Wen-Hsien Li (李文献)

Center for Neutron Beam Applications

(中子束應用研究中心)

Department of Physics (物理系)

National Central University (中央大學)

中子散射原理、實驗設施、

與應用實例簡介

(Principles, facilities & applications

of neutron scattering techniques)

whli@phy.ncu.edu.tw

National Central University

散射概念

(Scattering process)

中子束源

(Neutron beam sources)

常用中子散射儀簡介

(Neutron instruments)

應用實例

(Examples)

Content

散射概念

Scattering process

奈米物性實驗室

Viewing atomic landscape

Solid: periodic arrangement of atoms,

consisting of unit cell blocks

Momentum and energy changes of the probes

→ Understanding the atomic arrangement and dynamics

Momentum exchange: yes

Energy exchange: no

Momentum exchange: yes

Energy exchange: yes

Elastic scattering

Inelastic scattering

Incident

neutron

ki

kf

2q ∆k

Elastic scattering (彈性散射) 4 sink = 0

q

22 2

neutron f i f iE = E - E = (k - k ) = 02m

Diffraction for structure

(繞射尋靜態結構)

Incident

neutron

ki

kf

2q ∆k

Inelastic scattering (非彈性散射) 4 sink = 0

q

22 2

neutron f i f iE = E - E = (k - k ) 02m

Excitation for dynamics

(激發尋動態組合)

Physical quantities

Energy scale

o 12.4(A)

(keV)E

Photon : Energy dispersion of

with h = 4.1310-15 eVs and c = 2.998108 m/s.

for photons.

For an x-ray photon of = 1.5 Å E = 8.3 keV.

For a laser photon of = 5145 Å E = 2.41 eV.

/E h hc

2 2 2 2

22 2 2

k pE

m m m

o 0.28 9.04(A)

(eV) (meV)E E

Neutron : Energy dispersion of

with h = 4.1310-15 eVs and m = 1.67510-24 g.

for neutrons.

For a thermal neutron of = 1.5 Å E = 36.3 meV.

Neutron: in the meV (10-3 電子伏特) range

Comparable to the dynamical energy of solids

Epithermal neutron (超熱中子): 200 meV, 0.64 Å

Thermal neutron(熱中子): 20 meV, 2 Å

Cold neutron(冷中子): 2 meV, 6.4 Å

X-ray: in the keV range

Laser: in the eV range

Electron: in the 100 eV range

Energy scale

中子束源

奈米物性實驗室

Reactor neutron source

1. Nuclear fusion processes → proving continuous

free neutrons

2. n + 235U → 36Ba + 56Kr + free n (平均2.5) + betas

3. D2O moderator: 減速核分裂所滋生中子能量

(~1 MeV)至熱中子(eV) 增加連鎖反應速率。

Beam guides

Energetic proton

以高能量質子(500MeV)

撞擊金屬靶

平均每次撞擊可滋生約10個中子

Spallation neutron source

Types of neutron source

Reactor source:

穩態，能量依Maxwellian分佈

以H2O/D2O/石墨降低能量至meV範圍

Cold neutron source:

爐内增設致冷器(液態氫: 20 K)

Spallation source:

脈衝式，瞬時通量較高，TOF techniques

Energy: meV(good for dynamics studies)

Average flux

1 MW spallation source

≈ 10 MW reactor source

Neutron:

carries no charge

small in size relative to atomic radius

heavy in weight relative to electron

mneutron = 1.675 × 10−27 kg

mproton = 1.673 × 10−27 kg

melectron = 9.109 × 10−31 kg

mneutron / melectron = 1838

Strong neutron-nucleus interaction

→ Determine the atom position with high precision

Incident

neutron

atom

What makes neutron so special for diffraction

To detect cation substitution, distribution,

site occupancies and order-disorder processes

Mn Fe Co

X-ray

Neutron

ex.: (Fe, Mn)2SiO4, Al-Mg order-disorder in spinel structure

Al-Si distribution in silicates

What makes neutron so special for diffraction

Strong neutron-nucleus interaction

→ Discriminate elements with similar atomic number

Relative Scattering Powers of the Elements

Neutrons scatter strongly from light elements,

since neutrons scatter mainly from the nuclei.

Scattering length

中子散射作用力

散射作用力:

中子–原子核:強交互作用力

(見到原子核，散射機率並非隨原子序增加而增大)

偵測原子核位置 原子排列方式(晶體結構)

中子自旋–未成對電子自旋:磁偶矩交互作用力

偵測未成對電子自旋 自旋排列方式(磁結構)

對樣品穿透力:

除少數元素(Gd、Cd、Sm、B)外，基本上全然穿透

散射長度因同位素而異:

對比調變(contrast variation)技術

中子束基本功能

˙為一非破壞性探測的工具。

˙能深入系統的內部。

˙目前唯一能探測磁性結構的工具

→ 磁性材料。

˙在重原子間判定輕原子

→ 生化分子裡氫原子的測定。

˙動力組態探討。

→ 所具能量與動力激發子相當。

˙中子影像。

→ 漸層分析，觀看動態氫。

D

H

O Ca Si

Scattering power:

中子能量: meV

中子為電中性

中子具磁耦矩

Amorphous (glass, liquid, gas…)

Elastic scattering (∆E=0)

shows where atoms are

Yarnell, J. L. et. al. Phys. Rev. A (1973) 7, 2130

Peak positions → unit cell size

Peak intensity → positions of atoms

Peak width → block size

20 30 40 50 60 70 80

0

2

4

6

8

10

12 Ho0.82

La0.18

Mn2O

5

Inte

nsi

ty (

10

3 c

ou

nts

)

Scattering angle 2q ( deg. )

T=300 K

g(r

)

0 5 10 15 20 25

r(Å )

1

3

2

0

radial distance

distribution

0 10 20 30 40 θ (deg.)

1000

3000

2000

0

Inte

nsi

ty

Liquid Ar at 85 K

Neutron powder diffraction

Neutron activation analysis

Neutron imaging Inelastic neutron scattering (TOF)

Small angle neutron diffraction

大小 形狀

Motion of H atoms

in a fuel cell

Ancient Greek

hanging bronze oil lamp

Neutron x-ray

Neutron imaging

Neutron x-ray

打火機

Small angle neutron scattering

大小 形狀

常用中子散射儀

簡介

奈米物性實驗室

*

Australian Nuclear Science and

Technology Organisation

OPAL

reactor

Guide

Hall

澳洲雪梨ANSTO

Taiwan

office

Thermal source

20 K liquid H2

cooled cold source

9.045

E meV

1 Å = 82 meV

2 Å = 20.5 meV

4 Å = 5 meV

Neutron flux of OPAL OPAL cold source

Cold head

(liquid H2)

Heat

exchanger

Opal guide and reactor halls

TOF DCS

飛逝時間散射儀

Reflectometer

反射儀

Residual stress

diffractometer

殘餘應力繞射儀

HIPD

高強度 中子繞射儀

SANS

小角度散射儀

Quasi-Laue

diffractometer

準勞厄繞射儀

Thermal-TAS

熱三軸散射儀

HRPD

高解析度 中子繞射儀

Cold-TAS

冷三軸散射儀

Neutron instruments at ANSTO

ANSTO 2nd phase projects:

3He polarizer, USANS, 2nd SANS, Back scattering, Neutron radiography

7+2+5散射儀

Opal neutron beam facility

www.ncnr.nist.gov

NCNR NBSR

TSB

美國華盛頓NIST

Center for Neutron Research

4 new guides

5 new instruments

30+ Neutron Beam Line Instruments

NBSR guide and reactor halls

SAMPLE AREA

GRANITE FLOOR

NIST BT-7 TAS

NIST guide hall

繞射

diffraction

奈米物性實驗室

1. Crystalline structure

atomic composition,

atomic separation

2. Spin arrangement

transition temperature,

magnetic moment,

correlation length,

dimensionality

3. Particle size

The interference pattern of neutrons

being diffracted by the periodic

lattice of solid.

Results of 3D interference.

Cu(2)

O(2)

Cu(1) O(1)

O(4)

Ba

2.4654(15) Å

2.7736(4) Å

74.32°(9)

O(3)

O(5)

2.4458(16) Å

Pr

104.92°(9)

105.68°(9)

75.08°(9)

Purpose

A macroscopic point of view:

Crystals are made out of

parallel planes of spacing d.

θ:Bragg angle, 2θ: scattering angle

Electric scattering:

Momentum transfer:

k k

( )K k k

Constructive interference occurs whenever nλ=2dsinθ,

which is known as the Bragg reflection law.

Bragg reflection (1913)

A, B: lattice points

X: Viewing point

A: origin

Incident wave at B :

Scattered wave at X due to scattering by B:

with

Final scattered wave due to scattering by all lattices:

jik Re

( ) - j j jik R ik r R iK Rik re e e e K k k

- -( ) j jiK R iK Rik r ik r

s

j j

r e e e e

Information on lattice structure, 含晶格結構資訊

Incident wave:

Scattered wave:

ik r

ik r

e

e

: Direct lattice vectorjR

Diffraction wave

幾何結構因子 Structure factor

Two basis at B and B

Scattered wave at X due to scattering

by B:

by B:

with is known as the geometrical structure

factor, which provides the information on the relative

positions between B and B.

( ) -j j jik R ik r R iK Rik re e e e

( ) ( ) - -j j jik R r ik r R r iK R iK rik re e e e e

- - -- -( ) j j jiK R iK R iK RiK r iK rik r ik r ik r

s Kj j j

r e e e e e e e e S

-iK r

KS e

-iK r

KS e

Structural factor of a bcc lattice

bcc lattice = sc lattice + basis at 1 2 1 2 3

10,

2r r a a a

1 2 3Recall K hb kb lb

1

2

0

2

2 2 2

K r

h k lK r h k l

( ) 0 for odd

1 2 for even

i h k lh k l

S hkl eh k l

1. No Bragg peaks at position with

h+k+l is an odd integer.

2. Bragg peaks appear at positions

with h+k+l is an even integer.

Structural factor of an fcc lattice

fcc lattice = sc lattice + basis at

1 2 2 3 3 3 1 4 1 2

1 1 10, , ,

2 2 2r r a a r a a r a a

No Bragg peaks at positions for the indices are partly

even or partly odd.

( ) ( ) ( )( ) 1

4 , , all even

4 , , all odd

0 otherwise

i k l i h l i h kS hkl e e e

h k l

h k l

Atomic form factor

Basis with internal structure

Introduce atomic form factor f so that

KiK r

KS f e

31 ( ) iK rf K d r r e

e

1. X-ray diffraction: scattered by electron density

→ f = Fourier transform of change density

→

2. Neutron nuclear diffraction: nucleus are “size less”

→ f = 1, use scattering length b to describe the

neutron-nucleus scattering probability with (4b2)

is the scattering cross section, so that biK r

KS e

22

2ˆ ˆ 1 ( )

sinθ sin2θ

h k lM Z M

MeI C F m

m c

Magnetic scattering

Scattering intensity

Magnetic moment Moment direction

2 sinθ sin2θ

h k lN N

MI C F

Nuclear scattering

2

2

j

rik

jNjebF

2

2 (0.0729) 2

(100) 774 sinθ sin2θ 0.16794(110) 1061

(0.0726) 3sinθ sin2θ 0.3195

h k lz

M

h k lN

MC

I

MIC

2 2 2

(001) (010) (001)

If points at the (001) direction:

ˆ ˆ ˆˆ ˆ ˆ1 ( ) 0, 1 ( ) 1, 1 ( ) 1

m

m m m

(1 0 0)+(0 1 0)+(0 0 1)

Moment calculation

BGive 1.07 μZ

Observations:

Nuclear {100} integrated intensity of 1061

Magnetic {110} integrated intensity of 774

應用實例

奈米物性實驗室

SAMPLE AREA

128 Position sensitive

detectors

Monochromator

shielding

GRANITE FLOOR

Neutron

guide

Dr Klaus-Dieter Liss

高解析度

粉末繞射譜圖

High Resolution Powder Diffractometer (HRPD)

- Complex crystalline structure

- Magnetic structure

- Cation ordering

- High pressure study

- Phase transition (vs T, P, H)

- Solid state chemical reaction

- Location of light anion or oxygen vacancy

2q

Neutrons

High resolution powder

diffraction pattern

Scattered by nuclei

Bi

O Cu S

20 40 60 80 100 120 140

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0Tetragonal P4/nmm

a = 3.8645(1) Å

c = 8.5493(3) Å

Rp = 3.81 %

Rwp

= 4.74 %

2 = 2.297

Neutron = 1.6208 Å

T = 293 K

Scattering angle (deg.)

Inte

nsi

ty (

103 c

oun

ts )

BiOCu0.94

S

1. Seeing nuclei 2. Well-defined Bragg profiles

3. Insignificant form factor variations

Neutron powder diffraction (粉末繞射)

Cu(2)

O(2)

Pr

Cu(1) O(1)

O(4)

Ba

2.4882(12) Å

2.7991(9) Å

76.49°(7)

103.51°(7)

c

b a

Rietveld refining analysis

General Structure Analysis System

晶體結構分析 (PrBa2Cu3O6.338)

0 20 40 60 80 100 120 140 160

0

500

1000 P 4/m m m

χ2 = 1.175

Rwp =

8.47%

Rp = 6.66%

1500

PrBa2Cu3O6.338

λ = 1.5402 Å

15'-20'-7'

Neu

tron

cou

nts

Scattering angle (deg)

50 100 150 200 250 300 350-48

-45

-42

-39

-36

-33

-30

-27

Jd

Ja

Jc

Ex

cha

nge i

nte

gra

l (

arb

. u

nit

s )

Temperature ( K )

Jb

(b)Jahn-Teller

distortion

(a)

c

a y=½ b

Mn(1) Mn(2)

Mn(3)

Mn(1) Mn(2)

O(8)

O(8)

O(7)

O(7)

O(6)

O(6)

O(5)

O(5)

O(6) O(7)

O(8) O(5)

O(8) O(7)

O(6) O(5)

Jb

Jc

Ja

Jd

50 100 150 200 250 300 3509

12

15

18

21

24

Jg

Jf

Je

Mn4+

(3)-Mn4+

(3)

Mn3+

(2)-Mn3+

(2)

Mn3+

(1)-Mn3+

(1)E

xch

an

ge i

nte

gra

l (

arb

. u

nit

s )

Temperature ( K )

Jahn-Teller distortion

(b)

(a) z=0c

b

a

Mn(2)

Mn(2) Mn(1)

3 1

Mn(1)

Bi Je Jf

z=½ c

b

a

4 3 Bi Bi

Mn(3) Mn(3)

2 2

Mn(3) Mn(3)

Bi Jg Bi Jg

Bi0.37Ca0.63Mn0.96Cr0.04O2.98

Mn-O-Mn superexchange

coupling strength

TN

Exchange integral calculation

High Intensity Powder Diffractometer (HIPD)

APPLICATIONS

• Real time: Single shot (kinetic) measurements

• Real time: Stroboscopic (cyclic, periodic) measurements

• Small sample volumes

• Magnetic studies at “long” wavelengths (2.36 Å and 4 Å)

Dr Andrew Studer

High intensity

powder diffraction

pattern

Neutron magnetic diffraction (磁繞射)

Magnetic dipole moment of neutron & unpaired electrons

→ Magnetic scattering High intensity

diffraction pattern

Polyaniline-intercalated

FeOCl 4000

3000

2000

1000

0

-1000

Inte

nsity (

co

un

ts / m

in.)

3530252015

Scattering angle 2 q (deg.)

(PANI)0.16FeOCl

{0

1}- ,

{0

0}+

{1 1

}- , {

1 0

}-

1. Coupled bi-layered quasi-2D

magnetic scattering profile.

2. No magnetic correlation

between the adjacent bilayers.

Magnetic modulation vector K=(1/3 1/2)

c

a

Along b: antiparallel

Van-der-Waals gap

• Direct exchange (DE):

Fe–Fe → Ferromagnetic

• Superexchange (SE):

Mediated through O between the Fe

ions Fe–O–Fe → Antiferromagnetic

• Competition bet. FMDE & AFMSE:

Non-collinear spin arrangement

Non-collinear spin arrangement

Fe Fe O

Bi-layer magnetic order

Calculated pattern

20 25 30 35 40 45 50 55

0

3

6

9

12

15Bi0.37Ca0.63Mn0.96Cr0.04O2.99

I30 K - I150 K

{1 1

1/2

}

{1 1

3/2

} +

{3

1 1

/2}

{3 1

0}

+ {

0 1

3/2

}

{0 1

0}{2 1

0}

+ {

0 1

1}

{2 0

0}

+ {

1 1

1/2

} +

{0

0 1

}

Inte

nsi

ty (

10

3 C

ou

nts

/ m

in.

)

Scattering angle 2q ( deg. )

{1 1

0}

+ {

0 1

1/2

}

a

c

b

θ= 45° φ=90°

101

θ= -135°

b a

c φ=90°

101

Mn4+(3), 4f

Mn3+(1), 2a

Mn4+(3), 4f

Mn3+(2), 2b Mn4+(3), 4f

Mn3+(1), 2a

Mn3+(1), 2a

Mn4+(3), 4f Mn3+(2), 2b

Ferromagnetic clusters

created by Cr-doping.

Spin-charge coupling

CMR

Bi0.37Ca0.63Mn0.96Cr0.04O2.98

Magnetic cluster

4 nm Au

1. Langevin M(H): alignment

of moment in Au by H.

2. Moments confirmed by

neutron diffraction.

3. Moments appear in the core.

0 10 20 30 40 50 60

0

1

2

3

4

MI

MP

15 K

300 K 55 K

10 K

7.5 K

Mag

net

iza

tio

n (

10

-2 e

mu

/g )

Applied magnetic field Ha (kOe)

4 nm Au 5 K

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

T = 2.1 K5

4

3

2

M (

10

-2 e

mu

/ g

)

Applied magnetic field Ha ( kOe )

4 nm Au

1

30 45 60 75 90 105 120 135

0

2000

4000

6000

Ha= 0 Oe

(420)(331)

(400)

(222)

(311)

(220)

(200)

Inte

nsi

ty (

co

un

ts /

19

0 m

in.

)

Scattering angle 2q ( deg. )

I5 K

- I100 K

4 nm Au

(111)

0 5 10 15 20 25 30

0.00

0.01

0.02

0.03

0.04

1.15

1.20

1.25

1.30

1.35

1.40

1.45(b)

Magn

eti

zati

on

( e

mu

/g )

Applied magnetic field Ha ( kOe )

T = 5 K

4 nm Au

Inte

grated

inte

nsity

( arb

. un

it )

(400) 0 50 100 150 200 250 300

1.10

1.15

1.20

1.25

1.30

1.16

1.20

1.24

1.28

1.32

(220)

Inte

gra

ted

inte

nsity

(arb

. un

it)

(200)

(111)

(400)

Ha = 1 kOe

Inte

gra

ted

in

ten

sity

(a

rb

. u

nit

)

Temperature (K)

4 nm Au

Confirmation of magnetic moment

X-rays are best (synchrotrons) for solving structures

Easier to find the heavy atoms first

Neutrons are best for refining structures

All atoms are ‘equal’ for neutrons

Few systematic errors (average over big samples etc…)

Easier sample environment (low temperatures etc…)

Interest of very precise structure measurements

Precise bond lengths

Study charge ordering, metal-insulator transitions…

Magnetic structures: difficult with x-ray powders

Best combinations for structural analysis

APPLICATIONS

• Complex fluids under flow

• Polymer coatings and interdiffusion

• Protein adsorption in biological membranes

• Magnetic multilayers

掠角反射(干涉)譜圖

Time-of-flight Reflectometer (反射儀)

PolymerProtein

Air

Water

Neutron Beam

Lipid

Layer thickness

Interface roughness

Mass density

Spin arrangement

Interference pattern

Reflectivity & grazing-incident scattering

磁性薄膜：鐵磁雙交換

與反鐵磁超交換建構成

canted spin arrangement

HIV protein and how it

penetrates a lipid monolayer

Protein penetration Spin exchange

Dr Elliot Gilbert

APPLICATIONS

• Large scale structures (1-100 nm)

• Colloids/emulsions/micelles

• Nanomagnetic materials

• Polymers and polymer processing

• Biomineralisation & biomimetics

• Biomembrane physics

• Zeolites & mesoporous materials

Small Angle Neutron Scattering (小角度散射儀)

Information may be obtained by neutrons

˙ Structure - exact arrangement of atoms.

˙ Overall shape - related to their function.

˙ Dynamic changes within a molecular

structure - correct functioning. 1

10

100

1000

0.004 0.007 0.01 0.04

Wave vector transfer Q(Å -1)

Inte

nsi

ty

Shape

Size

Small angle scattering (小角度散射)

Hydrogen/Deuterium contrast matching

H與D對中子的散射方式

非常不同

(bH = -3.74 fm bD = 6.67 fm)

以D取代部分H來調配背

景溶液或樣品的散射強度

判定H的位置、隱藏部份

分子

Increasing %D2O in the solvent 0% 100%

結構組態&受熱分解(鄰苯二酚加氧酵素)

0.00 0.05 0.10 0.15

1.5

2.0

2.5

3.0

3.5

log

I

S,A-1

Rg = 290 Å

83oC A B

C D

C23O(SH1) thermal cycle

52.5 oC 62.5 oC 5 oC

72.5 oC 80 oC 5 oC

A B

D C

0 10 20 30 40 50 60 70 80

30

40

50

60

70

80

90

100

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Rg

Rg (

)

Temperature ( oC )

ActivityÅ

Activ

ity (u

nit)

Enlargement of the

enzyme size: due to

partial unfolding of the

tetrameric subunits of

the enzyme.

Spins in Fe2O3 nanoparticle 極化中子小角度散射

磁性奈米顆粒的核(內部)與殼

(表面)的自旋排列方式相互垂

直，使得奈米顆粒的磁矩小於

塊材者。

Oil/surfactant mixtures, repeat layer constant,

but membrane thickness (dip) changes

Membrane thickness

Inelastic scattering (非彈性散射)

Filter

selector

Beam shutter

Collimator

exchanger

Collimator

Monochromator

Sample table

Collimator Analyser

Beam stop

Bea

m sto

p

Collimator

Detector

Beam aperture

Monochromator drum

Analyzer-detector system

1st axis

(monochromator)

2nd axis

(sample) 3rd axis

(anlyzer)

Triple-axis

spectrometer

Sika

Cold Three-Axis-Spectrometer (TAS)

Dr. Chun-Ming Wu

For low energy excitations

Thermal Three-Axis-Spectrometer (TAS)

APPLICATIONS

Inelastic scattering - excitations

• collective - phonons and magnons

• diffusive - spin fluctuations

• localised - crystal-field levels

Dr Sergey Danilkin

W. -H. Li et. al. PRB 39 4119 (1989).

1. Coexistence of antiferromagnetic

order and superconductivity.

2. Very low Neel temperature,

hence the crystalline electric

field (CEF) effects play

important roles in its magnetic

and superconducting properties.

Crystal field scheme of Ho3+ in HoPd2Sn

Powder sample

Crystal field excitations

Crystal field

level scheme

of HoPd2Sn

and

isostructures

HoPd2Sn

Crystal field scheme

Maxons

Phonons

Rotons

T=1.1 K

He-II

A. D. B. Woods & R. A. Cowley, Rep. Prog. Phys. 36 1135 (1973 .)

smdP

dEvg / 239

Phase diagram of He

Excitations in superfluid 4He

Cu

T=49 K

Cu (FCC), Bravais lattice,

no optical branches

R. M. Nickow et. al. (1967), PR 164, 922

1. 1 Longitudinal +2 Transverse modes.

2. Transverse modes degenerate alone high symmetry

directions.

3. Sound speed: VL>VT

4. Phonon density of state → calculating thermal properties

Fm3m

a=3.516 Å FBZ: Octahedron

Phonon dispersion of Crystalline field scheme

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0

20

40

60

80

q (Å -1)

Ma

gn

on

en

ergy

(m

eV)

B. Antonini & V. J. Minikiewicz, Solid State Comm. 10 203 (1972)

G. Shirane et. al., JAP 39, 383 (1968)

2cos12 kqJSkqJS

Magnon dispersion

Wetting of root

上圖左下部分的放大圖:

At day 2 the soil next to roots was darker

and probably wetter than the soil far

from the roots.

At day 6, just after rewetting, the region

next to roots appeared bright, indicating

that it was not rewetted.

Day1-5: drying period

Day 6: immediately after rewetting

中子

影像圖

Seeing

H2O

Conclusions

Welcome to

neutron

scattering

community

Thank you for your attention

whli@phy.ncu.edu.tw

CNBA Center for Neutron Beam Applications, National Central University, Taiwan