Chemical potentials calculated by pycalphad are discontinuous

[yangshenglan]

By means of pycalphad, the curved surface of the chemical potentials calculated are discontinuous. As is shown in the figure1, this is the scatter diagram of the chemical potentials of component Ni of the Al-Ni-Cr ternary system at 1273K. In the figure1, some of the chemical potentials change dramatically in different compositions.

Selecting a composition corresponding to the dramatically variational chemical potential from figure1, calculate the chemical potentials of different compositions around that composition. As is shown figure2, this is the diagram of the chemical potentials of component Ni of compositions of the area.

How to solve the problem that the chemical potentials are discontinuous calculated by pycalphad?

Chemical potentials calculated by pycalphad are dis.docx

[richardotis]

Can you verify that this problem exists in the latest release of pycalphad, 0.3.5?

[zhongjingjogy]

Hi Otis,

It seems that we are working with the 0.3.5., and I installed this version for her the other day.

>>> pycalphad._version.get_versions()
{'version': '0.3.5-py2.7.egg', 'full': ''}

Best wishes!

[richardotis]

Can you provide the TDB and Python file used to perform this calculation so I can try to reproduce the bug?

As a workaround, you can try passing calc_opts={'pdens': 1000} to equilibrium()

[yangshenglan]

TDB

$ Database file written 2016- 5-19
$ From database: TTNI5                   
 ELEMENT /-   ELECTRON_GAS              0.0000E+00  0.0000E+00  0.0000E+00!
 ELEMENT VA   VACUUM                    0.0000E+00  0.0000E+00  0.0000E+00!
 ELEMENT AL   FCC_A1                    2.6982E+01  4.5400E+03  2.8300E+01!
 ELEMENT CR   BCC_A2                    5.1996E+01  4.0500E+03  2.3543E+01!
 ELEMENT NI   FCC_A1                    5.8690E+01  4.7870E+03  2.9796E+01!


 FUNCTION GHSERAL   298.14 -7976.15+137.093038*T-24.3671976*T*LN(T)
     -.001884662*T**2-8.77664E-07*T**3+74092*T**(-1); 700 Y
      -11276.24+223.048446*T-38.5844296*T*LN(T)+.018531982*T**2
     -5.764227E-06*T**3+74092*T**(-1); 933.47 Y
      -11278.378+188.684153*T-31.748192*T*LN(T)-1.231E+28*T**(-9); 2900 N !
 FUNCTION ZERO      298.15 +0.0; 6000 N !
 FUNCTION GFCCCR    298.15 +7284+.163*T+GHSERCR#; 6000 N !
 FUNCTION GHSERNI   298.14 -5179.159+117.854*T-22.096*T*LN(T)-.0048407*T**2; 
     1728 Y
      -27840.655+279.135*T-43.1*T*LN(T)+1.12754E+31*T**(-9); 3000 N !
 FUNCTION GHSERCR   298.14 -8856.94+157.48*T-26.908*T*LN(T)+.00189435*T**2
     -1.47721E-06*T**3+139250*T**(-1); 2180 Y
      -34869.344+344.18*T-50*T*LN(T)-2.88526E+32*T**(-9); 6000 N !
 FUNCTION UN_ASS 298.15 +0; 300 N !

 TYPE_DEFINITION % SEQ *!
 DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
 DEFAULT_COMMAND DEF_SYS_ELEMENT VA /- !


 TYPE_DEFINITION & GES A_P_D FCC_A1 MAGNETIC  -3.0    2.80000E-01 !
 PHASE FCC_A1  %&  2 1   1 !
    CONSTITUENT FCC_A1  :AL,CR,NI% : VA% :  !

   PARAMETER G(FCC_A1,AL:VA;0)            298.15 +GHSERAL#; 6000 N REF0 !
   PARAMETER TC(FCC_A1,AL:VA;0)           298.15 +ZERO#; 6000 N REF0 !
   PARAMETER BMAGN(FCC_A1,AL:VA;0)        298.15 +ZERO#; 6000 N REF0 !
   PARAMETER G(FCC_A1,CR:VA;0)            298.15 +GFCCCR#; 6000 N REF0 !
   PARAMETER TC(FCC_A1,CR:VA;0)           298.15 -1109; 6000 N REF0 !
   PARAMETER BMAGN(FCC_A1,CR:VA;0)        298.15 -2.46; 6000 N REF0 !
   PARAMETER G(FCC_A1,NI:VA;0)            298.15 +GHSERNI#; 6000 N REF0 !
   PARAMETER TC(FCC_A1,NI:VA;0)           298.15 +633; 6000 N REF0 !
   PARAMETER BMAGN(FCC_A1,NI:VA;0)        298.15 +.52; 6000 N REF0 !
   PARAMETER G(FCC_A1,AL,CR:VA;0)         298.15 -45900+6*T; 6000 N REF0 !
   PARAMETER G(FCC_A1,AL,CR,NI:VA;0)      298.15 +30500-5*T; 6000 N REF0 !
   PARAMETER G(FCC_A1,AL,NI:VA;0)         298.15 -173950+19.35*T; 6000 N 
  REF0 !
   PARAMETER G(FCC_A1,AL,NI:VA;1)         298.15 +28500; 6000 N REF0 !
   PARAMETER G(FCC_A1,AL,NI:VA;2)         298.15 +47000; 6000 N REF0 !
   PARAMETER G(FCC_A1,CR,NI:VA;0)         298.15 +8030-12.8801*T; 6000 N 
  REF0 !
   PARAMETER G(FCC_A1,CR,NI:VA;1)         298.15 +33080-16.0362*T; 6000 N 
  REF0 !
   PARAMETER TC(FCC_A1,CR,NI:VA;0)        298.15 -3605; 6000 N REF0 !
   PARAMETER BMAGN(FCC_A1,CR,NI:VA;0)     298.15 -1.91; 6000 N REF0 !


 TYPE_DEFINITION ' GES A_P_D GAMMA_PRIME MAGNETIC  -3.0    2.80000E-01 !
 PHASE GAMMA_PRIME  %'  2 .75   .25 !
    CONSTITUENT GAMMA_PRIME  :AL,CR,NI% : AL%,CR,NI :  !

   PARAMETER G(GAMMA_PRIME,AL:AL;0)       298.15 +GHSERAL#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,CR:AL;0)       298.15 -8606+1.125*T+.75*GFCCCR#
  +.25*GHSERAL#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,NI:AL;0)       298.15 -39860+3.175*T+.75*GHSERNI#
  +.25*GHSERAL#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL:CR;0)       298.15 -8606+1.125*T+.75*GHSERAL#
  +.25*GFCCCR#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,CR:CR;0)       298.15 +GFCCCR#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,NI:CR;0)       298.15 -1915-.91*T+.75*GHSERNI#
  +.25*GFCCCR#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL:NI;0)       298.15 -35000+5*T+.75*GHSERAL#
  +.25*GHSERNI#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,CR:NI;0)       298.15 +10000-3.92*T+.75*GFCCCR#
  +.25*GHSERNI#; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,NI:NI;0)       298.15 +GHSERNI#; 6000 N REF0 !
   PARAMETER TC(GAMMA_PRIME,NI:NI;0)      298.15 +633; 6000 N REF0 !
   PARAMETER BMAGN(GAMMA_PRIME,NI:NI;0)   298.15 +.52; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL,NI:AL;0)    298.15 -59500+20*T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL,NI:AL;1)    298.15 +53350; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL:AL,NI;0)    298.15 +10000; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL:AL,CR;0)    298.15 -2869+.375*T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,CR:AL,NI;0)    298.15 +10000; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,CR:AL,CR;0)    298.15 -2869+.375*T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,NI:AL,NI;0)    298.15 +9100-1.5*T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,NI:AL,NI;1)    298.15 -5400; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,NI:AL,CR;0)    298.15 -6250+T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL,NI:CR;0)    298.15 -60000+20*T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL,NI:NI;0)    298.15 -50000; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,AL,CR:*;0)     298.15 -25819+3.375*T; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,*:CR,NI;0)     298.15 +3000; 6000 N REF0 !
   PARAMETER G(GAMMA_PRIME,CR,NI:*;0)     298.15 -1500; 6000 N REF0 !

 LIST_OF_REFERENCES
 NUMBER  SOURCE
  ! 

python file 1

import matplotlib.pyplot as plt
from pycalphad import equilibrium
from pycalphad import Database, Model
import pycalphad.variables as v
import numpy as np

db = Database('NiAlCr.tdb')
my_phases = ['FCC_A1', 'GAMMA_PRIME']

xal = np.linspace(0.12, 0.13, 50)
xcr = np.linspace(0.15, 0.1846, 100)
m = []
a = []
b = []
c = []
d = []
e = []
for i in range(50):
    for j in range(100):
        eq = equilibrium(db, ['AL', 'NI', 'CR', 'VA'], my_phases, {v.X('AL'): xal[i], v.X('CR'): xcr[j], v.T: 1273, v.P: 101325}, calc_opts={'pdens': 1000})
        m.append(eq)
        a.append(eq.get("X"))
        b.append(eq.get("Y"))
        c.append(eq.get("MU"))
        d.append(eq.get("GM"))
        e.append(eq.get("NP"))

f = open('equilibrium_data1.txt','w')
print >>f,m
print >>f,a
print >>f,b
print >>f,c
print >>f,d
print >>f,e
f.close()

python file 2

import matplotlib.pyplot as plt
from pycalphad import equilibrium
from pycalphad import Database, Model
import pycalphad.variables as v
import numpy as np

db = Database('NiAlCr.tdb')
my_phases = ['FCC_A1', 'GAMMA_PRIME']

xal = np.linspace(0.1211, 0.1233, 50)
xcr = np.linspace(0.15, 0.1788, 100)
m = []
a = []
b = []
c = []
d = []
e = []
for i in range(50):
    for j in range(100):
        eq = equilibrium(db, ['AL', 'NI', 'CR', 'VA'], my_phases, {v.X('AL'): xal[i], v.X('CR'): xcr[j], v.T: 1273, v.P: 101325}, calc_opts={'pdens': 1000})
        m.append(eq)
        a.append(eq.get("X"))
        b.append(eq.get("Y"))
        c.append(eq.get("MU"))
        d.append(eq.get("GM"))
        e.append(eq.get("NP"))
#
f = open('equilibrium_data2.txt','w')
print >>f,m
print >>f,a
print >>f,b
print >>f,c
print >>f,d
print >>f,e
f.close()

[richardotis]

Thanks. I will take a look at this problem this weekend.

[richardotis]

I can't reproduce this on Linux with Python 2.7 or 3.5, using either pycalphad 0.3.5 or the pycalphad develop branch. I cut your example down a bit to reduce the computation time. (The next version of pycalphad will be 100x faster for mapping.)

import matplotlib.pyplot as plt
from pycalphad import equilibrium
from pycalphad import Database, Model
import pycalphad.variables as v
import numpy as np

db = Database('NiAlCr.tdb')
my_phases = ['FCC_A1', 'GAMMA_PRIME']

xcr = np.linspace(0.17, 0.18, 10)

eq = equilibrium(db, ['AL', 'NI', 'CR', 'VA'], my_phases,
                 {v.X('AL'): .12, v.X('CR'): xcr, v.T: 1273, v.P: 101325})
print(eq)
fig = plt.figure(figsize=(12,12))
ax = fig.gca()
X = eq.X_CR.values
ax.set_xlabel('X(CR)')
Y = eq.MU.sel(component='AL')
ax.scatter(X, Y)
plt.show()

[yangshenglan]

The same to your example, I get the result that chemial potentials of component Al are continuous. However, chemical potentials of component Ni are discontinuous. Could you give the example about calculating chemical potentials of component Ni al the same composition.
xal = 0.12 xcr = np.linspace(0.17, 0.18, 10)

[zhongjingjogy]

Hi,

I'm not sure whether we have make mistakes about the pycalphad version. So I ran some new tests anyway, as I have reconfirmed that a 0.3.5 version had been installed.
Codes are presented as following, which is the similiar to the previous one, but I varied the composition of the Al from 0.15 to 0.1846.

from pycalphad import equilibrium
from pycalphad import Database, Model
import pycalphad.variables as v
import numpy as np

db = Database('NiAlCr.tdb')
my_phases = ['FCC_A1', 'GAMMA_PRIME']

x = np.empty((50, 100))
y = np.empty((50, 100))
mu_al, mu_cr, mu_ni = np.empty((50, 100)), np.empty((50, 100)), np.empty((50, 100))
gm = np.empty((50, 100))

xal = np.linspace(0.12, 0.13, 50)
xcr = np.linspace(0.15, 0.1846, 100)

for i in range(50):
    xcr = np.linspace(0.15, 0.1846, 100)
    eq = equilibrium(db, ['AL', 'NI', 'CR', 'VA'], my_phases,
                 {v.X('AL'): xal[i], v.X('CR'): xcr, v.T: 1273, v.P: 101325})
    print eq.X_AL
    print eq.MU.sel(component='AL')
    print eq.MU.sel(component='CR')
    print eq.MU.sel(component='NI')

ps: there are too much brakets in the output result, and I just manual came across the result manually rather than walking through the brakets with some iterations.

I came across the outputs the other day in order to figure out whether there are anything tricky. And I did observe some discontinous when the composition of Alumimum is 0.1241. Here follows the figure.

Maybe the minimizer has been performed perfectly enough, and we are just stressing too much on the precision, which is not necessary.

What's more, there might a misibility gap in the Gibbs energy of FCC_A1 and I have no idea whether it bothers the calculation of the equilibirum or not.

Thanks!

[richardotis]

Thanks again for the details. I'll try to debug exactly this case and get back to you on the next 7-10 days.

[richardotis]

I can reproduce this error now. It appears to be related to the global minimization point density. If I increase pdens from default 100 to 200, the discontinuity goes away.

[richardotis]

It appears to be a convergence failure in that composition range. I will look into this further.