VITESS Modules to simulate Neutron Scattering in Samples

There are 8 VITESS modules to simulate scattering of neutrons in samples:
sample_elasticisotr can be used to simulate isotropic scattering
sample_sans is meant for samples in SANS measurements, but also allows isotropic scattering.
sample_s_q assuming any function S(Q) is more general.
sample_reflectom is used for reflectometer samples.
sample_powder or sample_nxs can be used for powder samples.
sample_singcryst simulates scattering of a single crystal.
sample_inelast is used for inelastic virtual experiments.
sample_ncrystal is used for virtual experiments leveraging the Ncrystal sample database.

In all cases, parameters of both the sample (position, size, ...) and the scattering have to be given, partly in files. Usually, input is expected in form of tables showing scattering cross-sections or reflectivities as a function of momentum transfer or d-spacing. However, the modules sample_sans, sample_s_q and sample_nxs can do the calculation themselves.

In VITESS 3.n, the parameter input is separated between direct input parameters that are given on the main window ('Parameters for module sample_environment') and others that are stored in a file ('File input parameters'). In VITESS 4.n, all parameters can be given as direct input parameters, but using the file is still possible. If a parameter is given in both ways, the direct input parameter will be used.

While neutron transport is treated classically in VITESS, the scattering process is treated using quantum mechanics.

VITESS Module 'sample_elasticisotr' for isotropic scattering

This module simulates a sample scattering isotropically and elasticly (conforming to a delta-function at energy 0), which can have the following geometries: cuboid, sphere, cylinder or hollow cylinder.

The probability weight P provided by the former module is multiplied by the following factors:

P' = P x (1 - exp(- μ_s d)) x Attenuation x solid_angle/4π,

where μ_s = σ_s ρ is the macroscopic scattering coefficient [cm^-1], i.e. the scattering cross section σ multiplied by the particle density ρ. Attenuation means a wavelength and path length (before and after the scattering) dependent exponential factor: exp(-(μ_abs x pathlength)), where μ_abs ~ λ. And the usual tabulated value for 1.798 Å has to be converted to 1 Å in order to calculate the input value absorption coeff..
Note that there is currently no beam of unscattered neutrons - even if the scattering probability is low.

The sample structure is considered as homogeneous and absorbent. The geometrical parameters of the sample are: position, horizontal and vertical offset angles with reference to the final coordinate system of the antecedent module, and size of the sample.

Detailed parameter definitions can be read from the tables in section A.

In the output frame X'Y'Z', all neutron coordinates are referring to the moment when the neutrons are just crossing the sample walls after the scattering . Multiple scattering is not yet included. The effect of sample size and geometry on the scattered intensity can be calculated by calibration taking into account that I / I' = V/V' (V - illuminated sample volume).

Main parameters

File Input Parameters

Example for hollow cylinder V sample:

VITESS Module 'sample_sans' for SANS measurement

The module sample_sans describes small angle scattering at monodispers hard particles. The coordinate system of an incoming neutron is defined by the preceding module. The direction of the beamline defines the +x-axis. The y-axis is defined as the horizontal axis to the left and the z-axis as the vertical one upwards. The module SANS sample uses the angles θ and φ. θ is defined as the angle between a vector a vector R defining the flight direction of the neutron and the +x-axis and covers a range of [0..π]. φ is the angle between the projection of the vector r in the yz-plane and the +y-axis and has a range of [0..2π[.

A neutron is written to the output by this module, if the neutron arrives at the sample surface after scattering. The coordinate system has still the same orientation, but the origin has moved to the center of the sample. All sample modules consider the divergence of each neutron without any approximation to obtain the true direction of the flightpath after the scattering process.

Description of the scattering

First of all it is determined if the neutron intersects the sample. If the neutron does not intersect the sample, it is discarded. Otherwise the neutron is scattered along its path through the sample at a certain distance L_s from its entrance, which is determined by a Monte Carlo choice.
The scattering is restricted to an angular range of [θ-Δθ, θ+Δθ] by the input values for θ, Δθ, φ and Δφ. The direction of the trajectory i after the sample is given by (θ_i, φ_i). For both, coherent scattering and incoherent scattering, both angles θ_i and φ_i are determined by a Monte Carlo choice in these ranges. Therefore, the number of trajectories per solid angle in this range depends on the choice of the range. To get the real flux into this solid angle, this has to be considered by the factors

(see below). The differential cross section is given by the square of the scattering amplitude (see e.g. Feigin, Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering (2.2), or P. Fratzl in 'PSI Proceedings 97-01, Cold Neutrons - High Resolution'):

Integration yields for N identical particles of volume V_p and scattering length density ρ_p:

with the Form Factor F(Q) = |S(Q)|² = | ∫ exp(iQ*r)dV / V_p|². Considering also the scattering length density ρ_s of the solution:

where f_p is the volume fraction of the particles and V_smpl the sample volume. Now it is possible to calculate the cross section for scattering into a solid angle Ω. For a discrete number of orientations (θ_i,φ_i):

(The meaning of N_i is explained below). Here, we get:

The probability of scattering neutrons into this solid angle is:

I_in denotes the incoming neutron current, I_out,coh the current of the neutrons scattered into the solid angle Ω. A_smpl is the area of the sample perpendicular to the beam direction. With the preceding equation:

L_i denotes the total length of the flightpath of the trajectory under consideration through the sample. N_i is the number of trajectories times the number of repetitions, the sum is over these N_i orientations. (In practice, the influence of the number of trajectories on the probability is already taken into account in the module 'Source', but the number N_r of repetitions must be considered here.) p_coh is the probability that a neutron is scattered at all.
The values for F(Q) can be calculated from size and shape for particles of a simple geometry, e.g. for spheres

Apart from spheres, the form factors of ellipsoids, cylinders and parallelepipeds are introduced in the program. The formula are taken from the literature mentioned above. Additionally, isotropicscttering can be chosen for testing normalization purposes. Apart from the spheres, the orientation of the particle relatively to the neutron flight direction is determined by a Monte Carlo choice before the treatment of the scattering event.

In addition to the coherent scattering, the incoherent scattering can be treated. This gives an isotropic distribution of the incoherently scattered neutrons. This scattering probability is given by

σ_inc is the incoherent scattering cross section of the unit cell; μ_inc = σ_inc/v is the macroscopic incoherent scattering cross section, which can be given as an input in the sample file.

For all trajectories, an attenuation A_t is considered as follows:

L_n is the total neutron flight path in the sample (surface -> point of scattering -> surface). μ_tot = σ_tot/v₀ denotes the total macroscopic scattering cross section to be interpreted as wavelength independent, μ_abs = σ_abs/v₀is the macroscopic absorption cross section (to be provided for λ= 1.798 Å).

For each incoming trajectory, N_r - only coherent scattering - or 2*N_r - with incoherent scattering - trajectories are generated. Summing over these trajectories, the probability for the scattering of a trajectory is then composed by:

where sin θ_i considers the θ-dependence of the isotropic distribution of the scattering orientations.

Module parameters

Parameter Unit	Description	Range, Examples	Command Option
sample file	The sample file describes the geometry and properties of the sample.		-S
max. theta [deg]	In SANS, neutrons are always scattered in a cone around the positive x-axis This parameter defines the edge of the cone, i.e. the maximal deviation from the forward direction.	0° - 180°	-M
repetitions	'repetitions' specifies the number of data sets (trajectories) generated for each scattered trajectory. A larger number of repetitions enriches the population on the detector and gives therefore better statistics in the spectrum, but the number of density of events in the parameter space is not increases, e.g. the number of different wavelength values remains the same. Therefore, an increase of the number of trajectories created by the source module is favorable.	≥ 1	-A
incoherent scattering	yes: neutrons are additionally scattered incoherently no: incoherent scattering is omitted	yes, no	-I

Sample file parameters

Example:
(The order written to the sample file differs from the sequence in the GUI. Anything after the # character is interpreted as a comment.)

  2.0 0.0 0.0        # sample position relative to the coordinate system defined by the preceding module is: 2 cm along the x-axis
  cub                # sample has the geometry of a cuboid
  0.1 1.0 1.0        # thickness, height and width of the cuboid are 0.1 x 1 x 1 cm
  1.0 0.0 0.0        # orientation of the cuboid: thickness is in x-direction, height in z-direction (vector need not be normalised)
  S 500.0            # sperical particles of radius 500 Å
  1.0E10 3.0E10 0.03 # scattering length densities: particles 1010 1/cm², solution 3x1010 1/cm², 3 % vol. frac. of particles
  0.0 0.5 0.05       # Scattering cross sections: incoherent=0, total=0.5 cm-1 and absorption=0.05 cm-1Å-1
  

VITESS Module 'sample_s_q' for Samples of S(Q) Dependent Scattering

The module S(Q)-sample describes the coherent and incoherent elastic scattering of a S(Q)-sample. The coordinate system of an incoming neutron is defined by the preceding module as well as the main flight path of the neutrons. The main flight direction of the neutrons defines the +x-axis. The y-axis is defined as the horizontal axis and the z-axis as the vertical one. The module S(Q)-sample uses the angles θ and φ. θ is defined as the angle between a vector r and the +x-axis and covers the range from [0..π]. φ is the angle between the projection of the vector r in the yz-plane and the +y-axis and has the range of [0..2π[.

A neutron is written to the output by this module, if the neutron arrives at the sample surface after scattering. The coordinate system has still the same orientation, but the origin has moved to the center of the sample. All sample modules consider the divergence of each neutron without any approximation to obtain the true direction of the flightpath after the scattering process.

Description of the scattering:

First of all it is determined if the neutron intersects the sample. If the neutron does not intersect the sample, it is discarded. Otherwise the neutron is scattered along its path through the sample at a certain distance L_s from its entrance, which is determined by a Monte Carlo choice.

The scattering is restricted to an angular range of [θ-Δθ θ+Δθ], [φ-Δφ, φ+Δφ] by the input values for θ, Δθ, φ, Δφ. The direction of the trajectory i after the sample is given by (θ_i, φ_i ). For both, coherent scattering and incoherent scattering, both angles θ_i and φ_i are determined by a Monte Carlo choice in these ranges. Therefore, the number of trajectories per solid angle in this range depends on the choice of the range. To get the real flux into this solid angle, this has to be considered by the factors

(see below). With the equation for the differential cross section (Squires, Thermal Neutron Scattering (5.29)):

it is possible to calculate the cross section for scattering into a solid angle Ω. (N is the number of nuclei in the scattering system.) For a discrete number of orientations (θ_i, φ_i ):

(The meaning of N_i is explained below). Here we get:

The probability of scattering neutrons into this solid angle is:

I_indenotes the incoming neutron current, I_out,coh the current of the neutrons scattered into the solid angle Ω. A_smpl is the area of the sample perpendicular to the beam direction. With the preceding equation:

S(Q) denotes the structure factor as a function of the momentum transfer Q, V_smpl the sample volume, and v₀ the volume per nuclei. μ_coh = σ_coh/v₀ denotes the macroscopic coherent scattering cross section and L_i the total length of the flightpath of the trajectory under consideration through the sample.
N_i is the number of trajectories times the number of repetitions, the sum is over these N_i orientations. (In practice, the influence of the number of trajectories on the probability is already taken into account in the module 'Source', but the number N_rof repetitions must be considered here.) p_coh is the probability that a neutron is scattered at all.
The values for S(Q) can be taken from the structure factor file or be calculated in the function "CalcStructureFactor" in "sample_s_q.c". As default, a function using the Percus-Yevick hard sphere model with special parameters is called.

In addition to the coherent scattering, the incoherent scattering can be treated. This gives an isotropic distribution of the incoherently scattered neutrons. This scattering probability is given by

σ_inc is the incoherent scattering cross section of the unit cell; μ_inc = σ_inc / v is the macroscopic incoherent scattering cross section, which can be given as an input in the sample file.

For all trajectories, an attenuation A_t is considered as follows:

L_n is the total neutron flight path in the sample (surface -> point of scattering -> surface). μ_tot = σ_tot / v₀ denotes the total macroscopic scattering cross section to be interpreted as wavelength independent, μ_abs = σ_abs / v₀ is the macroscopic absorption cross section (to be provided for λ=1.798 Ang).

For each incoming trajectory, N_r- only coherent scattering - or 2 N_r - with incoherent scattering - trajectories are generated. Summing over these trajectories, the probability for the scattering of a trajectory is then composed by:

where sin θ_i considers the θ-dependence of the isotropic distribution of the scattering orientations.

Module parameters:

Sample file parameters

Example:
(The order written to the sample file differs from the sequence in the GUI. Anything after the # character is interpreted as a comment.)

  100.0 0.0 0.0        # sample position relative to the coordinate system defined by the preceding module
  cyl                  # sample geometry (cyl, bal or cub)
  2.0 10.0             # radius and height of the cylinder in cm
  1.0 0.0 0.0          # orientation of the cylinder; need not be normalised
  D                    # S(Q) data from file
  SiO_300.str          # file containing the structure factor data for the unit cell
  0.0082 0.0824 0.0139 # Scattering cross sections: incoherent, total and absorption
  

VITESS Module 'sample_reflectom' for virtual experiments on reflectomters

This module simulates a sample of a reflectometer.
The reflectivity data of a sample are taken from a file that contains the reflectivity R as a function of momentum transfer Q. To be able to get a simulated function R(Q), it is possible to simulate a reference measurement. The reference sample has a reflectivity of 1 for all Q-values.
If offspecular scattering mode is desired, the reflectivity file should contain a look-up table in the form: q_i, q_f,j, R(q_i, q_f,j). Here, q_i is the incoming neutron "scattering" vector: q_i = 2*pi/lambda * sin(theta), where theta is the angle between the sample and the beam axis. q_f,j is an array of possible outgoing scattered vector components : q_f,j = 2*pi/lambda * sin(theta_j), where theta_j=theta is the specular case and theta_j=-theta stands for the direct beam. The reflectivity table thus looks like this:

q_i.................q_f,j.......R(q_i, q_f,j)
0.00255028 -0.0800882 0.001
0.00255028 -0.0797596 0.0005
0.00255028 -0.079431 0.0005
0.00255028 -0.0791025 0.0015
...
0.00255028 0.0876443 0.0005
0.00255028 0.0879728 0.0005

0.00280531 -0.0798336 0.0005
0.00280531 -0.079505 0.0005
0.00280531 -0.0791764 0.0005
0.00280531 -0.0788478 0.0005
0.00280531 -0.0785192 0.001
...

An empty line between two subsequent q_i values is recommended to match the plotting format of gnuplot. An example file with a generic offspecular look-up table is provided in the FILES folder.

The reflectometry sample can now handle incoherent isotropic scattering. It requires information on the scattering path length mu, with P=μ*x being the scattering probability (0.00288 1/cm for D₂O), and on some detector parameters. Besides, if the ratio between the area containing the specular signal and the total detector area is known, this is used to scale the incoherent trajectories such that eval_elast can provide the correct backgroun level without additional data treatment inside and outside the specular signal area.

The reflection of neutrons at several angles can be done in one simulation. In this case, a minimal value, a maximal value, and a step size for the reflection angle must be given (see chapter C). If only one angle shall be considered, the step size must be set to zero or minimal and maximal value must be identical.

Main parameters

File input parameters

Data evaluation

If several reflection angles are considered simultaneously, one incoming neutron can cause up to
    N_max = (θ_max - θ_min) / Δθ + 1
outgoing neutrons. (This number is reached, if the sample is hit by the neutron at all angles.)

So the overall neutron flux at the detector is no longer comparable to the flux before the sample. Thus it is senseful to evaluate the data (using the module EVAL_ELAST) to separate the neutrons reflected at the different angles.
An evaluation in scattering angle is possible, if the angle difference Δθ is larger than the fluctuation in the orientation of the incoming neutrons. For an evaluation in the momentum transfer Q, the variation in Q of the incoming neutrons (caused by fluctuation in orientation and wavelength) must be smaller than the difference in Q caused by the angle difference Δθ.

VITESS Module 'sample_powder' for polycrystalline samples

The module sample_powder describes the coherent and incoherent elastic scattering of a powder sample. All parameter data are taken from file.
The coordinate system of an incoming neutron is defined by the preceding module. The direction of the beamline defines the +x-axis. The y-axis is defined as the horizontal axis to the left and the z-axis as the vertical one upwards. The powder sample module uses the angles θ and φ. θ is defined as the angle between a vector R defining the flight direction of the neutron and the +x-axis and covers a range of [0..π]. φ is the angle between the projection of the vector R to the yz-plane and the +y-axis and has a range of [0..2 π[.

A neutron is written to the output by this module, if the neutron arrives at the sample surface after scattering. The coordinate system has still the same orientation, but the origin has moved to the center of the sample. All sample modules consider the divergence of each neutron without any approximation to obtain the true direction of the flightpath after the scattering process.

Description of the scattering:
First of all it is determined if the neutron intersects the sample. If the neutron does not intersect the sample, it is discarded. Otherwise the neutron is scattered along its path through the sample at a certain distance L_s from its entrance, which is determined by a Monte Carlo choice. The probability p_coh (see e.g. Squires (3.103)) of the scattering process results from summing up the single contributions P_{coh, d} for all d-spacings which satisfy the Bragg equation for a neutron with wavelength λ_i:

F_d denotes the structure factor; it is the sum over all reciprocal lattice vectors with the same d-spacing d. (d and |F_d|² are taken from the structure factor file.) θ_sc,i is the scattering angle of the i-th trajectory, V_smpl the sample volume, and v₀ the unit cell volume.  I_in denotes the incoming neutron current, I_out,coh the current of the neutrons scattered to the cone. A_smpl is the area of the sample perpendicular to the beam direction. L_i denotes the total length of the flightpath of the trajectory under consideration through the sample. The values for |F_d|²  contain the Debye-Waller factor.
The direction of the trajectory i after the sample is given by (θ_i, φ_i). The angle θ_i is determined by &theta_sc,i ; φ_i is given by a Monte Carlo choice between &phi - Δφ and &phi + Δφ.

In addition to the coherent scattering, incoherent scattering can be treated. This gives an isotropic distribution of the incoherently scattered neutrons. The scattering probability is given by

σ_inc is the incoherent scattering cross section of the unit cell; μ_inc = σ_inc/v is the macroscopic incoherent scattering cross section, which can be given as an input in the sample file.

The scattering is restricted to an angular range of [θ-Δθ, θ+Δθ],[φ-Δφ, φ+Δφ] by the input values θ, Δθ, φ and Δφ. For coherent scattering, θ_i is determined by the Bragg condition . If it is out of the range [θ-Δθ, θ+Δθ], the trajectory is discarded. Therefore, no correction for this angle is necessary. For incoherent scattering, θ_i is determined by a Monte Carlo choice in the range [θ-Δθ, θ+Δθ]. Therefore, the intensity in this range depends on the choice of the range. This is corrected by a factor Δθ. A limitation of the φ-range must be corrected for both kinds of scattering, because the value is chosen by a Monte Carlo choice in the given range (see above). So, the restricted solid angle is taken into account by using the factors

For all trajectories, an attenuation A_t is considered as follows:

L_n is the total neutron flight path in the sample (surface  ->  point of scattering  ->  surface). μ_tot = σ_tot/v₀ denotes the total macroscopic scattering cross section to be interpreted as wavelength independent, μ_abs = σ_abs/v₀ is the macroscopic absorption cross section (to be provided for λ = 1.798 Å).

For one incoming trajectory, N_r(N_coh + 1) trajectories are generated, where N_r denotes the number of repetitions. Summing over these trajectories, the total probability for the scattering of a trajectory is then given by:

sin θ_i considers the θ-dependence of the isotropic distribution of the scattering orientations. Due to considering all accessible Bragg peaks, N_coh is often greater than 1, even if N_r = 1. So don't worry about obtaining more output than input trajectories.

Module parameters

Parameter Unit	Descripton	Range, Examples	Command Option
sample file	The sample file describes the geometry and properties of the sample.		-S
θ, Δθ φ, Δφ [deg]	These parameters describe the solid angle into which scattering occurs. The direction (θ,φ) points to the middle of the covered range, which extends from [θ-Δθ, θ+Δθ] and [φ-Δφ, φ+Δφ]. θ is the scattering angle defined as the angle between +x-axis (main flight direction of the neutrons) and the vector R describing the flight direction after scattering. φ is the direction on the cone defined as the angle between the +y-axis and the projection of R to the yz-plane. (x,y and z form a right-handed system.) The default is Theta=DelTheta=90°, Phi=DelPhi=180° corresponding to a coverage of 4π.	Example: 20° to 160° scattering to the right in +/-20° vert.: θ=90°, Δθ=70° φ=180° Δφ=20°	-D, -d, -P, -p
repetitions	'repetitions' specifies the number of data sets (trajectories) generated for each scattered trajectory. A larger number of repetitions enriches the population at the detector and gives therefore better statistics in the spectrum, but the number of density of events in the parameter space is not increased, e.g. the number of different wavelength values remains the same. Therefore, an increase of the number of trajectories created by the source module is favorable.	≥ 1 default: 1	-A
colour	Colour of the neutrons scattered by the powder sample If no color, color=0 or color=-1 is chosen, the colour of the trajectories is not changed	-1,0: no action: ≥ 1: colour is set	-c
incoherent scattering	yes: neutrons are additionally scattered incoherently no: incoherent scattering is omitted	yes, no	-I
treat all neutrons	yes: treats neutrons not hitting the sample no : treats only neutrons hitting the sample (This is the right option for background simulations.)	yes, no	-a

Sample file parameters

first an example (the order written to the sample file differs from the sequence chosen in the GUI):
(Anything after the # character is interpreted as a comment.)

  100.0 0.0 0.0            # sample position relative to the coordinate system defined by the preceding module
  cyl                      # sample geometry (cyl, bal or cub)
  2.0 10.0                 # radius and height of the cylinder in cm
  1.0 0.0 0.0              # orientation of the cylinder; need not be normalised
  Al_300.str               # file containing the structure factor data for the unit cell. If the format is neither .str nor .laz, the meaning of individual columns needs to be specified (see below).
  0.000494 0.09057 0.01392 # macroscopic cross sections: incoherent, total and absorption
  66.38                    # unit cell volume in cubic Angstrom
  6 13 0 17 0 1            # Structure file format, if the file is not given as .str or .laz. The last number is the scale factor that is needed to express the squared structure factor in barn, if it is given in a different unit in the used structure factor file.
  

VITESS Module 'sample_nxs' for polycrystalline samples

The sample_nxs module describes a polycrystalline sample based on its unit cell definition and was originally developed to simulate Bragg edge neutron transmission experiments. The module handles coherent and incoherent scattering, as well as absorption and transmission. The individual probabilities for those events are determined using the calculation of wavelength-dependent neutron cross sections (nxs). These cross sections are computed for each atom contributing to a unit cell, such that complex material compositions can be simulated. The nxs concept is briefly described.

CONTENT

1. Simulation description

1.1 Unit cell initialisation

• Space group number (Schönflies and Hermann-Mauguin symbols are also possible),
• Lattice parameters (a, b, c, α, β and γ),
• Properties of atoms contributing to the unit cell (σ_coh, σ_inc, σ_abs, M and θ_D)
• Arrangment of atoms inside the unit cell (given by the Wyckoff position).

1.2 Neutron cross section calculation

1.3 Neutron-sample interactions

2. Module parameters

3. Input files

3.1 Sample geometry file

  10.0 0.0 0.0    # sample position in [cm] the coordinate system of the preceding module   (-x, -y, -z)
  cub             # sample geometry (cyl, bal or cub)                                       (-G)
  2.0 1.0 2.3     # thickness or radius, height and widthheight of the sample in [cm]       (-t, -h, -w)
  1.0 0.0 0.0     # orientation of the cylinder (does not need not be normalised)           (-X, -Y, -Z)
  Fe.nxs          # nxs parameter file to describe the unit cell composition                (-s)
        

From VITESS 4 on, these parameters can also given as input parameters. The command options are shown in brackets at the end of the table.

• Cylinder: the vector is always perpendicular to the top of the cylinder (standard cyl. position (001), height along the z-axis).
• Cuboid: Standard is the (1,0,0) direction, i.e. the sample has a thickness in x-direction, a width in y-direction and height in z-direction. By giving a different vector the whole sample is rotated in this direction, i.e. the planes separated by 'thickness' remain perpendicular to this vector.
• Sphere: no values required.

The sample geometry file is assigned by the command line parameter -S. This option is mandatory. The VITESS GUI provides input fields to edit the described parameters.

3.2 NXS parameter file

# define the unit cell parameters:
#   space_group                      - the space group number or Hermann or Hall symbol [string]
#   lattice_a, ...b, ...c            - the lattice spacings a,b,c [angstrom]
#   lattice_alpha, ...beta, ...gamma - the lattice angles alpha,beta,gamma [degree]
#   debye_temp                       - the Debye temperature [K]

space_group    = -F 4 2 3 # space group number is also allowed (= 225)
lattice_a = 4.049
lattice_b = 4.049
lattice_c = 4.049
lattice_alpha = 90
lattice_beta = 90
lattice_gamma = 90
debye_temp = 429.0

# add atoms to the unit cell:
# notation is "atom_number = name b_coh sigma_inc sigma_abs_2200 molar_mass x y z"
#   name           - labels the current atom/isotope  [string]
#   b_coh          - the coherent scattering length [fm]
#   sigma_inc      - the incoherent scattering cross section [barns]
#   sigma_abs_2200 - the absorption cross sect. at 2200 m/s [barns]
#   molar_mass     - the Molar mass [g/mol]
#   debye_temp     - the Debye temperature [K]
#   x y z          - the Wyckoff postion of the atom inside the unit cell

[atoms]
add_atom = Al 3.449 0.008 0.23 26.98 0.0 0.0 0.0

4. Further developments

• M. Boin, A. Hilger, N. Kardjilov, S.Y. Zhang, E.C. Oliver, J.A. James, C. Randau & R.C. Wimpory (2011), J. Appl. Cryst. 44(5), 1040-1046, doi:10.1107/S0021889811025970
• Strobl, M.; Hilger, A.; Boin, M.; Kardjilov, N.; Wimpory, R.; Clemens, D.; M\"uhlbauer, M.; Schillinger, B.; Wilpert, T.; Schulz, C.; Rolfs, K.; Davies, C. M.; O'Dowd, N.; Tiernan, P. & Manke, I. (2011), Nucl. Instrum. Methods Phys. Res., Sect. A 651, 149-155, doi:10.1016/j.nima.2010.12.121
• M. Boin (2012), J. Appl. Cryst. 45, 603-607, doi:10.1107/S0021889812016056
• M. Boin, R.C. Wimpory, A. Hilger, N. Kardjilov, S.Y. Zhang, M. Strobl (2012), J. Phys.: Conf. Ser. 340, 012022, doi:10.1088/1742-6596/340/1/012022
• Kittelmann, T.; Stefanescu, I.; Kanaki, K.; Boin, M.; Hall-Wilton, R. & Zeitelhack, K. (2014), J. Phys.: Conf. Ser. 513, 022017, doi:10.1088/1742-6596/513/2/022017
• Peetermans, S.; Tamaki, M.; Hartmann, S.; Kaestner, A.; Morgano, M. & Lehmann, E. H. (2014), Nucl. Instrum. Methods Phys. Res., Sect. A 757, 28-32, doi:10.1016/j.nima.2014.04.033

5. References

• K. Binder (1970), Phys. Stat. Sol. B 41(5), 767-779, doi:10.1002/pssb.19700410233
• J.R. Granada (1984), Z. Naturforsch. Teil A 39, 1160-1167.
• R.W. Grosse-Kunstleve (1995), SgInfo - a Comprehensive Collection of ANSI C Routines for the Handling of Space Groups, http://cci.lbl.gov/sginfo/
• S.C. Vogel (2000), PhD thesis, Christian-Albrecht University, Kiel, Germany.
• A.K. Freund (1983), Nucl. Instr. Meth. 213, 495-501.

VITESS Module 'sample_singcryst' for single crystal samples

The integrated intensity I of a particular reflection measured in a TOF neutron diffraction experiment can be written as a function of the wavelength and the Bragg angle:

where h, k, l are the Miller indices designating the Bragg peaks, and the wavelength dependent correction factors are in the order given above: the incident
spectral neutron flux, the detector efficiency, the absorption correction, the extinction correction, and alfa= I_TDS/I_Bragg, the thermal diffuse scattering (TDS) correction.
( J. Peters and W. Jauch, Science Progress (2002), 85 (4), 297–317).
In this module we can treat the extinction, TDS correction by combining a normalisation factor, d-spacing spread or by a reflection dependent coefficient multiplying Fhkl² in the structure factor file.
The program expects a complete list of h k l reflections. (see 'Module Parameters'|'structure factor file' below).

Module Parameters

File Input Parameters

The parameter file contains in the first 3 lines the reciprocal lattice vectors, and you can give a normalisation containing the number denstity or other factors.

Example:

  1.2892     0       0       recipr. unit v. A X [1/A], recipr. unit v. A  Y [1/A], recipr. unit v. A  Z [1/A]
  0          1.2892  0       recipr. unit v. B X [1/A], recipr. unit v. B  Y [1/A], recipr. unit v. B  Z [1/A]
  0          0       1.8982  recipr. unit v. C X [1/A], recipr. unit v. c  Y [1/A], recipr. unit v. C  Z [1/A]
  1          0.01            normalisation [a.u.], absorbtion [1/cm/A]
  900        0       0       position X [cm],  position Y [cm], position Z [cm],
  30       -15       0       phi(Z) [deg], chi(X) [deg], omega(Z) [deg]
  cub                        sample geometry: 'cub', 'cyl'inder, 'ball'
  1          1       1       thickness or diameter [cm], height [cm], width [cm]
  109.3      20.7            output angle horiz. [deg], output angle vert. [deg]
  

VITESS rotation convention: Smaller index axis rotated towards higher index axis is positive!

  no. refl    h     k     l      Fhkl2
  

(a Debye-Waller factor can be included here).
All incoming trajectories will sample each reflection and the successful ones are written out i.e. number of incoming trajectories will be larger than the number of incoming trajectories.
The third coordinate 'colour' will contain which reflection has happened (no.refl), this can be seen if you use 'writeout' to view the ASCII output (as in the example, but for longer runs do not forget to cancel 'writeout' to save memory and computing time).

Example:

  1 14 -11 -1 0.08057
  2 15 -11 -1 0.00616
  3 16 -11 -1 0.02162
  4 17 -11 -1 0.01906
  5 18 -11 -1 5.35824E-5
  6 12 -10 -1 5.929E-7
  7 13 -10 -1 0.00652
  8 14 -10 -1 0.00228
  9 15 -10 -1 0.49332
 10 17 -10 -1 7.66736E-4
 11 18 -10 -1 0.00165
 12 19 -10 -1 5.67392E-4
  

VITESS Module 'sample_inelast' for inelastic scattering samples

The probability weight P provided by the former module is multiplied by the known factors:

P' = exp ( -μt ) x |k_f|/|k_i| x S(q,ω) x (ΔΩ/4π)  x  P,

σ_coh and σ_inc are both calculated from the respective linear coefficients, using the density, assuming in both cases that the linear coefficients given as input are the usual tabular values at λ = 1.8 Â.

The geometrical parameters of the sample are: position, horizontal and vertical offset angles with reference to the final coordinate system of the antecedent module, and size of the sample.

Detailed parameter definitions can be read from the tables in section B. The functions used to approximate S(q,w) are given in section C.

In the output frame X'Y'Z', all neutron coordinates are referring to the moment when the neutrons are just crossing the sample walls after the scattering . Multiple scattering is not yet included. The effect of sample size and geometry on the scattered intensity can be calculated by calibration taking into account that I / I' = V/V' (V - illuminated sample volume).

A. Options

B. Parameter and file descriptions

Main parameters

File Input parameters

Quasi-elastic scattering

Set P1=P4=0 for quasi-elastic scattering and lambda final equal to lambda initial. Delta lambda final should be matched to the HWHM parameter P2: lambda and delta lambda final determine the wavelength/energy range in which neutrons are simulated, while the P parameters determine the Lorentzian shape via the neutron weight. The delta lambda final should cover several times the FWHM to see the tails of the Lorentzian distribution. Note that in order to see a broadening of the elastic peak, the width of the incoming neutron wavelength has to be smaller than the energy transfer / delta lambda final.

C. Functions used

1) Scattering functions:

S(q,ω) = σ_cohS_coh(q,ω) + σ_incohS_incoh(q,ω)

\( S_{coh}(q,\omega)= \frac{ BF(\omega,T) P_3 }{\pi} \left( \frac{P_2}{(\omega - P_1 - \epsilon (Q) )^2 + P_2^2 } - P_4 \frac{P_2}{(\omega + P_1 + \epsilon (Q) )^2 + P_2^2 } \right) \)

if \(P_4 = -1 \) it's divided by 2, in this way the normalization is 1 in all cases. For continuity reasons exact ω = 0 events are skipped and P₂ > 0.0001 meV. For computation of non-coupled multipeak dynamic structure factors it is recommended to run separate simulations for each single peak and add the resulting TOF or energy spectra.

\( S_{incoh}(q,\omega)= \frac{1}{\Delta \omega}\), where \(\Delta \omega\) is the energy transfer range within which neutrons are scattered.

2) Dispersion function:

By considering \(P_1\) as a reference energy, the dispersion relation \(\omega(q)\) is:

\(\omega(q) = P_1 + \epsilon (q) \)

with

\(\epsilon (q) = D_1 q_x + D_2 q_y + D_3 q_z\).

3) Bose factor:

If option 'No Bose factor' has been chosen, BF is set to 1 for all cases.

If T = 0, BF = 1 for ω> 0 and BF = 0 for ω< 0.

\( BF(\omega,T) = \left\{ \begin{array}{lr} \frac{1}{e^{{\hbar \omega}/{k_B T}} - 1} +1 : \omega\gt 0\\ \frac{1}{e^{-{\hbar \omega}/{k_B T}} - 1} : \omega\lt 0 \\ \end{array} \right.\)

VITESS Module 'sample_ncrystal' for scattering with NCrystal sample database.

This module integrates the NCrystal library into the Vitess simulation framework.
This module facilitates advanced neutron transport simulations by enabling coherent and incoherent scattering, absorption, and spin-flip effects in materials described using NCrystal's scattering models.
The module computes scattering cross-sections (coherent and incoherent) for neutrons interacting with materials using NCrystal's S(q,w) scattering kernel.
It supports neutron spin-flip processes during incoherent scattering.
It handles multiple material geometries such as cylinders, spheres, and hollow cylinders.
If the state of matter of the sample is solid, the crystal directions are set in the lab framework, indenpendentently from the scattering volume orientation. The two offset angles enable to align the scattering volume to the crystal axes, if this is desired.

The neutron scattering follows this process:
1. Vitess propagates the neutron until the scattering point.
2. Ncrystal defines the probability of a scattering event and defines the final neutron properties.
3. Vitess reads the neutron properties from NCrystal and propagates further.

Workflow

The key function S(q,ω)

Sample material setup