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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

In [2]:

    

%matplotlib inline
# %matplotlib notebook # for interactive


    

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%config InlineBackend.figure_format = 'retina'


    

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


    

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v0 = 3.9231**3
v = np.linspace(v0, v0 * 0.8, 20)


    

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p_th = eos.dorogokupets2007_pth(v, 2000., v0, 2.82, 1.83, 8.11, 220., 1, 4)


    

In [7]:

    

help(eos.zharkov_panh)


    

    




Help on function zharkov_panh in module pytheos.eqn_anharmonic:

zharkov_panh(v, temp, v0, a0, m, n, z, t_ref=300.0, three_r=24.943379399999998)
    calculate pressure from anharmonicity for Zharkov equation
    the equation is from Dorogokupets 2015
    
    :param v: unit-cell volume in A^3
    :param temp: temperature in K
    :param v0: unit-cell volume in A^3 at 1 bar
    :param a0: parameter in K-1 for the Zharkov equation
    :param m: parameter for the Zharkov equation
    :param n: number of elements in a chemical formula
    :param z: number of formula unit in a unit cell
    :param three_r: 3 times gas constant
    :return: anharmonic contribution for pressure in GPa

In [8]:

    

p_anh = eos.zharkov_panh(v, 2000., v0, -166.9e-6, 4.32, 1, 4)


    

In [9]:

    

help(eos.zharkov_pel)


    

    




Help on function zharkov_pel in module pytheos.eqn_electronic:

zharkov_pel(v, temp, v0, e0, g, n, z, t_ref=300.0, three_r=24.943379399999998)
    calculate electronic contributions in pressure for the Zharkov equation
    the equation can be found in Sokolova and Dorogokupets 2013
    
    :param v: unit-cell volume in A^3
    :param temp: temperature in K
    :param v0: unit-cell volume in A^3 at 1 bar
    :param e0: parameter in K-1 for the Zharkov equation
    :param g: parameter for the Zharkov equation
    :param n: number of atoms in a formula unit
    :param z: number of formula unit in a unit cell
    :param t_ref: reference temperature, 300 K
    :param three_r: 3 times gas constant
    :return: electronic contribution in GPa

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p_el = eos.zharkov_pel(v, 2000., v0, 260.e-6, 2.4, 1, 4)


    

In [11]:

    

plt.plot(v, p_th, label='$P_{th}$')
plt.plot(v, p_el, label='$P_{el}$')
plt.plot(v, p_anh, label='$P_{anh}$')
plt.legend();


    

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dorogokupets2007_pt = eos.platinum.Dorogokupets2007()


    

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help(dorogokupets2007_pt)


    

    




Help on Dorogokupets2007 in module pytheos.scales.platinum object:

class Dorogokupets2007(pytheos.scales.objs.MGEOS)
 |  Dorogokupets and Dewaele. 2007. HPR 27, 431+
 |  
 |  Method resolution order:
 |      Dorogokupets2007
 |      pytheos.scales.objs.MGEOS
 |      builtins.object
 |  
 |  Methods defined here:
 |  
 |  __init__(self, v0=60.37930856339099)
 |      :param params_st: elastic parameters for static EOS in an OrderedDict
 |          [v0 in A^3, k0 in GPa, k0p]
 |      :param params_th: thermal parameters for thermal EOS in an OrderedDict.
 |          The component can differ depending on the equation used.
 |      :param params_anh: anharmonic parameters for anharmonic correction in
 |          an OrderedDict.  The component can differ depending on the
 |          equation used.
 |      :param params_el: electronic parameters for electronic correction in
 |          an OrderedDict. The component can differ depending on the
 |          equation used.
 |      :param eqn_st: equation type for the static EOS. 'bm3', 'vinet', or
 |          'kunc'
 |      :param eqn_th: equation type for the thermal EOS. 'constq', 'tange',
 |          'speziale', 'dorogokupets2007', 'dorogokupets2015', 'alphakt'
 |      :param eqn_anh: equation type for anharmonic correction. 'zharkov',
 |      :param eqn_el: equation type for electonic correction. 'zharkov',
 |          'tsuchiya'
 |      :param t_ref: reference temperature, 300 K
 |      :param three_r: 3 times gas constant.
 |          Jamieson modified this value to compensate for mismatches
 |      :param reference: reference for the EOS
 |  
 |  ----------------------------------------------------------------------
 |  Methods inherited from pytheos.scales.objs.MGEOS:
 |  
 |  cal_p(self, v, temp)
 |      calculate total pressure at given volume and temperature
 |      
 |      :param v: unit-cell volume in A^3
 |      :param temp: temperature in K
 |      :return: pressure in GPa
 |      :note: 2017/05/10 temp must be numpy array.  If not, such as list,
 |          create an error.
 |  
 |  cal_panh(self, v, temp)
 |      calculate pressure from anharmonic contributions
 |      
 |      :param v: unit-cell volume in A^3
 |      :param temp: temperature in K
 |      :return: pressure in GPa
 |  
 |  cal_pel(self, v, temp)
 |      calculate pressure from electronic contributions
 |      
 |      :param v: unit-cell volume in A^3
 |      :param temp: temperature in K
 |      :return: pressure in GPa
 |  
 |  cal_pst(self, v)
 |      calculate static pressure at 300 K.
 |      
 |      :param v: unit-cell volume in A^3
 |      :return: static pressure at t_ref (=300 K) in GPa
 |  
 |  cal_pth(self, v, temp)
 |      calculate thermal pressure
 |      
 |      :param v: unit-cell volume in A^3
 |      :param temp: temperature in K
 |      :return: thermal pressure in GPa
 |  
 |  cal_v(self, p, temp, min_strain=0.2, max_strain=1.0)
 |      calculate unit-cell volume at given pressure and temperature
 |      
 |      :param p: pressure in GPa
 |      :param temp: temperature in K
 |      :param min_strain: minimum strain searched for volume root
 |      :param max_strain: maximum strain searched for volume root
 |      :return: unit-cell volume in A^3
 |      :note: 2017/05/10 I found wrap function is not compatible with
 |          OrderedDict. So I convert unp array to np array.
 |  
 |  print_equations(self)
 |      show equations used for the EOS
 |  
 |  print_parameters(self)
 |      show thermoelastic parameters for the EOS
 |  
 |  print_reference(self)
 |      show reference for the EOS
 |  
 |  ----------------------------------------------------------------------
 |  Data descriptors inherited from pytheos.scales.objs.MGEOS:
 |  
 |  __dict__
 |      dictionary for instance variables (if defined)
 |  
 |  __weakref__
 |      list of weak references to the object (if defined)

In [14]:

    

p = dorogokupets2007_pt.cal_p(v, 2000.)


    

In [15]:

    

plt.plot(unp.nominal_values(p), p_th, label='$P_{th}$')
plt.plot(unp.nominal_values(p), p_el, label='$P_{el}$')
plt.plot(unp.nominal_values(p), p_anh, label='$P_{anh}$')
plt.legend();


    

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