[cig-commits] [commit] add_thermodynamic_potentials: Add einstein thermal model (618ce37)

[cig_noreply at geodynamics.org]

Repository : https://github.com/geodynamics/burnman

On branch  : add_thermodynamic_potentials
Link       : https://github.com/geodynamics/burnman/compare/2e5646d93cedbbf8eae54cc37cffc14e0aa85180...d5ddad03ff9f30f5a4efaddb4e3ec585ea1a7c51

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commit 618ce379545e169ec6f1038848cba24954f4d112
Author: ian-r-rose <ian.r.rose at gmail.com>
Date:   Wed Aug 27 14:06:41 2014 -0700

    Add einstein thermal model


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618ce379545e169ec6f1038848cba24954f4d112
 burnman/einstein.py | 57 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)

diff --git a/burnman/einstein.py b/burnman/einstein.py
new file mode 100644
index 0000000..a96b29d
--- /dev/null
+++ b/burnman/einstein.py
@@ -0,0 +1,57 @@
+# BurnMan - a lower mantle toolkit
+# Copyright (C) 2012, 2013, 2014, Heister, T., Unterborn, C., Rose, I. and Cottaar, S.
+# Released under GPL v2 or later.
+
+import numpy as np
+
+"""
+Functions for the Einstein model of a solid.
+"""
+
+R = 8.314462175
+
+def thermal_energy(T, einstein_T, n):
+    """
+    calculate the thermal energy of a substance.  Takes the temperature,
+    the Einstein temperature, and n, the number of atoms per molecule.
+    Returns thermal energy in J/mol
+    """
+    if T == 0:
+        return 3.*n*R*einstein_T*0.5 # zero point energy
+    x = einstein_T/T
+    E_th = 3.*n*R*einstein_T*( 0.5 + 1. / (np.exp( x ) - 1.0) ) # include the zero point energy
+    return E_th
+
+def heat_capacity_v(T,einstein_T,n):
+    """
+    Heat capacity at constant volume.  In J/K/mol
+    """
+    if T ==0:
+        return 0
+    x = einstein_T/T
+    C_v = 3.0*n*R* ( x * x * np.exp( x ) / np.power( np.exp( x ) - 1.0, 2.0 ) ) 
+    return C_v
+
+
+
+
+if __name__ == "__main__":
+
+    import matplotlib.pyplot as plt
+
+    temperatures = np.linspace(0,5000, 200)
+    vibrational_energy = np.empty_like(temperatures)
+    heat_capacity = np.empty_like(temperatures)
+    Einstein_T = 1000.
+    for i in range(len(temperatures)):
+      vibrational_energy[i] = thermal_energy(temperatures[i], Einstein_T, 1.0)
+      heat_capacity[i] = heat_capacity_v(temperatures[i], Einstein_T, 1.0)
+
+    plt.subplot(121)
+    plt.plot(temperatures, vibrational_energy)
+    plt.subplot(122)
+    plt.plot(temperatures, heat_capacity)
+    plt.show()
+
+
+