# coding: utf-8

import matplotlib.pyplot as plt

from pycalphad import Database, binplot, calculate

import pycalphad.variables as v

from pycalphad.plot.utils import phase_legend

import numpy as np

from scipy.optimize import curve_fit, newton

import os.path

def func(x, a, b, c, d, e, f, g, h, i, j, k):

return a*x**10 + b*x**9 + c*x**8 + d*x**7 + e*x**6 + f*x**5 + g*x**4 + h*x**3 + i*x**2 + j*x + k

def fprime(x, a, b, c, d, e, f, g, h, i, j):

return 10*a*x**9 + 9*b*x**8 + 8*c*x**7 + 7*d*x**6 + 6*e*x**5 + 5*f*x**4 + 4*g*x**3 + 3*h*x**2 + 2*i*x + j

# Cu-Ni (S. an Mey 1999)

db_cuni = Database('CuNi_RWTH.tdb')

my_phases_cuni = ['FCC_A1', 'LIQUID', 'BCC_A2', 'HCP_A3']

# Calculate Isobaric Binary Phase Diagram

if not os.path.isfile('CuNi.png'):

fig = plt.figure(figsize=(9,6))

binplot(db_cuni, ['CU', 'NI', 'VA'] , my_phases_cuni, {v.X('NI'):(0,1,0.01), v.T: (1300, 1800, 5), v.P:101325}, ax=fig.gca())

plt.savefig('CuNi.png', dpi=400, bbox_inches='tight')

plt.close()

# It is very common in CALPHAD modeling to directly examine the Gibbs energy surface of all the constituent phases in a system.

# Below we show how the Gibbs energy of all phases may be calculated as a function of composition at a given temperature (1550 K).

# Calculate Energy Surfaces of Binary Systems

if not os.path.isfile('CuNi_energy.png'):

legend_handles, colorlist = phase_legend(my_phases_cuni)

fig = plt.figure(figsize=(9,6))

ax = fig.gca()

xref = np.linspace(-0.1,1.1,150)

for name in my_phases_cuni:

result = calculate(db_cuni, ['CU', 'NI', 'VA'], name, T=1550, output='GM')

x = np.ravel(result.X.sel(component='NI'))

y = np.ravel(7.124e-4*result.GM)

ax.scatter(x, y, marker='.', s=5, color=colorlist[name.upper()])

popt, pcov = curve_fit(func, x, y)

print name, popt

ax.plot(xref, func(xref,popt[0],popt[1],popt[2],popt[3],popt[4],popt[5],popt[6],popt[7],popt[8],popt[9],popt[10]), '-', color=colorlist[name.upper()])

roo = newton(fprime, 0.5, args=(popt[0],popt[1],popt[2],popt[3],popt[4],popt[5],popt[6],popt[7],popt[8],popt[9]),maxiter=1000)

print name, "Equilibrium x_Ni near ", roo

ax.set_xlim((-0.1, 1.1))

ax.legend(handles=legend_handles, loc='center left', bbox_to_anchor=(1, 0.6))

plt.savefig('CuNi_energy.png',dpi=400,bbox_inches='tight')

plt.close()