def test_default(self):
for rx in [
get_ionic_radii("Sr", charge=2, coordination=8),
get_ionic_radii("Mn", charge=2, coordination=8),
get_ionic_radii("Mg", charge=2, coordination=8),
get_ionic_radii("Ba", charge=2, coordination=8),
]:
D_j = self.D0 * strain_coefficient(
self.ri, rx, r0=self.r0, E=self.E, T=self.Tk
)
self.assertTrue(D_j > 0.0)
self.assertTrue(D_j < self.D0)
def setUp(self):
elements = [i for i in REE(dropPm=True) if i != "Eu"] # drop Pm, Eu
self.xs = np.array(get_ionic_radii(elements, coordination=8, charge=3))
self.default_degree = 5
self.expect = [
(),
(1.05477,),
(1.00533, 1.12824),
(0.99141, 1.06055, 1.14552),
(0.98482, 1.03052, 1.10441, 1.15343),
]
def test_params(self):
# the first three all have the same result - defaulting to ONeill 2016
# the two following use a full REE set for the OP basis function definition
# the last illustrates that custom parameters could be used
degree = self.default_degree
for params in [
None,
"ONeill2016",
"O'Neill (2016)",
"full",
"Full",
orthogonal_polynomial_constants(
get_ionic_radii(REE(), charge=3, coordination=8), # xs
degree=self.default_degree,
),
]:
with self.subTest(params=params):
ret = calc_lambdas(self.df, params=params, degree=degree)
self.assertTrue(ret.columns.size == self.default_degree)
def setUp(self):
self.xs = np.array(get_ionic_radii(REE(), coordination=8, charge=3))
self.default_degree = 4
"""
Ionic Radii
=============
:mod:`pyrolite` incldues a few sets of reference tables for ionic radii in aangstroms
(Å) from [Shannon1976]_ and [WhittakerMuntus1970]_, each with tables indexed
by element, ionic charge and coordination. The easiset way to access these is via
the :func:`~pyrolite.geochem.ind.get_ionic_radii` function. The function can be used
to get radii for individual elements:
"""
from pyrolite.geochem.ind import get_ionic_radii, REE
Cu_radii = get_ionic_radii("Cu")
print(Cu_radii)
########################################################################################
# Note that this function returned a series of the possible radii, given specific
# charges and coordinations of the Cu ion. If we completely specify these, we'll get
# a single number back:
#
Cu2plus6fold_radii = get_ionic_radii("Cu", coordination=6, charge=2)
print(Cu2plus6fold_radii)
########################################################################################
# You can also pass lists to the function. For example, if you wanted to get the Shannon
# ionic radii of Rare Earth Elements (REE) in eight-fold coordination with a valence of
# +3, you should use the following:
#
shannon_ionic_radii = get_ionic_radii(REE(), coordination=8, charge=3)
print(shannon_ionic_radii)
########################################################################################
# The function defaults to using the Shannon ionic radii consistent with [Pauling1960]_,
# but you can adjust to use the set you like with the `pauling` boolean argument
def setUp(self):
self.r0 = get_ionic_radii("Ca", charge=2, coordination=8) # angstroms
self.ri = get_ionic_radii("Ca", charge=2, coordination=8)
self.D0 = 4.1
self.E = 120 * 10 ** 9 # Pa
self.Tk = 1200.0 # kelvin
def test_modulus_not_specified(self):
rx = get_ionic_radii("Sr", charge=2, coordination=8)
D_j = self.D0 * strain_coefficient(self.ri, rx, r0=self.r0, z=2, T=self.Tk)
self.assertTrue(D_j > 0.0)
self.assertTrue(D_j < self.D0)
Ionic Radii
==============
:mod:`pyrolite` incldues a few sets of reference tables for ionic radii in aangstroms
(Å) from [Shannon1976]_ and [WhittakerMuntus1970]_, each with tables indexed
by element, ionic charge and coordination. The easiset way to access these is via
the :func:`~pyrolite.geochem.ind.get_ionic_radii` function. The function can be used
to get radii for individual elements, using a :code:`source` keyword argument to swap
between the datasets:
"""
import pandas as pd
import matplotlib.pyplot as plt
from pyrolite.geochem.ind import get_ionic_radii, REE
REE_radii = pd.Series(get_ionic_radii(REE(),
coordination=8,
charge=3,
source="Whittaker"),
index=REE())
REE_radii
########################################################################################
REE_radii.pyroplot.spider(color="k", logy=False)
plt.show()
########################################################################################
# References
# ----------
# .. [Shannon1976] Shannon RD (1976). Revised effective ionic radii and systematic
# studies of interatomic distances in halides and chalcogenides.
# Acta Crystallographica Section A 32:751–767.
# `doi: 10.1107/S0567739476001551 <https://doi.org/10.1107/S0567739476001551>`__.
# .. [WhittakerMuntus1970] Whittaker, E.J.W., Muntus, R., 1970.
# Ionic radii for use in geochemistry.
from pyrolite.mineral.lattice import strain_coefficient
# sphinx_gallery_thumbnail_number = 3
########################################################################################
# First, we need to define some of the necessary parameters including temperature, the Young's
# moduli for the :math:`X^{2+}` and :math:`X^{3+}` sites in plagioclase (:math:`E_2`,
# :math:`E_3`), and some reference partition coefficients and radii for calcium and
# sodium:
D_Na = 1.35 # Partition coefficient Plag-Melt
D_Ca = 4.1 # Partition coefficient Plag-Melt
Tc = 900 # Temperature, °C
Tk = Tc + 273.15 # Temperature, K
E_2 = 120 * 10**9 # Youngs modulus for 2+ site, Pa
E_3 = 135 * 10**9 # Youngs modulus for 3+ site, Pa
r02, r03 = 1.196, 1.294 # fictive ideal cation radii for these sites
rCa = get_ionic_radii("Ca", charge=2, coordination=8)
rLa = get_ionic_radii("La", charge=3, coordination=8)
########################################################################################
# We can calculate and plot the partitioning of :math:`X^{2+}` cations relative to
# :math:`Ca^{2+}` at a given temperature using their radii and the lattice strain function:
#
fontsize = 8
fig, ax = plt.subplots(1)
site2labels = ["Na", "Ca", "Eu", "Sr"]
# get the Shannon ionic radii for the elements in the 2+ site
site2radii = [
get_ionic_radii("Na", charge=1, coordination=8),
*[
get_ionic_radii(el, charge=2, coordination=8)
for el in ["Ca", "Eu", "Sr"]
import numpy as np
import matplotlib.pyplot as plt
from pyrolite.plot import pyroplot
from pyrolite.plot.spider import REE_v_radii
from pyrolite.geochem.ind import REE, get_ionic_radii
# sphinx_gallery_thumbnail_number = 4
########################################################################################
# Where data is not specified, it will return a formatted axis which can be used for
# subsequent plotting:
ax = REE_v_radii(
index='radii') # radii mode will put ionic radii on the x axis
# create some example data
ree = REE()
xs = get_ionic_radii(ree, coordination=8, charge=3)
ys = np.linspace(1, 20, len(xs))
ax.plot(xs, ys, marker='D', color='k')
plt.show()
########################################################################################
# Here we generate some example data:
#
no_analyses = 10
data_ree = REE(dropPm=True)
data_radii = np.array(get_ionic_radii(data_ree, coordination=8, charge=3))
data_radii = np.tile(data_radii,
(1, no_analyses)).reshape(no_analyses,
data_radii.shape[0])
dataframes = []
"""
Shannon Radii
=============
"""
import matplotlib.pyplot as plt
from pyrolite.geochem.ind import get_ionic_radii, REE
REE_radii = get_ionic_radii(REE(), coordination=8, charge=3)
fig, ax = plt.subplots(1)
ax.plot(REE_radii, c='k', marker='D')
ax.set_xticks(range(len(REE())))
ax.set_xticklabels(REE())
ax.set_ylabel('Ionic Radius ($\AA$)')
ax.set_title('Rare Earth Element Shannon Ionic Radii')
########################################################################################
# .. seealso:: `Pandas Lambda Ln(REE) Function <../lambdas/pandaslambdas.html>`__,
# `Lambdas for Dimensional Reduction <../lambdas/lambdadimreduction.html>`__,
# `REE Radii Plot <../plotting/REE_radii_plot.html>`__
from pyrolite.geochem.ind import REE, get_ionic_radii
from pyrolite.mineral.lattice import strain_coefficient
# sphinx_gallery_thumbnail_number = 3
########################################################################################
# First, we need to define some of the necessary parameters including temperature, the Young's
# moduli for the :math:`X^{2+}` and :math:`X^{3+}` sites in plagioclase (:math:`E_2`,
# :math:`E_3`), and some reference partition coefficients and radii for calcium and
# sodium:
D_Na = 1.35 # Partition coefficient Plag-Melt
D_Ca = 4.1 # Partition coefficient Plag-Melt
Tc = 900 # Temperature, °C
Tk = Tc + 273.15 # Temperature, K
E_2 = 120 * 10 ** 9 # Youngs modulus for 2+ site, Pa
E_3 = 135 * 10 ** 9 # Youngs modulus for 3+ site, Pa
r02, r03 = 1.196, 1.294 # fictive ideal cation radii for these sites
rCa = get_ionic_radii("Ca", charge=2, coordination=8)
rLa = get_ionic_radii("La", charge=3, coordination=8)
########################################################################################
# We can calculate and plot the partitioning of :math:`X^{2+}` cations relative to
# :math:`Ca^{2+}` at a given temperature using their radii and the lattice strain function:
#
fontsize = 8
fig, ax = plt.subplots(1)
site2labels = ["Na", "Ca", "Eu", "Sr"]
# get the Shannon ionic radii for the elements in the 2+ site
site2radii = [
get_ionic_radii("Na", charge=1, coordination=8),
*[get_ionic_radii(el, charge=2, coordination=8) for el in ["Ca", "Eu", "Sr"]],
]
# plot the relative paritioning curve for cations in the 2+ site
f = np.ones_like(xs) * w
for c in p:
f *= xs - np.float(c)
if log:
f = np.exp(f)
label = ("$r^{}: \lambda_{}".format(len(p), len(p)) +
["\cdot f_{}".format(len(p)), ""][int(len(p) == 0)] + "$")
ax.plot(xs, f, label=label, **kwargs)
########################################################################################
# First we generate some example data:
#
data_ree = REE(dropPm=True)
data_radii = np.array(get_ionic_radii(data_ree, charge=3, coordination=8))
lnY = (np.random.randn(*data_radii.shape) * 0.1 +
np.linspace(3.0, 0.0, data_radii.size) + (data_radii - 1.11)**2.0 - 0.1)
for ix, el in enumerate(data_ree):
if el in ["Ce", "Eu"]:
lnY[ix] += np.random.randn(1) * 0.6
Y = np.exp(lnY)
########################################################################################
# Now we can calculate the lambdas:
#
exclude = ["Ce", "Eu"]
if exclude:
subset_ree = [i for i in data_ree if not i in exclude]
subset_Y = Y[[i in subset_ree for i in data_ree]]
