Nucleation Rate
This example will compute the nucleation rate with various precipitate parameters.
Note: the computeSteadyStateNucleation function does not account for the number of nucleation sites
Comparing multiple phases in Al-Mg-Si system
1 import numpy as np
2 import matplotlib.pyplot as plt
3
4 from kawin.thermo import MulticomponentThermodynamics
5 from kawin.precipitation.NucleationRate import computeSteadyStateNucleation
6 from kawin.precipitation.PrecipitationParameters import MatrixParameters, PrecipitateParameters
7
8 phases = ['FCC_A1', 'MGSI_B_P', 'MG5SI6_B_DP', 'B_PRIME_L', 'U1_PHASE', 'U2_PHASE']
9 therm = MulticomponentThermodynamics('AlMgSi.tdb', ['AL', 'MG', 'SI'], phases)
10
11 matrix = MatrixParameters(['MG', 'SI'])
12 matrix.volume.setVolume(1e-5, 'VM', 4)
13
14 gamma = {
15 'MGSI_B_P': 0.18,
16 'MG5SI6_B_DP': 0.084,
17 'B_PRIME_L': 0.18,
18 'U1_PHASE': 0.18,
19 'U2_PHASE': 0.18
20 }
21
22 precipitates = []
23 for p in phases[1:]:
24 params = PrecipitateParameters(p)
25 params.gamma = gamma[p]
26 params.volume.setVolume(1e-5, 'VM', 4)
27 precipitates.append(params)
28
29 fig, ax = plt.subplots(figsize=(5,5))
30 T = np.linspace(50, 400, 100) + 273.15
31 for prec in precipitates:
32 nucRate = computeSteadyStateNucleation(therm, [0.0072, 0.0057], T, prec, matrix)
33 ax.plot(nucRate.nucleation_rate, T-273.15, label=prec.name)
34 ax.set_ylim([100, 400])
35 ax.set_xlim([1e-24, 1e-3])
36 ax.set_xscale('log')
37 ax.set_xlabel(r'Nucleation Rate ($s^{-1}$)')
38 ax.set_ylabel(r'Temperature ($\degree C $)')
39 ax.legend()
40 plt.show()
Comparing nucleation on different nucleation sites for Al-Zr
41 from kawin.thermo import BinaryThermodynamics
42
43 therm = BinaryThermodynamics('AlScZr.tdb', elements=['AL', 'ZR'], phases=['FCC_A1', 'AL3ZR'])
44 therm.setGuessComposition(0.24)
45
46 D0 = 0.0768 #Diffusivity pre-factor (m2/s)
47 Q = 242000 #Activation energy (J/mol)
48 diff = lambda T: D0 * np.exp(-Q / (8.314 * T))
49 therm.setDiffusivity(diff, 'FCC_A1')
50
51 a = 0.405e-9 # nm
52 Va = a**3 # nm^3
53 atomsPerCell = 4
54
55 matrix = MatrixParameters(solutes=['ZR'])
56 matrix.volume.setVolume(Va, 'VA', atomsPerCell)
57 matrix.GBenergy = 0.3
58 matrix.nucleationSites.setDislocationDensity(1e15)
59 matrix.nucleationSites.setGrainSize(100)
60
61 precipitate = PrecipitateParameters('AL3ZR')
62 precipitate.gamma = 0.25 # J/m2
63 precipitate.volume.setVolume(Va, 'VA', atomsPerCell)
64 precipitate.nucleation.gbEnergy = matrix.GBenergy
65
66 nucleationSites = ['dislocations', 'grain boundaries', 'grain edges', 'grain corners']
67 N0 = {
68 'dislocations': matrix.nucleationSites.dislocationN0,
69 'grain boundaries': matrix.nucleationSites.GBareaN0,
70 'grain edges': matrix.nucleationSites.GBedgeN0,
71 'grain corners': matrix.nucleationSites.GBcornerN0
72 }
73
74 fig, ax = plt.subplots(figsize=(5,5))
75 T = np.linspace(300, 1200, 100)
76 for site in nucleationSites:
77 precipitate.nucleation.setNucleationType(site)
78 nucRate = computeSteadyStateNucleation(therm, 4e-3, T, precipitate, matrix)
79 ax.plot(N0[site]*nucRate.nucleation_rate, T, label=site.capitalize())
80 ax.legend()
81 ax.set_xlim([1e-20, 1e20])
82 ax.set_xscale('log')
83 ax.set_ylim([300, 1300])
84 ax.set_xlabel('Nucleation Rate (#/s)')
85 ax.set_ylabel('Temperature (K)')
86 plt.show()
