added MACAW EoS

Author: bobmyhill

burnman/eos/__init__.py

@@ -26,6 +26,7 @@
 from .vinet import Vinet
 from .morse_potential import Morse
 from .reciprocal_kprime import RKprime
+from .macaw import MACAW
 from .dks_liquid import DKS_L
 from .dks_solid import DKS_S
 from .aa import AA

burnman/eos/helper.py

@@ -11,6 +11,7 @@
 from . import birch_murnaghan as bm
 from . import birch_murnaghan_4th as bm4
 from . import modified_tait as mt
+from . import macaw
 from . import dks_liquid
 from . import dks_solid
 from . import hp
@@ -70,6 +71,8 @@ def create(method):
             return bm4.BM4()
         elif method == "mt":
             return mt.MT()
+        elif method == "macaw":
+            return macaw.MACAW()
         elif method == "hp98":
             return hp.HP98()
         elif method == "hp_tmt":

burnman/eos/macaw.py

@@ -0,0 +1,188 @@
+from __future__ import absolute_import
+
+# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit
+# for the Earth and Planetary Sciences.
+# Copyright (C) 2012 - 2024 by the BurnMan team, released under the GNU
+# GPL v2 or later.
+
+
+import scipy.optimize as opt
+from . import equation_of_state as eos
+import warnings
+import numpy as np
+
+
+# Try to import the jit from numba.  If it is
+# not available, just go with the standard
+# python interpreter
+try:
+    from numba import jit
+except ImportError:
+
+    def jit(fn):
+        return fn
+
+
+@jit(nopython=True)
+def make_params(K0, K0_prime, K_infinity_prime):
+    a = (
+        16.0 * np.power(K0_prime, 3.0)
+        + 84.0 * np.power(K0_prime, 2.0)
+        + 192.0 * K0_prime
+        - 972.0 * K_infinity_prime
+        + 1177.0
+    )
+    b = 2.0 * np.power(K0_prime, 2.0) + 7.0 * K0_prime - 27.0 * K_infinity_prime + 38.0
+    omega = np.power((a + np.sqrt(a * a - 32.0 * b * b * b)), 1.0 / 3.0)
+    C = (
+        (11.0 / 6.0)
+        + (1.0 / 3.0) * K0_prime
+        - K_infinity_prime
+        + (np.power(2, -1.0 / 3.0) / 6) * omega
+        + (np.power(2, 1.0 / 3.0) / 3) * (b / omega)
+    )
+    B = K_infinity_prime - 1.0
+    A = K0 / (B - 0.5 * C + np.power(B + C, 2.0))
+    return A, B, C
+
+
+class MACAW(eos.EquationOfState):
+    """
+    Class for the MACAW equation of state
+    detailed in Lozano and Aslam (2022; https://doi.org/10.1063/5.0076897).
+
+    This equation of state has no temperature dependence.
+    """
+
+    def isothermal_bulk_modulus_reuss(self, pressure, temperature, volume, params):
+        """
+        Returns isothermal bulk modulus :math:`K_T` :math:`[Pa]` as a function of pressure :math:`[Pa]`,
+        temperature :math:`[K]` and volume :math:`[m^3]`.
+        """
+        A, B, C = make_params(params["K_0"], params["Kprime_0"], params["Kprime_inf"])
+        Vrel = volume / params["V_0"]
+        term1 = A * np.power(Vrel, -(B + 1))
+        term2 = np.exp((2.0 / 3.0) * C * (1 - np.power(Vrel, 1.5)))
+        term3 = np.power(C * np.power(Vrel, 1.5) + B, 2.0) - (
+            0.5 * C * np.power(Vrel, 1.5) - B
+        )
+        return term1 * term2 * term3
+
+    def volume(self, pressure, temperature, params):
+        """
+        Get the Vinet volume at a reference temperature for a given
+        pressure :math:`[Pa]`. Returns molar volume in :math:`[m^3]`
+        """
+
+        def delta_pressure(x):
+            return self.pressure(0.0, x, params) - pressure
+
+        V = opt.brentq(delta_pressure, 0.1 * params["V_0"], 1.5 * params["V_0"])
+        return V
+
+    def pressure(self, temperature, volume, params):
+        """
+        Returns pressure :math:`[Pa]` as a function of volume :math:`[m^3]`.
+        """
+        A, B, C = make_params(params["K_0"], params["Kprime_0"], params["Kprime_inf"])
+        Vrel = volume / params["V_0"]
+        term1 = A * np.power(Vrel, -(B + 1.0))
+        term2 = np.exp((2.0 / 3.0) * C * (1.0 - np.power(Vrel, 1.5)))
+        term3 = C * np.power(Vrel, 1.5) + B
+        return term1 * term2 * term3 - A * (B + C) + params["P_0"]
+
+    def molar_internal_energy(self, pressure, temperature, volume, params):
+        """
+        Returns the internal energy :math:`\\mathcal{E}` of the mineral. :math:`[J/mol]`
+        """
+        A, B, C = make_params(params["K_0"], params["Kprime_0"], params["Kprime_inf"])
+        Vrel = volume / params["V_0"]
+        I1 = -params["V_0"] * (
+            np.power(Vrel, -B) * np.exp((2.0 / 3.0) * C * (1.0 - np.power(Vrel, 1.5)))
+            - 1.0
+        )
+        I0 = (-A * (B + C) + params["P_0"]) * params["V_0"] * (Vrel - 1.0)
+        return -A * I1 - I0
+
+    def gibbs_free_energy(self, pressure, temperature, volume, params):
+        """
+        Returns the Gibbs free energy :math:`\\mathcal{G}` of the mineral. :math:`[J/mol]`
+        """
+        return (
+            self.molar_internal_energy(pressure, temperature, volume, params)
+            + pressure * volume
+        )
+
+    def isentropic_bulk_modulus_reuss(self, pressure, temperature, volume, params):
+        """
+        Returns adiabatic bulk modulus :math:`K_s` of the mineral. :math:`[Pa]`.
+        """
+        return self.isothermal_bulk_modulus_reuss(pressure, temperature, volume, params)
+
+    def shear_modulus(self, pressure, temperature, volume, params):
+        """
+        Returns shear modulus :math:`G` of the mineral. :math:`[Pa]`
+        """
+        return 1.0e99
+
+    def entropy(self, pressure, temperature, volume, params):
+        """
+        Returns the molar entropy :math:`\\mathcal{S}` of the mineral. :math:`[J/K/mol]`
+        """
+        return 0.0
+
+    def molar_heat_capacity_v(self, pressure, temperature, volume, params):
+        """
+        Since this equation of state does not contain temperature effects, return a very small number. :math:`[J/K/mol]`
+        """
+        return 1.0e-99
+
+    def molar_heat_capacity_p(self, pressure, temperature, volume, params):
+        """
+        Since this equation of state does not contain temperature effects, return a very small number. :math:`[J/K/mol]`
+        """
+        return 1.0e-99
+
+    def thermal_expansivity(self, pressure, temperature, volume, params):
+        """
+        Since this equation of state does not contain temperature effects, return zero. :math:`[1/K]`
+        """
+        return 0.0
+
+    def grueneisen_parameter(self, pressure, temperature, volume, params):
+        """
+        Since this equation of state does not contain temperature effects, return zero. :math:`[unitless]`
+        """
+        return 0.0
+
+    def validate_parameters(self, params):
+        """
+        Check for existence and validity of the parameters.
+        The value for :math:`K'_{\\infty}` is thermodynamically bounded
+        between 5/3 and :math:`K'_0` :cite:`StaceyDavis2004`.
+        """
+
+        if "E_0" not in params:
+            params["E_0"] = 0.0
+        if "P_0" not in params:
+            params["P_0"] = 1.0e5
+
+        # Check that all the required keys are in the dictionary
+        expected_keys = ["V_0", "K_0", "Kprime_0", "Kprime_inf"]
+        for k in expected_keys:
+            if k not in params:
+                raise KeyError("params object missing parameter : " + k)
+
+        # Finally, check that the values are reasonable.
+        if params["P_0"] < 0.0:
+            warnings.warn("Unusual value for P_0", stacklevel=2)
+        if params["V_0"] < 1.0e-7 or params["V_0"] > 1.0e-3:
+            warnings.warn("Unusual value for V_0", stacklevel=2)
+        if params["K_0"] < 1.0e9 or params["K_0"] > 1.0e13:
+            warnings.warn("Unusual value for K_0", stacklevel=2)
+        if params["Kprime_0"] < 0.0 or params["Kprime_0"] > 10.0:
+            warnings.warn("Unusual value for Kprime_0", stacklevel=2)
+        if params["Kprime_inf"] < 1 + 45.0 / 29.0:
+            warnings.warn("Value for Kprime_inf below recommended value", stacklevel=2)
+        if params["Kprime_inf"] > params["Kprime_0"]:
+            warnings.warn("Kprime_inf should be less than Kprime_0", stacklevel=2)

misc/benchmarks/figures/Lozano_Aslam_2022_Fig6c_HMX.png

@@ -0,0 +1,44 @@
+from __future__ import absolute_import
+
+from burnman.tools.eos import check_eos_consistency
+from burnman import Mineral
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.image as mpimg
+
+HMX_params = {
+    "P_0": 1.0e5,
+    "V_0": 1.0e-6,  # arbitrary value
+    "K_0": 15.22e9,
+    "Kprime_0": 7.54,
+    "Kprime_inf": 2.63,
+    "molar_mass": 0.296155,
+    "equation_of_state": "macaw",
+}
+
+HMX = Mineral(HMX_params)
+
+
+if check_eos_consistency(HMX, tol=1.0e-5, including_shear_properties=False):
+    print("The MACAW EoS is internally consistent.\n")
+
+pressures = np.linspace(0.0, 100.0e9, 6)
+temperatures = 0.0 + 0.0 * pressures
+V, K_T = HMX.evaluate(["V", "K_T"], pressures, temperatures)
+
+for i in range(6):
+    print(
+        f"{pressures[i]/1.e9:3.0f} GPa: "
+        f"V/V_0 = {V[i]/HMX_params['V_0']:.3f}, "
+        "K_T = {K_T[i]/1.e9:6.2f} GPa"
+    )
+
+pressures = np.linspace(0.0, 100.0e9, 101)
+temperatures = 0.0 + 0.0 * pressures
+K_T = HMX.evaluate(["K_T"], pressures, temperatures)[0]
+
+fig1 = mpimg.imread("figures/Lozano_Aslam_2022_Fig6c_HMX.png")
+plt.imshow(fig1, extent=[0.0, 100.0, 0, 500.0], aspect="auto")
+
+plt.plot(pressures / 1.0e9, K_T / 1.0e9, linestyle=":", c="red")
+plt.show()

misc/benchmarks/macaw_benchmarks.py

@@ -0,0 +1,8 @@
+The MACAW EoS is internally consistent.
+
+  0 GPa: V/V_0 = 1.000, K_T =  15.22 GPa
+ 20 GPa: V/V_0 = 0.704, K_T = 127.87 GPa
+ 40 GPa: V/V_0 = 0.626, K_T = 218.49 GPa
+ 60 GPa: V/V_0 = 0.579, K_T = 300.87 GPa
+ 80 GPa: V/V_0 = 0.546, K_T = 378.32 GPa
+100 GPa: V/V_0 = 0.520, K_T = 452.36 GPa