Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1...
Transcript of Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1...
![Page 1: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/1.jpg)
Quasielastic Neutron Scattering (QENS)
Joachim WuttkeForschungszentrum JülichJülich Centre for Neutron Science at MLZ GarchingScientific Computing Grouphttp://apps.jcns.fz-juelich.de
SISN data analysis school, June 2016
MLZ is a cooperation between
![Page 2: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/2.jpg)
outline
What is QENS?What makes QENS analysis special and difficult?What software do we need?
2
![Page 3: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/3.jpg)
ressources
http://apps.jcns.fz-juelich.deposters and talks > slides of this talkpublications > Quasielastic Scattering, spring school 2012Frida > download, installation instructions, tutorial
3
![Page 4: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/4.jpg)
TOF spectracoenzyme Q10
Smuda
etal:J
ChemPhys
2008,measured
onTO
FTOF
(FRMII)
4
![Page 5: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/5.jpg)
quasielastic scatteringcoenzyme Q10
Smuda
etal:J
ChemPhys
2008,measured
onTO
FTOF
(FRMII)
5
![Page 6: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/6.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
6
![Page 7: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/7.jpg)
decoupling scattering ←→ sample physics
∂2σ
∂ω∂Ω=
kfki
Nσ4π S(q, ω)
7
![Page 8: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/8.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
Def 2broadened elastic peak
8
![Page 9: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/9.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
Def 2broadened elastic peak
8
![Page 10: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/10.jpg)
methyl group dynamics in a molecular solidtetramethylpyrazine : picric acid
Sawka-Dobrowolska
etal:J.M
ol.Struct.
2010
9
![Page 11: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/11.jpg)
methyl group dynamics in a molecular solidtetramethylpyrazine : picric acid
−5 −2.5 0 2.5 5
hω (µeV)
10
100
1000
S(q
,ω)
(µe
V−
1)
80 K
50 K
Sawka-Dobrowolska
etal:J.M
ol.Struct.
2010,measured
onSPH
ERES(JCN
SatFRM
II)
10
![Page 12: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/12.jpg)
methyl group dynamics in a molecular solidtetramethylpyrazine : picric acid
−5 −2.5 0 2.5 5
hω (µeV)
10
100
1000
S(q
,ω)
(µe
V−
1)
80 K
50 K
35 K
Sawka-Dobrowolska
etal:J.M
ol.Struct.
2010,measured
onSPH
ERES(JCN
SatFRM
II)
10
![Page 13: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/13.jpg)
methyl group dynamics in a molecular solidtetramethylpyrazine : picric acid
−5 −2.5 0 2.5 5
hω (µeV)
10
100
1000
S(q
,ω)
(µe
V−
1)
80 K
50 K
35 K
30 K
Sawka-Dobrowolska
etal:J.M
ol.Struct.
2010,measured
onSPH
ERES(JCN
SatFRM
II)
10
![Page 14: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/14.jpg)
methyl group dynamics in a molecular solidtetramethylpyrazine : picric acid
−5 −2.5 0 2.5 5
hω (µeV)
10
100
1000
S(q
,ω)
(µe
V−
1)
80 K
50 K
35 K
30 K
4 K
Sawka-Dobrowolska
etal:J.M
ol.Struct.
2010,measured
onSPH
ERES(JCN
SatFRM
II)
10
![Page 15: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/15.jpg)
rotational tunnelingmethyl group CH3
ψA = ψ1 + ψ2 + ψ3
ψE = ψ1 + e±i2π/3ψ2 + e∓i2π/3ψ3
Press,Single-particlerotation
inm
olecularcrystals(1981)
11
![Page 16: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/16.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
Def 2broadened elastic peak
Def 3slow modes
Def 4measured on TOF/BS/NSE spectrometer
Def 5presented at QENS conference
12
![Page 17: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/17.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
Def 2broadened elastic peak
Def 3slow modes
Def 4measured on TOF/BS/NSE spectrometer
Def 5presented at QENS conference
12
![Page 18: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/18.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
Def 2broadened elastic peak
Def 3slow modes
Def 4measured on TOF/BS/NSE spectrometer
Def 5presented at QENS conference
12
![Page 19: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/19.jpg)
what does ‘quasielastic’ mean ?
Def 1|ℏω| ≪ Ei
Def 2broadened elastic peak
Def 3slow modes
Def 4measured on TOF/BS/NSE spectrometer
Def 5presented at QENS conference
12
![Page 20: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/20.jpg)
quasielastic light scattering
Quasielastic light scattering
dynamic light scatteringphoton-correlation spectroscopy
figurefrom
wikipedia
13
![Page 21: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/21.jpg)
confused terminology
Quasielastic light scattering
photon-correlation spectroscopy |E|4 µs …s
Raman-Brillouin scattering
grating spectrometer, interferometer |E|2 GHz …THz
Neutron scattering
quasielastic ≃ high-resolution |ψ|2 GHz …THz
14
![Page 22: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/22.jpg)
scattering kinematicsgeneric case
2ϑ
kf (ω>0)
kf (ω=0)
kf (ω<0)
ki
q (ki,ϑ,ω)
15
![Page 23: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/23.jpg)
scattering kinematics
−15 −10 −5 0 5
Ei − Ef (meV)
0
1
2
3
4q (
A−
1)
Ei = 4 meV0°
60°
120°
180°
16
![Page 24: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/24.jpg)
scattering kinematicsquasielastic case |ℏω| ≪ Ei
ϑ
kf (ω≈0)
ki
q = 2 ki sin ϑ
17
![Page 25: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/25.jpg)
resolution broadening
−10 −5 0 5 10
ω
10−4
10−3
10−2
10−1
S (
ω)
ΩS :
0.025
0.1
0.4
1.6
scattering function:
S(ω) = 1π
ΩSω2+Ω2
S
resolution:
R(ω) = 1√2πΩR
exp(− ω2
2Ω2R
)convolution:
SR(ω) =∫
dω′ R(ω−ω′)S(ω′)
18
![Page 26: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/26.jpg)
resolution broadening
−10 −5 0 5 10
ω / ΩR
10−4
10−3
10−2
10−1
S (
ω)
(ΩR
−1)
ΩS / ΩR :
0.025
0.1
0.4
1.6
scattering function:
S(ω) = 1π
ΩSω2+Ω2
S
resolution:
R(ω) = 1√2πΩR
exp(− ω2
2Ω2R
)
convolution:
SR(ω) =∫
dω′ R(ω−ω′)S(ω′)
18
![Page 27: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/27.jpg)
resolution broadening
−10 −5 0 5 10
ω / ΩR
10−4
10−3
10−2
10−1
S (
ω)
(ΩR
−1)
ΩS / ΩR :
0.025
0.1
0.4
1.6
scattering function:
S(ω) = 1π
ΩSω2+Ω2
S
resolution:
R(ω) = 1√2πΩR
exp(− ω2
2Ω2R
)convolution:
SR(ω) =∫
dω′ R(ω−ω′)S(ω′)
18
![Page 28: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/28.jpg)
resolution histogram ⊗ sharply peaked theory
−2 0 2
hω (µeV)
0.1
1
10
100
1000
S(q
,ω)
(µe
V−
1)
(R⊗ T)(ω) =∑
ω′ R(ω − ω′)T(ω′)
must be replaced by
(R⊗ T)(ω) =∑
ω′ R(ω − ω′) [P(ω′+∆ω/2)− P(ω′−∆ω/2]
Wuttke,Algorithm
s(2012)
19
![Page 29: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/29.jpg)
![Page 30: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/30.jpg)
-10 -5 0 5 10
hω (µeV)
0.001
0.01
S (
q,ω
) (
µeV
-1)
1.0 ± 0.15 A-1
300 K274 K250 K240 K230 K217 K200 K100 K
0 0.5 1
hω (µeV)
0.1
1
S (
q,ω
) /
S (
q,0
)
3 4 5 6
1000 K / T
10-11
10-10
10 -9
10 -8
10 -7
10 -6
10 -5
⟨τ⟩ (s
)
CPC improved fit
CPC standard fit
lysozyme
myoglobin
myoglobin (NMR)
myoglobin (diel)
TL
(∆ω)-1
![Page 31: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/31.jpg)
Fourier deconvolutionrelaxation in a molecular glass former
SR(ω) =∫
dω′ R(ω−ω′)S(ω′) =⇒ I(t) = IR(t)/R(t)
IN13IN6IN5
o-terphenyl 1.2A-1
293 K
298 K
306 K
312 K
320 K
327 K
1 10 1000
0.2
0.4
0.6
0.8
t (psec)
I (q
,t)
Wuttke
etal:Z.Phys.
B(1993),m
easuredatthe
ILL
22
![Page 32: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/32.jpg)
S(ω) vs I(t)
0
ω
0
S (
ω)
t
0
1
I (t
)
23
![Page 33: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/33.jpg)
S(ω) vs I(t)
10−13 s−1 0 10−13 s−1
ω
0
S (
ω)
ps
log t
0
1
f
I (t
)
S(ω) = fδ(ω) + (1− f)Sphonons(ω)
f =
Debye-Waller factor (coherent scattering)Lamb-Mössbauer factor (incoherent scattering)
24
![Page 34: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/34.jpg)
S(ω) vs I(t)localized motion
10−13 s−1 0 10−13 s−1
ω
0
S (
ω)
ps
log t
0
1
f
f A
I (t
)
S(ω) = f [Aδ(ω) + (1− A)Squasiel.(ω)] + (1− f)Sphonons(ω)
A = elastic incoherent structure factor (EISF)
25
![Page 35: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/35.jpg)
elastic incoherent structure factor2-site jump model, jump length 1.2 Å
0 2.5 5 7.5 10 12.5
q (A−1)
0
0.25
0.5
0.75
1
EIS
F
IN10, IN16, HFBS, SPHERES
IN13
Bée:Q
uasielasticneutron
scattering(1988,outofprint)
26
![Page 36: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/36.jpg)
S(ω) vs I(t)localized motion
10−13 s−1 0 10−13 s−1
ω
0
S (
ω)
ps
log t
0
1
f
f A
I (t
)
S(ω) = f [Aδ(ω) + (1− A)Squasiel.(ω)] + (1− f)Sphonons(ω)
A = elastic incoherent structure factor (EISF)
27
![Page 37: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/37.jpg)
S(ω) vs I(t)long-ranged motion
10−13 s−1 0 10−13 s−1
ω
0
S (
ω)
ps
log t
0
1
f
f A
I (t
)
S(ω) = fSquasiel.(ω) + (1− f)Sphonons(ω)
28
![Page 38: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/38.jpg)
basic functions for Squasiel.(ω)
ballistic short-time limit:S(ω) ∼ exp(−τ2ω2/2) I(t) = 1− t2/2τ2 + . . .
diffusion, rotational diffusion, jump models:
S(ω) ∼(1 + τ2ω2)−1 I(t) = exp(−t/τ)
complex relaxation: e.g.S(ω) ∼ Re (1 + i(ωτ)α)−γ I(t) = exp(−(t/τ)β)
29
![Page 39: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/39.jpg)
localized motion: rotation in a molecular solid(CH3NH3)5Bi2Br11
−10 0
hω (µeV)
0.1
1
10
100
S(q
,ω)
(ve
rtic
ally
sh
ifte
d) (CH3NH3)5Bi2Br
65 K
75 K
85 K
100 K 10 12.5 15 17.5
1000 K / T
0.1
1
10
τ (
ns)
Tc
weight 2
weight 3
Piechaetal,publication
overdue,measured
onSPH
ERES(JCN
SatFRM
II)
30
![Page 40: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/40.jpg)
Ni diffusion in Ni:Zr melt
Ni36Zr64
Q = 0.9 A−1
T = 1650 K
T = 1290 K
0 1 2
hω (meV)
0.01
0.1
1
S(q
,ω)
(m
eV
−1)
Ni36Zr64
T = 1650 K
T = 1345 K
T = 1210 K
1 2 3
Q2 (A−2)
0
0.2
0.4
0.6
Γ Q (m
eV
)
Lorentzian fits ⇒ width Γ ⇒ diffusion coefficents D = Γ/q2
Holland-M
oritzetal:
PhysRev
B(2009),m
easuredon
TOFTO
F(FRM
II)
31
![Page 41: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/41.jpg)
H motion in n-alkanes
CnH2n+2
NMR
QENS
100 1000
molecular mass
10−10
10−9
10−8
D
(m2/s
)
C32H66
1 10 100 1000
resolution time (ps)
0
1
2
3
D (1
0−
9 m
2/s
)
small-q (NMR): center-of-mass diffusionlarge-q (QENS): intra-chain (Rouse) motion
Smuda
etal:J
ChemPhys;Unruh
etal:ibid
(2008),measured
onTO
FTOF
(FRMII)
32
![Page 42: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/42.jpg)
two steps of data analysis
neutron counts N(j,i)
data reduction
scattering law S(q,ω)
data analysis, fitting, interpretation
results
33
![Page 43: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/43.jpg)
two steps of data analysisbut: reduced data still contain resolution and multiple scatering
neutron counts N(j,i)
data reduction
scattering law S(q,ω) ⊗ R(ω)
data analysis, fitting, interpretation
results
34
![Page 44: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/44.jpg)
data analysis is circular
neutron counts N(j,i)
data reduction
scattering law Sexp(q,ω) ⊗ R(ω)
inspection fit
fit model Stheo(q,ω) ⊗ R(ω)
fit parameters
35
![Page 45: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/45.jpg)
shall we fit raw data?
neutron counts N(j,i)
data reduction
scattering law Sexp(q,ω) ⊗ R(ω)
inspection
fit
fit model Stheo(q,ω) ⊗ R(ω) ⊗ D(q,ω)
fit parameters
36
![Page 46: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/46.jpg)
rank of datarank 3:S(q, ω;T) inelastic temperature scanS(q, ω; t) other inelastic time scan
rank 2:S(q, ω) regular scanS(ω; t) q-averaged/selected time scanS(q, 0; t) elastic time scan
rank 1:S(ω) q-averaged/selected spectrumS(q, 0) elastic intensity
37
![Page 47: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/47.jpg)
inelastic T scan at SPHERES
Mg(NH3)6Cl2
|E| < 0.25µeV
|E| > 1.2 µeV
inelast x 100
elast
0 50 100 150 200 250
T (K)
0
200
400
600
800
counts
(s
−1)
Q.Lietal,m
easuredon
SPHERES,unpublished
38
![Page 48: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/48.jpg)
Real-time kineticsdecomposition of sodium alanate
3 NaAlH4 → Na3AlH6 + 2 Al + 3 H2
Na3AlH6 → 3 NaH + Al + 1.5 H2
3 NaH → 3 Na + 1.5 H2
-5 0 5
hω (µeV)
0.01
0.1
1
S(q
,ω)
(µe
V-1
)
NaAlH4
177°C 0.. 5 h
15..20 h
30..35 h
45..50 h
64..69 h
Léon&
Wuttke,J
PhysCondensed
Matt(2011),m
easuredon
SPHERES
(JCNS
atFRMII)
39
![Page 49: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/49.jpg)
real-time kineticsdecomposition of sodium alanate
-5 0 5
hω (µeV)
0.01
0.1
1
S(q
,ω)
(µe
V-1
)
NaAlH4
177°C 0.. 5 h
15..20 h
30..35 h
45..50 h
64..69 h
0 25 50 75 100
t (h)
0
0.2
0.4
0.6
0.8
am
plit
udes
0 25 50 75 100
t (h)
0
0.2
0.4
0.6
0.8
am
plit
udes
NaAlH4 → Na3AlH6 → NaH
total
elastic
Lorentzian (Na3AlH6)
d[A]/dt = −k00[A]− k01[A][B]2
d[B]/dt = −d[A]/dt− d[C]/dtd[C]/dt = k10[B]4/3 + k11[B]4/3[C]2/3
Léon&
Wuttke,J
PhysCondensed
Matt(2011),m
easuredon
SPHERES
(JCNS
atFRMII)
40
![Page 50: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/50.jpg)
rank reduction cascadescattering law Sexp(ω; q,T) ⊗ R(ω)
inspection fits for individual q,T
fit model Stheo(ω) ⊗ R(ω)
parameters Pexp(q;T)
inspection fits for individual T
fit model Ptheo(q)
parameters pexp(T)
inspection fit
fit model ptheo(T)
global parameters
41
![Page 51: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/51.jpg)
feed outcome back into modelscattering law Sexp(ω; q,T) ⊗ R(ω)
fit model Stheo(ω) ⊗ R(ω) global fit Stheo(ω,q,T) ⊗ R(ω)
fit
parameters Pexp(q;T)
fit model Ptheo(q) derive constraints
parameters pexp(T)
fit model ptheo(T)
global parameters
42
![Page 52: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/52.jpg)
software: Unix vs workbench principle
file plot
tool
file plot
tool
file plot
tool
file plot
tool
file
file
workspaceworkspaceworkspaceworkspaceworkspace
transform
fit
file plot
43
![Page 53: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/53.jpg)
why workbench?
file
workspaceworkspaceworkspaceworkspaceworkspace
transform
fit
file plot
advantages:saves disk I/Opermanent storage only when requiredcan be GUIfiedefficient CLIsupport out of one hand
disadvantages:less concurrence for best toolsscripting less easy, less standard
perspective:Jupyter notebook
44
![Page 54: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/54.jpg)
QENS data analysis software
1990s:INX, SQW data reduction for time-of-flight / backscatteringIDA → Frida command-line workbench for data analysis
2000s:LAMP GUI workbench for data reduction and analysisDAVE, DANSE
2010s:Mantid GUI workbench for spallation data reduction
2020s ???
45
![Page 55: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/55.jpg)
Frida
a Swiss Army Knife forfast reliable interactive data analysis
History:1990−2001 Ida → Frida1 in Fortran772001− Frida2 in C++
46
![Page 56: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/56.jpg)
Frida
a Swiss Army Knife forfast reliable interactive data analysis
Usage:used by a few groupstaught to users of SPHERES
47
![Page 57: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/57.jpg)
Frida
a Swiss Army Knife forfast reliable interactive data analysis
Status:legacy one-man projectnot an official project of MLZ Scientific Computing Group
48
![Page 58: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/58.jpg)
Frida
a Swiss Army Knife forfast reliable interactive data analysis
Hasopen-source licencedownload page, CMakeversion controlfrequent releasessome tutorialssome tests
Hasn’tGUIuser manualfull test coverage
49
![Page 59: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/59.jpg)
Frida
a Swiss Army Knife forfast reliable interactive data analysis
a collection of algorithmsoperating on data files in RAM (»workspaces«)controlled by a concise (cryptic) command-line interfacewith dedicated fit models for QENSgenerating human editable PostScript graphics
50
![Page 60: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/60.jpg)
−10 0 10
E (ueV)
0.1
1
10
S(E
,q)
(u
eV
−1
)
gly5 mfj # gly5 is merger of: − gly255 glycerol measured on SPHERES by J.Wuttke reduced data set for Frida tutorial fs gly255.y08 # Fri Aug 10 16:16:30 2012 mpaf 3 mr j==8 − gly275 ===fs gly275.y08 # Fri Aug 10 16:16:31 2012 − gly295 ===fs gly295.y08 # Fri Aug 10 16:16:31 2012 − gly305 ===fs gly305.y08 # Fri Aug 10 16:16:31 2012
0 254.107 1.41697 1 274.146 1.41697 2 293.905 1.41697 3 304.177 1.41697
fit_gly5 cc p0*pconv(kwwp(t,p1,p2)) # z from gly5 p0*pconv(kwwp(t,p1,p2)) data file: 14, conv file: 13, weighing: with reciprocal variance (data and curve) j z0 z1 p0 p1 p2 oc chi^2 1−R^2
0 254.107 1.41697 24.1952 292.671 0.414796 1 1.80418 0.134212 1 274.146 1.41697 23.3787 22.3248 0.484547 1 3.21818 0.352675 2 293.905 1.41697 21.9556 1.25831 0.551861 1 1.21577 0.599272 3 304.177 1.41697 20.9664 0.521076 0.586763 1 1.34236 1.75922
plot −> /home/jwu/pub/V/17/1704−Frida/gly_join.ps
8 minutes manual editing
−10 0 10
hω (µeV)
0.1
1
10
S(q
,ω)
(µe
V−
1)
304 K
294 K
274 K
254 K
180 K
51
![Page 61: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/61.jpg)
PS file → original data points
1 [ 254.107 1.41697 ] zValues1 pstyle % (E (ueV) -> S(E,q) (ueV -1))0.36000 1.58792 0.21947 ti % -13.92 wx 0.04215903 wy0.44000 1.46066 0.23179 t % -13.68 wx 0.03785536 wy0.52000 1.81438 0.19977 t % -13.44 wx 0.051063 wy[...]
52
![Page 62: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/62.jpg)
fl g*msr! 8mpaf! 31:4 mfj1:4 fdel1 cc p0*pconv(kwwp(t,p1,p2))cv 02 op2 .6cx 2cfcu 2cfg20 p1:2 a :gp graphic_file_name
−10 0 10
E (ueV)
0.1
1
10
S(E
,q)
(ueV
−1)
gly180
glycerol
measured on SPHERES by J.Wuttke
reduced data set for Frida tutorial
fs gly180.y08 # Fri Aug 10 16:16:30 2012
mpaf 3
8 1.41697
gly255
....
53
![Page 63: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/63.jpg)
2 oi .6582*p1/p2*gamma(1/p2)ecy <tau>(ns)ox! 1000/xcc p0*exp(p1*t)cwlcfga3,4 pgp graphic_file_name
3.4 3.6 3.8
1000/T (1/(K))
1
10
100
<ta
u>
(n
s)
fit_gly5
cc p0* pconv(kwwp(t,p1 ,p2)) # z from gly5
oi .6582*p1/p2*gamma(1/p2)
ecy <tau>(ns) # old: 0.658200*p1/p2*gamma(1/p2)()
ox 1000/x
0
fit_fit_gly5
cc p0*exp(p1*t) # z from fit_gly5
p0*exp(p1*t)
data file: 5, weighing: logarithmic
j p0 p1 oc chi^2 1−R^2
0 9.1608e−16 10.367 5 0.203248 8.32178e−07
plot −> /home/jwu/pub/V/17/1704−Frida/gly−tau.ps
54
![Page 64: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/64.jpg)
y is shorthand for y[,,] is shorthand for y[k,j,i]
Command oy f(y) is executed asfor k in file_selection:
for j in [0,nj) spectra in filefor i in [0,ni) points in spectrum
y_out[k_out,j,i] := f(y[k,j,i])
This allows foroy y/y[0] normalize to file 0oy y/y[,0] normalize to spec 0 of current fileoy y/y[,,0] normalize to point 0 of current specoy y/y[k-4,0,j] normalize spec j to point j of spec 0 of file k-4
55
![Page 65: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/65.jpg)
−10 0 10
hω (µeV)
0.1
1
10
S(q
,ω)
(µe
V−
1)
304 K
294 K
274 K
254 K
180 K
3.4 3.6 3.8
1000/T (1/(K))
1
10
100
<ta
u>
(n
s)
extract fit parameter
reduce rank
xω
y
Sq(ω;T)
zT
xT
y
τq(T)
56
![Page 66: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/66.jpg)
x
y
z0
z1
z2
x ← z0
y
z0 ← z1
z1 ← z2
Rank-reducing operations:p0 fit parameter 0ni number of points in spectrumsum(y)
∑y[, , i]
avge(y)∑
y[, , i] / niintegral(x,y)
∫dx y(x) per midpoint rule
valmax(y) maxi y[, , i]idxmin(y) index i for which y[, , i] is minimalcog(x,y) center of gravity in x weighed with ywidth(x,y) standard variation in x weighed with ycorr(x,y) correlation coefficient of x and yfirstwith(expr) first i for which expr is true
57
![Page 67: Quasielastic Neutron Scattering (QENS)apps.jcns.fz-juelich.de/doku/sc/_media/1806-qens.pdf0.01 0.1 1 S(q,w) (m eV-1) NaAlH4 177 C 0.. 5 h 15..20 h 30..35 h 45..50 h 64..69 h 0 25 50](https://reader034.fdocuments.in/reader034/viewer/2022042310/5ed7bddebb7a0a285033353a/html5/thumbnails/67.jpg)
Other functionality:command line as pocket calculatorfunction plotter handling singularities and frame crossingsfunction integration2D color plotsimport/export from/to various tabular formats
58