Jim Rhyne Deputy Director Lujan Neutron Scattering Center Los Alamos National Laboratory What's Cool...
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Transcript of Jim Rhyne Deputy Director Lujan Neutron Scattering Center Los Alamos National Laboratory What's Cool...
Jim Rhyne
Deputy DirectorLujan Neutron Scattering Center
Los Alamos National Laboratory
What's Cool About Neutron Scattering -- the Basics with a bias toward Magnetism
Summer Student Lecture Series June 8, 2007
LA-UR-06-4041
2
Magnetic Materials and Devices (a realization of the technological potential of magnetism that has only been speculated about by others in the past)
4
On to Neutron Scattering PhenomenaOutline -- References
• Neutron Sources• General Concepts of Scattering• Diffractometers and Diffraction• Magnetic Diffraction• Reflectometry• Inelastic Scattering
• References:– Neutron Diffraction, G.E. Bacon, 5th edition, Oxford Press, 1975– Theory of Neutron Scattering From Condensed Matter, S.W.
Lovesey, Oxford Press 1984– Introduction to the Theory of Neutron Scattering, G.L. Squires,
Dover, 1996.– Solid State Physics, N.W. Ashcroft, N.D. Mermin, Holt, Rinehart &
Winston, 1976
What Can Neutrons Do?
• Diffraction (the momentum [direction] change of the neutron is measured)
– Atomic Structure via nuclear positions
– Magnetic Structure(neutron magnetic moment interacts with internal fields)
– Disordered systems - radial distribution functions
– Depth profile of order parameters from neutron reflectivity
– Macro-scale structures from Small Angle Scattering (1 nm to 100 nm)
• Inelastic Scattering (the momentum and energy change of the neutron is measured)
– Dispersive and non-dispersive phonon and magnon excitations
– Density of states
– Quasi-elastic scattering
Neutrons measure the space and time-dependent correlation function of atoms and spins – All the Physics!
What do we need to do neutron scattering?
• Neutron Source – produces neutrons
• Diffractometer or Spectrometer– Allows neutrons to interact with sample
– Sorts out discrete wavelengths by monochromator (reactor) or by time of flight (pulse source)
– Detectors pick up neutrons scattered from sample
• Analysis methods to determine material properties
• Brain power to interpret results
Sources of neutrons for scattering?
• Nuclear Reactor– Neutrons produced from fission of 235U
– Fission spectrum neutrons moderated to thermal energies (e.g. with D20)
– Continuous source – no time structure
– Common neutron energies -- 3.5 meV < E < 200 meV
• Proton accelerator and heavy metal target (e.g., W or U)
– Neutrons produced by spallation
– Higher energy neutrons moderated to thermal energies
– Neutrons come in pulses (e.g. 20 Hz at LANSCE)
– Wider range of incident neutron energies
Lujan Neutron Scattering Center
WNR Facility
Proton Radiography
800 MeV Proton Linear Accelerator
Isotope ProductionFacility
Proton Storage Ring
High-FluxIsotope Reactor
Spallation Neutron Source (first neutrons in
May -- operational instruments late in 2006)
(1000 kW)
Intense Pulsed Neutron Source(7 kw)
Manuel Lujan Jr. Neutron Scattering
Center(100 kW)
National User National User FacilitiesFacilitiesHFIR 1966 HFIR 1966 NCNR 1969 NCNR 1969 IPNS 1981 IPNS 1981 Lujan 1985 Lujan 1985 (SNS 2006) (SNS 2006)
Local/Regional Local/Regional FacilitiesFacilities(University (University Reactors)Reactors)MITMITMissouriMissouri……
NIST Center NIST Center for Neutron for Neutron ResearchResearch
There are four National User Facilities for neutron scattering in the US
Neutron scattering machines
• Spectrometers or diffractometers– typically live in a beam room
– are heavily shielded to keep background low and protect us
– receive neutrons from the target (or reactor)
– correlate data with specific neutron wavelengths by time of flight
– accommodate sample environments (high/low temperature, magnetic fields, pressure apparatus)
12
General Properties of the Neutron The kinetic energy of a 1.8 Å neutron is equivalent to T = 293K
(warm coffee!), so it is called a thermal neutron. The relationships between wavelength (Å) and the energy (meV),
and the speed (m/s, mi/hr) of the neutron are:
e.g. the 1.8 Å neutron has E = 25.3 meV and v = 2200 m/s = 4900 mi/hr
The wavelength if of the same order as the atomic separation so interference occurs between waves scattered by neighboring atoms (diffraction).
Also, the energy is of same order as that of lattice vibrations (phonons) or magnetic excitations (magnons) and thus creation of annihilation of a lattice wave produces a measurable shift in neutron energy (inelastic scattering).
/3960 and /89.81 2 vE
13
COMPARATIVE PROPERTIES OF X-RAY AND NEUTRON SCATTERING
Property X-Rays Neutrons
Wavelength Characteristic line spectra such as Cu K
= 1.54 Å
Continuous wavelength band, or single = 1.1 0.05 Å separated out from Maxwell spectrum by crystal monochromator or chopper
Energy for = 1 Å 1018 h 1013 h (same order as energy of elementary excitations)
Nature of scattering by atoms
ElectronicForm factor dependence on [sin]/Linear increase of scattering amplitude with atomic number, calculable from known electronic configurations
Nuclear, Isotropic, no angular dependent factor Irregular variation with atomic number. Dependent on nuclear structure and only determined empirically by experiment
Magnetic Scattering Very weak additional scattering ( 10-5) Additional scattering by atoms with magnetic moments (same magnitude as nuclear scattering) Amplitude of scattering falls off with increasing [sin ]/
Absorption coefficient
Very large, true absorption much larger than scattering abs 102 - 103
increases with atomic number
Absorption usually very small (exceptions Gd, Cd, B …) and less than scattering abs 10-1
Method of Detection Solid State Detector, Image Plate Proportional 3He counter
14
Golden Rule of Neutron Scattering
We don’t take pictures of atoms!
Job preservation for neutron scatterers – we live in reciprocal space
Atoms in fcc crystal
Inte
nsit
y
15
How are neutrons scattered by atoms (nuclei)?
Short-range scattering potential:
The quantity “b” (or f) is the strength of the potential and is called the scattering length – depends on isotopic composition
Thus “b” varies over N nuclei – can find average defines coherent scattering amplitude leads to
diffraction – turns on only at Bragg peaks But what about deviations from average? This defines the
incoherent scattering
Incoherent scattering doesn’t depend on Bragg diffrac. condition, thus has no angular dependence – leads to background (e.g., H)
bbcoh b
)(2
)(2
rbm
rV
2/122 bbbinc
16
Scattering of neutrons by nuclei
A single isolated nucleus will scatter neutrons with an intensity (isotropic)– I = I0 [4b2]
where I0 = incident neutron intensity, b = scattering amplitude for nucleus
What happens when we put nucleus (atom) in lattice?– Scattering from N neuclei can add up because they are on a lattice– Adding is controlled by phase relationship between waves scattered
from different lattice planes– Intensity is no longer isotropic Bragg law gives directional dependence
– Intensity I (Q, or ) is given by a scattering cross-section or scattering function
sin2d
17
Observed Coherent Scattering Intensity of diffracted x-ray or neutron beam produces series of peaks at discrete
values of 2 [or d or K (also Q)]Note: d = /(2 sin) or K = 4sin/ = 2/d are more fundamental since values are independent of and thus characteristic only of material.
Benzine Pattern (partial) Note: Inversion of scales - 2 f(1/d)
18
Scattering Factors f, cont’d For x-rays the magntude of f is proportional to Z For neutrons nuclear factors determine f, thus no regular with Z (different
isotopes can have different f s)
Shaded (negative) --> phase changeFor neutrons conventionally f = b (Scattering length - constant for an element)
19
Magnetic Powder Diffraction
Neutron has a magnetic moment -- will interact with any magnetic fields within a solid, e.g., exchange field
Magnetic scattering amplitude for an atom (equivalent to b)
where g = Lande “g” factor, J = total spin angular momentum, f = magnetic electrons form factor
Magnetic scattering comes from polarizedspins (e.g., 3d [Fe] or 4f [RE]) not fromnucleus -- Therefore scattering amplitudeis Q-dependent (like for x-rays) via f
at Q = 0 for Fe = gJ = 2.2 Bohr magnetonsp = 0.6 (comparable to nuclear b = 0.954)all in units of 10-12cm
Refinement gives moment magnitudes oneach site and x,y,z components(if symmetry permits)
)(10269.02
122
2
cmfgJxfgJmc
ep
Mn+2
21
Magnetic Powder Diffraction II In diffraction with unpolarized neutrons (polarized
scattering is a separate topic) the nuclear and magnetic cross sections are independent and additive:
q2 is a “switch” reflecting fact that only the component of the magnetic moment scattering vector K (or Q) contributes to the scattering
magnnuclmagnnucl SSSqSQSd
d 22 cos1)(
K
22
Basic Types of Magnetic Order and Resulting Scattering
Ferromagnet (parallel spins)– Single Magnetic site (e.g., Fe, Co,
Tb)
– Scattering only at Bragg peak positions (adds to nuclear), but not necessarily all (q2 switch)
– Multi Site Ferromagnet
(e.g. Y6Fe23 (4 distinct Fe sites) -- no new peaks in scattering
Antiferromagnet (parallel spins with alternate sites reversed in direction)
– equivalent to new magnetic unit cell doubled in propagation direction of AFM
– Purely magnetic scattering peaks at half Miller index positions (e.g., 1,1,1/2)
– Overall net magnetic moment adds to 0 [job security for neutrons!!]
c
a
Polarized Neutron Reflectometry
Detector
SampleAl-Coil Spin Flipper
Spin Polarizing Supermirror
Specular Reflectivity
Incident Polarized Neutrons
Al-Coil Spin Flipper
]n1)[4/k()z( 22i
22 dz)ikzexp()z()z(
iQ
4)Q(r
cospN2
1n
sinpbN2
1n
2
2
• index of refraction: sensitive to
• scattering length density: used to model reflectivity
• reflectivity: measured quantity
spin-flip
non spin-flip
Ga1-xMnxAs
• Dilute ferromagnetic semiconductor
• Spintronics applications
• Annealing increases magnetization & Tc
• Interstitial Mn go to the surface! – K. W. Edmonds et al., PRL, 92, 37201, (2004) - Auger
• Depth-dependence of chemical order and magnetization determined Polarized-Beam Neutron Reflectivity
• Compared similar as-grown and annealed films
– T = 13 K, H = 1 kOe (in plane)
J. Blinowski et al, Phys. Rev. B 67, 121204 (2003)
Ga1-xMnxAs As-Grown & Annealedt = 110 nm, x = 0.08, TC = 50 K, 120 K
0.01 0.02 0.03 0.04 0.0510-10
10-9
10-8
Q (Å-1)
Re
flect
ivity
x Q
4 (Å
-4)
As-Grown Film measured R
++ fit to R
++
measured R- -
fit to R- -
Annealed Film measured R
++ fit to R
++
measured R- -
fit to R- -
0.01 0.02 0.03 0.04 0.05
-0.1
0.0
0.1
0.2
Annealed Film measured SA fit from SLD model
Q (Å-1)
Spi
n A
sym
met
ry
0.01 0.02 0.03 0.04 0.05
-0.1
0.0
0.1
0.2
Q (Å-1)
As-Grown Film measured SA fit from SLD model
Sp
in A
sym
met
ry
0 200 400 600 800 1000 12000
2
4
6
8
290
300
310
320
As-Grown Film
Depth (Å)
Mavg = 17 emu cm-3
moment per Mn = 1.2 B
m
-2
nuc
mag
0
10
20
30
substratesurface
M (e
mu
cm-3)
0 200 400 600 800 1000 12000
5
10
15
290
300
310
320
nuc
mag
Mavg = 48 emu cm-3
moment per Mn = 3.4 B
(m
-2)
substratesurface Depth (Å)
Annealed Film
0
20
40
60
M (em
u cm
-3)
• Measured reflectivities & fits– Spin up & spin down splitting due to
sample magnetization– Spin up reflectivities are different– “Slope” at high Q different – Fits are good
• Magnetic signal: spin asymmetry– SA = (up – down) / (up + down)– Larger amplitude for annealed film– Better defined for annealed film
• SLD Models (mag. & chem.)– As-grown M doubles near surface – M increases and more uniform for
annealed film– Both films show magnetic depletion at
surface– Drastic chemical change at annealed
film’s surface– Interstitial Mn have diffused to
surface! (combined with N2 during annealing)
Inelastic Scattering
• Inelastic Scattering (the momentum and energy change of the neutron is measured)
– Dispersive and non-dispersive phonon and magnon excitations
– Density of states
– Quasi-elastic scattering
27
Triple Axis Neutron Scattering Spectrometer
Want Thermal neutronse.g., E=14mev, =2.4Å
i = 2dmsin m |ki| = 2/i
n
ii m
kE
2
22
f = 2dasina
|kf| = 2/f
dEd
dcountsI
m
kE
n
ff
2det
22
)(
2
kTEE e
kT
E
kT
nn /
2
1
02
28
MURR Triple Axis Neutron Spectrometer (TRIAX)
Analyzer Assembly
Monochromator Drum
Sample Table andGoniometer
Detector Shieldand Collimator
Beam Stop (pivots withdrum and sample)
29
22
nf2
2
ni 2E
2E fi k
mk
m
2
222
ifN kk
mE
Qqkk if
2
P
0
i f
Inelastic Neutron Scattering ***
The measurement of the functional dependence of wave vector q and the energy E = h of an elementary excitation (e.g., magnon or phonon dispersion) Energy and Momentum Conservation Conditions: * ki = wave vector of incident neutron * kf = wave vector of scattered neutron
* Neutron energies
Change of EN creates (EN < 0) or annihilates (EN > 0) an excitation of energy
Neutron - excitation system
momentum conservation:
Constant q scan (Einc fixed)
Rotate P [kf,and ki] about 0
30
P h y s i c a l P h e n o m e n a S t u d i e d w i t h I n e l a s t i c N e u t r o n S c a t t e r i n g * * * a c c e s s i b l e e n e r g y a n d m o m e n t u m
t r a n s f e r ( Q ) r a n g e s * * *
N o t e : C o l d a n d h o t s o u r c e s a t R e a c t o r s a n d p a r t i c u l a r l y S p a l l a t i o n N e u t r o n S o u r c e s h a v e g r e a t l y e x t e n d e d t h e u s e f u l r a n g e o f Q a n d E .
[ F r o m J . D . A x e , N e u t r o n s : T h e K i n d e r , G e n t l e r P r o b e o f C o n d e n s e d M a t t e r , M a t l s . R e s . S y m p . P r o c . 1 6 6 , 3 ( 1 9 9 0 ) ] .
310 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0
[ q q q ]
[ q q 0 ]
[ q 0 0 ]
En
erg
y (m
eV
)
q ( r l u )
D i s p e r s i o n i n a H e i s e n b e r g F e r r o m a g n e t
A t l o w q d i s p e r s i o n i s q u a d r a t i c ( t o l o w e s t o r d e r ) :
E ( q ) = ( q ) = + D q 2
D i s t h e s p i n w a v e s t i f f n e s s p a r a m e t e r ( m a y b e a n i s o t r o p i c i n q d i r e c t i o n
i s t h e g a p e n e r g y ( m a y b e 0 - - r e f l e c t s c r y s t a l f i e l d a n i s o t r o p y e n e r g y )
F u l l B r i l l o u i n z o n e d i s p e r s i o n f o r a s i n g l e n e a r e s t n e i g h b o r e x c h a n g e c o n s t a n t J 1 i s o f t h e f o r m :
q ) = + 4 J 1 S ( 3 – c o s q x a o – c o s q y a o – c o s q z a o )
w h i c h r e d u c e s a t s m a l l q ( c o s x 1 - x 2 / 2 ) t o ( 1 1 1 ) :
q 1 1 1 ) 6 J 1 S a 2 q 2 D q 2
F u l l z o n e d i s p e r s i o n f o r a f c c l a t t i c e
J 1 T c
I n m e a n f i e l d a p p r o x :
T c = 4 J 1 S ( S + 1 ) / k B
32
Exam ples of Inelastic Scattering D ata
Ferrom agnetic A m orphous m etallic glass Fe0.86B 0.14 Constant q scans left panel -
varying T right panel -
varying q) [Rhyne, Fish, and Lynn,
JAP 53 , 2316 (1982)]
Q uadratic dispersion (E
vs. q2) [J.A . Fernandez-Baca, J.W . Lynn, J.J.
Rhyne, and G .E. Fish, Physics B 136B, 53 (1986)
34
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FLORSHEIM SHOES PULLS ITS MAGNETIC HEALTH CLAIMS
Faced with a consumer lawsuit in California, and ridicule from the scientific community, Florsheim has yanked the brochures that described the "science" behind its MagneForce shoes ($125). Its web page, which once claimed that its magnetic insole, "increases circulation: reduces foot, leg and back fatigue; provides natural pain relief and increased energy level," now simply says it's, "the first shoe with its own power supply." What's New for Sep 01, 2000
35
Using Powder DiffractionInput Information -- Structure Determination
Know instrument-dependent scattering line-shape– Gaussian for fixed
– Convolution of rising and falling exponentials with Gaussian for TOF
– Sample distortions (pseudo Voigt) linear comb. of Lorentzian and Gaussian
Know or parameterize resolution and background functions
Know Space Group (or a limited # choices) [coordinates of atoms in cell - may be variables x,y,z]
2.00 2.040
1000
2000
3000
4000
5000
Gaussian
Inte
nsity
Q (Å-1)0.45 0.50 0.55
Lorentzian
Gaussian
2
22ln4
2
2ln4)(
oQQ
eQR
2
o
'
)Q-2(Q1
1 '
2)(
QR
)()()( zerfceyerfceNTR vu (VonDreele, Jorgensen & Windsor)