In [1]:

    

%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


    

In [3]:

    

%config InlineBackend.figure_format = 'retina'


    

In [4]:

    

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


    

In [5]:

    

eta = np.linspace(0., 0.34, 18)
print(eta)


    

    




[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]

In [6]:

    

heinz_au = eos.gold.Heinz1984()


    

In [7]:

    

help(heinz_au)


    

    




Help on Heinz1984 in module pytheos.scales.gold object:

class Heinz1984(pytheos.scales.objs.MGEOS)
 |  Heinz and Jeanloz. 1984. JAP 55, 885+
 |  
 |  Method resolution order:
 |      Heinz1984
 |      pytheos.scales.objs.MGEOS
 |      builtins.object
 |  
 |  Methods defined here:
 |  
 |  __init__(self, v0=67.84742110765599)
 |      :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 [8]:

    

heinz_au.print_equations()


    

    




P_static:  bm3
P_thermal:  constq
P_anharmonic:  None
P_electronic:  None

In [9]:

    

heinz_au.print_equations()


    

    




P_static:  bm3
P_thermal:  constq
P_anharmonic:  None
P_electronic:  None

In [10]:

    

heinz_au.print_parameters()


    

    




Static:  OrderedDict([('v0', 67.84742110765599+/-0.001), ('k0', 166.65+/-5.0), ('k0p', 5.4833+/-0.43)])
Thermal:  OrderedDict([('v0', 67.84742110765599+/-0.001), ('gamma0', 2.95+/-0.43), ('q', 1.7+/-0.7), ('theta0', 170.0+/-0)])
Anharmonic:  None
Electronic:  None

In [11]:

    

v0 = 67.84742110765599


    

In [12]:

    

heinz_au.three_r


    

    
Out[12]:





24.943379399999998

In [13]:

    

v = v0 * (1.-eta) 
temp = 3000.


    

In [14]:

    

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


    

In [15]:

    

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
 0.000  19.42+/-2.83
 0.020  22.70+/-2.80
 0.040  26.47+/-2.81
 0.060  30.80+/-2.85
 0.080  35.76+/-2.93
 0.100  41.45+/-3.06
 0.120  47.97+/-3.26
 0.140  55.44+/-3.53
 0.160  64.00+/-3.90
 0.180  73.82+/-4.41
 0.200  85.09+/-5.07
 0.220  98.05+/-5.93
 0.240  112.96+/-7.03
 0.260  130.14+/-8.43
 0.280  149.98+/-10.17
 0.300  172.94+/-12.32
 0.320  199.56+/-14.98
 0.340  230.51+/-18.25

In [16]:

    

v = heinz_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]

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