provides Waasmaier and Kirfel form factor approximations

praxes/io/spec/mapping.pyx

@@ -1,4 +1,4 @@
-import abc
+import collections
 
 
 cdef class Mapping:
@@ -35,4 +35,4 @@ cdef class Mapping:
         return self._index.values()
 
 
-abc.Mapping.register(Mapping)
+collections.Mapping.register(Mapping)

praxes/physref/waasmaier/__init__.py

@@ -0,0 +1,3 @@
+from .atomicdata import AtomicData
+
+atomic_data = AtomicData()

praxes/physref/waasmaier/atomicdata.py

@@ -0,0 +1,114 @@
+# -*- coding: utf-8 -*-
+"""
+Parameters for calculating the atomic scattering factors for free
+atoms and ions, as reported by D. Waasmaier and A. Kirfel, Acta.
+Cryst. A, v 51, p 416-431 (1995)
+ ┌ ┐ ┌              ┐
+ │a│ │a₁ a₂ a₃ a₄ a₅│
+ │b│=│b₁ b₂ b₃ b₄ b₅│
+ │c│ │c₁ 0  0  0  0 │
+ └ ┘ └              ┘
+"""
+
+#from __future__ import absolute_import
+
+import json
+import os
+import sqlite3
+
+import numpy as np
+
+from praxes.physref.lib.mapping import Mapping
+from praxes.lib.decorators import memoize
+
+class AtomicData(Mapping):
+
+    @Mapping._keys.getter
+    def _keys(self):
+        cursor = self.__db.cursor()
+        res = cursor.execute(
+            '''select ion from f0 order by id'''
+            )
+        return tuple(i[0] for i in res)
+
+    def __init__(self):
+        self.__db = sqlite3.connect(
+            os.path.join(os.path.split(__file__)[0], 'waasmaier_kirfel.db')
+            )
+
+    def __hash__(self):
+        hash(type(self))
+
+    def __getitem__(self, key):
+        if key not in self:
+            raise KeyError(
+                'Form factor approximations not reported for %s' % key
+                )
+        return FormFactor(key, self.__db)
+
+
+class FormFactor(object):
+    """
+    NondispersiveScatterer('Si')
+
+    NondispersiveScatterer instances are elements with methods to
+    calculate nondispersive scattering factors and properties based
+    on these values.
+
+    Parameters for calculating the nondispersive scattering factors
+    for free atoms and ions, as reported by D. Waasmaier and A.
+    Kirfel, Acta. Cryst. A, v 51, p 416-431 (1995)
+    ┌ ┐ ┌              ┐
+    │a│ │a₁ a₂ a₃ a₄ a₅│
+    │b│=│b₁ b₂ b₃ b₄ b₅│
+    │c│ │c₁ 0  0  0  0 │
+    └ ┘ └              ┘
+    """
+
+    def _get_data(self, id):
+        cursor = self.__db.cursor()
+        result = cursor.execute('''select %s from f0
+            where ion=?''' % id, (self._symbol, )
+            ).fetchone()
+        assert result is not None
+        return result[0]
+
+    @property
+    @memoize
+    def _a(self):
+        return tuple(json.loads(self._get_data('scale')))
+
+    @property
+    @memoize
+    def _b(self):
+        return tuple(json.loads(self._get_data('exponent')))
+
+    @property
+    @memoize
+    def _c(self):
+        return self._get_data('offset')
+
+    def __init__(self, symbol, db):
+        """symbol is a string, like 'Ca' or 'Ca2+'"""
+        self._symbol = symbol
+        self.__db = db
+
+    def __call__(self, Q):
+        """
+        Calculate the Q-dependent, energy-independent, scattering
+        factors:
+
+        f = f₀(Q)
+
+        Q-dependence is appproximated as reported by D. Waasmaier and
+        A. Kirfel, Acta. Cryst. A, v 51, p 416-431 (1995):
+
+        f₀(Q) = ∑_i a_i exp[-b_i(|Q|/4π)²] + c
+
+        This approximation is valid for |Q| ≤ 75 Å⁻¹
+        """
+        Q = Q.rescale('1/angstrom').magnitude
+        f = Q * 0.0 + self._c
+        for a, b in np.array([self._a, self._b]).transpose():
+            f += a * np.exp(-b * (Q / (4 * np.pi))**2)
+        return f

setup.py

@@ -47,9 +47,18 @@ def process_elam(self):
             'praxes/physref/elam/elam.db'
             )
 
+    def process_waasmaier(self):
+        return (
+            sys.executable,
+            'praxes/physref/waasmaier/create_db',
+            'praxes/physref/waasmaier/waasmaier_kirfel.dat',
+            'praxes/physref/waasmaier/waasmaier_kirfel.db'
+            )
+
     def run(self):
         to_process = [
             self.process_elam(),
+            self.process_waasmaier(),
             ]
 
         if sys.platform.startswith('win'):