`Sample`

class nexus.Sample(layers, geometry='f', angle=0.0, length=10, roughness='a', effective_thickness=0.3, drive_detuning=[], function_time=None, divergence=0.0, id='')

Bases: NxObject

Constructor for Sample.

Parameters:

layers (list) – List of Layer in order of beam propagation.
geomerty (string) –
Scattering geometry of the sample.
- f - forward scattering
- r - reflection in grazing incidence scattering
- t - transmission in grazing incidence scattering
angle (float or Var) – Angle of incidence for grazing geometry (degree).
length (float) – length of the sample along beam direction. Only used for grazing geometry.
roughness (string) –
Roughness model in grazing geometry.
- n - no roughness
- a - analytical model
- e - effective density model
effective_thickness (float) – Layer thickness in the effective density model (nm).
drive_detuning (list or ndarray) – Detuning values for a sample on a Moessbauer drive.
function_time (FunctionTime) – A FunctionTime implementation of the user to describe sample motion. Must return the phase factor \(\phi(t) = k x(t)\), where \(k\) is the photon wave vector along beam direction and \(x(t)\) the sample motion along the beam propagation direction.
divergence (float or Var) – Divergence of the incidence angle given as the FWHM of the divergence (deg).
id (string) – User identifier.

layers

List of Layer in order of beam propagation.

Type:: list

geometry

Scattering geometry of the sample.

f - forward scattering
r - reflection in grazing incidence scattering
t - transmission in grazing incidence scattering

Type:: string

angle

Angle of incidence for grazing geometry (degree).

Type:: float or Var

length

length of the sample along beam direction. Only used for grazing geometry.

Type:: float

roughness

Roughness model in grazing geometry.

n - no roughness
a - analytical model
e - effective density model

Type:: string

effective_thickness

Layer thickness in the effective density model (nm).

Type:: float

drive_detuning

Detuning values for a sample on a Moessbauer drive.

Type:: list or ndarray

function_time

A FunctionTime implementation of the user to describe sample motion. Must return the phase factor \(\phi(t) = k x(t)\), where \(k\) is the photon wave vector along beam direction and \(x(t)\) the sample motion along the beam propagation direction.

Type:: FunctionTime

divergence

Divergence of the incidence angle given as the FWHM of the divergence (deg).

Type:: float or Var

id

User identifier.

Type:: string

effective_coordinates

Layer coordinates in the effective density model.

Type:: list

effective_layers

List of EffectiveLayer objects.

Type:: list

ClearLayers(): Clear the layers list.

EffectiveLayerSystem(eff_layer_thickness, nuclear)

Create an effective density model from the sample. Electronic scattering factors and matrices are always calculated.

Parameters:

eff_layer_thickness (float) – Layer thickness in the effective density model.
nuclear (bool) – Calculate the matrices for nuclear scattering in addition to the electronic ones.

ElectronicAmplitude(energy)

Calculates the relative electronic amplitude behind the sample. It is given by the product of the complex transmission or layer matrices of the sample layers. The geometry is determined from the geometry.

Parameters:: energy (float) – X-ray energy (eV)
Returns:: Electronic amplitude.
Return type:: complex

ElectronicAmplitudeMatrix(energy)

Calculates the relative electronic amplitude matrix behind the sample. It is given by the product of the complex transmission or layer matrices of the sample layers. The geometry is determined from the geometry.

Parameters:: energy (float) – X-ray energy (eV)
Returns:: Electronic amplitude.
Return type:: complex

ElectronicFieldAmplitude(energy, num_points=101, angle=0.0)

Calculates the electronic X-ray field amplitude in the sample.

Parameters:

energy (float) – X-ray energy (eV).
num_points (int) – Number of points of the output.
angle (float) – Incidence angle in grazing incidence geometry.

Returns:

Electronic field amplitude in the sample.

Return type:

complex

ElectronicFieldIntensity(energy, num_points=101, angle=0.0)

Calculates the electronic X-ray field intensity in the sample.

Parameters:

energy (float) – X-ray energy (eV).
num_points (int) – Number of points of the output.

Returns:

Electronic field intensity.

Return type:

float

ElectronicForwardAmplitude(energy)

Calculates the electronic amplitude behind the sample in forward geometry .

Parameters:: energy (float) – X-ray energy (eV).
Returns:: Forward amplitude.
Return type:: complex

ElectronicForwardTransmission(energy)

Calculates the electronic transmission behind the sample in forward geometry .

Parameters:: energy (float) – X-ray energy (eV).
Returns:: Forward transmission.
Return type:: float

ElectronicGrazingReflectivity(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the reflectivity intensity of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – Thickness of the layers in the effective layer model (e).

Returns:

Reflectivity.

Return type:

float

ElectronicGrazingReflectivityAmplitude(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the complex reflectivity amplitude of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex reflectivity amplitude.

Return type:

complex

ElectronicGrazingSampleMatrix(*args)

Overload 1:

Calculates the electronic 2x2 sample matrix in grazing incidence geometry. It is the product of all layer matrices.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex 2x2 matrix.

Return type:

ndarray

Overload 2:

Calculates the electronic 2x2 sample matrix up to a certain sample thickness in grazing incidence geometry. It is the product of all layer matrices up to this thickness.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
thickness (float) – Thickness at which the sample matrix should be calculated (nm).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex 2x2 matrix.

Return type:

ndarray

ElectronicGrazingTransmission(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the transmission intensity of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – Thickness of the layers in the effective layer model (e).

Returns:

Transmission.

Return type:

float

ElectronicGrazingTransmissionAmplitude(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the complex transmission amplitude of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex reflectivity amplitude.

Return type:

complex

ElectronicTransmission(energy)

Calculates the relative electronic transmission behind the sample. It is given by the product of the complex transmission or layer matrices of the sample layers. The geometry is determined from the geometry.

Parameters:: energy (float) – X-ray energy (eV)
Returns:: Electronic transmission.
Return type:: float

ForwardEffectiveThickness()

Returns the effective thickness \(t_{eff} = \sigma \sum_i \rho_{i} f^{LM}_i t_i\) of the sample in forward geometry, where \(\sigma\) is the nuclear cross section, \(\rho_{i}\) is the number density of the resonant nuclei in the i-th layer, \(f^{LM}_i\) is the Lamb Moessbauer factor of the i-th layer, \(t_i\) is the thickness of the layer i-th layer.

Returns:: Effective thickness.
Return type:: double

Ids()

List with all layer id of the sample.

Returns:: Layers ids.
Return type:: list

Interfaces()

A list with the positions of the layer interfaces.

Returns:: Position of the Layer interfaces.
Return type:: list

KzSigma(energy, angle_kz)

Calculates the product \(k_z \sigma\) for each layer in the sample. The product should be << 1 for the validity of the W matrix calculation.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence angle (deg).

Returns:

List of \(k_z \sigma\) values for each layer.

Return type:

list

LayerCenters()

A list with the center coordinates of all layers in the sample.

Returns:: Position of the Layer centers.
Return type:: list

LayerPointers()

Returns a list of all layer pointers. Useful in order to check if layers have the same reference.

Returns:: List of layer pointers
Return type:: list

ObjectMatrix(isotope, detuning, calc_transitions)

Calculates the detuning-dependent complex 2x2 object matrix.

Parameters:

isotope (MoessbauerIsotope) – Moessbauer isotope of the experiment.
detuning (list or ndarray) – n-dimensional array with detuning values.
calc_transitions (bool) – Set to True for calculations of the nuclear transitions in the object.

Returns:

List of complex 2x2 matrices.

Return type:

list

PrintLayerPointers()

Print the pointer of each Layer. Useful in order to check if layers have the same reference.

Returns:: Prints the layer pointers to the output

SampleMatrix(*args)

Calculates the sample matrix - the product of all layer matrices in the given sample geometry. Same as the ObjectMatrix.

Parameters:

isotope (MoessbauerIsotope) – Moessbauer isotope.
detuning (list or ndarray) – Detuning values of the calculation.
angle (float) – Angle in grazing geometry (degree).
calc_roughness (string) –
Calculation mode for roughness.

n - no roughness a - analytical model e - effective density model
eff_layer_thickness (float) – Layer thickness for the effective density model (nm).
calc_transitions (bool) – Specifies if the nuclear transitions should be updated or not. Set this value to True.

Returns:

List of complex 2x2 matrices.

Return type:

list

TotalThickness()

Calculates the total thickness of the sample.

Returns:: Total thickness of the sample (nm).
Return type:: float

TotalThicknessEffective()

Total thickness of the sample in the effective density model.

Returns:: Total thickness in the effective density model.
Return type:: float

nexus.Air(length, id='')

Creates a Sample type of air.

Parameters:

length (float) – length of the air distance in meter.
id (string) – optional string identifier.

Returns:

Sample object with material air.

Return type:

Sample

class nexus.SimpleSample(thickness, composition, density, isotope=None, abundance=0.0, lamb_moessbauer=0.0, hyperfine_sites=[], id='')

Bases: Sample

Creates a Sample with only one layer and material. All needed instances are created automatically. The layer and material parameters can be assigned directly via the SimpleSample attributes.

New in version 1.0.4.

Parameters:

thickness (float or Var) – Thickness of the layer (nm).
composition (list) – Composition of the material in the format [[“element symbol” (string), relative atomic fraction (float)] , … ].
density (float or Var) – Density (g/cm ³).
isotope (MoessbauerIsotope) – Moessbauer isotope.
abundance (float or Var) – Isotope abundance (0 to 1).
lamb_moessbauer (float or Var) – Lamb Moessbauer factor (0 to 1).
hyperfine_sites (list) – List of Hyperfine sites assigned to the material.
id (string) – user identifier.

thickness

Thickness of the layer (nm).

Type:: float or Var

composition

Composition of the material in the format [[“element symbol” (string), relative atomic fraction (float)] , … ].

Type:: list

density

Density (g/cm ³).

Type:: float or Var

isotope

Moessbauer isotope.

Type:: MoessbauerIsotope

abundance

Isotope abundance (0 to 1).

Type:: float or Var

lamb_moessbauer

Lamb Moessbauer factor (0 to 1).

Type:: float or Var

hyperfine_sites

List of Hyperfine sites assigned to the material.

Type:: list

id

user identifier.

Type:: string

layer

Layer instance of the SimpleSample.

Type:: Layer

material

Material instance of the SimpleSample.

Type:: Material

Returns:: Sample object.
Return type:: Sample

ClearLayers(): Clear the layers list.

EffectiveLayerSystem(eff_layer_thickness, nuclear)

Create an effective density model from the sample. Electronic scattering factors and matrices are always calculated.

Parameters:

eff_layer_thickness (float) – Layer thickness in the effective density model.
nuclear (bool) – Calculate the matrices for nuclear scattering in addition to the electronic ones.

ElectronicAmplitude(energy)

Calculates the relative electronic amplitude behind the sample. It is given by the product of the complex transmission or layer matrices of the sample layers. The geometry is determined from the geometry.

Parameters:: energy (float) – X-ray energy (eV)
Returns:: Electronic amplitude.
Return type:: complex

ElectronicAmplitudeMatrix(energy)

Calculates the relative electronic amplitude matrix behind the sample. It is given by the product of the complex transmission or layer matrices of the sample layers. The geometry is determined from the geometry.

Parameters:: energy (float) – X-ray energy (eV)
Returns:: Electronic amplitude.
Return type:: complex

ElectronicFieldAmplitude(energy, num_points=101, angle=0.0)

Calculates the electronic X-ray field amplitude in the sample.

Parameters:

energy (float) – X-ray energy (eV).
num_points (int) – Number of points of the output.
angle (float) – Incidence angle in grazing incidence geometry.

Returns:

Electronic field amplitude in the sample.

Return type:

complex

ElectronicFieldIntensity(energy, num_points=101, angle=0.0)

Calculates the electronic X-ray field intensity in the sample.

Parameters:

energy (float) – X-ray energy (eV).
num_points (int) – Number of points of the output.

Returns:

Electronic field intensity.

Return type:

float

ElectronicForwardAmplitude(energy)

Calculates the electronic amplitude behind the sample in forward geometry .

Parameters:: energy (float) – X-ray energy (eV).
Returns:: Forward amplitude.
Return type:: complex

ElectronicForwardTransmission(energy)

Calculates the electronic transmission behind the sample in forward geometry .

Parameters:: energy (float) – X-ray energy (eV).
Returns:: Forward transmission.
Return type:: float

ElectronicGrazingReflectivity(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the reflectivity intensity of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – Thickness of the layers in the effective layer model (e).

Returns:

Reflectivity.

Return type:

float

ElectronicGrazingReflectivityAmplitude(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the complex reflectivity amplitude of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex reflectivity amplitude.

Return type:

complex

ElectronicGrazingSampleMatrix(*args)

Overload 1:

Calculates the electronic 2x2 sample matrix in grazing incidence geometry. It is the product of all layer matrices.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex 2x2 matrix.

Return type:

ndarray

Overload 2:

Calculates the electronic 2x2 sample matrix up to a certain sample thickness in grazing incidence geometry. It is the product of all layer matrices up to this thickness.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
thickness (float) – Thickness at which the sample matrix should be calculated (nm).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex 2x2 matrix.

Return type:

ndarray

ElectronicGrazingTransmission(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the transmission intensity of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – Thickness of the layers in the effective layer model (e).

Returns:

Transmission.

Return type:

float

ElectronicGrazingTransmissionAmplitude(energy, angle, calc_roughness, eff_layer_thickness)

Calculates the complex transmission amplitude of the sample in grazing incidence geometry.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence-angle of the sample (degree).
calc_roughness (string) – Assumed roughness model, either n, a, e.
eff_layer_thickness (float) – thickness of the layers in the effective layer model (e).

Returns:

Complex reflectivity amplitude.

Return type:

complex

ElectronicTransmission(energy)

Calculates the relative electronic transmission behind the sample. It is given by the product of the complex transmission or layer matrices of the sample layers. The geometry is determined from the geometry.

Parameters:: energy (float) – X-ray energy (eV)
Returns:: Electronic transmission.
Return type:: float

ForwardEffectiveThickness()

Returns the effective thickness \(t_{eff} = \sigma \sum_i \rho_{i} f^{LM}_i t_i\) of the sample in forward geometry, where \(\sigma\) is the nuclear cross section, \(\rho_{i}\) is the number density of the resonant nuclei in the i-th layer, \(f^{LM}_i\) is the Lamb Moessbauer factor of the i-th layer, \(t_i\) is the thickness of the layer i-th layer.

Returns:: Effective thickness.
Return type:: double

Ids()

List with all layer id of the sample.

Returns:: Layers ids.
Return type:: list

Interfaces()

A list with the positions of the layer interfaces.

Returns:: Position of the Layer interfaces.
Return type:: list

KzSigma(energy, angle_kz)

Calculates the product \(k_z \sigma\) for each layer in the sample. The product should be << 1 for the validity of the W matrix calculation.

Parameters:

energy (float) – X-ray energy (eV).
angle (float) – Incidence angle (deg).

Returns:

List of \(k_z \sigma\) values for each layer.

Return type:

list

LayerCenters()

A list with the center coordinates of all layers in the sample.

Returns:: Position of the Layer centers.
Return type:: list

LayerPointers()

Returns a list of all layer pointers. Useful in order to check if layers have the same reference.

Returns:: List of layer pointers
Return type:: list

ObjectMatrix(isotope, detuning, calc_transitions)

Calculates the detuning-dependent complex 2x2 object matrix.

Parameters:

isotope (MoessbauerIsotope) – Moessbauer isotope of the experiment.
detuning (list or ndarray) – n-dimensional array with detuning values.
calc_transitions (bool) – Set to True for calculations of the nuclear transitions in the object.

Returns:

List of complex 2x2 matrices.

Return type:

list

PrintLayerPointers()

Print the pointer of each Layer. Useful in order to check if layers have the same reference.

Returns:: Prints the layer pointers to the output

SampleMatrix(*args)

Calculates the sample matrix - the product of all layer matrices in the given sample geometry. Same as the ObjectMatrix.

Parameters:

isotope (MoessbauerIsotope) – Moessbauer isotope.
detuning (list or ndarray) – Detuning values of the calculation.
angle (float) – Angle in grazing geometry (degree).
calc_roughness (string) –
Calculation mode for roughness.

n - no roughness a - analytical model e - effective density model
eff_layer_thickness (float) – Layer thickness for the effective density model (nm).
calc_transitions (bool) – Specifies if the nuclear transitions should be updated or not. Set this value to True.

Returns:

List of complex 2x2 matrices.

Return type:

list

TotalThickness()

Calculates the total thickness of the sample.

Returns:: Total thickness of the sample (nm).
Return type:: float

TotalThicknessEffective()

Total thickness of the sample in the effective density model.

Returns:: Total thickness in the effective density model.
Return type:: float

Sample

`Sample`