH = -µ(H+) / 2.303 kT = - log a(H+)(A1.2)

To modify the coordinates appropriate for the Pourbaix diagram,
1) pH is selected as X axis. For this purpose, first focus is moved on the firstline of (D:O) and double click on this line. A species, H+ (a), is first
selected and the coefficient of –1 is selected in the Coefficient Fom.
2) pE is selected as Y axis. For this purpose, focus is moved on the (D:pE)
and then click the upward arrow to move the (D:pE) to the second line.
3) The coordinate (D:Fe) is not changed.
Equilibria between condensed phases and aqueous species I generalized diagram- 100 -

Fig. A1.2 The generalized electrochemical potential diagram for the
Fe-O-H-e- system at 298.15 K under the condition of a(H2O) = 1.

Fig. A1.2 shows the generalized electrochemical potential diagram for the
Fe-O-H-e- system at 298.15 K under the condition of a(H2O) = 1. The
important point as the generalized diagram is that the chemical potential or theactivity of Fe is explicitly expressed in the diagram. In this diagram, thecondensed phase and the aqueous species are respectively shown as stable
polygon.
There are several points to be noted here:
1) Aqueous species are presented as the condition that their activity is equal tounity.
2) On the other hand, those species or compounds which do not contain theiron component form the frame within which the iron compounds can bedisplayed as stable compounds; namely, H+, H2O2(l), HO2-, and OH- form
such a frame as shown in Fig. A1.2.
Equilibria between condensed phases and aqueous species II Pourbaix diagram
Fig. A1. 3(a) and 3(b) are the diagram to reproduce the Pourbaix diagram.
Fig. A3(a) is the two dimensional chemical potential diagram which isconstructed under the same calculation conditions as Fig. A1.2. When
compared with the normal Pourbaix diagram, the regions beyond pH=0 or 14
are lacked. This is because the H+ and OH- species are explicitly included as- 101 -

Fig. A1.3 The generalized electrochemical potential diagram for the
Fe-O-H-e- system at 298.15 K under the condition of a(H2O) = 1. (a)with and (b) without H+, HO2-, and OH- species.

target compounds to be included as stable species and their activity is definedas unity.
To reproduce the Pourbaix diagram which shows the equilibria beyond theselimits, the following can be made.
1) In the menu of “Chemical System / Selection of compounds,”“ReSelection” button is clicked and the species, H+, HO2- and OH-, areexcluded.
- 102 -

2) Other conditions are the same as before.
Resulting diagram is shown in Fig. A1. 3(b). The species, Fe3+, appears as
stable species.
Predominant area diagram
Pourbaix also proposed to use the predominant area diagram which indicate
what aqueous species is predominant in the given thermodynamic conditionsin terms of pH and pE.
To reproduce the predominant area diagram, the following setting can be
made:1) In the menu of “Chemical System / Selection of Compounds, the default
setting is made only on the aqueous species.
2) Then, “ReSelection” button is clicked and those species which do notcontain the iron component will be excluded; namely, O2, O3, H+, HO2-,
OH-, H2O2 will be excluded.
Fig. A1. 4 shows the predominant area diagram in which only the ironcontaining aqueous species are presented as predominant species.

Fig. A1.4 The predominant area diagram for the Fe-containing species at
298.15 K.

- 103 -

S-O-H-e- System
Chemical System:
The same user database is used to retrieve the thermodynamic data for the
S-O-H-e- system.
The Pourbaix diagram and the predominant area diagram for the S-O-H-esystem can be constructed in the same procedures as those in the Fe-O-H-e-Fig. A1.5 The Pourbaix diagram for the S-O-H-e- system at 298.15 K.

Fig. A1.6 The predominant area diagram for the S-containing species at
298.15 K.

- 104 -

system.
Fig. A1.5 shows the two dimensional chemical potential diagram for the
S-O-H-e- system. As sulfur compounds, only S appears as stable compounds.
Fig. A1. 6 shows the predominant area diagram for the sulfur aqueous species.
This is very similar to Fig. A1. 5 where except S, aqueous species are the stableones.
Fe-S-O-H-e- System
The most powerful point of the present CHD program is to construct the
Pourbaix diagram for the multicomponent system without any difficulty. As
described above, we do not need to have any other algorithms for constructing
the Pourbaix diagram or the predominant area diagram. What is needed inconstructing such diagrams is only the following:
1) Select the species to be included in construction of diagram.
2) Specify the condition that a(H2O) = 1.
3) Select the coordinates appropriate for the Pourbaix diagrams. Particularly,
pH and pE should be correctly selected.
The same procedures will be adopted below to construct the Pourbaix diagram
for the Fe-S-O-H-e- multicomponent system.
Chemical System
The thermodynamic data for the Fe-S-O-H-e- system are retrieved from the
MALT main database and the user database: FeSAqueous.udb.
Three Dimensional Chemical Potential Diagram
Selection of Compounds
Condensed phases and also aqueous species are included, although species in
the O-H-e- system are excluded to eliminate the limits derived from H+ etc.
Fixation
Only the activity of water is fixed at unity.
Diagram Coordinates-log a(H+) (=pH)- 105 -

pE
log a(Fe) – log a(S)(D:Fe)
After execute the command Run, the range limits are modified as follows:-log a(H+)
pE
log a(Fe)-log a(S)
min
-2
-40
-100
max
16
40
150
step
2
10
50
factor
1
0.25
0.125
Fig. A1.7 shows the three dimensional Pourbaix diagram for the Fe-S-O-H-esystem ate 298.15 K under a(H2O)=1. As the third axis, we select the valuableof log a(Fe) – log a(S). The type of axis variable is convenient for treating two
metals in equivalent manner. Here, we are treating two elements, iron andsulfur.
In Fig. A1.7, the phase equilibrium information for the Fe-O-H-e- subsystemappears in front of the diagram. On the right hand side, the dissection at pH=16
appears as a function of log a(Fe)-log a(S).
Conventional diagram for the Fe-S-H2O system
Traditionally, the Pourbaix diagram for the Fe-S-H2O system has been
constructed under the assumption that the redox element of the target diagram
is Fe so that only species which contain the iron component will appears in the
diagram.
To reproduce such a diagram in CHD, the following should be made:1) the third axis is changed to – log a(Fe) + log a(S). This is to present thesulfur containing compounds before the iron containing compounds which
do not include sulfur.
2) In the menu of rotation of 3D diagram, the conversion matrix is changed to
as follows;
X-axisY-axisZ-axisHorizontal
1.0
0.0
0.0
Vertical
0.0
1.0
0.0
Depth
0.0
0.0
1.0

- 106 -

Fig. A1.7 The Three Dimensional Pourbaix diagram for the Fe-S-O-H-esystem at 298.15 K.

Fig. A1.8 The Three Dimensional Pourbaix Diagram projected on the
pH-pE plane.

3) In the menu of Graph Inspector / “Compounds” page, the transparency of- 107 -

the displayed compounds is changed in the following compounds:
H2O2 (l)S_Rhombohedral (cs)
H2S (a)S-2(a)
SO4- (a)HS-(a)
HSO4- (a)Fig. A1. 8 shows the three dimensional diagram which is rotated so as to givethe normal two dimensional Pourbaix diagram. There are several blue lines
which are not related with the stable polygons of the species. These areborderlines for species which are converted to be transparent.
The phase equilibria become complicated so that it is not easy to distinguishthe respective stable area. For example, in Fig. A1. 8, it is not easy where thestability region of Fe3O4. To make clear the relative relations among thestability areas, the option of zoom can be used. Fig. A1.9 shows the enlarged
diagram; here, the stability region can be well recognized in relations to otherstability areas.

Fig. A1.9 The Three Dimensional Pourbaix Diagram projected on the
pH-pE plane. This is enlarged diagram to show clearly the stability areaof Fe3O4.

- 108 -Dissections
There are many ways to specify another fixation to obtain the two dimensional
diagram or the three dimensional surface diagram. One of the most attractive
ways is to make a dissection on the three dimensional diagram.
Fig. 1A.10 shows the dissection diagram which was constructed on the basis of
the previously constructed three dimensional diagram (Fig.A1. 8,9).
The menu of Run / Dissection is selected. The dissection plane is defined by
selecting the variable of pH, that is, H+ is selected and the coefficient of –1 isselected.
“Dissection Swing” should be checked.
“Profile Diagram” should be also checked. The diagram type is specified as
dissected diagram(2D). The coordinates are selected as follows;

Fig. A1.10 The dissection diagram at pH=7 for the three Dimensional
Pourbaix Diagram at 298.at K.

- 109 -

1) The axis variable, –log a(Fe) + log a(S), is moved to the x-axis.
2) The axis variable, pE, is moved to the y-axis.
3) As a result, the working variable pH is moved to the z-axis that will not be
used in 2D dissection diagram.
4) When the Selection of Swing Values appears, the range limits are changed
by right-hand-mouse click; the new values should be changed from –2 to16.
Fig. A1. 10 shows the dissection at pH=7. In the left hand side, the phaserelations in the Fe-O-H-e- system are presented, whereas the phase relations in
the corresponding sulfur system are shown in the right hand side. In between,
those species which contain both iron and sulfur appear.
Relation among diagrams for dry, hydrated and wet systems
Since the chemical potential diagram for the Fe-S-O system and theelectrochemical potential diagram for the Fe-S-O-H-e- system can beconstructed by the same algorithm and the same program, it is very easy tocompare those diagrams under the same conditions. One interesting
comparison from the chemical point of view is the construction of diagramswith the same coordinates for the dry, the hydrated and the wet systems. By
hydrated system, the diagram is constructed for the Fe-S-O-H system without
any aqueous species. Even so, the activity of water is fixed at unity in thesystem, some hydrated compounds can be formed. By wet system, the diagram
can contain the aqueous species in addition to the compounds appearing in thehydrated system.
Fig.A1.11 compares three diagrams for the Fe-S-O (-H-e-) systems. As wet
systems, pH=7 is adopted.
In the hydrated system, FeSO4 disappears and instead, FeSO4*7H2O appears.
In addition, H2SO4*H2O appear in the upper-right corner.
In the aqueous system, the aqueous species, SO4(a), appears instead of FeSO4,
FeSO4*7H2O or H2SO4+H2O. In addition, the aqueous species, HS-, appears
in the left hand side. This diagram should be compared with the Pourbaix-type
dissection diagram in Fig. A2.10.

- 110 -

Fig. A1.11 The chemical potential diagrams for the Fe-S-O system: (a) wet
system, (b) hydrated system (c) dry system- 111 -

A2 Electrochemical potential diagrams for Li-Mn-O-H-esystem
The present electrochemical potential diagram can be applied to many
materials issues associated with the electrochemical devices. One of suchapplications is the lithium batteries.
Here, an attempt will be made to construct the electrochemical potential
diagram for the Li-Mn-O-H-e- system. Although the electrolyte for lithium
battery does not contain water in it, it will be interesting to know the phaseequilibria associated with the Li-Mn-O-H system because it has been alreadypointed out that the presence of a small amount of acidic water that is causedby the oxidation of the electrolyte may enhance the manganese dissolution.
Chemical System
The thermodynamic data for the Li-Mn-O-H-e- system can be completed when
the user database, LiMnOHAqueous.txt is used.
Pourbaix diagram for the Mn-O-H-e- system
The thermodynamic data for the Mn-O-H-e- system are retrieved as follows:
1) user database “LiMnOHAqueous.udb” is loaded in the menu “Options /User data /load user database.”
2) In the menu “Tools / Customize MALT Setting ,” check should be madefor the “including Aqueous species” in the Options for Search in“General” page.
3) In the menu “Search Compounds,” “Get compounds” with “Search by
Elements” is selected. In the form of “Search Compounds by Elements,”
the mode of “Compounds consisting of combination of the elements” ischecked and then “Mn,” “O,” and “H” are selected.
4) After preparing the thermodynamic data in MALT with above procedures ,the “MALT Direct” is used to transfer the data to CHD.
In a similar manner described in Appendix 1, the two dimensional Pourbaix
diagram for the Mn-O-H-e- system can be constructed as in Fig. A2.1.
5) In the chemical system, the selection of compounds is made by first
selecting the “Select by Default” with check on the condensed phases andthe aqueous species and then by clicking “ReSelction” button to remove
the species of O2(a), O3(a), H+(a), OH-(a), HO2-(a), H2O2(a).
- 112 -

Fig. A2.1 The Two Dimensional Pourbaix Diagram for the Mn-O-H-esystem at 298.15 K.

6) In the menu “Project / Specify Diagram,” the fixation is made to select thewater, H2O(a), with the fixed value at unity and the diagram type of 2D
chemical potential diagram with the coordinates of -log a(H+) as the x axis
and the (D:pE) as the y axis and (D:Mn) as the z-axis.
7) Since the resulting diagram has a display range wider than the normal, thedisplay range of diagram should be changed by selecting the menu
“Diagram / Range.” The proper range for the x- and the y-axes are thefollowings-log a(H+)
pE
min -2-40
max 1640
step 2
10
factor1
0.25
The chemical feature of the Pourbaix diagram for Mn is that the aqueous
species Mn2+ as well as MnO4- and MnO4-2 are present.

Pourbaix Diagram for the Li-O-H-e- system- 113 -

In the same manner, the Pourbaix diagram for the Li-O-H-e- system can beconstructed as given in Fig. A2.2. In this system, only Li+ species apears as theFig. A2.2 The Two Dimensional Pourbaix Diagram for the Li-O-H-esystem at 298.15 K.

stable species. However, the stability region of Li+ is quite wide comparedwith the corresponding species in the Mn-O-H system.
Three dimensional Pourbaix diagram for the Li-Mn-O-H e- system
The three dimensional Pourbaix diagram can be set up by the following
procedures:
1) Data retrieval for the Li-Mn-O-H-e- system from the MALT main database
and the user database: LiMnOHAqueous.udb.
2) Remove of aqueous species which do not include Li or Mn.
3) Fixation of water, H2O, at the activity of unity
4) The diagram type of 3D chemical potential diagram
5) Change of the coordinates as follows:
X axis : -log a(H+) (=pH)
Y-axis : pE

- 114 -

Z-axis : log a(Mn) – log a(Li)6) Diagram Range is defined as-log a(H+)
pE
log a(Mn)-log a(Li)
min
-2
-40
-90
max
16
40
60
step
2
10
10
factor
1
0.25
0.125
Fig. A2.3 shows the resulting diagram. Phase equilibria in the Mn-O-H-esubsystem shown in Fig. A2.1 appears in the front plane in Fig. A2.3, whereas
in the right hand side plane, the phase equilibria at pH=16 appear.
Since this is the three dimensional diagram so that some additional procedures
are needed to know more detailed information of the target chemical equilibria.
The followings are the possible procedures
1) To make some compounds transparent.

Fig. A2.3 The Three Dimensional Pourbaix Diagram for the
Li-Mn-O-H-e- system at 298.15 K.

- 115 -

Fig. A2.4 The Diagram Specification / One Dissection for the three
Dimensional Pourbaix Diagram for the Li-Mn-O-H-e- system at 298.15 K.

2) To make one dissection and to swing the dissection value.
3) To make a series of dissections
One dissection at log a(Li) = -60
Here, an attempt is made to make a dissection by fixing the lithium activity.
The menu “Dissection” is selected. Thus, the dialog for the Diagram
Specification / One Dissection page will appear as Fig. A2.4. One dissection
plane is selected by clicking the Add button and the Li(cs) is selected among
the Compound candidate. At this time, the fixed value is input as –60.
When profile diagram is checked, the diagram can be selected between thedissected diagram (2D)or the dissected diagram (3D). Here, the dissected
diagram (2D) is selected. In Fig. A2.4, the X-axis for the 2D dissection
diagram is defined as –log a(H+), the Y-axis being log a(Mn) – log a(Li).
A resulting dissection diagram is shown in Fig. A2.5. In this diagram, the- 116 -

display form for the dissection diagram is docked in the right-hand side
docking panel.
The CHD Main form has the two docking panels; that is, the right-handpanel and the bottom-side panel. When the top frame of the display formis dragged by putting the control key and left click of mouse, the positionof cursor appearing with the dragging square frame can be adjusted
between the Right-hand frame of the Main Form and the scroll bar of theMain Display Panel. Then, the Dissection Display Form will be docked tothe panel as shown in Fig. A2.5. The relative size of the main display
panel and the additional display panel can be adjusted by manipulating
the position of splitting bar adjacent to the vertical scroll bar of the main
display panel.

Fig. A2.5 The Three Dimensional Pourbaix Diagram for the Li-Mn-O-H-esystem at 298.15 K with the dissected diagram (2D) at log a(Li)=-60. In
the upper right corner, the Form for Selection of Swing values appears.
The dissected value can be changed by manipulating the scroll bar.

- 117 -

Fig. A2.6 The Three Dimensional Pourbaix Diagram for the Li-Mn-O-H-esystem at 298.15 K with the dissected diagram (2D) at -log a(H+)=6.3.

When the Dissection Swing option is checked, the small form for selecting theswing value appears as in Fig. A2.5. Whenever the dissection value ischanged, a new diagram is constructed and updated in the same display panel.
Fig. A2. 6 shows the dissection diagram for another dissection. Here, the pH,that is, -loga(H+), is defined as a dissection at 6.3. As the X-axis, thelogarithmic activity difference, log a(Mn)-log a(Li), is adopted. The equilibria
in the manganese system appear in the right-hand side, whereas those in thelithium system are given in the left-hand side.
In the chemical potential diagrams shown in Figs. A2.5 and 6, the chemical
stability of LiMn2O4 against the dissolution into aqueous solutions can be
discussed by using the following considerations.
First, the electrode reaction of LiMn2O4 can be written as follows;- 118 -

LiMn2O4 = Li+(a) + Mn2O4 + e-

(A2.1)The right-hand side direction is the charging process and the left-hand side
direction is the discharging process. In Fig. A2.5, the lithium activity is fixedat log a(Li)=-60, and the equilibria between LiMn2O4 and Li+(a) is shown.
Since E/V = -(2.303 RT / F) log a(Li), log a(Li)=-60 corresponds to E=3.55
VThis indicates that this lithium activity corresponds to the discharging process
where Li+(a) is inserted into Mn2O4 phase. In Fig. A2.6, the three phasecombination of Li+(a) / LiMn2O4/Mn2O4 corresponds well the above electrodereaction.
In addition to the normal electrode reaction, there is some possibility that side
reactions can occur during the charge/discharge processes. The manganesedissolution is one of the most important side reactions. It has been pointed outthat the manganese dissolution is enhanced by the acidic environments caused
from the oxidation of electrolyte component. Since LiMn2O4 is dissolved into
Li+ and Mn2+, this reaction can be written as follows:
LiMn2O4 + 8H+ + 3e- = Li+(a) + 2Mn2+(a) + 4 H2O(a)(A2.2)In Fig.A2.5, the stability regions of Li+ and Mn2+ appear in the low values of
pH=–log a(H+), whereas LiMn2O4 appears in the high pH region. This wellcorresponds to the fact that LiMn2O4 is dissolved under the acidic condition.
This is the reaction that consumes the electron so that this can be regarded asdischarge-process-enhancing reaction. Actually, during the discharge process,the lithium activity increases (the electrode potential value decreases); In Fig.
A2.5, the dissection value can be changed from –60 to –58. This corresponds
to a change in lithium activity on discharge. On this change in the lithium
activity, the stability area of LiMn2O4 becomes small. In other wards, thethree-phase point of Li+/LiMn2O4/Mn2+ shifts to the more basic side; that is,
the manganese dissolution is enhanced.

- 119 -

Fig. A2.7 The Three Dimensional Pourbaix Diagram for the Li-Mn-O-H-esystem at 298.15 K in the normal high temperature coordinates for the
Li-Mn-O systems.

In Fig. A2. 6, the interesting phase equilibria are plotted. Here, three-phase
point of Li+/LiMn2O4/Mn2+ is represented as the vertex point of their stability
polygons. There is however, a new feature appearing in this diagram. That is,
the spinel phase, Mn3O4, becomes very close to that three-phase point. This
thermodynamically implies that the dissolved manganese ions, Mn2+, can be
precipitated as the spinel phase. Since the LiMn2O4 itself has the spinel
structure, it is suggested that there is no kinetic barrier for Mn3O4 to beprecipitated.
3Mn2+ + 4H2O = Mn3O4 + 8H+ + 2e-(A2.3)

By combining with (A2.1), the following reaction can be written:
3LiMn2O4 + 8H+ + 5e-= 3Li+ + 2Mn3O4 + 4H2O

(A2.4)

By comparing Eqa. (A2.4) and (A2.1), the following is obvious:- 120 -

The

manganese ions remain without change in the ionic configuration after thelithium ion is removed in (A2.1), whereas the manganese ions in (A2.4) can be
regarded as reconstructed from aqueous solution; in such a case, there are nolithium sites in the new spinel precipitate.
Thus, these diagrams can give the reasonable explanation for the following
facts in the lithium batteries.
1) Manganese dissolution is enhanced in the acidic situation after theoxidation of electrolyte component.
2) Manganese dissolution becomes more severe on discharge process.
3) Even so, the manganese dissolution tends to be mild on heavily discharge
state.
4) The capacity loss is also associated with the manganese dissolution. The
loss of the lithium site due to the occupation of manganese ions should be
the reason for the capacity fading.

Relation among the Pourbaix diagram for the multi-component system and the hightemperature chemical potential diagram.
Since the Li-Mn-O system is one part of the subsystems of the Li-Mn-O-H-esystem, it can be possible to compare the phase relation appears in Fig. A2. 5
and 6 with those chemical potential diagrams proposed for high temperatureuse.
The main chemical potential diagram in Fig. A2.7shows the three dimensional
diagram for Li-Mn-O-H-e- system at a(H2O)=1.0. Although the aqueous
species are shown in this diagram, they are not well shown because the axis of
pH now disappears. In other wards, the phase equilibria developing along the
pH axis are degenerated into the non-pH axis. Actually, there should be many
species at one point in the three chemical potential diagram.
To display the diagram in Fig.A2.7, the species of MnO4- and MnO42- arechanged to be transparent.
The comparison is made in Fig. A2. 7 where the same phase equilibria as inFig. A2. 6 are plotted in the normal three dimensional diagram. In thisdiagram, the stable polygons for Li+ and Mn2+ appear in addition to the
non-aqueous species. This clearly shows how the aqueous species affect on
the normal phase equilibria.

- 121 -