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public release 2.2.0 - see README.md and CHANGES.md for details

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muntwiler_m
2020-09-04 16:22:42 +02:00
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commit 7c61eb1b41
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pmsco/elements/__init__.py Normal file
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"""
@package pmsco.elements
extended properties of the elements
this package extends the element table of the `periodictable` package
(https://periodictable.readthedocs.io/en/latest/index.html)
by additional attributes like the electron binding energies.
the package requires the periodictable package (https://pypi.python.org/pypi/periodictable).
@author Matthias Muntwiler
@copyright (c) 2020 by Paul Scherrer Institut @n
Licensed under the Apache License, Version 2.0 (the "License"); @n
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
"""
import periodictable.core
def _load_binding_energy():
"""
delayed loading of the binding energy table.
"""
from . import bindingenergy
bindingenergy.init(periodictable.core.default_table())
def _load_photoionization():
"""
delayed loading of the binding energy table.
"""
from . import photoionization
photoionization.init(periodictable.core.default_table())
periodictable.core.delayed_load(['binding_energy'], _load_binding_energy)
periodictable.core.delayed_load(['photoionization'], _load_photoionization)

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"70": {"1s": 61332.0, "2s": 10486.0, "2p1/2": 9978.0, "2p3/2": 8944.0, "3s": 2398.0, "3p1/2": 2173.0, "3p3/2": 1950.0, "3d3/2": 1576.0, "3d5/2": 1528.0, "4s": 480.5, "4p1/2": 388.7, "4p3/2": 339.7, "4d3/2": 191.2, "4d5/2": 182.4, "4f5/2": 2.5, "4f7/2": 1.3, "5s": 52.0, "5p1/2": 30.3, "5p3/2": 24.1},
"71": {"1s": 63314.0, "2s": 10870.0, "2p1/2": 10349.0, "2p3/2": 9244.0, "3s": 2491.0, "3p1/2": 2264.0, "3p3/2": 2024.0, "3d3/2": 1639.0, "3d5/2": 1589.0, "4s": 506.8, "4p1/2": 412.4, "4p3/2": 359.2, "4d3/2": 206.1, "4d5/2": 196.3, "4f5/2": 8.9, "4f7/2": 7.5, "5s": 57.3, "5p1/2": 33.6, "5p3/2": 26.7},
"72": {"1s": 65351.0, "2s": 11271.0, "2p1/2": 10739.0, "2p3/2": 9561.0, "3s": 2601.0, "3p1/2": 2365.0, "3p3/2": 2108.0, "3d3/2": 1716.0, "3d5/2": 1662.0, "4s": 538.0, "4p1/2": 438.2, "4p3/2": 380.7, "4d3/2": 220.0, "4d5/2": 211.5, "4f5/2": 15.9, "4f7/2": 14.2, "5s": 64.2, "5p1/2": 38.0, "5p3/2": 29.9},
"73": {"1s": 67416.0, "2s": 11682.0, "2p1/2": 11136.0, "2p3/2": 9881.0, "3s": 2708.0, "3p1/2": 2469.0, "3p3/2": 2194.0, "3d3/2": 1793.0, "3d5/2": 1735.0, "4s": 563.4, "4p1/2": 463.4, "4p3/2": 400.9, "4d3/2": 237.9, "4d5/2": 226.4, "4f5/2": 23.5, "4f7/2": 21.6, "5s": 69.7, "5p1/2": 42.2, "5p3/2": 32.7},
"74": {"1s": 69525.0, "2s": 12100.0, "2p1/2": 11544.0, "2p3/2": 10207.0, "3s": 2820.0, "3p1/2": 2575.0, "3p3/2": 2281.0, "3d3/2": 1872.0, "3d5/2": 1809.0, "4s": 594.1, "4p1/2": 490.4, "4p3/2": 423.6, "4d3/2": 255.9, "4d5/2": 243.5, "4f5/2": 33.6, "4f7/2": 31.4, "5s": 75.6, "5p1/2": 45.3, "5p3/2": 36.8},
"75": {"1s": 71676.0, "2s": 12527.0, "2p1/2": 11959.0, "2p3/2": 10535.0, "3s": 2932.0, "3p1/2": 2682.0, "3p3/2": 2367.0, "3d3/2": 1949.0, "3d5/2": 1883.0, "4s": 625.4, "4p1/2": 518.7, "4p3/2": 446.8, "4d3/2": 273.9, "4d5/2": 260.5, "4f5/2": 42.9, "4f7/2": 40.5, "5s": 83.0, "5p1/2": 45.6, "5p3/2": 34.6},
"76": {"1s": 73871.0, "2s": 12968.0, "2p1/2": 12385.0, "2p3/2": 10871.0, "3s": 3049.0, "3p1/2": 2792.0, "3p3/2": 2457.0, "3d3/2": 2031.0, "3d5/2": 1960.0, "4s": 658.2, "4p1/2": 549.1, "4p3/2": 470.7, "4d3/2": 293.1, "4d5/2": 278.5, "4f5/2": 53.4, "4f7/2": 50.7, "5s": 84.0, "5p1/2": 58.0, "5p3/2": 44.5},
"77": {"1s": 76111.0, "2s": 13419.0, "2p1/2": 12824.0, "2p3/2": 11215.0, "3s": 3174.0, "3p1/2": 2909.0, "3p3/2": 2551.0, "3d3/2": 2116.0, "3d5/2": 2040.0, "4s": 691.1, "4p1/2": 577.8, "4p3/2": 495.8, "4d3/2": 311.9, "4d5/2": 296.3, "4f5/2": 63.8, "4f7/2": 60.8, "5s": 95.2, "5p1/2": 63.0, "5p3/2": 48.0},
"78": {"1s": 78395.0, "2s": 13880.0, "2p1/2": 13273.0, "2p3/2": 11564.0, "3s": 3296.0, "3p1/2": 3027.0, "3p3/2": 2645.0, "3d3/2": 2202.0, "3d5/2": 2122.0, "4s": 725.4, "4p1/2": 609.1, "4p3/2": 519.4, "4d3/2": 331.6, "4d5/2": 314.6, "4f5/2": 74.5, "4f7/2": 71.2, "5s": 101.7, "5p1/2": 65.3, "5p3/2": 51.7},
"79": {"1s": 80725.0, "2s": 14353.0, "2p1/2": 13734.0, "2p3/2": 11919.0, "3s": 3425.0, "3p1/2": 3148.0, "3p3/2": 2743.0, "3d3/2": 2291.0, "3d5/2": 2206.0, "4s": 762.1, "4p1/2": 642.7, "4p3/2": 546.3, "4d3/2": 353.2, "4d5/2": 335.1, "4f5/2": 87.6, "4f7/2": 84.0, "5s": 107.2, "5p1/2": 74.2, "5p3/2": 57.2},
"80": {"1s": 83102.0, "2s": 14839.0, "2p1/2": 14209.0, "2p3/2": 12284.0, "3s": 3562.0, "3p1/2": 3279.0, "3p3/2": 2847.0, "3d3/2": 2385.0, "3d5/2": 2295.0, "4s": 802.2, "4p1/2": 680.2, "4p3/2": 576.6, "4d3/2": 378.2, "4d5/2": 358.8, "4f5/2": 104.0, "4f7/2": 99.9, "5s": 127.0, "5p1/2": 83.1, "5p3/2": 64.5, "5d3/2": 9.6, "5d5/2": 7.8},
"81": {"1s": 85530.0, "2s": 15347.0, "2p1/2": 14698.0, "2p3/2": 12658.0, "3s": 3704.0, "3p1/2": 3416.0, "3p3/2": 2957.0, "3d3/2": 2485.0, "3d5/2": 2389.0, "4s": 846.2, "4p1/2": 720.5, "4p3/2": 609.5, "4d3/2": 405.7, "4d5/2": 385.0, "4f5/2": 122.2, "4f7/2": 117.8, "5s": 136.0, "5p1/2": 94.6, "5p3/2": 73.5, "5d3/2": 14.7, "5d5/2": 12.5},
"82": {"1s": 88005.0, "2s": 15861.0, "2p1/2": 15200.0, "2p3/2": 13035.0, "3s": 3851.0, "3p1/2": 3554.0, "3p3/2": 3066.0, "3d3/2": 2586.0, "3d5/2": 2484.0, "4s": 891.8, "4p1/2": 761.9, "4p3/2": 643.5, "4d3/2": 434.3, "4d5/2": 412.2, "4f5/2": 141.7, "4f7/2": 136.9, "5s": 147.0, "5p1/2": 106.4, "5p3/2": 83.3, "5d3/2": 20.7, "5d5/2": 18.1},
"83": {"1s": 90526.0, "2s": 16388.0, "2p1/2": 15711.0, "2p3/2": 13419.0, "3s": 3999.0, "3p1/2": 3696.0, "3p3/2": 3177.0, "3d3/2": 2688.0, "3d5/2": 2580.0, "4s": 939.0, "4p1/2": 805.2, "4p3/2": 678.8, "4d3/2": 464.0, "4d5/2": 440.1, "4f5/2": 162.3, "4f7/2": 157.0, "5s": 159.3, "5p1/2": 119.0, "5p3/2": 92.6, "5d3/2": 26.9, "5d5/2": 23.8},
"84": {"1s": 93105.0, "2s": 16939.0, "2p1/2": 16244.0, "2p3/2": 13814.0, "3s": 4149.0, "3p1/2": 3854.0, "3p3/2": 3302.0, "3d3/2": 2798.0, "3d5/2": 2683.0, "4s": 995.0, "4p1/2": 851.0, "4p3/2": 705.0, "4d3/2": 500.0, "4d5/2": 473.0, "4f5/2": 184.0, "4f7/2": 184.0, "5s": 177.0, "5p1/2": 132.0, "5p3/2": 104.0, "5d3/2": 31.0, "5d5/2": 31.0},
"85": {"1s": 95730.0, "2s": 17493.0, "2p1/2": 16785.0, "2p3/2": 14214.0, "3s": 4317.0, "3p1/2": 4008.0, "3p3/2": 3426.0, "3d3/2": 2909.0, "3d5/2": 2787.0, "4s": 1042.0, "4p1/2": 886.0, "4p3/2": 740.0, "4d3/2": 533.0, "4d5/2": 507.0, "4f5/2": 210.0, "4f7/2": 210.0, "5s": 195.0, "5p1/2": 148.0, "5p3/2": 115.0, "5d3/2": 40.0, "5d5/2": 40.0},
"86": {"1s": 98404.0, "2s": 18049.0, "2p1/2": 17337.0, "2p3/2": 14619.0, "3s": 4482.0, "3p1/2": 4159.0, "3p3/2": 3538.0, "3d3/2": 3022.0, "3d5/2": 2892.0, "4s": 1097.0, "4p1/2": 929.0, "4p3/2": 768.0, "4d3/2": 567.0, "4d5/2": 541.0, "4f5/2": 238.0, "4f7/2": 238.0, "5s": 214.0, "5p1/2": 164.0, "5p3/2": 127.0, "5d3/2": 48.0, "5d5/2": 48.0, "6s": 26.0},
"87": {"1s": 101137.0, "2s": 18639.0, "2p1/2": 17907.0, "2p3/2": 15031.0, "3s": 4652.0, "3p1/2": 4327.0, "3p3/2": 3663.0, "3d3/2": 3136.0, "3d5/2": 3000.0, "4s": 1153.0, "4p1/2": 980.0, "4p3/2": 810.0, "4d3/2": 603.0, "4d5/2": 577.0, "4f5/2": 268.0, "4f7/2": 268.0, "5s": 234.0, "5p1/2": 182.0, "5p3/2": 140.0, "5d3/2": 58.0, "5d5/2": 58.0, "6s": 34.0, "6p1/2": 15.0, "6p3/2": 15.0},
"88": {"1s": 103922.0, "2s": 19237.0, "2p1/2": 18484.0, "2p3/2": 15444.0, "3s": 4822.0, "3p1/2": 4490.0, "3p3/2": 3792.0, "3d3/2": 3248.0, "3d5/2": 3105.0, "4s": 1208.0, "4p1/2": 1058.0, "4p3/2": 879.0, "4d3/2": 636.0, "4d5/2": 603.0, "4f5/2": 299.0, "4f7/2": 299.0, "5s": 254.0, "5p1/2": 200.0, "5p3/2": 153.0, "5d3/2": 68.0, "5d5/2": 68.0, "6s": 44.0, "6p1/2": 19.0, "6p3/2": 19.0},
"89": {"1s": 106755.0, "2s": 19840.0, "2p1/2": 19083.0, "2p3/2": 15871.0, "3s": 5002.0, "3p1/2": 4656.0, "3p3/2": 3909.0, "3d3/2": 3370.0, "3d5/2": 3219.0, "4s": 1269.0, "4p1/2": 1080.0, "4p3/2": 890.0, "4d3/2": 675.0, "4d5/2": 639.0, "4f5/2": 319.0, "4f7/2": 319.0, "5s": 272.0, "5p1/2": 215.0, "5p3/2": 167.0, "5d3/2": 80.0, "5d5/2": 80.0},
"90": {"1s": 109651.0, "2s": 20472.0, "2p1/2": 19693.0, "2p3/2": 16300.0, "3s": 5182.0, "3p1/2": 4830.0, "3p3/2": 4046.0, "3d3/2": 3491.0, "3d5/2": 3332.0, "4s": 1330.0, "4p1/2": 1168.0, "4p3/2": 966.4, "4d3/2": 712.1, "4d5/2": 675.2, "4f5/2": 342.4, "4f7/2": 333.1, "5s": 290.0, "5p1/2": 229.0, "5p3/2": 182.0, "5d3/2": 92.5, "5d5/2": 85.4, "6s": 41.4, "6p1/2": 24.5, "6p3/2": 16.6},
"91": {"1s": 112601.0, "2s": 21105.0, "2p1/2": 20314.0, "2p3/2": 16733.0, "3s": 5367.0, "3p1/2": 5001.0, "3p3/2": 4174.0, "3d3/2": 3611.0, "3d5/2": 3442.0, "4s": 1387.0, "4p1/2": 1224.0, "4p3/2": 1007.0, "4d3/2": 743.0, "4d5/2": 708.0, "4f5/2": 371.0, "4f7/2": 360.0, "5s": 310.0, "5p1/2": 232.0, "5p3/2": 232.0, "5d3/2": 94.0, "5d5/2": 94.0},
"92": {"1s": 115606.0, "2s": 21757.0, "2p1/2": 20948.0, "2p3/2": 17166.0, "3s": 5548.0, "3p1/2": 5182.0, "3p3/2": 4303.0, "3d3/2": 3728.0, "3d5/2": 3552.0, "4s": 1439.0, "4p1/2": 1271.0, "4p3/2": 1043.0, "4d3/2": 778.3, "4d5/2": 736.2, "4f5/2": 388.2, "4f7/2": 377.4, "5s": 321.0, "5p1/2": 257.0, "5p3/2": 192.0, "5d3/2": 102.8, "5d5/2": 94.2, "6s": 43.9, "6p1/2": 26.8, "6p3/2": 16.8}
}

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"""
@package pmsco.elements.bindingenergy
electron binding energies of the elements
extends the element table of the `periodictable` package
(https://periodictable.readthedocs.io/en/latest/index.html)
by the electron binding energies.
the binding energies are compiled from Gwyn Williams' web page
(https://userweb.jlab.org/~gwyn/ebindene.html).
please refer to the original web page or the x-ray data booklet
for original sources, definitions and remarks.
usage
-----
this module requires the periodictable package (https://pypi.python.org/pypi/periodictable).
~~~~~~{.py}
import periodictable as pt
import pmsco.elements.bindingenergy
# read any periodictable's element interfaces, e.g.
print(pt.gold.binding_energy['4f7/2'])
print(pt.elements.symbol('Au').binding_energy['4f7/2'])
print(pt.elements.name('gold').binding_energy['4f7/2'])
print(pt.elements[79].binding_energy['4f7/2'])
~~~~~~
note that attributes are writable.
you may assign refined values in your instance of the database.
the query_binding_energy() function queries all terms with a particular binding energy.
@author Matthias Muntwiler
@copyright (c) 2020 by Paul Scherrer Institut @n
Licensed under the Apache License, Version 2.0 (the "License"); @n
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
"""
import json
import numpy as np
import os
import periodictable as pt
from pmsco.compat import open
index_energy = np.zeros(0)
index_number = np.zeros(0)
index_term = []
def load_data():
data_path = os.path.join(os.path.dirname(__file__), "bindingenergy.json")
with open(data_path) as fp:
data = json.load(fp)
return data
def init(table, reload=False):
if 'binding_energy' in table.properties and not reload:
return
table.properties.append('binding_energy')
pt.core.Element.binding_energy = {}
pt.core.Element.binding_energy_units = "eV"
data = load_data()
for el_key, el_data in data.items():
try:
el = table[int(el_key)]
except ValueError:
el = table.symbol(el_key)
el.binding_energy = el_data
def build_index():
"""
build an index for query_binding_energy().
the index is kept in global variables of the module.
@return None
"""
global index_energy
global index_number
global index_term
n = 0
for element in pt.elements:
n += len(element.binding_energy)
index_energy = np.zeros(n)
index_number = np.zeros(n)
index_term = []
for element in pt.elements:
for term, energy in element.binding_energy.items():
index_term.append(term)
i = len(index_term) - 1
index_energy[i] = energy
index_number[i] = element.number
def query_binding_energy(energy, tol=1.0):
"""
search the periodic table for a specific binding energy and return all matching terms.
@param energy: binding energy in eV.
@param tol: tolerance in eV.
@return: list of dictionaries containing element and term specification.
the list is ordered arbitrarily.
each dictionary contains the following keys:
@arg 'number': element number
@arg 'symbol': element symbol
@arg 'term': spectroscopic term
@arg 'energy': actual binding energy
"""
if len(index_energy) == 0:
build_index()
sel = np.abs(index_energy - energy) < tol
idx = np.where(sel)
result = []
for i in idx[0]:
el_num = int(index_number[i])
d = {'number': el_num,
'symbol': pt.elements[el_num].symbol,
'term': index_term[i],
'energy': index_energy[i]}
result.append(d)
return result
def export_flat_text(f):
"""
export the binding energies to a flat general text file.
@param f: file path or open file object
@return: None
"""
if hasattr(f, "write") and callable(f.write):
f.write("number symbol term energy\n")
for element in pt.elements:
for term, energy in element.binding_energy.items():
f.write(f"{element.number} {element.symbol} {term} {energy}\n")
else:
with open(f, "w") as fi:
export_flat_text(fi)

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"""
@package pmsco.elements.photoionization
photoionization cross-sections of the elements
extends the element table of the `periodictable` package
(https://periodictable.readthedocs.io/en/latest/index.html)
by a table of photoionization cross-sections.
the data is available from (https://vuo.elettra.eu/services/elements/)
or (https://figshare.com/articles/dataset/Digitisation_of_Yeh_and_Lindau_Photoionisation_Cross_Section_Tabulated_Data/12389750).
both sources are based on the original atomic data tables by Yeh and Lindau (1985).
the Elettra data includes interpolation at finer steps,
whereas the Kalha data contains only the original data points by Yeh and Lindau
plus an additional point at 8 keV.
the tables go up to 1500 eV photon energy and do not resolve spin-orbit splitting.
usage
-----
this module requires python 3.6, numpy and the periodictable package (https://pypi.python.org/pypi/periodictable).
~~~~~~{.py}
import numpy as np
import periodictable as pt
import pmsco.elements.photoionization
# read any periodictable's element interfaces as follows.
# eph and cs are numpy arrays of identical shape that hold the photon energies and cross sections.
eph, cs = pt.gold.photoionization.cross_section['4f']
eph, cs = pt.elements.symbol('Au').photoionization.cross_section['4f']
eph, cs = pt.elements.name('gold').photoionization.cross_section['4f']
eph, cs = pt.elements[79].photoionization.cross_section['4f']
# interpolate for specific photon energy
print(np.interp(photon_energy, eph, cs)
~~~~~~
the data is loaded from the cross-sections.dat file which is a python-pickled data file.
to switch between data sources, use one of the load functions defined here
and dump the data to the cross-sections.dat file.
@author Matthias Muntwiler
@copyright (c) 2020 by Paul Scherrer Institut @n
Licensed under the Apache License, Version 2.0 (the "License"); @n
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
"""
import numpy as np
from pathlib import Path
import periodictable as pt
import pickle
import urllib.request
import urllib.error
from . import bindingenergy
def load_kalha_data():
"""
load all cross-sections from csv-files by Kalha et al.
the files must be placed in the 'kalha' directory next to this file.
@return: cross-section data in a nested dictionary, cf. load_pickled_data().
"""
data = {}
p = Path(Path(__file__).parent, "kalha")
for entry in p.glob('*_*.csv'):
if entry.is_file():
try:
element = int(entry.stem.split('_')[0])
except ValueError:
pass
else:
data[element] = load_kalha_file(entry)
return data
def load_kalha_file(path):
"""
load the cross-sections of an element from a csv-file by Kalha et al.
@param path: file path
@return: (dict) dictionary of 'nl' terms.
the data items are tuples (photon_energy, cross_sections) of 1-dimensional numpy arrays.
"""
a = np.genfromtxt(path, delimiter=',', names=True)
b = ~np.isnan(a['Photon_Energy__eV'])
a = a[b]
eph = a['Photon_Energy__eV'].copy()
data = {}
for n in range(1, 8):
for l in 'spdf':
col = f"{n}{l}"
try:
data[col] = (eph, a[col].copy())
except ValueError:
pass
return data
def load_kalha_configuration(path):
"""
load the electron configuration from a csv-file by Kalha et al.
@param path: file path
@return: (dict) dictionary of 'nl' terms mapping to number of electrons in the sub-shell.
"""
p = Path(path)
subshells = []
electrons = []
config = {}
with p.open() as f:
for l in f.readlines():
s = l.split(',')
k_eph = "Photon Energy"
k_el = "#electrons"
if s[0][0:len(k_eph)] == k_eph:
subshells = s[1:]
elif s[0][0:len(k_el)] == k_el:
electrons = s[1:]
for i, sh in enumerate(subshells):
if sh:
config[sh] = electrons[i]
return config
def load_elettra_file(symbol, nl):
"""
download the cross sections of one level from the Elettra webelements web site.
@param symbol: (str) element symbol
@param nl: (str) nl term, e.g. '2p' (no spin-orbit)
@return: (photon_energy, cross_section) tuple of 1-dimensional numpy arrays.
"""
url = f"https://vuo.elettra.eu/services/elements/data/{symbol.lower()}{nl}.txt"
try:
data = urllib.request.urlopen(url)
except urllib.error.HTTPError:
eph = None
cs = None
else:
a = np.genfromtxt(data)
try:
eph = a[:, 0]
cs = a[:, 1]
except IndexError:
eph = None
cs = None
return eph, cs
def load_elettra_data():
"""
download the cross sections from the Elettra webelements web site.
@return: cross-section data in a nested dictionary, cf. load_pickled_data().
"""
data = {}
for element in pt.elements:
element_data = {}
for nlj in element.binding_energy:
nl = nlj[0:2]
eb = element.binding_energy[nlj]
if nl not in element_data and eb <= 2000:
eph, cs = load_elettra_file(element.symbol, nl)
if eph is not None and cs is not None:
element_data[nl] = (eph, cs)
if len(element_data):
data[element.symbol] = element_data
return data
def save_pickled_data(path, data):
"""
save a cross section data dictionary to a python-pickled file.
@param path: file path
@param data: cross-section data in a nested dictionary, cf. load_pickled_data().
@return: None
"""
with open(path, "wb") as f:
pickle.dump(data, f)
def load_pickled_data(path):
"""
load the cross section data from a python-pickled file.
the file can be generated by the save_pickled_data() function.
@param path: file path
@return: cross-section data in a nested dictionary.
the first-level keys are element symbols.
the second-level keys are 'nl' terms (e.g. '2p').
note that the Yeh and Lindau tables do not resolve spin-orbit splitting.
the data items are (photon_energy, cross_sections) tuples
of 1-dimensional numpy arrays holding the data table.
cross section values are given in Mb.
"""
with open(path, "rb") as f:
data = pickle.load(f)
return data
class Photoionization(object):
def __init__(self):
self.cross_section = {}
self.cross_section_units = "Mb"
def init(table, reload=False):
"""
loads cross section data into the periodic table.
this function is called by the periodictable to load the data on demand.
@param table:
@param reload:
@return:
"""
if 'photoionization' in table.properties and not reload:
return
table.properties.append('photoionization')
# default value
pt.core.Element.photoionization = Photoionization()
p = Path(Path(__file__).parent, "cross-sections.dat")
data = load_pickled_data(p)
for el_key, el_data in data.items():
try:
el = table[int(el_key)]
except ValueError:
el = table.symbol(el_key)
pi = Photoionization()
pi.cross_section = el_data
pi.cross_section_units = "Mb"
el.photoionization = pi

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pmsco/elements/spectrum.py Normal file
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"""
@package pmsco.elements.spectrum
photoelectron spectrum simulator
this module calculates the basic structure of a photoelectron spectrum.
it calculates positions and approximate amplitude of elastic peaks
based on photon energy, binding energy, photoionization cross section, and stoichiometry.
escape depth, photon flux, analyser transmission are not accounted for.
usage
-----
this module requires python 3.6, numpy, matplotlib and
the periodictable package (https://pypi.python.org/pypi/periodictable).
~~~~~~{.py}
import numpy as np
import periodictable as pt
import pmsco.elements.spectrum as spec
# for working with the data
labels, energy, intensity = spec.build_spectrum(800., {"Ti": 1, "O": 2})
# for plotting
spec.plot_spectrum(800., {"Ti": 1, "O": 2})
~~~~~~
@author Matthias Muntwiler
@copyright (c) 2020 by Paul Scherrer Institut @n
Licensed under the Apache License, Version 2.0 (the "License"); @n
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
"""
from matplotlib import pyplot as plt
import numpy as np
import periodictable as pt
from . import bindingenergy
from . import photoionization
def get_element(number_or_symbol):
"""
return the given Element object of the periodic table.
@param number_or_symbol: atomic number (int) or chemical symbol (str).
@return: Element object.
"""
try:
el = pt.elements[number_or_symbol]
except KeyError:
el = pt.elements.symbol(number_or_symbol)
return el
def get_binding_energy(photon_energy, element, nlj):
"""
look up the binding energy of a core level and check whether it is smaller than the photon energy.
@param photon_energy: photon energy in eV.
@param element: Element object of the periodic table.
@param nlj: (str) spectroscopic term, e.g. '4f7/2'.
@return: (float) binding energy or numpy.nan.
"""
try:
eb = element.binding_energy[nlj]
except KeyError:
return np.nan
if eb < photon_energy:
return eb
else:
return np.nan
def get_cross_section(photon_energy, element, nlj):
"""
look up the photoionization cross section.
since the Yeh/Lindau tables do not resolve the spin-orbit splitting,
this function applies the normal relative weights of a full sub-shell.
the result is a linear interpolation between tabulated values.
@param photon_energy: photon energy in eV.
@param element: Element object of the periodic table.
@param nlj: (str) spectroscopic term, e.g. '4f7/2'.
@return: (float) cross section in Mb.
"""
nl = nlj[0:2]
try:
pet, cst = element.photoionization.cross_section[nl]
except KeyError:
return np.nan
# weights of spin-orbit peaks
d_wso = {"p1/2": 1./3.,
"p3/2": 2./3.,
"d3/2": 2./5.,
"d5/2": 3./5.,
"f5/2": 3./7.,
"f7/2": 4./7.}
wso = d_wso.get(nlj[1:], 1.)
cst = cst * wso
# todo: consider spline
return np.interp(photon_energy, pet, cst)
def build_spectrum(photon_energy, elements, binding_energy=False, work_function=4.5):
"""
calculate the positions and amplitudes of core-level photoemission lines.
the function looks up the binding energies and cross sections of all photoemission lines in the energy range
given by the photon energy and returns an array of expected spectral lines.
@param photon_energy: (numeric) photon energy in eV.
@param elements: list or dictionary of elements.
elements are identified by their atomic number (int) or chemical symbol (str).
if a dictionary is given, the (float) values are stoichiometric weights of the elements.
@param binding_energy: (bool) return binding energies (True) rather than kinetic energies (False, default).
@param work_function: (float) work function of the instrument in eV.
@return: tuple (labels, positions, intensities) of 1-dimensional numpy arrays representing the spectrum.
labels are in the format {Symbol}{n}{l}{j}.
"""
ekin = []
ebind = []
intens = []
labels = []
for element in elements:
el = get_element(element)
for n in range(1, 8):
for l in "spdf":
for j in ['', '1/2', '3/2', '5/2', '7/2']:
nlj = f"{n}{l}{j}"
eb = get_binding_energy(photon_energy, el, nlj)
cs = get_cross_section(photon_energy, el, nlj)
try:
cs = cs * elements[element]
except (KeyError, TypeError):
pass
if not np.isnan(eb) and not np.isnan(cs):
ekin.append(photon_energy - eb - work_function)
ebind.append(eb)
intens.append(cs)
labels.append(f"{el.symbol}{nlj}")
ebind = np.array(ebind)
ekin = np.array(ekin)
intens = np.array(intens)
labels = np.array(labels)
if binding_energy:
return labels, ebind, intens
else:
return labels, ekin, intens
def plot_spectrum(photon_energy, elements, binding_energy=False, work_function=4.5, show_labels=True):
"""
plot a simple spectrum representation of a material.
the function looks up the binding energies and cross sections of all photoemission lines in the energy range
given by the photon energy and returns an array of expected spectral lines.
the spectrum is plotted using matplotlib.pyplot.stem.
@param photon_energy: (numeric) photon energy in eV.
@param elements: list or dictionary of elements.
elements are identified by their atomic number (int) or chemical symbol (str).
if a dictionary is given, the (float) values are stoichiometric weights of the elements.
@param binding_energy: (bool) return binding energies (True) rather than kinetic energies (False, default).
@param work_function: (float) work function of the instrument in eV.
@param show_labels: (bool) show peak labels (True, default) or not (False).
@return: (figure, axes)
"""
labels, energy, intensity = build_spectrum(photon_energy, elements, binding_energy=binding_energy,
work_function=work_function)
fig, ax = plt.subplots()
ax.stem(energy, intensity, basefmt=' ', use_line_collection=True)
if show_labels:
for sxy in zip(labels, energy, intensity):
ax.annotate(sxy[0], xy=(sxy[1], sxy[2]), textcoords='data')
ax.grid()
if binding_energy:
ax.set_xlabel('binding energy')
else:
ax.set_xlabel('kinetic energy')
ax.set_ylabel('intensity')
ax.set_title(elements)
return fig, ax