T7: Calculating
phase boundaries
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb
Contents
- Using "Search phase boundary" with temperature variation
to determine solidus and liquidus
- Determining austenite <-> ferrite transformation temperatures
- Finding phase boundaries for carbide phases in terms of temperature
and element content
- Tracing a phase boundary on axes of temperature versus element
content
It was seen in Tutorial
3 that MatCalc evaluates solubility temperatures
(Tsol) or compositions (Xsol) during the course of stepped equilibrium
calculations. It is also possible to calculate these individually
using the 'Search phase boundary' function.
1. Setting up the system
Create a new workspace file and set up the system with elements
Fe, C and Nb and phases FCC_A1, BCC_A2, LIQUID and CEMENTITE. Enter
the composition as 0.1 wt.%C, 0.3
wt.% Nb and calculate an equilibrium
at 1000°C (Refer to Tutorial
1 and Tutorial
2 if necessary.)
Note the results in the 'Phase details' window. A second FCC_A1
phase has automatically been created, and examination of its composition
shows that its approximate formula is NbC.
#### /FCC_A1/ moles: 0,99669, gm: -62332,5 (-62332,5), sff: 0,996959
Phasestatus: entered - active
FE +9,96862e-001 C +3,04147e-003 NB +9,65398e-005
#### /FCC_A1#01/ moles: 0,0033101, gm: -112964 (-112964), sff: 0,514554
Phasestatus: entered - active
NB +5,14395e-001 C +4,85446e-001 FE +1,59079e-004
### inactive ###
#### /BCC_A2/ moles: 0, gm: -62262,4 (-62262,4), sff: 0,999701
Phasestatus: entered - not active (dfm=-82,83)
FE +9,99572e-001 C +2,99148e-004 NB +1,28385e-004
#### /LIQUID/ moles: 0, gm: -58601,3 (-58601,3), sff: 1
Phasestatus: entered - not active (dfm=-3777)
FE +9,75342e-001 C +2,34126e-002 NB +1,24525e-003
#### /CEMENTITE/ moles: 0, gm: -52390,6 (-27518,5), sff: 0,25
Phasestatus: entered - not active (dfm=-9077)
FE +7,50000e-001 C +2,50000e-001 NB +6,86980e-008
It is the following line in the database file mc_sample_fe.tdb which
causes the second FCC_A1 phase to be created:
ADD_COMPOSITION_SET FCC_A1 :TI,NB,V:C,N: !
This creates that a new phase of type FCC_A1 with Ti, Nb or V
as the major constituents on the first sublattice and C or N as
the major constituents on the second when the system contains these
elements. The 'General' tab in the 'Phase
status' box ('Global > Phase
status') shows the major constituents for each phase, :FE:VA: and
:NB:C: respectively for FCC_A1 and FCC_A1#01.
2. Calculating phase boundaries
Solidus and liquidus temperatures
The solidus temperature is defined by zero phase fraction of liquid.
To calculate this, choose 'Search phase boundary' from
the 'Calc' menu or click on the icon.
The box below appears. Select 'Temperature' in
the left-hand column and 'LIQUID' in
the 'Target
phase' column, then click on 'Go'.

The following message appears in the output window.
Tsol 'LIQUID': 1480.30 C (1753.46 K) iter: 16, time used: 0.02
s
The liquidus temperature is the dissolution temperature of the
last solid phase, which in this case is BCC_A2. Selecting 'BCC_A2' as the target phase gives the following result:
Tsol 'BCC_A2': 1452.43 C (1725.59 K) iter: 5, time used: 0.00
s
Of course, this is not a liquidus temperature, as it cannot be lower than the solidus temperature. This result is given because MatCalc finds the zero phase fraction temperature of BCC_A2 phase next to the temperature of the last calculation which is 1480.30°C in this case (the liquidus temperature). Information given in 'Phase summary' window explains that at 1452.43°C, BCC_A2 appears next to FCC_A1 phase (inactive BCC_A2 phase has the driving force value of zero). It is recommended to look at the 'Phase summary' window in order to check if the found phase boundary is the desired one!
The liquidus phase can be easily found if an equilibrium calculation in the liquid system is performed first. Calculate an equlibrium at 1600°C (or any temperature in which system contains only a liquid) and search again for the phase boundary of BCC_A2 phase. This time the following result should be given:
Tsol 'BCC_A2': 1527,33 C (1800,49 K) iter: 4, time used: 0,03 s
In general, the correct phase boundaries are found if the initial equilibrium describes the system in the neighbouring phase field which does not contain the searched phase - in the case presented above, the liquidus temperature (which is the border between the "BCC+LIQUID" and "LIQUID" phases) was found from the "LIQUID" phase field. Also, the algorithm used to search for phase boundaries might fail to converge
if the starting point is too far away from the boundary.
Austenite-ferrite transformation temperatures
Low-alloy steels undergo a ferrite - austenite phase transformation
between 700 and 800°C (see, for example, Tutorial
4). To find
the exact temperatures of the transformation in the Fe-0.1wt.%C-0.3wt.%Nb
system, calculate an equilibrium at 700°C and use again 'Search phase boundary'. Select 'FCC_A2' as a target
phase to identify the zero-phase boundary temperature for austenite.
Tsol 'FCC_A1': 726.62 C (999.78 K) iter: 11, time used: 0.00 s
The zero-phase boundary of BCC_A2 for this transformation can
be identified by calculating an equilibrium at 900°C and then
searching for the boundary.
Tsol 'BCC_A2': 883,07 C (1156,23 K) iter: 5, time used: 0,05 s
Dissolution temperatures of carbides
Cementite is only stable to relatively low temperatures, so calculate
an equilibrium at 800°C as a starting point, then search for
the phase boundary.
Tsol 'CEMENTITE': 726,62 C (999,78 K) iter: 9, time used: 0,05 s
Note that this is the same temperature as the zero-phase boundary
of FCC_A1. Niobium carbide, by contrast, remains stable at higher
temperatures. Calculate an equilibrium at 1200°C before searching
for the boundary.
Tsol 'FCC_A1#01': 1345,99 C (1619,15 K) iter: 5, time used: 0,03 s
Element content for zero-phase fractions
Phase boundaries can also be found in terms of element content
at a fixed temperature. To illustrate this, the zero-phase boundary
of cementite at 700°C will be evaluated in terms of carbon
content. Calculate an equilibrium at 700°C, then open the 'Search
phase boundary' box and select 'Element
content' in the left-hand
column. Set the target phase to 'CEMENTITE', the element to be varied to 'C', and the temperature
to '700', then click 'Go'.

The output gives the carbon content for zero phase fraction of
cementite in mole fraction and in weight percent.
iter: 2, time used: 0,05 s, GibbsEnergy: -40682,347 J
X(C): 0,0024577702, WP(C): 0,052897996, T: 700 C (973,16 K) - OK -
Note: After the search for the phase boundary with element content variation, the composition of the system is changed to the found value! (check 'Global > Composition')
In the same way, the zero phase fraction boundary for niobium
carbide at 1000°C can be evaluated in terms of the niobium
content. Firstly, open 'Global > Composition' and reset the
carbon content to 0.1 wt.%. Calculate an equilibrium at 1000°C,
then search for the phase boundary for 'FCC_A1#01', this time setting
the element to be varied to 'Nb'.
iter: 14, time used: 0,05 s, GibbsEnergy: -62319,958 J
X(NB): 6,6538713e-005, WP(NB): 0,011109209, T: 1000 C (1273,16 K) - OK -
Tracing phase boundaries
Once a point on a phase boundary has been identified using the
process described above, the boundary can be traced as a function
of element content. In the following example, the effect of
the niobium content on the temperature of the FCC_A1#01 (NbC)
zero-phase boundary will be calculated.
Firstly, reset the composition to 0.1 wt.% C, 0.3 wt.% Nb. Calculate
an equilibrium at 1000°C, then search for the temperature of
the FCC_A1#01 zero-phase boundary. Having established this point
on the boundary, open the 'Step equilibrium' window using 'Calc > Stepped
calculation' and select 'Phase boundary' from the left-hand column.
In the 'Boundary conditions' box,
set the element to 'Nb', the target phase to 'FCC_A1#01' and the max.
T-step to '100'. (The use of this parameter will be discussed in
Tutorial 8.) Enter '0.01', '0.6' and '0.01' as the start, stop and step
interval values in the 'Range' box.

Create a new X-Y plot window (Tutorial 4)
and drag and drop 'T$c' into it. The plot should look like this:

Right-click in the plot window outside the plot area and choose
'Duplicate and lock series' from the window (see Tutorial
5). Double-click
on the name of the series to duplicate it. In the 'Options' window,
change the name of the original series ('*_T$c') to '0.1
wt.%C'.
Change the carbon content of the system to 0.05 wt.% C, calculate
an equilibrium at 1000°C and search for the phase boundary,
then make a stepped calculation using the same conditions as before.
The phase boundary for 0.05 wt.% C should follow the green curve
in the plot below, which also shows the same phase boundary for
0.01 wt.%C.

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