T3: Stepped
equilibrium calculations
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb
Contents
- Re-opening a saved file and loading a calculation state
- Calculating a stepped equilibrium with varying temperature
- Understanding the results in the Output window
- Working with multiple buffers
- Calculating a stepped equilibrium with varying composition
- The "Edit buffer states" window
Before starting...
Re-open the file saved from Tutorial 2 and
load the calculation state 'Equil @ 600°C'.
1. Stepped equilibrium calculation with varying temperature
Running the stepped calculation
Select 'Stepped calculation...' from
the 'Calc' menu or click
on the icon.
The 'Step equilibrium' window will appear. Select 'Temperature' (the
uppermost choice in the left-hand column).
In the 'Range' box, the default 'Start', 'Stop' and 'Step
interval' values are 400, 1600 and 25 respectively.
Keep these values and verify that the 'Temperatures
in Celsius' option has been selected.
The step direction is unimportant, and it is not necessary to enter
the interval as '-25' if stepping
in a negative direction. The contents of the 'Vary' and 'Boundary
conditions' boxes are currently
greyed-out because they are not applicable to a temperature-step
calculation. Click on the 'Go' button
at the bottom right of the window.

Output
The 'Output' window should show the
following series of messages:
1, 0,00 s, 600,00 C (873,16 K), its 2, BCC_A2 CEMENTITE - OK -
2, 0,00 s, 625,00 C (898,16 K), its 4, BCC_A2 CEMENTITE - OK -
3, 0,00 s, 650,00 C (923,16 K), its 4, BCC_A2 CEMENTITE - OK -
4, 0,02 s, 675,00 C (948,16 K), its 4, BCC_A2 CEMENTITE - OK -
5, 0,00 s, 700,00 C (973,16 K), its 4, BCC_A2 CEMENTITE - OK -
6, 0,00 s, 725,00 C (998,16 K), its 4, BCC_A2 CEMENTITE - OK -
Tsol 'FCC_A1': 726,62 C (999,78 K) iter: 4, time used: 0,00 s
Tsol 'CEMENTITE': 726,62 C (999,78 K) iter: 5, time used: 0,00 s
7, 0,01 s, 750,00 C (1023,16 K), its 5, FCC_A1 BCC_A2 - OK -
8, 0,02 s, 775,00 C (1048,16 K), its 5, FCC_A1 BCC_A2 - OK -
Tsol 'BCC_A2': 787,14 C (1060,30 K) iter: 4, time used: 0,00 s
9, 0,00 s, 800,00 C (1073,16 K), its 4, FCC_A1 - OK -
10, 0,00 s, 825,00 C (1098,16 K), its 2, FCC_A1 - OK -
11, 0,00 s, 850,00 C (1123,16 K), its 2, FCC_A1 - OK -
12, 0,00 s, 875,00 C (1148,16 K), its 2, FCC_A1 - OK -
13, 0,00 s, 900,00 C (1173,16 K), its 2, FCC_A1 - OK -
14, 0,00 s, 925,00 C (1198,16 K), its 2, FCC_A1 - OK -
15, 0,00 s, 950,00 C (1223,16 K), its 2, FCC_A1 - OK -
16, 0,00 s, 975,00 C (1248,16 K), its 2, FCC_A1 - OK -
17, 0,00 s, 1000,00 C (1273,16 K), its 2, FCC_A1 - OK -
18, 0,00 s, 1025,00 C (1298,16 K), its 2, FCC_A1 - OK -
19, 0,00 s, 1050,00 C (1323,16 K), its 2, FCC_A1 - OK -
20, 0,00 s, 1075,00 C (1348,16 K), its 2, FCC_A1 - OK -
21, 0,00 s, 1100,00 C (1373,16 K), its 2, FCC_A1 - OK -
22, 0,00 s, 1125,00 C (1398,16 K), its 2, FCC_A1 - OK -
23, 0,00 s, 1150,00 C (1423,16 K), its 2, FCC_A1 - OK -
24, 0,00 s, 1175,00 C (1448,16 K), its 2, FCC_A1 - OK -
25, 0,00 s, 1200,00 C (1473,16 K), its 2, FCC_A1 - OK -
26, 0,00 s, 1225,00 C (1498,16 K), its 2, FCC_A1 - OK -
27, 0,00 s, 1250,00 C (1523,16 K), its 2, FCC_A1 - OK -
28, 0,00 s, 1275,00 C (1548,16 K), its 2, FCC_A1 - OK -
29, 0,00 s, 1300,00 C (1573,16 K), its 2, FCC_A1 - OK -
30, 0,00 s, 1325,00 C (1598,16 K), its 2, FCC_A1 - OK -
31, 0,00 s, 1350,00 C (1623,16 K), its 2, FCC_A1 - OK -
32, 0,02 s, 1375,00 C (1648,16 K), its 2, FCC_A1 - OK -
33, 0,00 s, 1400,00 C (1673,16 K), its 2, FCC_A1 - OK -
34, 0,00 s, 1425,00 C (1698,16 K), its 2, FCC_A1 - OK -
35, 0,00 s, 1450,00 C (1723,16 K), its 2, FCC_A1 - OK -
Tsol 'LIQUID': 1453,05 C (1726,21 K) iter: 3, time used: 0,00 s
36, 0,02 s, 1475,00 C (1748,16 K), its 3, LIQUID FCC_A1 - OK -
Tsol 'FCC_A1': 1494,60 C (1767,76 K) iter: 16, time used: 0,00 s
Tsol 'BCC_A2': 1494,60 C (1767,76 K) iter: 5, time used: 0,00 s
37, 0,02 s, 1500,00 C (1773,16 K), its 5, LIQUID BCC_A2 - OK -
Tsol 'BCC_A2': 1505,64 C (1778,80 K) iter: 4, time used: 0,00 s
38, 0,00 s, 1525,00 C (1798,16 K), its 4, LIQUID - OK -
39, 0,00 s, 1550,00 C (1823,16 K), its 2, LIQUID - OK -
40, 0,00 s, 1575,00 C (1848,16 K), its 2, LIQUID - OK -
41, 0,00 s, 1600,00 C (1873,16 K), its 2, LIQUID - OK -
changing step direction ...
42, 0,00 s, 575,00 C (848,16 K), its 5, BCC_A2 CEMENTITE - OK -
43, 0,02 s, 550,00 C (823,16 K), its 5, BCC_A2 CEMENTITE - OK -
44, 0,00 s, 525,00 C (798,16 K), its 5, BCC_A2 CEMENTITE - OK -
45, 0,00 s, 500,00 C (773,16 K), its 5, BCC_A2 CEMENTITE - OK -
46, 0,00 s, 475,00 C (748,16 K), its 5, BCC_A2 CEMENTITE - OK -
47, 0,00 s, 450,00 C (723,16 K), its 5, BCC_A2 CEMENTITE - OK -
48, 0,00 s, 425,00 C (698,16 K), its 5, BCC_A2 CEMENTITE - OK -
49, 0,00 s, 400,00 C (673,16 K), its 5, BCC_A2 CEMENTITE - OK -
50, 0,00 s, 400,00 C (673,16 K), its 2, BCC_A2 CEMENTITE - OK -
Steps: 51, CalcTime: 0,50 s
AktStepVal: 673,160000
- OK -
Each line corresponds to an equilibrium calculated at a single
temperature value and comprises a line number, the calculation
time, the temperature, the number of iterations, the stable phases
at that temperature and an '- OK -' message indicating that the
equilibrium calculation was successful.
Note that the temperature-stepping
starts from the equilibrium at 600°C loaded from the calculation
state. Initially, the temperature is increased by the 'Step
interval' each time until the upper temperature limit is reached. Then, a
'changing step direction' message is displayed and, again starting
from the equilibrium at 600°C, the temperature is decreased
until the lower limit is reached.
Also note the lines beginning with 'Tsol':
phase solubility temperatures are automatically evaluated during
the stepped calculation. Thus it is seen in the output below that
from 600°C to 726.62°C,
the two stable phases are BCC_A2 (ferrite)
and CEMENTITE. At 726.62°C,
FCC_A1 (austenite) becomes stable,
and cementite becomes unstable. The two phases in equilibrium are
ferrite and austenite between this temperature and 787.14°C,
when ferrite becomes unstable. Austenite is then the only stable
phase, and this situation persists up to the liquid solubility
temperature of 1453.05°C. The BCC_A2 phase
known as delta-ferrite is stable in a narrow temperature range
at high temperature, and by 1600°C the
only equilibrium phase is liquid.
There are no changes in phase stability between 600°C and 400°C,
as can be seen from the block of lines below 'changing
step direction'.
The final three lines of output give the number of steps and total
calculation time, the current value of the stepped variable (673.16
K = 400°C) and an 'OK' message indicating that the calculation
was carried out successfully.
The contents of the 'Phase summary' and 'Phase
details' are not
modified during the stepped calculation, but still display the
information loaded from the calculation state 'Equil
@ 600°C'.
Buffers
All the equilibria listed above are stored in a buffer. The default
buffer is named '_default_', and its
contents are overwritten when a new stepped calculation is carried
out.
To be able to keep more than one set of stepped equilibria, additional
buffers must be created. Firstly, rename the existing default buffer
using 'Global > Buffers > Rename'.
Type 'T
= 400 to 1600°C' into the 'New
buffer name' box and click 'OK'.
Then, create a new buffer using 'Global > Buffers > Create'.
This new buffer will contain the results from a new stepped equilibrium
calculation in which the carbon content is varied from 0 to 1.5
wt.% at 500°C,
so enter the name 'C=0 to 1.5 at 500°C'.
Note that buffers can be selected from the drop-box in the toolbar
area or using 'Global > Buffers > Select'.

2. Stepped equilibrium calculation with varying carbon content
Running the calculation
Calculate an equilibrium at 500°C. Open the 'Step
equilibrium' window again, but this time select 'Element
cont..' instead of
'Temperature' in the 'Type' box. Enter '0', '1.5' and '0.05' respectively
as the start, stop and step interval values. (Note that, as shown
in the image below, MatCalc accepts either a decimal point or a
comma as the decimal separator.)
In the 'Boundary conditions' box,
ensure that the element selected is 'C', and enter the temperature
as '500'. Ensure that in the 'vary' box, 'global
comp' is selected,
and that in the 'Options' column, 'Temperatures
in Celsius' and
'Composition in weight percent' are
both selected, then click on 'Go'.

The contents of the 'Output' window should appear as follows:
1, 0,00 s, 0,4, its 2, BCC_A2 CEMENTITE - OK -
2, 0,00 s, 0,45, its 2, BCC_A2 CEMENTITE - OK -
3, 0,00 s, 0,5, its 2, BCC_A2 CEMENTITE - OK -
4, 0,00 s, 0,55, its 2, BCC_A2 CEMENTITE - OK -
5, 0,00 s, 0,6, its 2, BCC_A2 CEMENTITE - OK -
6, 0,00 s, 0,65, its 2, BCC_A2 CEMENTITE - OK -
7, 0,00 s, 0,7, its 2, BCC_A2 CEMENTITE - OK -
8, 0,00 s, 0,75, its 2, BCC_A2 CEMENTITE - OK -
9, 0,00 s, 0,8, its 2, BCC_A2 CEMENTITE - OK -
10, 0,00 s, 0,85, its 2, BCC_A2 CEMENTITE - OK -
11, 0,00 s, 0,9, its 2, BCC_A2 CEMENTITE - OK -
12, 0,00 s, 0,95, its 2, BCC_A2 CEMENTITE - OK -
13, 0,00 s, 1, its 2, BCC_A2 CEMENTITE - OK -
14, 0,00 s, 1,05, its 2, BCC_A2 CEMENTITE - OK -
15, 0,00 s, 1,1, its 2, BCC_A2 CEMENTITE - OK -
16, 0,00 s, 1,15, its 2, BCC_A2 CEMENTITE - OK -
17, 0,00 s, 1,2, its 2, BCC_A2 CEMENTITE - OK -
18, 0,00 s, 1,25, its 2, BCC_A2 CEMENTITE - OK -
19, 0,00 s, 1,3, its 2, BCC_A2 CEMENTITE - OK -
20, 0,00 s, 1,35, its 2, BCC_A2 CEMENTITE - OK -
21, 0,00 s, 1,4, its 2, BCC_A2 CEMENTITE - OK -
22, 0,00 s, 1,45, its 2, BCC_A2 CEMENTITE - OK -
23, 0,00 s, 1,5, its 2, BCC_A2 CEMENTITE - OK -
changing step direction ...
24, 0,00 s, 0,35, its 2, BCC_A2 CEMENTITE - OK -
25, 0,00 s, 0,3, its 2, BCC_A2 CEMENTITE - OK -
26, 0,00 s, 0,25, its 2, BCC_A2 CEMENTITE - OK -
27, 0,00 s, 0,2, its 2, BCC_A2 CEMENTITE - OK -
28, 0,00 s, 0,15, its 2, BCC_A2 CEMENTITE - OK -
29, 0,00 s, 0,1, its 2, BCC_A2 CEMENTITE - OK -
30, 0,00 s, 0,05, its 2, BCC_A2 CEMENTITE - OK -
Xsol 'CEMENTITE': X(C): 5,6266917e-005, WP(C): 0,0012101846 - OK -
31, 0,03 s, 1e-009, its 13, BCC_A2 - OK -
Steps: 32, CalcTime: 0,75 s
AktStepVal: 0,000000
- OK -
Similarly to the temperature-step calculation, the output consists
of a series of equilibria evaluated at the specified step-values.
The first of these corresponds to the carbon content of 0.4 wt.%
entered in the 'System composition' box in Tutorial
2. The carbon
content is then increased in 0.05 wt.% steps up to the maximum
value of 1.5 wt.%. The 'Changing step direction' line marks the
beginning of the second set of equilibria, in which the carbon
content is decreased.
At 500°C, the stable phases are BCC_A2 and CEMENTITE across
almost the whole composition range, but between the final two equilibria
there is a line beginning with 'Xsol'. The line below this gives
the carbon content at which cementite becomes unstable, both in
mole fraction 'X(C)' and in weight percent 'WP(C)'.
Create a third buffer named 'C=0 to 1.5
at 800°C' and perform
a stepped calculation with the same composition range but at a
temperature of 800°C. The output in this case includes three
'Xsol' lines, corresponding to changes in phase stability:
1, 0,02 s, 0,4, its 49, FCC_A1 - OK -
2, 0,00 s, 0,45, its 4, FCC_A1 - OK -
3, 0,00 s, 0,5, its 3, FCC_A1 - OK -
4, 0,00 s, 0,55, its 3, FCC_A1 - OK -
5, 0,00 s, 0,6, its 3, FCC_A1 - OK -
6, 0,00 s, 0,65, its 3, FCC_A1 - OK -
7, 0,00 s, 0,7, its 3, FCC_A1 - OK -
8, 0,00 s, 0,75, its 3, FCC_A1 - OK -
9, 0,00 s, 0,8, its 3, FCC_A1 - OK -
10, 0,02 s, 0,85, its 3, FCC_A1 - OK -
11, 0,00 s, 0,9, its 3, FCC_A1 - OK -
Xsol 'CEMENTITE': X(C): 0,042627412, WP(C): 0,94852383 - OK -
12, 0,01 s, 0,95, its 4, FCC_A1 CEMENTITE - OK -
13, 0,00 s, 1, its 2, FCC_A1 CEMENTITE - OK -
14, 0,00 s, 1,05, its 2, FCC_A1 CEMENTITE - OK -
15, 0,00 s, 1,1, its 2, FCC_A1 CEMENTITE - OK -
16, 0,00 s, 1,15, its 2, FCC_A1 CEMENTITE - OK -
17, 0,00 s, 1,2, its 2, FCC_A1 CEMENTITE - OK -
18, 0,00 s, 1,25, its 2, FCC_A1 CEMENTITE - OK -
19, 0,00 s, 1,3, its 2, FCC_A1 CEMENTITE - OK -
20, 0,00 s, 1,35, its 2, FCC_A1 CEMENTITE - OK -
21, 0,00 s, 1,4, its 2, FCC_A1 CEMENTITE - OK -
22, 0,00 s, 1,45, its 2, FCC_A1 CEMENTITE - OK -
23, 0,00 s, 1,5, its 2, FCC_A1 CEMENTITE - OK -
changing step direction ...
24, 0,00 s, 0,35, its 4, FCC_A1 - OK -
Xsol 'BCC_A2': X(C): 0,015673339, WP(C): 0,34128475 - OK -
25, 0,02 s, 0,3, its 4, FCC_A1 BCC_A2 - OK -
26, 0,00 s, 0,25, its 2, FCC_A1 BCC_A2 - OK -
27, 0,00 s, 0,2, its 2, FCC_A1 BCC_A2 - OK -
28, 0,00 s, 0,15, its 2, FCC_A1 BCC_A2 - OK -
29, 0,00 s, 0,1, its 2, FCC_A1 BCC_A2 - OK -
30, 0,00 s, 0,05, its 2, FCC_A1 BCC_A2 - OK -
Xsol 'FCC_A1': X(C): 0,00055591189, WP(C): 0,011961202 - OK -
31, 0,01 s, 1e-009, its 9, BCC_A2 - OK -
Steps: 32, CalcTime: 0,30 s
AktStepVal: 0,000000
- OK -
Edit buffer states
The 'Output' window provides information on which phases are stable
at a given temperature and carbon content, but not on the phase
fractions or compositions. However, this detailed information is
stored in the buffers and can be found by selecting 'Global > Buffers > Edit
buffer states'.

The upper part of this window contains a drop-box for selecting
a buffer, and the lower part gives a list of the step-values at
which equilibria have been evaluated. These are either temperature
or carbon content values, depending on the buffer chosen, and their
units are those specified in the 'Step equilibrium' window when
setting up the calculation. The 'Tsol' or 'Xsol' values are also stored.
If the 'auto load' box at the bottom left is ticked, clicking on
a step-value loads the equilibrium, and the contents of the 'Phase
summary' and 'Phase details' are immediately updated with phase
fraction and composition details for this equilibrium.
The next two tutorials demonstrate how to produce graphical plots
of phase fractions, compositions and many other quantities as a
function of the stepped variable.
To finish...
Save the workspace file - it will be needed again in Tutorial
4.
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