structures.atoms

Classes:

Atom()	Smallest structural unit of which larger structures can be build.
AtomMixed()	Representation of mixed atoms in alloys and stochiometric mixtures.

class udkm1Dsim.structures.atoms.Atom(symbol, **kwargs)

Bases: object

Smallest structural unit of which larger structures can be build.

It holds real physical properties of on the atomic level.

Parameters:

symbol (str) – symbol of the atom.

Keyword Arguments:

• id (str) – id of the atom, may differ from symbol and/or name.

• ionicity (int) – ionicity of the atom.

• atomic_form_factor_path (str) – path to atomic form factor coeffs.

• atomic_form_factor_source (str) – either _henke_ or default _chantler_

• magnetic_form_factor_path (str) – path to magnetic form factor coeffs.

Attributes:

• symbol (str) – symbol of the element.

• id (str) – id of the atom, may differ from symbol and/or name.

• name (str) – name of the element (generic).

• atomic_number_z (int) – Z atomic number.

• mass_number_a (float) – A atomic mass number.

• ionicity (int) – ionicity of the atom.

• mass (float) – mass of the atom [kg].

• atomic_form_factor_coeff (ndarray[float]) – atomic form factor. coefficients for energy-dependent atomic form factor.

• cromer_mann_coeff (ndarray[float]) – cromer-mann coefficients for angular-dependent atomic form factor.

• magnetic_form_factor_coeff (ndarray[float]) – magnetic form factor coefficients for energy-dependent magnetic form factor.

• mag_amplitude (float) – magnetization amplitude -1 .. 1.

• mag_phi (float) – phi angle of magnetization [rad].

• mag_gamma (float) – gamma angle of magnetization [rad].

References

[1] (1,2)

B. L. Henke, E. M. Gullikson & J. C. Davis, X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92, Atomic Data and Nuclear Data Tables, 54(2), 181–342, (1993).

[2] (1,2)

C.T. Chantler, K. Olsen, R.A. Dragoset, J. Chang, A.R. Kishore, S.A. Kotochigova, & D.S. Zucker, Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coefficients for Z = 1-92 from E = 1-10 eV to E = 0.4-1.0 MeV, NIST Standard Reference Database 66.

[3] (1,2,3)

J. Als-Nielson, & D. McMorrow, Elements of Modern X-Ray Physics. New York: John Wiley & Sons, Ltd. (2001)

[4] (1,2,3)

D. T. Cromer & J. B. Mann, X-ray scattering factors computed from numerical Hartree–Fock wave functions, Acta Crystallographica Section A, 24(2), 321–324 (1968).

Methods:

read_atomic_form_factor_coeff()	The coefficients for the atomic form factor \(f\) in dependence of the photon energy \(E\) is read from a parameter file given by [1] or by [2] as default.
get_atomic_form_factor()	The complex atomic form factor for the photon energy \(E\) [eV] is calculated by:
read_cromer_mann_coeff()	The Cromer-Mann coefficients (Ref.
get_cm_atomic_form_factor()	The atomic form factor \(f\) is calculated in dependence of the photon energy \(E\) [eV] and the \(z\)-component of the scattering vector \(q_z\) [Å \(^{-1}\)] (Ref.
read_magnetic_form_factor_coeff()	The coefficients for the magnetic form factor \(m\) in dependence of the photon energy \(E\) is read from a parameter file.
get_magnetic_form_factor()	The complex magnetic form factor is claculated by:

read_atomic_form_factor_coeff(source='chantler', filename='')

The coefficients for the atomic form factor \(f\) in dependence of the photon energy \(E\) is read from a parameter file given by [1] or by [2] as default.

Parameters:

• source (str, optional) – source of atmoic form factors can be either _henke_ or _chantler_. Defaults to _chantler_.

• filename (str, optional) – full path and filename to the atomic form factor coefficients.

Returns:

f (ndarray[float]) – atomic form factor coefficients.

get_atomic_form_factor(energy)

The complex atomic form factor for the photon energy \(E\) [eV] is calculated by:

\[f(E)=f_1 - i f_2\]

Convention of Ref. [3] (p. 11, footnote) is a negative \(f_2\).

Parameters:

energy (ndarray[float]) – photon energy [eV].

Returns:

f (ndarray[complex]) – energy-dependent atomic form factors.

read_cromer_mann_coeff()

The Cromer-Mann coefficients (Ref. [4]) are read from a parameter file and are returned in the following order:

\[a_1\; a_2\; a_3\; a_4\; b_1\; b_2\; b_3\; b_4\; c\]

Returns:

cm (ndarray[float]) – Cromer-Mann coefficients.

get_cm_atomic_form_factor(energy, qz)

The atomic form factor \(f\) is calculated in dependence of the photon energy \(E\) [eV] and the \(z\)-component of the scattering vector \(q_z\) [Å \(^{-1}\)] (Ref. [4]). Note that the Cromer-Mann coefficients are fitted for \(q_z\) in [Å \(^{-1}\)]!

See Ref. [3] (p. 235).

\[f(q_z,E) = f_{CM}(q_z) + \delta f_1(E) -i f_2(E)\]

\(f_{CM}(q_z)\) is given in Ref. [4]:

\[f_{CM}(q_z) = \sum(a_i \, \exp(-b_i \, (q_z/4\pi)^2))+ c\]

\(\delta f_1(E)\) is the dispersion correction:

\[\delta f_1(E) = f_1(E) - \left(\sum^4_i(a_i) + c\right)\]

Thus:

\[f(q_z,E) = \sum(a_i \, \exp(-b_i \, q_z/2\pi)) + c + f_1(E)-i f_2(E) - \left(\sum(a_i) + c\right)\]

\[f(q_z,E) = \sum(a_i \, \exp(-b_i \, q_z/2\pi)) + f_1(E) -i f_2(E) - \sum(a_i)\]

Parameters:

• energy (ndarray[float]) – photon energy [eV].

• qz (ndarray[float]) – scattering vector [1/m].

Returns:

f (ndarray[complex]) – energy- and qz-dependent Cromer-Mann atomic form factors.

read_magnetic_form_factor_coeff(filename='')

The coefficients for the magnetic form factor \(m\) in dependence of the photon energy \(E\) is read from a parameter file.

Parameters:

filename (str) – optional full path and filename to the magnetic form factor coefficients.

Returns:

m (ndarray[float]) – magnetic form factor coefficients.

get_magnetic_form_factor(energy)

The complex magnetic form factor is claculated by:

\[m(E) = m_1 - i m_2\]

for the photon energy \(E\) [eV].

Convention of Ref. [3] (p. 11, footnote) is a negative \(m_2\)

Parameters:

energy (ndarray[float]) – photon energy [eV].

Returns:

m (ndarray[complex]) – energy-dependent magnetic form factors.

class udkm1Dsim.structures.atoms.AtomMixed(symbol, **kwargs)

Bases: Atom

Representation of mixed atoms in alloys and stochiometric mixtures.

All properties of the included sub-atoms of class Atom are averaged and weighted with their stochiometric ratio.

Parameters:

symbol (str) – symbol of the atom.

Keyword Arguments:

• id (str) – id of the atom, may differ from symbol and/or name.

• name (str) – name of the mixed atom, default is symbol.

• atomic_form_factor_path (str) – path to atomic form factor coeffs.

• magnetic_form_factor_path (str) – path to magnetic form factor coeffs.

Attributes:

• symbol (str) – symbol of the element.

• id (str) – id of the atom, may differ from symbol and/or name.

• name (str) – name of the mixed atom, default is symbol.

• atomic_number_z (int) – Z atomic number.

• mass_number_a (float) – A atomic mass number.

• ionicity (int) – ionicity of the atom.

• mass (float) – mass of the atom [kg].

• atomic_form_factor_coeff (ndarray[float]) – atomic form factor. coefficients for energy-dependent atomic form factor.

• magnetic_form_factor_coeff (ndarray[float]) – magnetic form factor coefficients for energy-dependent magnetic form factor.

• mag_amplitude (float) – magnetization amplitude -1 .. 1.

• mag_phi (float) – phi angle of magnetization [rad].

• mag_gamma (float) – gamma angle of magnetization [rad].

• atoms (list[Atoms]) – list of Atoms.

• num_atoms (int) – number of atoms.

Methods:

add_atom()	Add an Atom instance with its stochiometric fraction and recalculate averaged properties.
read_atomic_form_factor_coeff()	The coefficients for the atomic form factor \(f\) in dependence of the photon energy \(E\) must be read from an external file given by filename.
get_atomic_form_factor()	Averaged energy dependent atomic form factor.
get_cm_atomic_form_factor()	Averaged energy and qz-dependent atomic form factors.
read_magnetic_form_factor_coeff()	The coefficients for the magnetic form factor \(m\) in dependence of the photon energy \(E\) must be read from an external file given by filename.
get_magnetic_form_factor()	Mixed energy dependent magnetic form factors.

add_atom(atom, fraction)

Add an Atom instance with its stochiometric fraction and recalculate averaged properties.

Parameters:

• atom (Atom) – atom to add.

• fraction (float) – fraction of the atom - sum of all fractions must be 1.

read_atomic_form_factor_coeff(filename='')

The coefficients for the atomic form factor \(f\) in dependence of the photon energy \(E\) must be read from an external file given by filename.

Parameters:

filename (str, optional) – full path and filename to the atomic form factor coefficients.

Returns:

f (ndarray[float]) – atomic form factor coefficients.

get_atomic_form_factor(energy)

Averaged energy dependent atomic form factor. If atomic_form_factor_path was given on initialization this file will be used instead.

Parameters:

energy (ndarray[float]) – photon energy [eV].

Returns:

f (ndarray[complex]) – energy-dependent atomic form factors.

get_cm_atomic_form_factor(energy, qz)

Averaged energy and qz-dependent atomic form factors.

Parameters:

• energy (ndarray[float]) – photon energy [eV].

• qz (ndarray[float]) – scattering vector [1/m].

Returns:

f (ndarray[complex]) – energy- and qz-dependent Cromer-Mann atomic form factors.

read_magnetic_form_factor_coeff(filename='')

The coefficients for the magnetic form factor \(m\) in dependence of the photon energy \(E\) must be read from an external file given by filename.

Parameters:

filename (str) – optional full path and filename to the magnetic form factor coefficients.

Returns:

m (ndarray[float]) – magnetic form factor coefficients.

get_magnetic_form_factor(energy)

Mixed energy dependent magnetic form factors.

Parameters:

energy (ndarray[float]) – photon energy [eV].

Returns:

f (ndarray[complex]) – energy-dependent magnetic form factors.