Plotting Ternary Phase Diagrams and Using Triangular Axes

Often in thermodynamics, it is useful to use a two dimensional plot to express equilibria in a three component system with fixed potentials. The ternplot API provides a straightforward way to calculate equilibria and generate ternary phase diagrams. Alternatively, if you already have an equilibrium calculation, you can directly import and use eqplot.

ternplot

Here we will use the ternplot API to plot an isothermal section of the Al-Cu-Y system from the thermodynamic database found at Jacob et al, Calphad 54 (2016) (1-15) (https://doi.org/10.1016/j.calphad.2016.04.013)

%matplotlib inline
from pycalphad import Database, ternplot
from pycalphad import variables as v

db_cr_fe_nb = Database('CrFeNb_Jacob2016.tdb')
comps = ['CR', 'FE', 'NB', 'VA']
phases = list(db_cr_fe_nb.phases.keys())
conds = {v.T: 1323, v.P:101325, v.X('CR'): (0,1,0.015), v.X('FE'): (0,1,0.015)}

%time ternplot(db_cr_fe_nb, comps, phases, conds, x=v.X('CR'), y=v.X('FE'))

CPU times: total: 38.9 s
Wall time: 39.2 s

<TriangularAxes: title={'center': 'Cr-Fe-Nb'}, xlabel='X(Cr)', ylabel='X(Fe)'>

Here is another example for plotting the isothermal section of the Al-Cu-Y system from the thermodynamic database found at the NIST CALPHAD assessments assessed by Zhang et al. Calphad 35 (2011). Labels for phases in the three-phase equilibria can be added for clarity.

%matplotlib inline
from pycalphad import Database, ternplot
from pycalphad import variables as v

db_al_cu_y = Database('Al-Cu-Y.tdb')
comps = ['AL', 'CU', 'Y', 'VA']
phases = list(db_al_cu_y.phases.keys())
conds = {v.T: 830, v.P:101325, v.X('AL'): (0,1,0.015), v.X('Y'): (0,1,0.015)}

%time ternplot(db_al_cu_y, comps, phases, conds, x=v.X('AL'), y=v.X('Y'), label_nodes=True)

CPU times: total: 40.7 s
Wall time: 40.9 s

<TriangularAxes: title={'center': 'Al-Cu-Y'}, xlabel='X(Al)', ylabel='X(Y)'>

Molar Ratios and Linear Combination Conditions

from pycalphad import Database, Workspace, variables as v

db_al_cu_y = Database('Al-Cu-Y.tdb')
comps = ['AL', 'CU', 'Y', 'VA']
phases = list(db_al_cu_y.phases.keys())
conds = {v.T: 830, v.P:101325,
         v.X('AL')/v.X('CU'): 5, # molar ratio condition
         0.1 * v.X('Y') + v.X('AL'): 0.6} # linear combination of mole fractions condition
wks = Workspace(db_al_cu_y, comps, phases, conds)
print(wks.get('X(AL)', 'X(CU)', 'X(Y)'))

[array(0.56818182), array(0.11363636), array(0.31818182)]