INTRODUCTION TO NEUTRON SCATTERING

Boualem Hammouda

National Institute of Standards and Technology Center for Neutron Research

-- Why Use Neutrons? -- Neutron Sources -- Continuous vs Time-of-Flight -- Neutron Sources in the US -- The NIST Neutron Scattering Facilities -- Neutron interactions -- Elastic vs Inelastic Scattering -- Coherent and Incoherent Scattering -- Neutron Scattering Lengths and Contrast Factors -- Introduction to SANS WHY USE NEUTRONS?

-- Neutrons interact through short-range nuclear interactions. They have no charge and are very penetrating and do not destroy samples.

-- Neutron wavelengths are comparable to atomic sizes and interdistance spacings.

-- Neutrons interactions with hydrogen and deuterium are widely different making the deuterium labeling method an advantage. Fission Chain Reaction NEUTRON SOURCES fission fragment

2 to 3 fission incident neutrons neutron fissile nucleus radiative (U-235, Pu- capture 239) gamma neutrons used for neutron scattering

Spallation Nuclear Reaction

10 to 30 neutrons incident emitted H- ion

high Z nucleus (W-183, U-238) neutrons used for neutron scattering CONTINUOUS VS TIME-OF-FLIGHT

Pulsed Sources Continuous Reactors scattering collimation detection collimation scattering detection source source t chopper monochromation wavelength range time-of-flight single wavelength intensity intensity at source at source time time

intensity intensity at detector at detector time time

Measure some of the neutrons all of the time Measure all of the neutrons some of the time NEUTRON SOURCES IN THE US

Continuous Sources:

-- HFIR-Oak Ridge National Laboratory. http://neutrons.ornl.gov. -- NIST-National Institute of Standards and Technology. http://www.ncnr.nist.gov.

Pulsed Sources:

-- WNR/PSR LANSCE (Los Alamos). http://lansce.lanl.gov -- SNS (Oak Ridge National Lab). http://www.sns.gov.

NIST Thermal Instruments THE NIST NEUTRON SOURCE cold neutron source

NG1 NG2 NG3 NG4 NG5 NG6 NG7

USANS

The Cold Neutron Source neutron guides NG0 0 5 m

NG1 core NG2 NG3 NG4

NG5 NG6 NG7 USANS Instrument Upgrade and VSANS

New Guide Hall

10 m SANS

30 m SANS

Present Guide Hall Confinement Building 40 m VSANS

USANS

30 m SANS The NIST Guide Hall The NIST New Guide Hall NEUTRON INTERACTIONS

Nuclei Seen by X-Rays

H C O Si Cl Ti U X-rays interact with the electron cloud.

Nuclei Seen by Neutrons

H-1 C O Si Ti U Cl-35 Ti-46 D-2 Cl-37 Ti-47

Ti-48 Ti-49

Ti-50

Neutrons interact with the nuclei. Negative scattering lengths in dark.

ELASTIC vs INELASTIC NEUTRON SCATTERING

scattered neutrons

momentum kf, energy Ef

incident neutrons

momentum ki, energy Ei

k , E f f Q=ki-kf momentum transfer θ E=Ei-Ef energy transfer

ki, Ei

Elastic scattering corresponds to E=0. Investigate structures.

SANS and NR are elastic scattering techniques.

NEUTRON SCATTERING TECHNIQUES Lengths (Å) 100 10 1

10-13 +4 INELASTIC triple axis 10 time-of-flight

-11 10 10+2 Times (s) E (µeV) back- 10-9 scattering 10-0 QUASIELASTIC spin echo

-7 10 10-2 0.01 0.1 1 10 Q (Å-1)

Reflectometry ELASTIC Diffraction SANS SCATTERING LENGTH DENSITY CALCULATOR

Web address: http://www.ncnr.nist.gov/resources/sldcalc.html

Input: Compound: D2O Density: 1.11 g/ml

Output: Neutron Scattering Length Density: 6.39*10-6 Å-2

bA scattering length Scattering length density: ρA = = vA volume The Contrast Match Method

Finite contrast Zero contrast

Multiple contrasts Contrast match SANS GEOMETRY

source sample area aperture aperture detector

R =0.5 cm scattered 3 neutrons

θ θmin beam R1=2.5 cm incident neutrons R2=1.27 cm stop

source to sample sample to detector distance L1~15 m distance L2~15 m

-3 o θmin = (R1+R2)/L1+R2/L2+R3/L2 ~ 3.7*10 Rad ~ 0.2

REFLECTOMETRY GEOMETRY

source sample linear slit slit detector

Y =0.5 mm scattered 3 neutrons

θ θ incident neutrons min Y1=2.5 mm Y2=1.27 mm

source to sample sample to detector distance L1~1.5 m distance L2~1.5 m

-3 o θmin = (R1+R2)/L1+R2/L2+R3/L2 ~ 3.7*10 Rad ~ 0.2