inelastic (neutron) scattering: a brief introduction · 2018. 7. 19. · inelastic (neutron)...
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Inelastic (neutron) Scattering: a brief introduction
John A. Stride School of Chemistry, UNSW
"for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter"
"for the development of neutron spectroscopy"
"for the development of the neutron diffraction technique"
Bertram N. Brockhouse (1918-2003)
Clifford G. Shull (1915-2001)
McMaster University Hamilton, Ontario,
Canada
Massachusetts Institute of Technology (MIT) Cambridge, MA, USA
The Nobel Prize in Physics 1994
2-axis: diffraction
3-axis: dynamics
2
ki
ko Q
2
ki
ko
2
Q
ki
ko
2 x y
h
Q2 = y 2 + h2 = ki - ko cos 2q( )( )2
+ ko sin 2q( )( )2
Q2 = ki
2 + ko
2cos2 2q( ) - 2ki ko cos 2q( ) + ko
2sin2 2q( )
= ki
2 + ko
2cos2 2q( ) + sin2 2q( )[ ] - 2ki ko cos 2q( )
cos2 a + sin2 a =1:
Q2 = ki
2 + ko
2- 2ki ko cos 2q( )
Consider the properties of a photon
If we take X-rays, then ≈ 1 Å; what is the associated photon energy?
• If we take a typical vibration of ~1500 cm-1:
l =hc
E=
hc
h ¢ c u =
1
100 ´1500= 6.667 ´10-6 m
that diffracts << associated with atomic motions
Now consider the properties of a neutron
For neutrons of ≈ 1 Å, what is the associated energy?
Vibrations and lattice modes lie up to ~3500 cm-1
l =h
mnv(de Broglie's equation); E =
1
2mnv
2
\v =h
mnl® E =
1
2mn
h
mnl
æ
èç
ö
ø÷
2
=h2
2mnl2
=6.626´10-34( )
2
2 1.675´10-27( ) 1´10-10( )=1.311´10-20 J
E=1.311´10-20
1.602´10-19eV = 81.8meV» 660cm-1
that diffracts = associated with atomic motions
Neutron spectroscopy - why?….
Neutron spectroscopy - why?….
So, how do we do spectroscopy with neutrons..?
• Monochromators can be used to define ki
• However, need to determine ko to obtain E
1. use a second monochromator (analyzer) to set ko or use a filter to set ko
scan ki at the monochromator (and ko at analyzer)
2. time-of-flight (TOF) analysis with fixed ki (direct geometry) time-of-flight with fixed ko (indirect geometry)
need a precise knowledge of the instrument flight paths
Triple axis spectroscopy….. (Taipan & Sika)
IN2
0, I
LL Ideally suited to probing small regions of (Q,)
Very high flux, but low (Q,) coverage
Usually requires large single crystal samples
Time-of-flight spectroscopy….. (Pelican)
… for a given packet of neutrons, that start at some moment:
Time-of-flight spectroscopy….. (Pelican)
… for a given packet of neutrons, that start at some moment:
Time-of-flight spectroscopy….. (Pelican)
… for a given packet of monochromatic neutrons, that start at some moment and then scatter from a sample:
Whilst all neutrons arrive at the sample at the same time
- some will gain energy & others lose energy at the
sample
TOF basics….
De Broglie's equation: l =h
mnv=
ht
mns
But E =1
2mnv
2 ® v =2E
mn
DE = Ei - E f and tTOF = ti + t f
If L1 = clock start - to - sample distance
and L2 = sample - to - detector distance:
tTOF =L1
vi
+L2
v f
=L1
2Ei
mn
+L2
2E f
mn
ü
ý
ïïïïïïïïï
þ
ïïïïïïïïï
If distances are known:
either Ei can be fixed & tTOF measured (direct geometry)
OR
Ef can be fixed & tTOF gives Ei
(indirect geometry)
In BOTH cases, we then have E
TOF instruments Pelican Layout
Ideal instrument to start INS on:
can run many sample types single sample position set Ei & measure…. full spectra immediately (do not sequentially scan) large coverage of Q- space – ideal for survey scans
Correlation functions
Most of the analysis of scattering data is actually in the form of so-called pair correlation functions
Think of Bragg’s Law:
What we are measuring is the correlations between regions (planes) of
scattering density
- this may be electron density for X-rays (photons) & electrons - or nuclei (predominantly) for neutrons
What about inelastic scattering?
We measure the change in some parameter (polarizability, amplitude of
oscillation, etc.)
- if the wave vectors are similar in length to the distance between points
in the reciprocal lattice, then we can have structural and temporal
information!
- alternatively, mis-match gives either structural or temporal information…
Correlation functions
The intensity of elastic, coherent neutron scattering is proportional to the
spatial Fourier Transform of the Pair Correlation Function, G(r); the probability
of finding a particle at position r if there is simultaneously a particle at r = 0.
The intensity of inelastic coherent neutron scattering is proportional to the
space and time Fourier Transforms of the time-dependent pair correlation
function function, G(r,t) = probability of finding a particle at position r at time t
when there is a particle at r = 0 and t = 0.
For inelastic incoherent scattering, the intensity is proportional to the space
and time Fourier Transforms of the self-correlation function, Gs(r,t); the
probability of finding a particle at position r at time t when the same particle
was at r = 0 at t = 0.
Correlation functions
The intensity of elastic, coherent neutron scattering is proportional to the
spatial Fourier Transform of the Pair Correlation Function, G(r); the probability
of finding a particle at position r if there is simultaneously a particle at r = 0.
The intensity of inelastic coherent neutron scattering is proportional to the
space and time Fourier Transforms of the time-dependent pair correlation
function function, G(r,t) = probability of finding a particle at position r at time t
when there is a particle at r = 0 and t = 0.
For inelastic incoherent scattering, the intensity is proportional to the space
and time Fourier Transforms of the self-correlation function, Gs(r,t); the
probability of finding a particle at position r at time t when the same particle
was at r = 0 at t = 0.
Correlation functions
The intensity of elastic, coherent neutron scattering is proportional to the
spatial Fourier Transform of the Pair Correlation Function, G(r); the probability
of finding a particle at position r if there is simultaneously a particle at r = 0.
The intensity of inelastic coherent neutron scattering is proportional to the
space and time Fourier Transforms of the time-dependent pair correlation
function function, G(r,t) = probability of finding a particle at position r at time t
when there is a particle at r = 0 and t = 0.
For inelastic incoherent scattering, the intensity is proportional to the space
and time Fourier Transforms of the self-correlation function, Gs(r,t); the
probability of finding a particle at position r at time t when the same particle
was at r = 0 at t = 0.
Applications suited to TOF….
A typical TOF experiment gives all correlation functions:
G(r) along the elastic line
G(r,t) + Gs(r,t) outside of the elastic region
The given coverage of S(Q,) - kinematic limits - makes TOF ideal for dynamics that
are not restricted to regions or points of reciprocal space
There is no need for single crystal samples - although these can be accommodated
- polycrystalline, powder, amorphous, liquid,……
Molecular spectroscopy & lattice dynamics Guest:host interactions (confinement)
Dynamics of inclusions Magnetism (low dimensional & frustrated)
Single molecule magnets Amorphous materials & liquids (local dynamic/ structure relation)
Recent (unpublished) data…. PMB
Localised modes dominated by methyl group dynamics.
• Absence of dispersion • Increasing intensity as a f(Q) • Agreement between TAS & TOF data (a good thing)
Samples ca. 100 mg of powdered C6(CH3)5H Data collected < 10 K.
M. Mudge, B.K. Ng, M. Bhadbhade, K.C. Rule, R.A. Mole & J.A. Stride; unpublished
IN4, ILL
Taipan, ANSTO
kx
E=÷÷
ø
öççè
æ2
2
d
d
Numerical modelling
measure the
sum over all
wave-vectors
in S()
J.A. Stride, Acta Cryst. B, 61 (2005) 61 200
comparison of DFT to expt:
0.0 10.0 20.0 30.0 40.0
0
5
10
15
0 81 161 242 323
neutron energy loss / cm-1
S(w
) /
ar
bit
rary
un
its
neutron energy loss / meV
J.A. Stride, J.M. Adams & M.R. Johnson, Chem. Phys., 317 (2005) 143
IN4
, ILL
d-HMB: isotopic substitution
1.34
1.32
2 =1.41
HMB
d-HMB
IN4
, ILL
6
C 12.01
14
Si 28.09
32
Ge 72.59
50
Sn 118.71
82
Pb 207.19
Methyl tunnelling • Very low energy transitions (much lower than the torsional motions) can result in tunnelling
spectra – Very sensitive probe of the potential energy surface that the rotor sits in
– CH3, NH3, NH4+, etc.,
Stride et al., Chemistry, Eur. J., 2009, 15, 6569.
0 2! /3 4! /3
rotational angle
barr
ier
heig
ht
!
Tunnel
splitting
Methyl tunnelling • Very low energy transitions (much lower than the torsional motions) can result in tunnelling
spectra – Very sensitive probe of the potential energy surface that the rotor sits in
– CH3, NH3, NH4+, etc.,
Stride et al., Chemistry, Eur. J., 2009, 15, 6569.
0 2! /3 4! /3
rotational angle
ba
rrie
r he
igh
t
!
Tunnel
splitting
X-(C6H4-CH3)4
M.C.C. Ng, D.J. Craig, J.B. Harper, L. van-Eijck & J.A. Stride, Chemistry, Eur. J., 15 (2009) 6569 M.C.C. Ng, J.B. Harper, A.P.J. Stampfl, S. Rols, G.J. Kearley & J.A. Stride, Chem., Eur. J., 18 (2012) 13018
IN4, ILL Ta
ipan
, AN
STO
IN1
6, I
LL
magnetic sponges: M3(HCO2)6
M = Mn2+, Fe2+, Co2+, Ni2+, Zn2+
bulk ferro-, ferrri- & non-magnetic examples
porous structure
magneto-structural correlations?
Z. Wang, B. Zang, H. Fujiwara, H. Kobayashi & M. Kurmoo, Chem. Commun., (2004) 416
adsorbed species….
Currently >40 guests characterised
Z. Wang, B. Zang, H. Fujiwara, H. Kobayashi & M. Kurmoo, Chem. Commun., (2004) 416
[Mn3(HCO2)6] @ i = 3.6 Å; Ei = 6.3 meV
Tc = 8.0 K
T = 6 K
T=1.5 K T = 4 K
T = 15 K
J.A. Stride, M. Kurmoo and Z. Wang, Physica B, 385-386 (2006) 465
IN4
, ILL
[Mn3(HCO2)6] @ i = 4.1 Å; Ei = 4.9 meV
Pronounced degree of dispersion Magnetic Excitations (Q-dependence)
Samples ca. 500 mg of perdeuterated powders.
Strong long-range magnetic excitations
Chain-like coupling of spins
(unusually well-defined dispersion curves from a powder).
IN5
, ILL
adsorbed species…?
Unloaded, T = 1.5 K Loaded with C6H6, T = 1.5 K
Mn3(HCO2)6 i = 1.8 Å; Ei = 25.2 meV:
IN4
, ILL
adsorbed species…?
Mn3(HCO2)6 i = 1.8 Å; Ei = 25.2 meV:
• Assumes that the framework phonons are not very different upon loading
• all modes show Q2 phonon-like behaviour
• no indication of magnetic scattering in difference plot
IN4
, ILL
phonon density of states of confined
species:
2 4 6 8 10 12 14 16 18
16.1 32.3 48.4 64.5 80.6 96.8 112.9 129.0 145.2
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
neutron energy loss / cm-1
GD
OS
/
arb
itra
ry u
nit
s
neutron energy transfer / meV
IN4
, ILL
Conclusions (take home messages)
Inelastic neutron scattering can provide complementary – often unique - information to
other scattering techniques
The whole gamut of condensed matter dynamics is accessible to neutrons:
• from meV through to near eV
• largely motions of atoms & nuclei (coherent, incoherent, diffusive)
• sensitive to fluctuations in magnetic moments (magnons, spin waves)
Isotopic variation can ‘silence’ certain modes • incoherent scattering of 1H (when present) dominates spectra
• most molecular species have 1H – great sensitivity….
• dynamics on confinement
Absence of selection rules for vibrational modes • particle-particle interactions – ease of numerical modelling
World class facilities available at ANSTO – complementary techniques in Japan,
Europe & USA.
thank you