T2: Calculating
a single equilibrium
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb
This tutorial explains how to determine the equilibrium phases
at a given temperature, and their phase fractions and compositions.
Contents
- Opening a database and selecting elements and phases
- Entering a composition
- Calculating an equilibrium at a given temperature
- Interpretation of information displayed in the output, phase
summary and phase details windows
- Using the 'Options' window to modify the display
- Phase status indicators
- Calculation states
Before starting...
Create a new workspace file (Tutorial
1).
1. Setting up the system
Opening a thermodynamic database and selecting elements and phases
In the 'Global' menu, select 'Databases'.
A window will appear as shown below. The 'Equilibrium
database' box initially displays
the message 'database not open...'.
Click on the 'open...' button;
this will open the '...MatCalc/database' subdirectory,
allowing the user to choose a database. A small database on iron-based
materials,
'mc_sample_fe.tdb', is provided with
MatCalc for demonstration purposes. Select this database and click 'Open'.

A list of elements will appear in the left-hand box, with FE
and VA (vacancies) selected by default. In the
right-hand box is a list of the phases which can occur in a system
containing the selected elements. Click on 'C' in the elements
box; this will add to the list a number of other phases which
can occur in an Fe-C system, such as graphite and several carbides.
The 'show all available phases' box can be used to display all
the phases available in the database, irrespective of whether
they can form in the system in question.
From the phase list, select 'LIQUID', 'BCC_A2',
'FCC_A1', 'GRAPHITE' and 'CEMENTITE'.
Phases are described using crystallographic notation: BCC_A2 represents
the body-centred cubic phase, which corresponds to ferrite in
the iron-carbon system, and FCC_A1 is the face-centred cubic austenite
phase in Fe-C. Click 'Read' then 'close'

Entering the composition
In the 'Global' menu, select 'Composition'. This opens the 'System
composition' box. The lower part of the box gives options for
the units in which the composition is to be displayed: mole fraction,
weight fraction, u-fraction or weight percent. One of the elements,
usually the one with the highest mole fraction, is designated
as the 'reference element', and the amount of this element is
calculated as 1-(sum of the amounts of all
other elements) for
compositions expressed in fractional form, or 100-(sum
of the amounts of all other elements) for compositions expressed as percentages.
Iron is set as the reference element by default in the 'mc_sample_fe.tdb'
database, as can be seen from the 'Ref.
Elem' column in the composition
dialogue box. Another element can be set as the reference by selecting
the element name and clicking on the 'Set
reference element' button
on the right, or by double-clicking in the 'Ref.
Elem' column
by the side of the element name.
To enter a composition of 0.4 wt.% C, select 'weight
percent' as the unit, then highlight element C. Double-click in the 'Amount' column, click on the 'Change' button or press F2 to modify the
composition, then type in '0.4' and press 'Enter'.
The system is now ready to perform an equilibrium calculation.

2. Calculating an equilibrium
From the 'Calc' menu, select 'Set
start values'. This initialises
the calculation variables with reasonable values in order to
help the Gibbs free energy minimiser to find a solution which
satisfies all the boundary conditions. This command is useful
if the solution algorithm seems to be 'stuck' and unable to find
an equilibrium.
Once one valid equilibrium has been found, solutions
at other temperatures or boundary conditions are much easier to
obtain. From the 'Calc' menu, select 'Equilibrium', or click on the icon
in the toolbar. The following window appears:

Enter '700' in the temperature box
and ensure that 'temperature in C' is selected. Leave the pressure
at its default value. Click on 'Go' to
start the calculation.
Interpreting the results of the calculation
The 'Output', 'Phase
status' and 'Phase details' windows each
show information on the calculation which has just been performed.
The final three lines of the Output window list the number of
iterations, the calculation time, the temperature and the Gibbs
energy of the system. The '- OK -' message in the final line indicates
that the calculation was successful, with no errors reported.
If any errors do occur, the message '***
error ***' followed by
a description of the nature of the error will be displayed instead
of the 'OK' message. In this case, reset the calculation with 'Set
start values' and repeat it using 'Equilibrium'. It is always advisable to check the status
of the calculation in the Output window before proceeding.
The other lines visible in the Output window are messages relating
to the opening and reading of the thermodynamic database.

Information on the phase stabilities is shown in the 'Phase
summary' window. Those phases with non-zero phase fractions are termed
'active' and are listed in the first block. Inactive phases (those
which are unstable, with negative driving forces) are listed in
the second block. The third column gives the phase fraction and
the column after 'dfm:' gives the driving force in J/mole. It
can be seen that BCC_A2 (ferrite) and GRAPHITE are the stable
phases at 700°C.

The 'Phase details' window provides
more comprehensive information on the properties of the phases,
including the molar Gibbs free energy of the phase (the number
after 'gm:') and the phase compositions
(expressed in mole fraction by default), as well as the information
provided in the 'Phase summary'. The phases are again grouped
according to whether they are active or inactive.

Using the 'Options' window to modify the display
To change the units in which the composition is displayed in
the 'Phase details' window, first highlight this window and then
go to the 'Options' window. (If this is not shown on the screen,
make it appear by selecting 'View > Show options window' or
right-clicking in the toolbar area and selecting 'options' from
the menu.)
The 'Options' window provides display
options for the currently highlighted window. In the case of the 'Phase
details' window,
the composition can be displayed as a mole fraction, a weight
fraction or a u-fraction, and can also be expressed as a percentage
if required.

Phase status: suspended and dormant phases
The calculation has shown that at 700°C, BCC_A2 (ferrite)
and graphite are the equilibrium (i.e. most thermodynamically
stable) phases. However, it is observed in practice that in Fe-C
systems with relatively low carbon contents, graphite formation
is extremely slow, and can be considered not to occur over practical
timescales.
Since this is the case, it is useful to calculate a metastable
equilibrium, for which graphite formation is not allowed. Go to
'Global > Phase status' and highlight 'GRAPHITE'.
In the 'General' tab,
the uppermost section is labelled 'Flags...'.
Click to place a tick in the box next to 'suspended'.

Repeat the equilibrium calculation and note the difference in
results in the 'Phase
summary' window:
BCC_A2 * act 9.29184e-001 dfm: +0.00000e+000
CEMENTITE act 7.08156e-002 dfm: +0.00000e+000
### inactive ###
FCC_A1 - OK - 0.00000e+000 dfm: -1.19831e+002
LIQUID - OK - 0.00000e+000 dfm: -3.71988e+003
### suspended ###
GRAPHITE
Now BCC_A2 and CEMENTITE are active, FCC_A1 and LIQUID are inactive
and GRAPHITE is listed as 'suspended'. Suspending a phase causes
the program to consider it as if it were not there at all; the
next most stable phase (in this case, cementite) becomes the equilibrium
phase. Alternatively, the flag can be set to 'dormant' using the
same procedure. In this case, the phase is considered not to appear,
but its driving force is still evaluated. In this case, cementite
does not become active, as shown by the results below:
BCC_A2 * act 9.82166e-001 dfm: +0.00000e+000
### inactive ###
GRAPHITE dorm. 1.78337e-002 dfm: +0.00000e+000
FCC_A1 - OK - 0.00000e+000 dfm: -1.88361e+002
CEMENTITE - OK - 0.00000e+000 dfm: -5.82264e+002
LIQUID - OK - 0.00000e+000 dfm: -4.07901e+003
In order to eliminate graphite completely from the system, it
is necessary to re-load the thermodynamic data from the database.
Re-open 'Global > Databases' and click on GRAPHITE to unselect
it, then click on 'Read'. A warning will appear, stating that
all existing data will be deleted. Accept this by clicking on
'Yes'. A new message, with updated information on the thermodynamic
data, appears in the 'Output' window. Reading in new data from
the database erases any previous equilibrium calculation results,
so repeat the equilibrium calculation at 700°C to obtain an
equilibrium without graphite. The driving forces obtained should
be identical to those found in the previous calculation in which
graphite was suspended:
BCC_A2 * act 9.29184e-001 dfm: +0.00000e+000
CEMENTITE act 7.08156e-002 dfm: +0.00000e+000
### inactive ###
FCC_A1 - OK - 0.00000e+000 dfm: -1.19831e+002
LIQUID - OK - 0.00000e+000 dfm: -3.71988e+003
Calculation states
By default, the results from a previous equilibrium calculation
are overwritten when a new calculation is carried out. However,
it is sometimes useful to store the results from a calculation
for future use. The 'Calculation states' feature
is provided for this purpose; it can be found in the 'Global'
menu under 'CalcStates'. In the sub-menu, click on 'Create' and
type the name in the box:

The calculation state stores all information on an equilibrium
including the complete phase status, composition and any compositional
states which may apply. Calculate another equilibrium at 600°C
and store it in another calculation state. These states are now
both available in the calculation state drop-box on the toolbar:

Select a calculation state from this box and load the stored
equilibrium with the button
(This can also be done using 'Global > CalcStates > Select' and
then 'Load' ).
Note how the contents of the 'Phase details' and 'Phase
summary' windows are immediately
updated with the results stored in the calculation state, and
the temperature at which the equilibrium was calculated is shown
in the status bar towards the bottom right of the screen. The
results of the current equilibrium calculation can be saved into
an existing calculation state by selecting the name of the state
in the drop-box and then clicking on the button or using 'Global > CalcStates > Select' and
then 'Save'.
NB: Calculation states, like all other calculation results, are
erased when data is re-read from the database!
To finish...
Save the workspace using 'File > Save
as...'. Workspace files
are automatically given the file extension '.mcw'.
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