measurements of the thermal neutron scattering...
TRANSCRIPT
Measurements of the Thermal Neutron
Scattering Kernel
Li (Emily) Liu, Yaron Danon, Bjorn Becker, Devin P. Barry, Xin Li, Bin Wu
MANE, Rensselaer Polytechnic Institute
Alexander Kolesnikov
Oak Ridge National Lab/Spallation Neutron Source
Symposium on Nuclear Data for Criticality Safety and Reactor Applications, April 27, 2011.
2
Motivation and objectives
Approach-SEQUOIA
Present study
Results and discussions
Problems and Future study
Questions
3 M. Mattes and J. Keinert, Thermal Neutron Scattering Data for the Moderator Materials H2O, D2O and ZrHx in ENDF-6
Format and as ACE Library for MCNP(X) Codes, IAEA INDC(NDS)-0470, 2005.
IKE vs. ENDF/B-VI
Experimental Validation
4
The latest experimental data used was from 1973-1974!
M. Mattes and J. Keinert, Thermal Neutron Scattering Data for the Moderator Materials H2O, D2O and ZrHx in ENDF-6
Format and as ACE Library for MCNP(X) Codes, IAEA INDC(NDS)-0470, 2005.
Bischoff, F., et al., “Low Energy Neutron Inelastic
Scattering”, RPI-328-87, 1967.
The world’s most powerful neutron source, the $1.4 billion Spallation Neutron Source
At 1.4MW, SNS produces neutron flux ~8 times higher than ISIS, previous the
highest flux spallation neutron source in the world. SNS will feature 24 beamlines
for physics, chemistry, biology, materials research. www.sns.gov
Production of Neutrons for Materials
Research
• Reactors reaching a flux level limited by heat dissipation
• Pulsed source flux level not limited of heat dissipation, but pending further development of accelerator and target/moderator technology
• High peak flux and the time structure are advantageous to many applications
• Coproduction of epithermal, thermal and cold neutrons
SNS Instrument Beam Lines
8
1st
experiment proposed 2nd
experiment
SEQUOIA Fine-Resolution Fermi Chopper Spectrometer
Atomic-scale dynamics at thermal and epithermal energies – translations, rotations,
and vibrations.
EI = 10 to 2000 meV, 900 3He detector tubes,wide temperature/pressure capabilities
Horizontal -30 to -3 and 3 to 60, Vertical -30 to -3 and 3 to 30
Flux: > 1×105 neutrons/cm2s
E/EI ~ 1%
SEQUOIA spectrometer
Direct Geometry ToF
Fix the incident energy EI and use time of flight to determine the final energy EF
Detectors Moderator
Monochromating
chopper LC
LI
LF Sample
Phase time
at chopper
Flight time
at sample
Final flight
time
Energy transfer
E = EI - EF
18 m
2 m
5.5 m
F
FIF
E
LTTT 2284
I
II
E
LT 2284
I
CC
E
LT 2284
[msec]
[m]
[meV]
Ef kf
Sample
Ei ki
momentum = hk energy = (hk)2/(2m)
k=2p/l
Q = ki - kf
hw = Ei - Ef
Measure the number of scattered neutrons
as a function of Q and w
depends ONLY on the sample
Scattering Geometry
14
2 2Q / 2mkT
/ kT
S , kTS Q,
w
w
Transformation from S(Q,w) to S(α,).
where kT is the temperature in eV.
d2H
ddw 2N
H
4p
k f
kiSH(Q,w)
Experiment Measures Double Differential Cross Section
=> Dynamic Structure Factor S(Q,w)
(the Van Hove scattering function for quasi-elastic and inelastic
scattering)
Elastic
16
Inelastic Scattering from molecular vibrations
If atoms oscillate around fixed positions:
-intermediate scattering function I(q,t) has
oscillating component;
-the dynamic structure factor S(q,w) has an
inelastic component shifted in energy E=ħw. Also
significant elastic component is present.
Quasi-elastic Scattering from translation, rotation and conformation-jump motions
If atoms change their position:
-I(q,t) decays with a rate that is inversely
proportional to characteristic relaxation time of the
motion t;
-S(q,w) has quasielastic component (broadening of
the elastic line) with the width inversely proportional
to t. Depending on type of motion, elastic component
can be present.
)],([),( tQIFTQS w
17
Summary of the 1st SEQUOIA experiment (~ 4 days)
EI (eV) H2O PE Empty Can Vanadium
0.055 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
0.16 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
0.25 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
0.6 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
1 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
3 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
5 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs
Sample sizes: The vanadium sample is 50x50x2.12 mm3 size in the neutron beam. The
actual samples of H2O and PE were 0.1 mm thick samples, which means 50x 50x 0.1 mm3
in the neutron beam.
Temperature: Room – 27 oC.
Scattered angles : 5, 10, 15, 20, 35, 40, 45, 50, and 55 degrees.
Data Reduction
18
Vanadium White
CanEmpty from Counts - Sample from Counts
Counts vs. scattered energy is normalized
through vanadium file to double differential cross
section vs. scattered energy.
19 Esch et al., The Temperature Dependence of Neutron Inelastic Scattering
from Water, Nuclear Science and Engineering: 46, 223-235, 1971.
Ei=160 meV
20 Esch et al., The Temperature Dependence of Neutron
Inelastic Scattering from Water, Nuclear Science and
Engineering: 46, 223-235, 1971.
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 7500.01
0.1
1
10
100
S(Q
,w)
(ba
rn/s
r e
V)
Ef (meV)
40o
25o
14o
10o
Ei=600 meV
Etrans=40~130 meV: intermolecular librational vibrations of water
Etrans=200 meV: intramolecular H-O-H bending vibrations
Etrans=400~450 meV: intramolecular stretching O-H modes (symmetric and asymmetric)
0 50 100 150 200 250 300
1x104
2x104
3x104
4x104
5x104
6x104
7x104
8x104
d
dX
S [
co
un
ts]
E' [meV]
Exp. V (25 deg., 160 meV)
MCNP V (25 deg., 160 meV, normalized to Exp)
0 50 100 150 200 250 300
100
101
102
103
104
105
106
dd
XS
[co
un
ts]
E' [meV]
Exp. V (25 deg., 160 meV)
MCNP V (25 deg., 160 meV, normalized to Exp)
Vanadium
Discussions-H2O
0 20 40 60 80 100 120 140 160 180 200 220
2
10
100
1000
3000
dd
XS
[b
/sr/
eV
]
E' [meV]
Exp. (10 deg., 160 meV)
Exp. (old RPI, 10 deg., 154 meV)
ENDF/B VII (10 deg., 160 meV, E/E
i ~2.3%)
0 20 40 60 80 100 120 140 160 180 200 220
5
10
100
1000
2000
dd
XS
[b
/sr/
eV
]
E' [meV]
Exp. (15 deg., 160 meV)
Exp. (old RPI, 14 deg., 154 meV)
ENDF/B VII (15 deg., 160 meV, E/E
i ~2.3%)
0 20 40 60 80 100 120 140 160 180 200 220
5
10
100
1000
2000
dd
XS
[b
/sr/
eV
]
E' [meV]
Exp. (25 deg., 160 meV)
Exp. (old RPI, 25 deg., 154 meV)
ENDF/B VII (25 deg., 160 meV, E/E
i ~2.3%)
0 20 40 60 80 100 120 140 160 180 200 220
5
10
100
1000
dd
XS
[b
/sr/
eV
]
E' [meV]
Exp. (40 deg., 160 meV)
Exp. (old RPI, 40 deg., 154 meV)
ENDF/B VII (40 deg., 160 meV, E/E
i ~2.3%)
Discussions-H2O
0 20 40 60 80 100 120 140 160 180 200 220
5
10
100
1000
dd
XS
[b
/sr/
eV
]
E' [meV]
Exp. (40 deg., 160 meV)
ENDF/B VII (37.5 deg., 160 meV, E/E
i ~0.0%)
ENDF/B VII (40.0 deg., 160 meV, E/E
i ~2.3%)
ENDF/B VII (42.5 deg., 160 meV, E/E
i ~5.0%)
0 20 40 60 80 100 120 140 160 180 200 220
5
10
100
1000
dd
XS
[b
/sr/
eV
]
E' [meV]
Exp. (40 deg., 160 meV)
ENDF/B VII (37.5 deg., 160 meV, E/E
i ~2.3%)
ENDF/B VII (40.0 deg., 160 meV, E/E
i ~2.3%)
ENDF/B VII (42.5 deg., 160 meV, E/E
i ~2.3%)
2
4
Temperature Dependent Neutron Scattering Cross
Sections for Polyethylene
R. Hilla and C.-Y. Liu, arXiv:nucl-th/0309011v2
Discussions-PE
0 50 100 150 200 250 300 350 4000.01
0.1
1
10
100
1000
S(Q
,w)
(ba
rn/s
r e
V)
Ef (meV)
10o
40o
25o
14o
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 7500.01
0.1
1
10
100
S(Q
,w)
(ba
rn/s
r e
V)
Ef (meV)
10o
40o
25o
14o
0 50 100 150 200 250 3000.1
1
10
100
1000
S(Q
,w)
(ba
rn/s
r e
V)
Ef (meV)
10o
40o
25o
14o
Ei=160 meV
Ei=250 meV
Ei=600 meV
Etrans=360 meV: stretching vibrations of (covalent bond) C-H modes
Etrans=170 meV: bending C-H modes
Etrans=90~130 meV: other intramolecular vibrations
26
Problems and future study
Include time-independent background and multiple-scattering corrections into data reduction.
Analyze all data of H2O and PE.
Insufficient angle coverage of SEQUOIA. We will use ARCS (the Wide Angular-Range Chopper Spectrometer) in addition to SEQUOIA.
Proper identification of the reasons associated with the discrepancies.
27
Acknowledgement
Thanks for your attention.
Questions?
28 0 50 100 150 200 250 300
0
10
20
30
40
50
60
70
80
E = 231 meV; theta = 60 deg.
dd
XS
[b
/sr/
eV
]
E' [meV]
ENDF/B VII calculation
ENDF/B VI calculation
ENDF/B VI (Mattes paper)
IKE (Mattes paper)
Bischoff et al. (Mattes paper)
0 50 100 150 200
0
10
20
30
40
50
60
70
80
90
100
110
E = 154 meV; theta = 60 deg.
dd
XS
[b
/sr/
eV
]
E' [meV]
ENDF/B VII calculation
ENDF/B VI calculation
ENDF/B VI (Mattes paper)
IKE (Mattes paper)
Bischoff et al. (Mattes paper)