notebook.community



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%cat 0Source_Citation.txt









    



Source and citation

- This notebook is a part of the `pytheos` package.
- Website: http://github.com/SHDShim/pytheos.
- How to cite: S.-H. Shim (2017) Pytheos - a python tool set for equations of state. DOI: 10.5281/zenodo.802392



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%matplotlib inline
# %matplotlib notebook # for interactive

For high dpi displays.



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%config InlineBackend.figure_format = 'retina'

0. General note

This example compares pressure calculated from pytheos and original publication for the gold scale by Yokoo 2009.

1. Global setup



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import matplotlib.pyplot as plt
import numpy as np
from uncertainties import unumpy as unp
import pytheos as eos

3. Compare



In [5]:

    
eta = np.linspace(1., 0.60, 21)
print(eta)









    



[1.   0.98 0.96 0.94 0.92 0.9  0.88 0.86 0.84 0.82 0.8  0.78 0.76 0.74
 0.72 0.7  0.68 0.66 0.64 0.62 0.6 ]



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yokoo_au = eos.gold.Yokoo2009()



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yokoo_au.print_equations()









    



P_static:  bm3
P_thermal:  tange
P_anharmonic:  None
P_electronic:  tsuchiya



In [8]:

    
yokoo_au.print_equations()









    



P_static:  bm3
P_thermal:  tange
P_anharmonic:  None
P_electronic:  tsuchiya



In [9]:

    
yokoo_au.print_parameters()









    



Static:  OrderedDict([('v0', 67.84742110765599+/-0.001), ('k0', 167.5+/-0), ('k0p', 5.79+/-0.1)])
Thermal:  OrderedDict([('v0', 67.84742110765599+/-0.001), ('gamma0', 2.96+/-0), ('a', 0.45+/-0.09), ('b', 4.2+/-0.6), ('theta0', 170.0+/-0)])
Anharmonic:  None
Electronic:  OrderedDict([('v0', 67.84742110765599+/-0.001), ('a', -0.00021606+/-0), ('b', -4.3795e-06+/-0), ('c', 1.4526e-08+/-0), ('d', 7.8072e-14+/-0)])



In [10]:

    
v0 = 67.84742110765599



In [11]:

    
yokoo_au.three_r









    Out[11]:





24.943379399999998



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v = v0 * (eta) 
temp = 3000.



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p = yokoo_au.cal_p(v, temp * np.ones_like(v))



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print('for T = ', temp)
for eta_i, p_i in zip(eta, p):
    print("{0: .3f} {1: .2f}".format(eta_i, p_i))









    



for T =  3000.0
 1.000  19.60+/-0.00
 0.980  22.86+/-0.18
 0.960  26.66+/-0.34
 0.940  31.09+/-0.50
 0.920  36.24+/-0.66
 0.900  42.18+/-0.81
 0.880  49.06+/-0.96
 0.860  56.98+/-1.11
 0.840  66.12+/-1.26
 0.820  76.65+/-1.42
 0.800  88.79+/-1.61
 0.780  102.80+/-1.81
 0.760  118.96+/-2.06
 0.740  137.65+/-2.36
 0.720  159.28+/-2.72
 0.700  184.36+/-3.18
 0.680  213.52+/-3.74
 0.660  247.49+/-4.44
 0.640  287.17+/-5.30
 0.620  333.68+/-6.38
 0.600  388.35+/-7.70



In [15]:

    
v = yokoo_au.cal_v(p, temp * np.ones_like(p), min_strain=0.6)
print(1.-(v/v0))









    



[0.   0.02 0.04 0.06 0.08 0.1  0.12 0.14 0.16 0.18 0.2  0.22 0.24 0.26
 0.28 0.3  0.32 0.34 0.36 0.38 0.4 ]

I cannot quite reproduce the table values. The mismatch is about 3 GPa at 3000 K and 380 GPa.
This means his parameters may have been rounded.
Therefore, I readjusted the eos parameters from Yokoo to match their table values better. Users have a choice if they use the table values or the parameter values. If reproduce_table sets to True, the difference reduces to 0.1 GPa.



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yokoo_au = eos.gold.Yokoo2009(reproduce_table=True)



In [17]:

    
p = yokoo_au.cal_p(v, temp * np.ones_like(v))



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