[cig-commits] [commit] add_thermodynamic_potentials: Add another configurational entropy example (8cc2237)

[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 8cc22372deb8abef3fa6e89718e479a18b896877
Author: Bob Myhill <myhill.bob at gmail.com>
Date:   Wed Sep 3 20:45:43 2014 +0200

    Add another configurational entropy example


>---------------------------------------------------------------

8cc22372deb8abef3fa6e89718e479a18b896877
 solidsolution_benchmarks.py | 44 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 44 insertions(+)

diff --git a/solidsolution_benchmarks.py b/solidsolution_benchmarks.py
index d3778d2..ea8bb85 100644
--- a/solidsolution_benchmarks.py
+++ b/solidsolution_benchmarks.py
@@ -1,5 +1,6 @@
 # Benchmarks for the solid solution class
 import burnman
+from burnman import minerals
 from burnman.processchemistry import *
 
 import numpy as np
@@ -30,6 +31,49 @@ Solvus shapes (a proxy for Gibbs free energy checking
 Excess properties
 '''
 # Configurational entropy
+# Navrotsky and Kleppa, 1967
+class o_d_spinel(burnman.SolidSolution):
+    def __init__(self):
+        # Name
+        self.name='orthopyroxene'
+
+        # Endmembers (cpx is symmetric)
+        base_material = [[minerals.HP_2011.spinel(), '[Mg][Al]2O4'],[minerals.HP_2011.spinel(), '[Mg1/3Al2/3][Mg1/3Al2/3]2O4'] ]
+
+        # Interaction parameters
+        enthalpy_interaction=[[0.0]]
+
+        burnman.SolidSolution.__init__(self, base_material, \
+                          burnman.solutionmodel.SymmetricRegularSolution(base_material, enthalpy_interaction) )
+
+comp = np.linspace(0, 1.0, 100)
+sp=o_d_spinel()
+sp.set_method('mtait')
+sp_entropies = np.empty_like(comp)
+sp_S= np.empty_like(comp)
+for i,c in enumerate(comp):
+        molar_fractions=[1.0-c, c]
+        sp.set_composition( np.array(molar_fractions) )
+        sp.set_state( 1e5, 298.15 )
+        sp_entropies[i] = sp.solution_model.configurational_entropy( molar_fractions ) + \
+            (sum(molar_fractions[mbr]*sp.solution_model.endmember_configurational_entropies[mbr] for mbr in range(sp.solution_model.n_endmembers)))
+        x=c/1.5
+        if i > 0:
+            sp_S[i] = -8.3145*(x*np.log(x) + (1.-x)*np.log(1.-x) + x*np.log(x/2.) + (2.-x)*np.log(1.-x/2.))
+        else:
+            sp_S[i] = 0.
+
+#fig1 = mpimg.imread('configurational_entropy.png')  # Uncomment these two lines if you want to overlay the plot on a screengrab from SLB2011
+#plt.imshow(fig1, extent=[0.0, 1.0,0.,17.0], aspect='auto')
+plt.plot( comp, sp_S, 'b-', linewidth=3.)
+plt.plot( comp, sp_entropies, 'r--', linewidth=3.)
+plt.xlim(0.0,1.0)
+plt.ylim(0.,17.0)
+plt.ylabel("Configurational enthalpy of solution")
+plt.xlabel("disordered spinel fraction")
+plt.show()
+
+# Configurational entropy
 # Figure 3b of Stixrude and Lithgow-Bertelloni, 2011
 class enstatite (burnman.Mineral):
     def __init__(self):