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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 notebook shows an example of EOS fitting for static compression, focusing on applying a range of different pressure scales.
The result and data have been published in Nisr et al. (2017, JGR).

1. Global setup



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import numpy as np
from uncertainties import unumpy as unp
import pandas as pd
import pytheos as eos

2. Setup pressure scale and starting values

Setup dictionaries for pressure standard (au_eos) and equation to use (fit_model). This allows for eos fits with a wide range of different pressure scales.



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au_eos = {'Fei2007': eos.gold.Fei2007bm3(), 'Dorogokupets2007': eos.gold.Dorogokupets2007(),
          'Yokoo2009': eos.gold.Yokoo2009()}
fit_model = {'Fei2007': eos.BM3Model(), 'Dorogokupets2007': eos.VinetModel(),
             'Yokoo2009': eos.BM3Model()}

SiC has two polymorphs, 3C and 6H, at the studied pressure range. This notebook can conduct fitting for 3C. However, changing the sample variable between 3C and 6H allows for reading different data files and apply different initial conditions for different phases.



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sample = '3C' #'6H' #

Uncomment the following line to get some help.



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#help(eos.gold.Yokoo2009)

We use the values from Zhuravlev (2013) for initial guess.



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v0 = {'3C': 82.804, '6H': 124.27}
k0 = {'3C': 218., '6H': 218.}
k0p = {'3C': 3.75, '6H': 3.75}

3. Setup data

Read data file. Data points are stored in csv files.



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data = pd.read_csv('./data/'+sample+'-300EOS-final.csv')

Sort the data in a reverse order based on the unit-cell volume of pressure standard.



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n = data['V(Au)'].__len__()
ind = data['V(Au)'].argsort()[::-1][:n]

Make error propagation possible.



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v_std = unp.uarray(data['V(Au)'][ind], data['sV(Au)'][ind])
v = unp.uarray(data['V('+sample+')'][ind], data['sV('+sample+')'][ind])

4. Fitting

The cell below runs an iteration to generate fitting for three different pressure scales. We fix v0 in this fitting example.



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for key, value in au_eos.items():
    # set pressure standard to use
    p = au_eos[key].cal_pst(v_std)
    # set equation to fit
    model = fit_model[key]
    # assign initial values for the parameters
    params = model.make_params(v0=v0[sample], k0=k0[sample], k0p=k0p[sample])
    # fix v0
    params['v0'].vary = False
    # conduct fitting
    fitresult = model.fit(unp.nominal_values(p), params, v=unp.nominal_values(v))
    # generate text ouput for fitting result
    print('***'+key)
    print(fitresult.fit_report())
    # generate plots
    eos.plot.static_fit_result(fitresult, title=key)









    



***Fei2007
[[Model]]
    Model(bm3_p)
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 12
    # data points      = 44
    # variables        = 2
    chi-square         = 9.12605021
    reduced chi-square = 0.21728691
    Akaike info crit   = -65.2144926
    Bayesian info crit = -61.6461133
[[Variables]]
    v0:   82.804 (fixed)
    k0:   241.179946 +/- 2.00870449 (0.83%) (init = 218)
    k0p:  2.84051092 +/- 0.09815623 (3.46%) (init = 3.75)
[[Correlations]] (unreported correlations are < 0.100)
    C(k0, k0p) = -0.933

***Dorogokupets2007
[[Model]]
    Model(vinet_p)
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 13
    # data points      = 44
    # variables        = 2
    chi-square         = 9.32151503
    reduced chi-square = 0.22194083
    Akaike info crit   = -64.2820363
    Bayesian info crit = -60.7136571
[[Variables]]
    v0:   82.804 (fixed)
    k0:   243.007065 +/- 2.23301264 (0.92%) (init = 218)
    k0p:  2.67891704 +/- 0.13083708 (4.88%) (init = 3.75)
[[Correlations]] (unreported correlations are < 0.100)
    C(k0, k0p) = -0.944

***Yokoo2009
[[Model]]
    Model(bm3_p)
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 12
    # data points      = 44
    # variables        = 2
    chi-square         = 9.21241759
    reduced chi-square = 0.21934328
    Akaike info crit   = -64.8000421
    Bayesian info crit = -61.2316629
[[Variables]]
    v0:   82.804 (fixed)
    k0:   241.985853 +/- 2.01818712 (0.83%) (init = 218)
    k0p:  2.85352194 +/- 0.09839243 (3.45%) (init = 3.75)
[[Correlations]] (unreported correlations are < 0.100)
    C(k0, k0p) = -0.933



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