crystalpy.diffraction package

Submodules

crystalpy.diffraction.Diffraction module

Defines a crystal diffraction experiment setup.

class crystalpy.diffraction.Diffraction.Diffraction

Bases: object

This class contains methods to to make different diffraction calculations. It does not contain data.

classmethod calculateDiffractedComplexAmplitudePhoton(diffraction_setup, photon, calculation_method=0, is_thick=0, use_transfer_matrix=0, calculation_strategy_flag=0)

Parameters:

• diffraction_setup –

• photon –

• calculation_method (int, optional) – 0: Zachariasen, 1: Guigay (Default value = 0)

• is_thick (int, optional) – 0: No, 1: Yes (Default value = 0)

• use_transfer_matrix (int, optional) – 0: No, 1: Yes (Default value = 0)

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Return type:

ComplexAmplitudePhoton instance

classmethod calculateDiffractedComplexAmplitudePhotonBunch(diffraction_setup, incoming_bunch, calculation_method=0, is_thick=0, use_transfer_matrix=0, calculation_strategy_flag=0)

Calculates the diffraction/transmission given by the setup.

Parameters:

• diffraction_setup (DiffractionSetup instance) – The diffraction setup.

• incoming_bunch (ComplexAmplitudePhotonBeam instance) –

• calculation_method (int, optional) – 0: Zachariasen, 1: Guigay (Default value = 0)

• is_thick (int, optional) – 0: No, 1: Yes (Default value = 0)

• use_transfer_matrix (int, optional) – 0: No, 1: Yes (Default value = 0)

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Returns:

Bunch made of diffracted/transmitted photons.

Return type:

ComplexAmplitudePhotonBeam instance

classmethod calculateDiffractedComplexAmplitudes(diffraction_setup, incoming_photon, calculation_method=0, is_thick=0, use_transfer_matrix=0, calculation_strategy_flag=0)

Calculates the diffracted complex amplitude

Parameters:

• diffraction_setup –

• incoming_photon –

• calculation_method (int, optional) – 0: Zachariasen, 1: Guigay (Default value = 0)

• is_thick (int, optional) – 0: No, 1: Yes (Default value = 0)

• use_transfer_matrix (int, optional) – 0: No, 1: Yes (Default value = 0)

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Returns:

the complex amplitudes for sigma and pi polarizations: {“S”: float, “P”: float}

Return type:

dict

classmethod calculateDiffractedPolarizedPhoton(diffraction_setup, incoming_polarized_photon, inclination_angle, calculation_method=0, is_thick=0, use_transfer_matrix=0, calculation_strategy_flag=0)

Calculates the diffraction/transmission given by the setup.

Parameters:

• diffraction_setup (DiffractionSetup instance) – The diffraction setup.

• incoming_polarized_photon (ComplexAmplitudePhoton instance) –

• inclination_angle (float) – The inclination angle in rad.

• calculation_method (int, optional) – 0: Zachariasen, 1: Guigay (Default value = 0)

• is_thick (int, optional) – 0: No, 1: Yes (Default value = 0)

• use_transfer_matrix (int, optional) – 0: No, 1: Yes (Default value = 0)

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Returns:

Photon diffracted/transmitted.

Return type:

ComplexAmplitudePhoton instance

classmethod calculateDiffractedPolarizedPhotonBunch(diffraction_setup, incoming_bunch, inclination_angle, calculation_method=0, is_thick=0, use_transfer_matrix=0, calculation_strategy_flag=0)

Calculates the diffraction/transmission bunch given by the crystal in the setup.

Parameters:

• diffraction_setup (DiffractionSetup instance) – The diffraction setup.

• incoming_bunch (ComplexAmplitudePhotonBunch instance) –

• inclination_angle (float) – The inclination angle in rad.

• calculation_method (int, optional) – 0: Zachariasen, 1: Guigay (Default value = 0)

• is_thick (int, optional) – 0: No, 1: Yes (Default value = 0)

• use_transfer_matrix (int, optional) – 0: No, 1: Yes (Default value = 0)

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Returns:

PhotonBunch object made up of diffracted/transmitted photons.

Return type:

ComplexAmplitudePhotonBunch

classmethod calculateDiffraction(diffraction_setup, calculation_method=0, is_thick=0, use_transfer_matrix=0, calculation_strategy_flag=0)

Calculates the diffraction/transmission given by the setup.

Parameters:

• diffraction_setup (DiffractionSetup instance) –

• calculation_method (int, optional) – 0: Zachariasen, 1: Guigay (Default value = 0)

• is_thick (int, optional) – 0: No, 1: Yes (Default value = 0)

• use_transfer_matrix (int, optional) – 0: No, 1: Yes (Default value = 0)

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Returns:

DiffractionResult with the input setup.

Return type:

DiffractionResult instance

crystalpy.diffraction.DiffractionExceptions module

Exception classes with ad-hoc messages.

exception crystalpy.diffraction.DiffractionExceptions.DiffractionException(exception_text)

Bases: Exception

exception crystalpy.diffraction.DiffractionExceptions.ReflectionImpossibleException

Bases: DiffractionException

exception crystalpy.diffraction.DiffractionExceptions.StructureFactorF0isZeroException

Bases: DiffractionException

exception crystalpy.diffraction.DiffractionExceptions.StructureFactorFHbarIsZeroException

Bases: DiffractionException

exception crystalpy.diffraction.DiffractionExceptions.StructureFactorFHisZeroException

Bases: DiffractionException

exception crystalpy.diffraction.DiffractionExceptions.TransmissionImpossibleException

Bases: DiffractionException

crystalpy.diffraction.DiffractionResult module

Object to hold the diffraction results.

self._intensities = numpy.array((number_energies,number_angles,index_polarization)) self._phases = numpy.array((number_energies,number_angles,index_polarization))

index_polarization:

INDEX_POLARIZATION_S = 0 INDEX_POLARIZATION_P = 1 INDEX_DIFFERENCE_PS = 2

Note that INDEX_DIFFERENCE_PS=2 means for:

self._intensities: the RATIO of p-intensity / s-intensity self._phases: the DIFFERENCE of p-intensity - s-intensity

class crystalpy.diffraction.DiffractionResult.DiffractionResult(diffraction_setup, bragg_angle)

Bases: object

Constructor.

Parameters:

• diffraction_setup (DiffractionSetup instance) – Setup used for these results.

• bragg_angle (float) – Bragg angle in rad of the setup.

INDEX_DIFFERENCE_PS = 2

INDEX_POLARIZATION_P = 1

INDEX_POLARIZATION_S = 0

add(energy, deviation, s_complex_amplitude, p_complex_amplitude, difference_complex_amplitude)

Adds a new result for a given energy and deviation.

Parameters:

• energy (float) – The photon energy in eV.

• deviation (float) – The deviation angle in rad.

• s_complex_amplitude (float) – The complex amplitude for sigma polarization.

• p_complex_amplitude (float) – The complex amplitude for pi polarization.

• difference_complex_amplitude (float) – The ratio between the intensities of pi over sigma polarizations.

angleDeviations()

Returns the angle deviations used for these results.

Returns:

Angle deviations used for these results.

Return type:

numpy array

angles()

Returns the angles used for calculation of these results.

Returns:

The angles used for the calculation of these results.

Return type:

numpy array

braggAngle()

Returns Bragg angle used for these results.

Returns:

Bragg angle used for these results.

Return type:

float

differenceIntensityByDeviation(deviation)

Returns the intensities ratio for the two polarizations P/S .

Parameters:

deviation (float) – Deviation to return intensity for.

Returns:

Intensity ratio P / S for the two polarizations.

Return type:

float

differenceIntensityByEnergy(energy)

Returns the ratio of the intensity between P over S polarizations.

Parameters:

energy (float) – Energy to return intensity for.

Returns:

Ratio of the intensities P / S.

Return type:

float

differencePhaseByDeviation(deviation, deg=False)

Returns the difference of the phase between P and S polarizations.

Parameters:

• deviation (float) – Deviation to return phase for.

• deg (boolean, optional) – if True the phase is converted into degrees. (Default value = False)

Returns:

Different of phase between P and S polarization.

Return type:

float

differencePhaseByEnergy(energy, deg=False)

Returns the difference of phase between P and S polarizations.

Parameters:

• energy (float) – Energy to return phase for.

• deg (boolean, optional) – if True the phase is converted into degrees. (Default deg = False)

Returns:

Phase of the difference between S and P polarization.

Return type:

float

diffractionSetup()

Returns the diffraction setup used for the calculation of these results. :return:

Returns:

The diffraction setup used for the calculation of these results (referenced, not copied).

Return type:

DiffractionSetup instance

energies()

Returns the energies used for these results.

Returns:

Energies used for these results.

Return type:

numpy array

pIntensityByDeviation(deviation)

Returns the intensity of the P polarization.

Parameters:

deviation (float) – Deviation to return intensity for.

Returns:

Intensity of the P polarization.

Return type:

float

pIntensityByEnergy(energy)

Returns the intensity of the P polarization.

Parameters:

energy (float) – Energy for the intensity we are loking for.

Returns:

Intensity of the S polarization.

Return type:

float

pPhaseByDeviation(deviation, deg=False)

Returns the phase of the P polarization.

Parameters:

• deviation (float) – Deviation to return phase for.

• deg (boolean, optional) – if True the phase is converted into degrees. (Default value = False)

Returns:

Phase of the P polarization.

Return type:

float

pPhaseByEnergy(energy, deg=False)

Returns the phase of the P polarization.

Parameters:

• energy (float) – Energy for the phase we are loking for.

• deg (boolean, optional) – if True the phase is converted into degrees. (Default deg = False)

Returns:

Phase of the S polarization.

Return type:

float

sIntensityByDeviation(deviation)

Returns the intensity of the S polarization.

Parameters:

deviation (float) – Deviation to return intensity for.

Returns:

Intensity of the S polarization.

Return type:

float

sIntensityByEnergy(energy)

Returns the intensity of the S polarization.

Parameters:

energy (float) – Energy for the intensity we are loking for.

Returns:

Intensity of the S polarization.

Return type:

float

sPhaseByDeviation(deviation, deg=False)

Returns the phase of the S polarization.

Parameters:

• deviation (float) – Deviation to return phase for.

• deg (boolean, optional) – if True the phase is converted into degrees. (Default value = False)

Returns:

Phase of the S polarization.

Return type:

float

sPhaseByEnergy(energy, deg=False)

Returns the phase of the S polarization.

Parameters:

• energy (float) – Energy for the phase we are loking for.

• deg (boolean, optional) – if True the phase is converted into degrees. (Default deg = False)

Returns:

Phase of the S polarization.

Return type:

float

crystalpy.diffraction.DiffractionSetupAbstract module

Represents a diffraction setup abstract class. The super class should implement the methods to calculate structure factors

class crystalpy.diffraction.DiffractionSetupAbstract.DiffractionSetupAbstract(geometry_type=None, crystal_name='', thickness=1e-06, miller_h=1, miller_k=1, miller_l=1, asymmetry_angle=0.0, azimuthal_angle=0.0, debye_waller=1.0)

Bases: object

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• crystal_name (str) – The name of the crystal, e.g. “Si”.

• thickness (float) – The crystal thickness in m.

• miller_h (int) – Miller index H.

• miller_k (int) – Miller index K.

• miller_l (int) – Miller index L.

• asymmetry_angle (float) – The asymmetry angle between surface normal and Bragg normal (radians).

• azimuthal_angle (float) – The angle between the projection of the Bragg normal on the crystal surface plane and the Y axis (radians). It can also be called inclination angle.

• debye_waller (float) – The Debye-Waller factor exp(-M).

F0(energy=8000.0)

Calculate the structure factor F0.

Parameters:

energy (float) – photon energy in eV. (Default value = 8000.0)

Returns:

F0

Return type:

complex

FH(energy=8000.0)

Calculate the structure factor FH.

Parameters:

energy – photon energy in eV. (Default value = 8000.0)

Returns:

FH

Return type:

complex

FH_bar(energy=8000.0)

Calculate the structure factor FH_bar.

Parameters:

energy – photon energy in eV. (Default value = 8000.0)

Returns:

FH_bar

Return type:

complex

Fall(energy=8000.0)

Calculate the all structure factor (F0, FH, FH_bar).

Parameters:

energy – photon energy in eV. (Default value = 8000.0)

Returns:

(F0, FH, FH_bar).

Return type:

tuple

angleBragg(energy=8000.0)

Returns the Bragg angle for a given energy in radians.

Parameters:

energy – Energy to calculate the Bragg angle for. (Default value = 8000.0)

Returns:

Bragg angle in radians.

Return type:

float

angleBraggCorrected(energy=8000.0, use_exact_equation=True)

Returns the Bragg angle corrected for refraction for a given energy. An approximated formula is found in Zachariasen equation 3.145a. The exact formula is in Guigay % Sanchez del Rio equation 21.

Parameters:

energy (float or numpy array) – Energy in eV for calculating the Bragg angle. (Default value = 8000.0)

Returns:

Bragg angle(s) corrected.

Return type:

float or numpy array

asymmetryAngle()

Returns the asymmetry angle between surface normal and Bragg normal in degrees.

Returns:

Asymmetry angle.

Return type:

float

asymmetryFactor(energy, vector_k_in=None)

Returns asymmetric factor (after Zachariasen equation [3.115]).

Parameters:

• energy (float or numpy array) – The photon energy in eV.

• vector_k_in (Vector instance, optional) – The incident K0 (Default value = None, meaning that K0 is used.)

Return type:

float or numpy array

azimuthalAngle()

Returns the angle between the Bragg normal projection on the crystal surface plane and the x axis in degrees.

Returns:

Azimuthal angle.

Return type:

float

clone()

Returns a copy of this instance.

Returns:

A copy of this instance.

Return type:

DiffractionSetup instance

crystalName()

Returs the crystal name

Returns:

Crystal name.

Return type:

str

dSpacing()

Returns the lattice spacing d in A.

Returns:

Lattice spacing. in A

Return type:

float

dSpacingSI()

Returns the lattice spacing d in SI units (meters).

Returns:

Lattice spacing. in m

Return type:

float

darwinHalfwidth(energy)

Parameters:

energy –

darwinHalfwidthP(energy)

energyfloat or numpy array

Energy in eV for calculating the Bragg angle. (Default value = 8000.0)

Returns:

1/2 of the Darwin width(s) for pi polarization in radians.

Return type:

float or numpy array

darwinHalfwidthS(energy=8000.0)

energyfloat or numpy array

Energy in eV for calculating the Bragg angle. (Default value = 8000.0)

Returns:

1/2 of the Darwin width(s) for sigma polarization in radians.

Return type:

float or numpy array

deviationOfIncomingPhoton(photon_in)

Calculates deviation from the Bragg angle of an incoming photon in radians.

Parameters:

photon_in – Incoming photon.

Returns:

Deviation from Bragg angle in radians.

Return type:

float

duplicate()

Returns a copy of this instance.

Returns:

A copy of this instance.

Return type:

DiffractionSetup instance

geometryType()

Returns the GeometryType, e.g. BraggDiffraction, LaueTransmission,…

Returns:

The GeometryType.

Return type:

instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission.

millerH()

Returns the Miller H index.

Returns:

Miller H index.

Return type:

int

millerK()

Returns the Miller K index.

Returns:

Miller K index.

Return type:

int

millerL()

Returns the Miller L index.

Returns:

Miller L index.

Return type:

int

psi0(energy)

Calculate the structure factor psi0 (defined in Zachariasen [3-95]).

Parameters:

energy – photon energy in eV. (Default value = 8000.0)

Returns:

psi0

Return type:

complex

psiAll(energy1, rel_angle=1.0)

Calculate the psi structure factors (psi0, psiH, psiH_bar) (defined in Zachariasen [3-95]).

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – (Default = 1.0)

Returns:

(psi0, psiH, psiH_bar).

Return type:

tuple

psiH(energy, rel_angle=1.0)

Calculate the structure factor psiH (defined in Zachariasen [3-95]).

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – (Default = 1.0)

Returns:

psiH

Return type:

complex

psiH_bar(energy, rel_angle=1.0)

Calculate the structure factor psiH_bar (defined in Zachariasen [3-95]).

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – (Default = 1.0)

Returns:

psiH_bar

Return type:

complex

thickness()

Returns the crystal thickness in meters

Returns:

he crystal thickness.

Return type:

float

toDictionary()

Returns info of this setup in a dictionary.

Returns:

Info dictionary form of this setup.

Return type:

dict

unitcellVolume()

Returns the unit cell volume in A^3

Returns:

Unit cell volume in A^3.

Return type:

float

unitcellVolumeSI()

Returns the unit cell volume in SI units (m^3)

Returns:

Unit cell volume in m^3.

Return type:

float

vectorH()

Calculates the H vector, normal on the reflection lattice plane, with modulus 2 pi / d_spacing (SI).

The normal to Bragg planes is obtained by rotating vnor an angle equal to minuns asymmetry angle (-alphaXOP) around X using rodrigues rotation (in the screw direction (cw) when looking in the axis direction), and then an angle phi (azimuthal angle) around Z

Returns:

H vector

Return type:

vector instance

References

Sanchez del Rio, M., Perez-Bocanegra, N., Shi, X., Honkimäki, V. & Zhang, L. (2015). Simulation of X-ray diffraction profiles for bent anisotropic crystals. J. Appl. Cryst. 48, 477–491. http://dx.doi.org/10.1107/S1600576715002782

vectorHdirection()

Calculates the unitary vector parallel to the H vector (normal on the reflection lattice plane, with modulus 2 pi / d_spacing (SI)).

The normal to the Bragg planes is obtained by rotating vnor an angle equal to minuns asymmetry angle (-alphaXOP) around X using rodrigues rotation (in the screw direction (cw) when looking in the axis direction), and then an angle phi (azimuthal angle) around Z

Returns:

normal vector in direction of H.

Return type:

Vector instance

vectorIncomingPhotonDirection(energy, deviation, angle_center_flag=2)

Calculates the direction of the incoming photon (or photon stack). Parallel to k_0.

Parameters:

• energy (float of numpy array/) – Energy in eV.

• deviation (float or array.) – Deviation from the uncorrected Bragg angle. A positive deviation means the photon direction lies closer to the surface normal.

• angle_center_flag (int, optional) – Flag from where “deviation: is measured: 0: absolute angle, 1: from Bragg angle corrected for refraction, 2: from Bragg angle.

Returns:

Direction(s) of the incoming photon(s).

Return type:

Vector instance

vectorK0(energy)

Calculates the vector K0(along the Bragg position)

Parameters:

energy (float or numpy array.) – The photon energy in eV.

Returns:

The K0.

Return type:

Vector instance

vectorK0corrected(energy)

Calculates the vector K0corrected (along the corrected Bragg position)

Parameters:

energy (float or numpy array.) – The photon energy in eV.

Returns:

The K0corrected.

Return type:

Vector instance

vectorK0direction(energy)

Calculates the unitary vector parallel to the K0 vector (along the Bragg position)

Parameters:

energy (float or numpy array.) – The photon energy in eV.

Returns:

The normalized vector (or stack of vectors) with the directions of K0.

Return type:

Vector instance

vectorK0directionCorrected(energy)

Calculates the unitary vector parallel to the K0corrected vector (along the Bragg position corrected for refraction)

Parameters:

energy (float or numpy array.) – The photon energy in eV.

Returns:

The normalized vector (or stack of vectors) with the directions of K0corrected.

Return type:

Vector instance

vectorKh(energy)

returns KH that verifies Laue equation with K0

Parameters:

energy (float or numpy array) – The energy or energy array

Returns:

The KH vector or vector stack

Return type:

Vector instance

vectorKhdirection(energy)

returns an unitary vector along the KH direction (that that verifies Laue equation with K0).

Parameters:

energy (float or numpy array) – The energy or energy array

Returns:

The unitary vector(s) along the KH direction(s).

Return type:

Vector instance

vectorKscattered(K_IN=None, energy=8000.0)

returns the scattered K vector following the scattering equation at a surface:

K_parallel = K_IN_parallel + H_parallel |K| = |K_IN|

Parameters:

• K_IN (instance of Vector, optional) – The K vector. If None, used the vectorK0corrected(energy)

• energy (float, optional) – The energy value in eV (used only if K_IN=None)

Returns:

Vector with the scattered K.

Return type:

Vector instance

vectorNormalSurface()

Returns the normal to the surface. (0,0,1) by definition.

Returns:

Vector instance with Surface normal Vnor.

Return type:

Vector instance

vectorNormalSurfaceInwards()

Returns the inwards normal to the surface. -vectorNormalSurface() by definition.

Returns:

Vector instance with inwards surface normal Vnor.

Return type:

Vector instance

vectorParallelSurface()

Returns the direction parallel to the crystal surface. (0,1,0) by definition.

Returns:

Vector instance with Surface normal Vtan.

Return type:

vector instance

crystalpy.diffraction.DiffractionSetupDabax module

Represents a diffraction setup implementation using DABAX photon energy in eV dSpacing returns A units are in SI.

class crystalpy.diffraction.DiffractionSetupDabax.DiffractionSetupDabax(geometry_type=None, crystal_name='', thickness=1e-06, miller_h=1, miller_k=1, miller_l=1, asymmetry_angle=0.0, azimuthal_angle=0.0, crystal_data=None, dabax=None)

Bases: DiffractionSetupAbstract

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• crystal_name (str) – The name of the crystal, e.g. “Si”.

• thickness (float) – The crystal thickness in m.

• miller_h (int) – Miller index H.

• miller_k (int) – Miller index K.

• miller_l (int) – Miller index L.

• asymmetry_angle (float) – The asymmetry angle between surface normal and Bragg normal (radians).

• azimuthal_angle (float) – The angle between the projection of the Bragg normal on the crystal surface plane and the Y axis (radians). It can also be called inclination angle.

• debye_waller (float) – The Debye-Waller factor exp(-M).

• crystal_data (None or dict) – If None, the crystal data is loaded from dabax Crystals.dat file (entry: crystal_name). Alternatively, we can force using a user-structure entered here as a dictionary with the xraylib format.

• dabax (DabaxXraylib instance, optional) – Default : None, use DabaxXraylib()

F0(energy)

Calculate the structure factor F0.

Parameters:

energy (float) – photon energy in eV. (Default value = 8000.0)

Returns:

F0

Return type:

complex

FH(energy, rel_angle=1.0)

Calculate the structure factor FH.

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH

Return type:

complex

FH_bar(energy, rel_angle=1.0)

Calculate the structure factor FH_bar.

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH_bar

Return type:

complex

Fall(energy, rel_angle=1.0)

Calculate the all structure factor (F0, FH, FH_bar).

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

(F0, FH, FH_bar).

Return type:

tuple

angleBragg(energy)

Returns the Bragg angle for a given energy in radians.

Parameters:

energy – Energy to calculate the Bragg angle for. (Default value = 8000.0)

Returns:

Bragg angle in radians.

Return type:

float

dSpacing()

Returns the lattice spacing d in A.

Returns:

Lattice spacing. in A

Return type:

float

unitcellVolume()

Returns the unit cell volume in A^3

Returns:

Unit cell volume in A^3.

Return type:

float

crystalpy.diffraction.DiffractionSetupShadowPreprocessorV1 module

Represents a diffraction setup implementation using material data from shadow bragg preprocessor V1 photon energy in eV dSpacing returns A units are in SI.

class crystalpy.diffraction.DiffractionSetupShadowPreprocessorV1.DiffractionSetupShadowPreprocessorV1(geometry_type=None, crystal_name='', thickness=1e-06, miller_h=1, miller_k=1, miller_l=1, asymmetry_angle=0.0, azimuthal_angle=0.0, preprocessor_file='')

Bases: DiffractionSetupAbstract

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• crystal_name (str) – The name of the crystal, e.g. “Si”.

• thickness (float) – The crystal thickness in m.

• miller_h (int) – Miller index H.

• miller_k (int) – Miller index K.

• miller_l (int) – Miller index L.

• asymmetry_angle (float) – The asymmetry angle between surface normal and Bragg normal (radians).

• azimuthal_angle (float) – The angle between the projection of the Bragg normal on the crystal surface plane and the Y axis (radians). It can also be called inclination angle.

• debye_waller (float) – The Debye-Waller factor exp(-M).

• preprocessor_file (str) – The preprocessor file name.

F0(energy)

Calculate the structure factor F0.

Parameters:

energy (float) – photon energy in eV. (Default value = 8000.0)

Returns:

F0

Return type:

complex

FH(energy, rel_angle=1.0)

Calculate the structure factor FH.

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH

Return type:

complex

FH_bar(energy, rel_angle=1.0)

Calculate the structure factor FH_bar.

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH_bar

Return type:

complex

Fall(energy, rel_angle=1.0)

Calculate the all structure factor (F0, FH, FH_bar).

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

(F0, FH, FH_bar).

Return type:

tuple

angleBragg(energy)

Returns the Bragg angle for a given energy in radians.

Parameters:

energy – Energy to calculate the Bragg angle for. (Default value = 8000.0)

Returns:

Bragg angle in radians.

Return type:

float

dSpacing()

Returns the lattice spacing d in A.

Returns:

Lattice spacing. in A

Return type:

float

structure_factor(energy, ratio)

Calculate the structure factors (F_0, FH, FH_BAR, STRUCT, FA, FB)

Parameters:

• energy (float or numpy array) – The photon energy in eV.

• ratio (float or numpy array) – sin(theta)/lambda

Returns:

(F_0, FH, FH_BAR, STRUCT, FA, FB)

Return type:

tuple

unitcellVolume()

Returns the unit cell volume in A^3

Returns:

Unit cell volume in A^3.

Return type:

float

crystalpy.diffraction.DiffractionSetupShadowPreprocessorV2 module

Represents a diffraction setup implementation using material data from shadow bragg preprocessor V1 photon energy in eV dSpacing returns A units are in SI.

class crystalpy.diffraction.DiffractionSetupShadowPreprocessorV2.DiffractionSetupShadowPreprocessorV2(geometry_type=None, crystal_name='', thickness=1e-06, miller_h=1, miller_k=1, miller_l=1, asymmetry_angle=0.0, azimuthal_angle=0.0, preprocessor_file='')

Bases: DiffractionSetupAbstract

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) – The crystal geometry.

• crystal_name (str, optional) – The name of the crystal, e.g. “Si”.

• thickness (float, optional) – The crystal thickness in m.

• miller_h (int, optional) – Miller index H.

• miller_k (int, optional) – Miller index K.

• miller_l (int, optional) – Miller index L.

• asymmetry_angle (float, optional) – The asymmetry angle between surface normal and Bragg normal (radians).

• azimuthal_angle (float, optional) – The angle between the projection of the Bragg normal on the crystal surface plane and the x axis (radians).

• debye_waller (float, optional) – The Debye-Waller factor exp(-M).

• preprocessor_file (str, optional) – The preprocessor file name.

Return type:

instance of DiffractionSetupShadowPreprocessorV2.

F0(energy)

Calculate the structure factor F0.

Parameters:

energy (float or numpy array) – photon energy in eV. (Default value = 8000.0).

Returns:

F0.

Return type:

complex or numpy array

FH(energy, rel_angle=1.0)

Calculate the structure factor FH.

Parameters:

• energy (float or numpy array) – photon energy in eV.

• rel_angle (float or numpy array, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH.

Return type:

complex or numpy array

FH_bar(energy, rel_angle=1.0)

Calculate the structure factor FH_bar.

Parameters:

• energy (float or numpy array) – photon energy in eV.

• rel_angle (float or numpy array, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0).

Returns:

FH_bar.

Return type:

complex or numpy array

Fall(energy, rel_angle=1.0)

Calculate the all structure factor (F0, FH, FH_bar).

Parameters:

• energy (float or numpy array) – photon energy in eV.

• rel_angle (float or numpy array, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0).

Returns:

(F0, FH, FH_bar).

Return type:

tuple

angleBragg(energy)

Returns the Bragg angle for a given energy in radians.

Parameters:

energy (float or numpy array) – Energy to calculate the Bragg angle for. (Default value = 8000.0).

Returns:

Bragg angle in radians.

Return type:

float or numpy array

dSpacing()

Returns the lattice spacing d in A.

Returns:

Lattice spacing in A.

Return type:

float

unitcellVolume()

Returns the unit cell volume in A^3

Returns:

Unit cell volume in A^3.

Return type:

float

crystalpy.diffraction.DiffractionSetupShadowPreprocessorV2.crystal_fh(input_dictionary, phot_in, theta=None, forceratio=0)

Computes the structure factors and other parameters for a given photon energy (or array).

Parameters:

• input_dictionary (dict) – as resulting from bragg_calc().

• phot_in (float or numpy array) – photon energy in eV.

• theta (float or numpy array, optional) – incident angle (half of scattering angle) in rad (Default value = None).

• forceratio (int, float or numpy array, optional) – Value of sin(theta)/lambda to be used when calculating F0. By default, forceratio=0, it means that this ratio is automatically calculated used the Bragg angle.

Returns:

return {“PHOT”:phot, “WAVELENGTH”:r_lam0*1e-2 ,”THETA”:itheta, “F_0”:F_0, “FH”:FH, “FH_BAR”:FH_BAR, “STRUCT”:STRUCT, “psi_0”:psi_0, “psi_h”:psi_h, “psi_hbar”:psi_hbar, “DELTA_REF”:DELTA_REF, “REFRAC”:REFRAC, “ABSORP”:ABSORP, “RATIO”:ratio, “ssr”:ssr, “spr”:spr, “psi_over_f”:psi_over_f, “info”:txt}.

Return type:

dict

crystalpy.diffraction.DiffractionSetupSweeps module

Represents a diffraction setup (from where it inherits) and includes a photon beam with scanning photon energy and deviation angle (scattering plane is YZ plane)

Units are in SI except for photon energy in eV. Angles in radians.

class crystalpy.diffraction.DiffractionSetupSweeps.DiffractionSetupSweeps(geometry_type, crystal_name, thickness, miller_h, miller_k, miller_l, asymmetry_angle, azimuthal_angle, energy_min, energy_max, energy_points, angle_deviation_min, angle_deviation_max, angle_deviation_points)

Bases: DiffractionSetupXraylib

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• crystal_name (str) – The name of the crystal, e.g. “Si”.

• thickness (float) – The crystal thickness in m.

• miller_h (int) – Miller index H.

• miller_k (int) – Miller index K.

• miller_l (int) – Miller index L.

• asymmetry_angle (float) – The asymmetry angle between surface normal and Bragg normal (radians).

• azimuthal_angle (float) – The angle between the projection of the Bragg normal on the crystal surface plane and the Y axis (radians). It can also be called the inclination angle.

• energy_min (float) – The minimum energy in eV.

• energy_max (float) – The maximum energy in eV.

• energy_points (int) – Number of energy points.

• angle_deviation_min (float) – Minimal angle deviation in rad.

• angle_deviation_max (float) – Maximal angle in rad.

• angle_deviation_points (int) – Number of deviations points.

angleDeviationGrid()

Returns the grid of angle deviations according to this setup. :return: The angle deviations grid.

angleDeviationMax()

Returns the maximal angle deviation. :return: Maximal angle deviation.

angleDeviationMin()

Returns the minimal angle deviation. :return: Minimal angle deviation.

angleDeviationPoints()

Returns the angle deviation points. :return: Angle deviation points.

energies()

Returns the energies of this setup. :return: The angle deviations grid.

energyMax()

Returns the maximum energy in eV. :return: The maximum energy in eV.

energyMin()

Returns the minimum energy in eV. :return: The minimum energy in eV.

energyPoints()

Returns the number of energy points. :return: Number of energy points.

incomingPhotons()

Returns the incoming photons. :return: A list of photons.

toDictionary()

Returns this setup in InfoDictionary form. :return: InfoDictionary form of this setup.

crystalpy.diffraction.DiffractionSetupXraylib module

Represents a diffraction setup implementation using xraylib photon energy in eV dSpacing returns A units are in SI.

class crystalpy.diffraction.DiffractionSetupXraylib.DiffractionSetupXraylib(geometry_type=None, crystal_name='', thickness=1e-06, miller_h=1, miller_k=1, miller_l=1, asymmetry_angle=0.0, azimuthal_angle=0.0, crystal_data=None)

Bases: DiffractionSetupAbstract

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• crystal_name (str) – The name of the crystal, e.g. “Si”.

• thickness (float) – The crystal thickness in m.

• miller_h (int) – Miller index H.

• miller_k (int) – Miller index K.

• miller_l (int) – Miller index L.

• asymmetry_angle (float) – The asymmetry angle between surface normal and Bragg normal (radians).

• azimuthal_angle (float) – The angle between the projection of the Bragg normal on the crystal surface plane and the Y axis (radians). It can also be called inclination angle.

• crystal_data (None or dict) – If None, the crystal data is loaded from xraylib (entry: crystal_name). Alternatively, we can force using a user-structure entered here as a dictionary with the xraylib format.

• debye_waller (float) – The Debye-Waller factor exp(-M).

F0(energy)

Calculate the structure factor F0.

Parameters:

energy (float) – photon energy in eV. (Default value = 8000.0)

Returns:

F0

Return type:

complex

FH(energy, rel_angle=1.0)

Calculate the structure factor FH.

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH

Return type:

complex

FH_bar(energy, rel_angle=1.0)

Calculate the structure factor FH_bar.

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

FH_bar

Return type:

complex

Fall(energy, rel_angle=1.0)

Calculate the all structure factor (F0, FH, FH_bar).

Parameters:

• energy – photon energy in eV. (Default value = 8000.0)

• rel_angle (float, optional) – ratio of the incident angle and the Bragg angle (Default : rel_angle=1.0)

Returns:

(F0, FH, FH_bar).

Return type:

tuple

angleBragg(energy)

Returns the Bragg angle for a given energy in radians.

Parameters:

energy – Energy to calculate the Bragg angle for. (Default value = 8000.0)

Returns:

Bragg angle in radians.

Return type:

float

dSpacing()

Returns the lattice spacing d in A.

Returns:

Lattice spacing. in A

Return type:

float

unitcellVolume()

Returns the unit cell volume in A^3

Returns:

Unit cell volume in A^3.

Return type:

float

crystalpy.diffraction.GeometryType module

Represents geometry types/setups: Bragg diffraction, BraggTransmission, Laue diffraction, Laue transmission.

class crystalpy.diffraction.GeometryType.BraggDiffraction

Bases: GeometryType

Represents Bragg diffraction.

class crystalpy.diffraction.GeometryType.BraggTransmission

Bases: GeometryType

Represents Bragg transmission.

class crystalpy.diffraction.GeometryType.GeometryType(description)

Bases: object

Constructor.

Parameters:

description – Description of the geometry type, e.g. “Bragg transmission”

static allGeometryTypes()

Returns all possible geometry types. :return: All possible geometry types.

description()

Returns the description of this geometry type. :return: Description of this geometry type.

class crystalpy.diffraction.GeometryType.LaueDiffraction

Bases: GeometryType

Represents Laue diffraction.

class crystalpy.diffraction.GeometryType.LaueTransmission

Bases: GeometryType

Represents Laue transmission.

crystalpy.diffraction.PerfectCrystalDiffraction module

Calculates crystal diffraction according to Guigay and Zachariasen formalisms of the dynamic theory of crystal diffraction for perfect crystals. Except for energy all units are in SI. Energy is in eV.

class crystalpy.diffraction.PerfectCrystalDiffraction.PerfectCrystalDiffraction(geometry_type, bragg_normal, surface_normal, bragg_angle, psi_0, psi_H, psi_H_bar, thickness, d_spacing, calculation_strategy_flag)

Bases: object

PerfectCrystalDiffraction is the calculator of the perfect crystal.

Two steps: * create the PerfectCrystalDiffraction instance with the crystal data (usually picked up from DiffractionSetup). * call PerfectCrystalDiffraction.calculateDiffraction( photon(s) )

Notes: * arrays can be used, but compatible arrays in photons and in bragg_angle, psi_0, psi_H, psi_H, etc. * Both sigma and pi amplitudes can be calculated in the same call, not need to create different

instances for sigma and pi.

Constructor.

Parameters:

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• bragg_normal (instance of Vector) – The H vector.

• surface_normal (instance of Vector) – The n vector.

• bragg_angle (float or numpy array) – The Bragg angle(s).

• psi_0 (complex of numpy array) – The structire factor Psi0.

• psi_H (complex of numpy array) – The structire factor PsiH.

• psi_H_bar (complex of numpy array) – The structire factor Psi(-H).

• thickness (float) – the crystal thickness in m.

• d_spacing (float) – the crystal dSpacing in m.

• calculation_strategy_flag (int) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Psi0()

Returns Psi0 as defined in Zachariasen [3-95].

Returns:

The Psi0 value.

Return type:

complex or numpy array

PsiH()

Returns PsiH as defined in Zachariasen [3-95].

Returns:

The PsiH value.

Return type:

complex or numpy array

PsiHBar()

Returns PsiHBar as defined in Zachariasen [3-95].

Returns:

The PsiHBar value.

Return type:

complex or numpy array

braggAngle()

Returns the Bragg angle.

Returns:

The Bragg angle in rad.

Return type:

float or numpy array

braggNormal()

Returns the Bragg normal, i.e. normal on the reflection planes with modulus 2 pi / d_spacing.

Returns:

The H vector (normal to Bragg planes, modulus 2 pi / d_spacing in m^-1))

Return type:

instance of Vector

calculateDiffraction(photon_in, calculation_method=0, is_thick=0, use_transfer_matrix=0)

Calculate diffraction for incoming photon.

Parameters:

• photon_in (instance of ComplexAmplitudePhoton) – Incoming photon or Photon bunch.

• calculation_method (int) – 0 : Zachariasen, 1 : Guigay

• is_thick (int) – 0=No, 1=Yes (for calculation_method=1 only)

• use_transfer_matrix (int) – 0=No, 1=Yes (for calculation_method=1 only)

Returns:

The complex amplitudes of the diffraction weighted for power for the two polarizations are found in the kwys [“S”] and [“P”].

Return type:

dict

calculateDiffractionGuigay(photon_in, debug=0, s_ratio=None, is_thick=0, use_transfer_matrix=0)

Calculate diffraction for incoming photon.

Parameters:

• photon_in (instance of ComplexAmplitudePhoton) – Incoming photon or photon bunch.

• debug (int) – 0=No, 1=Yes.

• s_ratio (float) – the sin(theta)/lambda ratio (if None (default) it is calculated from Bragg law).

• is_thick (int) – 0=No, 1=Yes.

• use_transfer_matrix (int) – 0=No, 1=Yes. It is is faster to use use_transfer_matrix=0.

Returns:

The complex amplitudes of the diffraction weighted for power for the two polarizations are found in the kwys [“S”] and [“P”]. If use_transfer_matrix=1, other optional parameters are found at the keys: * sigma-polarized reflectivity: “s” * pi-polarized reflectivity: “p” * Transfer matrix: “m11_s” “m12_s” “m21_s” “m22_s” “m11_p” “m12_p” “m21_p” “m22_p” * Scattering matrix: “s11_s” “s12_s” “s21_s” “s22_s” “s11_p” “s12_p” “s21_p” “s22_p” * “gamma_0” * “alpha” * “b”

Return type:

dict

calculateDiffractionZachariasen(photon_in)

Calculate diffraction for incoming photon.

Parameters:

photon_in (instance of ComplexAmplitudePhoton) – Incoming photon or photon bunch.

Returns:

The complex amplitudes of the diffraction weighted for power for the two polarizations are found in the kwys [“S”] and [“P”].

Return type:

dict

calculatePhotonOut(photon_in, method=1, apply_reflectivity=False, calculation_method=0, is_thick=0, use_transfer_matrix=0)

Solves the scattering equation to calculates the outgoing photon from the incoming photon and the Bragg normal.

In case of diffracted photon (Laue or Bragg) 1) Calculates the parallel component of K: k_out_par = k_in_par + H_par 2) Uses the conservation of the wavevector modulus to calculate the k_out_perp

todo: In case of forward diffracted (transmitted) Bragg or Laue:

It is valid for diffraction not at the Bragg angle.

Warning

Note that the new photon has correct direction, but the complex amplitudes are not changed, just copied from the photon in.

Parameters:

• photon_in (instance of ComplexAmplitudePhoton) – Incoming photon or photon bunch.

• method (int) – select the calculated method: 0=old (to be deleted), 1=new

Returns:

Outgoing photon or photon bunch

Return type:

instance of ComplexAmplitudePhoton

calculateScatteringMatrix(photon_in, polarization=0, alpha=None, guigay_b=None, T=None)

Calculates the terms of the scattering matrix (see equation XXX in Guigay and Sanchez del Rio). :param photon_in: Incoming photon or photon bunch. :type photon_in: instance of ComplexAmplitudePhoton :param polarization: 0=sigma, 1=pi. :type polarization: int :param is_thick: Use thick crystal approximation: 0=No, 1=Yes. :type is_thick: int :param alpha: The alpha value (if None, it is internally calculated). :type alpha: float or numpy array :param guigay_b: The b (asymmetry factor) value (if None, it is internally calculated). :type guigay_b: float or numpy array :param T: The T (thickness along s0) value (if None, it is internally calculated). :type T: float or numpy array

Returns:

the terms of the scattering matrix: (s11, s12, s21, s22).

Return type:

tuple

classmethod calculateScatteringMatrixFromTransferMatrix(transfer_matrix)

Calculate the scattering matrix from the known transfer matrix (see equation XXX in Guigay and Sanchez del Rio).

Parameters:

transfer_matrix (tuple) – the terms of the transfer matrix: (m11, m12, m21, m22).

Returns:

the terms of the scattering matrix: (s11, s12, s21, s22).

Return type:

tuple

calculateTransferMatrix(photon_in, polarization=0, is_thick=0, alpha=None, guigay_b=None, T=None)

Calculates the transfer matrix (see equation XXX in Guigay and Sanchez del Rio).

Parameters:

• photon_in (instance of ComplexAmplitudePhoton) – Incoming photon or photon bunch.

• polarization (int) – 0=sigma, 1=pi.

• is_thick (int) – Use thick crystal approximation: 0=No, 1=Yes.

• alpha (float or numpy array) – The alpha value (if None, it is internally calculated).

• guigay_b (float or numpy array) – The b (asymmetry factor) value (if None, it is internally calculated).

• T (float or numpy array) – The T (thickness along s0) value (if None, it is internally calculated).

Returns:

the terms of the transfer matrix: (m11, m12, m21, m22).

Return type:

tuple

dSpacing()

Returns the distance between the reflection planes in A.

Returns:

Distance between the reflection planes in A.

Return type:

float or numpy array

geometryType()

Returns the geometry types, i.e. BraggTransmission, LaueDiffraction,…

Returns:

geometry_type

Return type:

instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission

classmethod initializeFromDiffractionSetupAndEnergy(diffraction_setup, energy, geometry_type=None, bragg_normal=None, surface_normal=None, thickness=None, d_spacing=None, calculation_strategy_flag=0)

Creates a PerfectCrystalDiffraction instance from parameters in a DiffractionSetupAbstract instance and a photon energy array.

Parameters:

• diffraction_setup (instance of PerfectCrystalDiffraction) –

• energy (numpy array) –

• geometry_type (instance of BraggDiffraction, LaueDiffraction, BraggTransmission, or LaueTransmission) –

• bragg_normal (instance of Vector, optional) – if None, retrieve from DiffractionSetup

• surface_normal (instance of Vector, optional) – if None, retrieve from DiffractionSetup

• thickness (float or numpy array, optional) – crystal thickness in m. If None, retrieve from DiffractionSetup

• d_spacing (float or numpy array) – d-spacing in m. If None, retrieve from DiffractionSetup

• calculation_strategy_flag (int, optional) – For computing exp, sin, cos: 0: use mpmath, 1: use numpy, 2=use numpy truncated.

Return type:

PerfectCrystalDiffraction instance

isDebug = False

log(string)

Logs (prints) a string.

Parameters:

string – String to log.

logDebug(string)

Logs (prints) a debug string.

Parameters:

string – String to log.

surfaceNormal()

Returns the surface normal that points outwards the crystal.

Returns:

The normal to the surface.

Return type:

instance of Vector

surfaceNormalInwards()

Returns the surface normal that points inwards the crystal.

Returns:

The normal to the surface.

Return type:

instance of Vector

thickness()

Returns crystal thickness.

Returns:

The thickness of the crystal in m.

Return type:

float or numpy array

Module contents