Introduction to RESTRAXlns00.psi.ch/mcworkshop/papers/RESTRAX_introduction.pdfModel describing phonons in diamond lattice (Si, Ge, α-Sn, Eigenvalues & eigenvectors are calculated

MC workshop, PSI Villigen, October 2-4, 2005

Contents:

• Overview of RESTRAX features• Example of TAS simulations with flat-cone multianalyzer

• Overview of SIMRES features

• Example: multichannel supermirror guides

Introduction to RESTRAX

Jan Šaroun1, Jiří Kulda2, Jiří Svoboda1, Vasyl Ryukhtin1

1Nuclear Physics Institute, Řež2Institute Laue-Langevin, Grenoble

RESTRAX homepage::http://omega.ujf.cas.cz/restrax/

http://omega.ujf.cas.cz/restrax/

RESTRAX package

What is RESTRAX?Virtual three-axis neutron spectrometer– Modeling of TAS resolution functions using both analytical (matrix) and

Monte Carlo ray-tracing methods.– 4D convolution with an “arbitrary” scattering kernel – S(q,ω) function– data analysis (non-linear χ2 fitting)

What is SIMRES?Ray-tracing simulation program for instruments with “TAS-like” layout (e.g. powder diffractometer) – More detailed simulation of some components (benders, crystals)– Absolute neutron fluxes and beam profiles in r, k, t space.– Tools for instrument design – mapping intensity/resolution in the space of

instrument parameters + numerical optimization

Win32 and Linux versions available at http://omega.ujf.cas.cz/restrax


RESTRAX

Resolution function ray-tracing + analytical calculations

S1(q,ω)

S2(q,ω)

S3(q,ω)

4D convolution

data fitting

dynamically loaded scattering models

5 collimator/guide segments

sample

focusing crystal assemblies

Source

detector



Resolution function: R(Q,ω)

∫ −−= ωωωωπ

σω ddRSkk

NIi

f QQQQQ ),(),(4

),( 0000

Defined as convolution ...

∫ Φ= fififiFI dddPWIFI

kkrkrkrkkkk kk ),(),(),(),(

… or neutron transport

Scattering probability

Flux distribution at the sample

Detection probability


Resolution function obtained by ray-tracing

Resolution function is represented by a cloud of points

weighted by event probability, αp

Em i f0

22 2

2≡ − ( ), ,k kα α

Q k kα α α≡ −f i, ,

A “specimen” scattering to all kf with equal probability:

( ),..., ααα EQX ≡


Monte Carlo convolution with S(Q,E)

step

Inte

nsity

scan step (∆Q, ∆E)

Event histogram∑ ∆+∆+=

αααα ),( EjEjSpI j QQ

All events are counted at each step:

Diffuse S(Q,ω)


Monte Carlo convolution with S(Q,E)

scan E=const.

QX

QY

Ener

gy

scan Q=const.Zero-width dispersion:

Events are sorted according to their distance from the dispersion branch


TAS: conventional arrangement

monochromator

sample

analyzer

detector


TAS: flat-cone analyzer

monochromator

sample

analyzer

detector


TAS: flat-cone multianalyzer

monochromator

sample

analyzer

detector


Mapping reciprocal space

New flat-cone analyzer for ILL TAS instruments, 32 channelsIN20: monochromator Si, ki=3 A-1

0 1 2 3-2

-1

0

1

2

3

ξ

[0 1

0]

E=0 meV

0 1 2 3

E=4 meV

ξ [1 0 0]0 1 2 3

E=12 meV

non-linear scans in rec. lattice

a3

a4


Example 1: Incommensurate satellites

Incommensurate satellites: ∆E →∞

210

010

200

210000

010110

E

raw data10 20 30 40 50 60 70 80

-40

-20

0

20

40

E=4 meV

a4 [deg]

a3 [d

eg]

M.C. ray-tracing & convolution with S(Q,E)


Example 1: Incommensurate satellites

0 1 2 3-2

-1

0

1

2

3

ξ [0

1 0

]

E=0 meV

0 1 2 3

E=4 meV

ξ [1 0 0]0 1 2 3

E=12 meV

... and transformed to rec. lattice space


Example 2: bond charge model (BCM)

Model describing phonons in diamond lattice (Si, Ge, α-Sn, ...)Eigenvalues & eigenvectors are calculated using coulombic potential of bond charges for each of Q,E points representing simulated TAS resolution functionW. Weber, Phys. Rev. B 15 (1977) 4789.

phonons in Si


E=20 meV

Phonons in Si

MC simulation for IN20kf=3A-1, E=20meV64 channels, ∆a4=1.25o

91 steps, ∆a3=0.75o

convolution with flat-cone resolutionsimulated by ray-tracingCPU time: 4 hours


SIMRESsource: arbitrary energy, spatial and angular distributions via look-up tables

crystals: focusing arrays of elastically bent or mosaic crystals (incl. simulated extinction effects, absorption, etc...)

collimators: universal components• coarse and Soller collimators• curved guides or benders• elliptic or parabolic guides

(multilamellar)

tools for• simulation of absolute neutron flux• Resolution and intensities for

inelastic scattering and powder diffraction

• numerical optimization for any of ~ 280 instrument parameters

7 collimator segments

sample

crystal assemblies

source

detector

M11M10

M9

M8M7

M6M5M4M3

M2

M1

M0


Source definition: lookup tables

Resampling TRIPOLI data for H53:

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

β [rad]

Y [m

m]

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15-30

-20

-10

0

10

20

30

α [rad]X

[mm

]

horizontal vertical

in the middle stream

)(4 λφλ

φπΩ∂∂

∂

0.1 1 100.01

0.1

1

10

100

H53 entry, middle stream, TRIPOLI HCS, by P. Ageron (1989)

dφ/d

λ [1

012 n

/s/c

m2 /A

]

λ [A]

used as look-up tables in RESTRAX ⇒


Mosaic and gradient crystals

• Random-walk model for secondary extinction

( ) ( )

⋅−⋅−∆=∆ −

segkin

PQ

graderferfgrad

t ξθθθ

η 1log1

( ) ( )θξ ∆⋅−−=∆ gQPt kinseg1log

( )θ∆g

mosaic

mosaic & gradientTilted segments of mosaic crystalsMigration between segmentsOptional uniform lattice gradient - theoretical

model by Hu H.-C., J. Appl. Cryst.26, 1993, 251-257.

Absorption - capture, TDS, incoherent scattering by Freund A. K., Nucl. Instr. Meth.A 213, 1983, 495-501.

• Random walk steps: ∆t

• Sampling procedure

Mosaic distribution:

where Pseg is the total scattering probability for 1 segment


Multichannel parabolic & elliptic guides

Test: point to point focusing:guides: 21x21 slots, space 1.8 mm, lam. thickness 0.2 mm, m=3 source: 1x1 mm2, λ=4.5 A

30 cm

300 cm

30 cm

-20 -10 0 10 20

-20

-10

0

10

20

X [mm]

Y [m

m]

spatial distribution

-0.04 -0.02 0.00 0.02 0.04

-0.04

-0.02

0.00

0.02

0.04

kY/k [rad]

k Y/k

[rad

]

angular distribution




30 cm

300 cm

30 cm

-20 -10 0 10 20

-20

-10

0

10

20

X [mm]

Y [m

m]


-0.04 -0.02 0.00 0.02 0.04

-0.04

-0.02

0.00

0.02

0.04

kY/k [rad]

k Y/k

[rad

]





30 cm

300 cm

30 cm

-20 -10 0 10 20

-20

-10

0

10

20

X [mm]

Y [m

m]


-0.04 -0.02 0.00 0.02 0.04

-0.04

-0.02

0.00

0.02

0.04

kY/k [rad]

k Y/k

[rad

]



Multichannel guide & focusing monochromator

Multichannel guide• 20 (hor.) or 30 (ver.) blades• thickness 0.5 mm• m=3 supermirror (concave sides)• elliptic & parabolic profiles• optimisation: entry & exit width

TAS - IN14 setup• cold source• straight 58Ni guide, 6x12 cm2

• monochromator: PG 002, doubly focusing, λ=4.05 Å

• target (sample) area: 3x3 mm2

• optimisation: crystal curvatures

50 cm30 cm

50 cm

8 cm12

.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.2

0.4

0.6

0.8

1.0

refle

ctiv

ity

m


Mapping of parameter space

-0.2 0.0 0.2 0.440

50

60

70

80

90

ρH [m-1]

exit

wid

th [m

m]

0.0 0.2 0.4 0.670

80

90

100

110

120

ρV [m-1]

exit

heig

ht [m

m]

Multiple instrument parameters can be optimized simultaneously

Example for parabolic guide exit width/height and monochromator curvature

Intensity/∆E Intensity

horizontal vertical


Multichannel guide & focusing monochromator

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

x [mm]

y [m

m]

-0.08 -0.04 0.00 0.04 0.08-0.08

-0.04

0.00

0.04

0.08

kx/k

k y/k

Parabolic blades


Incident beam in k-space

-0.05 0.00 0.051.51

1.52

1.53

1.54

1.55

1.56

1.57

1.58

1.59

horizontal divergence [rad]

k [A

-1]

transmitted

reflected

no dispersion of reflected neutrons=>

improved energy resolution

Sample at the focal point: the guide selects quasi-parallel beam after the monochromator


Resolution function

-0.10 -0.05 0.00 0.05 0.10-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(0 0 ξ)

∆E [m

eV]

-0.10 -0.05 0.00 0.05 0.10-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(ξ 0 0)

∆E [m

eV]

mul

ticha

nnel

gui

de

-0.2 -0.1 0.0 0.1 0.20

1000

2000

3000

4000

Inte

nsity

[rel

. uni

ts]

∆E [meV]

-0.10 -0.05 0.00 0.05 0.10-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(ξ 0 0)

∆E [m

eV]

-0.10 -0.05 0.00 0.05 0.10-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(0 0 ξ)∆E

[meV

]

no g

uide

-0.2 -0.1 0.0 0.1 0.20

1000

2000

3000

4000

Inte

nsity

[rel

. uni

ts]

∆E [meV]


Concluding remarksPlans for future development• GUI for SIMRES

• merging the ray-tracing codes of RESTRAX and SIMRES in a single kernel

• splitting code into client and server parts

• further development of neutron optics elements

RESTRAX homepage::http://omega.ujf.cas.cz/restrax/

http://omega.ujf.cas.cz/restrax/

Documents

Introduction to RESTRAXlns00.psi.ch/mcworkshop/papers/RESTRAX_introduction.pdfModel describing phonons in diamond lattice (Si, Ge, α-Sn, Eigenvalues & eigenvectors are calculated