VITESS New Monochromator-Analyser Module

The new monochromator module is an upgrade of the existing one. The older module is kept for backward-compatibility, however it is strongly recommended to change to the new one since only this module will be maintained. All known functionalities were kept and two were added: The "transmission" geometry and the handling of neutrons that are not reflected by the crystal lattice. They are explained below.
Moreover, the additional simulation run to determine the correct normalisation has become obsolete. The new module now handles the normalisation of the outgoing neutrons properly if the peak reflectivity, i.e. the reflectivity of the monochromator crystal for neutrons of the peak wavelength and negligible divergence, is given . The peak reflectivity is usually known from dedicated measurements. Note that a correct normalisation of the outgoing intensity is only possible, if realistic, non-zero values for the mosaicity and the d-spread are given. If an ideal crystal needs to be simulated, i.e. the mosaicity or d-spread are very close to zero, then it is possible that the outgoing intensity is larger than the incoming one. In this case you can set the reflectivity normalisation to a value below 1. If both the d-spread and the mosaicities are set to 0 then the crystal will only transmit the peak wavelength, resulting in a complete loss of intensity in a simulation.

A monochromator element is characterized by its geometric and crystallographic properties. The corresponding simulation parameters are set either on the main GUI window or in the parameter file. The module can handle flat crystals and focusing geometries. In addition, it is now possible to set up an array of monochromators/analyzers. The geometric parameters of a monochromator element are: position, horizontal and vertical offset angles (conforming to Eulerian rotation), horizontal and vertical 'Bragg angles' with reference to the final coordinate system of the previous module, and size of the CE. The Bragg angles can be rotated w.r.t. the crystal surface to allow for the transmission geometry (offcut orientation). For focusing geometries, additional parameters need to be specified to determine the curved shape of the monochromator element. The crystal structure can be characterized by setting the parameters d-spacing, d-spread (Lorentzian and Gaussian), mosaicity and reflectivity. Detailed parameter definitions can be read from the tables in section B. In the output frame X'Y'Z', all neutron coordinates are referring to the moment when the neutrons are just reflected from the crystal taking the new directions and probability weights.

There are two new features in the new monochromator module: The geometry choice "Transmission" handles a monochromator in transmission geometry. The option "transmission treated" creates a transmitted beam in addition to the one reflected by the crystal lattice. In this case, N_rep+1, i.e. usually 2, outgoing trajectories are generated for each incoming trajectory (hitting a crystal element), N_rep in the direction of reflection and 1 in the original direction. Important: In this mode, the global coordinate system is not altered by the 'standard frame generation', but needs to be defined as a 'user defined frame' or changed in a subsequent frame module.

The latest version of the new monochromator module also allows different movements of the monochromator/analyzer: an oscillation of the monochromator on a Doppler drive following a sinus function, a rotation on a chopper rotating about a horizontal axis to realize a phase space transformer (PST), and a rotation about the vertical axis.

Fig. CE

A. Options

For flat crystal simulation it is enough to use one single CE. The simulation of a curved focussing surface works with a matrix of CE-s (as they are really constructed), therefore one needs all positions, orientations and size parameters. For convenience, the deviations relative to the corresponding main values given in the Parameter File have to be defined and read from a Focus File properly formatted.

The options are:
 

1. Crystal_flat:	Simulates a flat rectangular generally (h,k,l) oriented offcut crystal.	-O1
2. Crystal_focus:	Activates the Focus File generation for a) λ-focussing, b) spherical c) vertically focussing cylinder or d) double focussing cylinder  M/A geometry.	-O2
3. Crystal_focus_dat:	Uses optional Focus File independently generated by separate programs not included in this module.	-O3

Option 2 takes advantage of an internal code of the module, which automatically generates the Focus File for a) l-focussing, b) spherical c) vertical cylinder d) or double focussing  M/A geometry. This option is suitable, for example, for setting analysers in a near-backscattering geometry to provide for example constant wavelength selection for neutrons scattered from the center of the sample.

B. Parameter and file descriptions

Option Crystal_Flat
 

File	Format	Examples Attached	Command Option
Parameter File	This files contains parameters describing a crystal element (CE). It can be read or created/modified by the VITESS shell.	crys.par	-P

- MAIN PARAMETERS

Parameter	Physical Symbol, Description	Range, Examples	Command Option
repetition [-]	If this integer > 1, the trajectory is used multiple times for better statistics.	>= 1	-A
mosaic fwhm horizontal, vertical [deg]	ξY, ξZ Horizontal and vertical fwhm components of the 2-dimensional Gaussian mosaic distribution. If it is set smaller than 0.001, then this minimum value is set automatically.	PG(002): 0.2 0.8 deg General: 0.001 1deg	-m, -M
d-spread  [-]	Δd / d Fwhm of the d-spacing distribution function (Lorentzian and Gaussian options) divided by lattice parameter under consideration. It is zero for a perfect crystal.	PG(002): 0.2 - 2´ 10-3 Si(111): 0.1 - 2´ 10-4	-D
peak reflectivity [-]	R (Experimentally determined) peak reflectivity of this monochromator.	0 ... 1 default: 1	-R
transmission treated [-]	If chosen, a tranmitted beam is generated in addition to the reflected beam(s). Please note that in both cases the 'standard frame generation' rotates the co-ordinate to the reflected beam. If you don't want that, choose the 'user defined frame' and set horizontal and vertical angle to zero to get the output frame aligned to the transmitted beam.	0 or 1	-o
movement [-]	Type of movement of the monochromator crystal(s): a) no movement b) rotation about a vertical axis c) rotation on a chopper about a horizontal axis parallel to the beam, usually used as phase space transformer (PST) d) oscillation along beam axis used to vary the wavelength via Doppler effect	'no movement' 'rotation vert. axis' 'rotation hor. axis (PST)' 'oscillation'	-b
randomize TOF [-]	no : the time of arrival at the monochromator is given by (the starting time at the source and) the time-of-flight to the monochromator. yes: the time of arrival at the monochromator is defined by a random choice within the time interval [-T/2,T/2] (T: period of the monochromator rotation or oscillation), i.e. the real TOF is ignored.	yes / no default: yes	-K
frequency [Hz]	f Frequency of the monochromator rotation or oscillation	Default: 0.0	-f
initial phase [deg]	ζ0 Zero time phase of the rotating or oscillating monochromator The phase at time t is calculated as ζ= 2 π f t + &zeta0; For ζ=0, the orientation of surface and reflecting planes are given by θ and ψ (see Table 'File Input Parameters')	Default: 0.0	-p
drive amplitude [cm]	Adop For Doppler drive only: Amplitude of the Doppler drive along x axis (= max. distance from zero position) A time depence of x(t) = Adop sin(ω t) is assumed; the direction is supposed be along the axis or close to it.	Default: 0.0 typical: 5 to 10 cm	-Q
number of areas [-]	Npst For PST only: number of identical areas, where the monochromator is mounted on the chopper	Default: 0.0 typical: 1 to 3	-n
area width [deg]	Wpst For PST only: angular range for each area, where the monochromator is mounted on the chopper	Default: 0.0 typical: 60 to 220 deg	-q
chopper radius [cm]	Rchop For PST only: distance from the chopper axle to the center of the monochromator	Default: 0.0 typical: 30 to 60 cm	-w
total scattering  [1/cm]	μtot Macroscopic total scattering cross-section in the crystal supposed to be wavelength independent	0 ... 1	-c
absorption [1/cm]	μabs Macroscopic absorption cross-section in the crystal for 1.798 Å supposed to be proportional to wavelength	0 ... 1	-C
geometry [-]	'Reflection' : Monochromator used in reflection geometry 'Transmission': Monochromator used in transmission geometry	1: Reflection 2: Transmission	-X
d-distribution	Lorentzian (1), Gaussian (2)	1, 2	-d

- FILE INPUT PARAMETERS
 

Parameter	Physical Symbol, Description	Range, Examples
main position [cm]	x, y, z Reference point (position) of the center of the monochromator/analyser-system in the frame provided by the former module. The position of each single CE is defined by (x,y,z) +deviation from (x,y,z). The deviation is read from focus data file. For the flat Geometry option, (x,y,z) is simply the center position of the rectangular CE.	x = distance to CE y = z = 0.0
thickness, width, height of CE [cm]	t, w, h Thickness, width and height give depth, horizontal and vertical dimensions of the rectangular CE. For each single CE the dimensions will be (t,w,h)+deviation from (t,w,h) the last being read from focus data file.	t = 0.0 0.5 cm w = h = 0.5 20 cm
'crystal offset' angle horizontal, vertical [deg]	θ,ψ: Offset from backscattering of the crystals determining the Bragg reflection. A rotation first about the Z axis (θ ) and then about the (new) Y axis (ψ ) gives the orientation of the planes of the center of the monochromator/analyzer. The orientation of each single CE is given by (θ, ψ) + deviation from (θ, ψ) the last being read from the focus data file. Zero angles means that diffraction planes are perpendicular to the incoming beam.	θ = ψ = 0.0 exact backscattering; θ: 0 ... 90 deg ψ;: -90 ... 90 deg
'Bragg offset' angle horizontal, vertical [deg]	If the (h,k,l) planes are parallel to the crystal surface, then 'Bragg offset' angles are identical with the 'crystal offset' angles (see previous row). For a focusing geometry this is always assumed. However, for a single monochromator/analyzer crystal the orientation of the reflecting crystal planes can be different from the surface orientation. In this case, the orientation of the planes has to be given as 'Bragg offset', while the 'crystal offset is regarded as the surface orientation.	see previous row
d-spacing [Å]	d Lattice distance corresponding to a reflection from a (h,k,l) crystal plane	PG(002): 3.332 Å Si(111): 3.135 Å Ge(113): 1.703 Å Cu(220): 1.272 Å
order of reflection [-]	N According to Braggs Law: N λ = 2 d sin φBr	1, 2, ...
output frame definition 'standard frame generation' 'user defined frame'	If 'user defined frame' is chosen, all parameters defining the output frame (X', Y', Z', hor. angle, vert. angle) are taken from the input values (see following two rows). If 'standard frame generation' is chosen, these values are generated (and the given values for the output frame ignored). 'Standard frame generation' is not useful if the monochromator is rotated. As the orientation is wavelength dependent it only considers the orientation (at t=0). In case of 'transmission treated', the co-ordinate system is not changed. Otherwise, it is moved to the center of the monochromator and directed along the reflected beam. After the co-ordinate transformation, the neutrons are written to the output file.	one point on the reflected beam axis
X', Y', Z' [cm]	x', y', z' In 'user defined frame': The position of the output frame in the original frame. (x', y', z') represents the translation vector applied to shift the origin of the original (input) frame to the new (output) position. In 'standard frame generation' without transmitted beam it is: (x', y', z') = (x, y, z) i.e. main position of the M/A system.	one point on the reflected beam axis
output horizontal, vertical angle [deg]	Θ, Ψ In 'user defined output frame', these angles are taken to generate the output frame: After the translation, a Θ rotation about the Z axis and then a Ψ rotation about the (new) Y axis defines a new orientation. If "standard frame generation" is chosen, the output frame is rotated until the new X axis is parallel to the reflected beam.	Θ = 180 deg, Ψ= 0.0: exact backscattering; Θ = 180 deg, Ψ= -2 ψ, with ψ being the 'vertical Bragg offset angle' and θ = 0.0

- Please note that the parameter file format used for the old monochromator module remains unchanged. However, the 'mosaic range' and 'd-range' parameters became obsolete and are not shown anymore, when the parameter file is open for editing.

Option Crystal_Focus

- same as Option Crystal_flat

-FOCUS PARAMETERS

Parameter	Physical Symbol, Description	Range, Examples	Command Option
focusing option:	This parameter defines the focusing geometry. 'no focusing' is chosen if the surface normals of all elements point into the same direction or that there is only 1 crystal element 'λ-focusing' builds a shape close to that of a sphere, but identical wavelengths will be focused to a point close to backscattering 'Spherical' puts the crystal elements on the surface of a sphere with radius 'radius vert.' The 'vert. cylinder' option forms a vertical cylinder The 'double focusing' option assumes a flat geometry, in which each element is rotated to give cylindrical focusing with different radii in vert. and hor. direction.	1 constant lambda 2 spherical 3 vert. cylinder 4 double focusing	-g
number of CE horizontal, vertical, layers [-]	The number of columns and rows (nH, nV) of the created CE-matrix. Number of layers > 1 means that crystals (or matrices of crystal elements) are put behind each other so that the transmitted beam is reflected again nH is not used for the option 'vert. cylinder', where only 1 element per row is assumed	1 50 1 for vert. foc. cylinder	-H,-V,-I
radius horiz. [cm]	Radius of focusing in horizontal direction for a double focusing monochromator. Not used for the other focusing options.	200 cm, 0 cm to focus only vertically	-s
radius vert. [cm]	λ-focusing: distance from the sample center to the bottom row of the CE-matrix. spherical : radius of the sphere vert. cylinder : radius of the vertical cylinder double focusing: Radius of focusing in vertical direction	200 cm	-r
angle vert. [deg]	Angular offset ψ0 of the bottom row of the crystal element-matrix relative to the horizontal plane containing the sample center. It is needed for all geometry options except 'double focussing', where a vertically symmetrical geometry is assumed.	-3 deg	-a
distance of layers [cm]	For number of layers > 1 only: Distance between two consecutive monochromator layers (measured from center to center along the normal of the crytals surface)	0.05	-o
max. layer\ndeclination [deg]	For number of layers > 1 only: max. hor. deviation Δζ of the CE from the mean orientation ζ. Values are set in equidistant steps from ζ-Δζ to ζ+Δζ.	default 0, range [-90°,90°]	-J
gap between columns, rows [cm]	The distance between adjacent crystal elements in horizontal and vertical direction horizontal: used for 'spherical' and 'double focusing' vertical : used for all options except for 'λ-focusing'	0.05	-h,-v
orient. dev. hor., vert. [deg]	Total range of the deviation Δθ, Δψ from the theoretical orientation (θ, ψ) of a crystal element in horizontal and vertical direction. The real orientation is determined by a Monte Carlo choice within [θ - 1/2Δθ, θ + 1/2Δθ] and [ψ - 1/2Δψ, ψ + 1/2Δψ] resp.	0.1	-t,-T

- Description of the focus file (filename must be given as input):

File	Format	Examples Attached	Command Option
focus file	First row includes 2 integer numbers: nH, nV, the number of columns and rows of the created CE-matrix. (H = horizontal, V = vertical.) Next nH, nV rows are created by two program loops (internal loop: V) computing 8 values representing deviations from the main values for each single CE. These are interpreted by the program as follows: The position of each single CE is (x,y,z) + deviation from (x,y,z) as read from columns 1 - 3. The dimension of each single CE (thickness, width, height) is (t,w,h) + deviation from (t,w,h) as read from columns 4 - 6. The orientation (hor., vert.) of each single CE is (θ, ψ) + deviation from (θ, ψ) as read from columns 7, 8.	lamb_foc.dat	-G

Option Crystal_focus_dat

For each incoming trajectory the d-spacing d is randomized according to the given d-spread. The randomization takes into account whether the distribution is Gaussian or Lorentzian. If the d-spread is zero, this step is obviously skipped. Then the Bragg-angle φ_Br of the trajectory is calculated taking into account its wavelength and the current d-spacing value: φ_Br = sin^-1(λ/(2*d)). Now one needs to calculate the probability that the monochromating crystal can reflect this neutron according to the Bragg condition.

In general, the Bragg condition is not fulfilled by the orientation of the CE, see Fig. Cone. The angle φ_CE between the incoming neutron k_i and the CE normal n_CE is usually not equal to φ_CE,Br = 90° - φ_Br, since the incoming beam can be divergent and the spectrum usually consists of a finite waveband. To assign a proper weight to the outgoing neutron the probability of finding a mosaic piece that fulfills the Bragg condition needs to be calculated. All possible normal orientarions of such mosaic elements describe a Bragg cone around k_i with the radius r_c = |k_i|tan(φ_CE,Br). Since all monochromators have a finite horizontal and vertical mosaicity, the Bragg cone can be reached starting from n_CE by two rotations around the y and z axes. To be in accordance with the given mosaic distributions and to obtain the correct probability, the rotation procedure is done as following: The first (e.g. vertical) rotation (Δφ_z) is randomised using a Gaussian with the given mosaic spread (FWHM of the corresponding distribution). Obviously, this first rotation fixes Δφ_y, the angle of the second (e.g. horizontal) rotation, since n_M must lie on the Bragg cone. The absolute probability for the reflection of this neutron is then determined by looking up the value of the Gaussian function of the latter (horizontal) mosaicity corresponding to Δφ_y. The norm of the Gaussian function is such that it is in accordance with the peak reflectivity of the monochromator element. This norm is determined in each simulation during the initialisation of the module and is based on the given Bragg angles, d-spread and mosaicity.

In the output, the new probability weight of a neutron mirrors adequately the given d- and mosaic distributions. The new coordinates and the direction of the neutron k_i are computed consecutively by taking into account the exact orientation of the reflecting mosaic piece n_M.

Fig. Cone

Last modified: Dec 03 15:00:00 MET 2013 , D. Nekrassov