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Neutron scattering in Earth
SciencesMartin Dove
1
2
The structure of the Earth
2
3
Properties under Earth conditions
3
Changes in structure
Phase changes, including displacive, cation
ordering and reconstructive
Changes in properties
Density, elasticity, diffusivity/conductivity, phonon
frequencies
4
What do we want to know?
‣ Same as in many fields …
‣ Structure, in absolute sense and also as function
of external variables
‣ Lattice dynamics, in part to understand flexibility,
also to use as basis for modelling
‣ Localised effects, such as motions of water
molecules within structures
‣ Magnetic structures
‣ … which can be obtained using standard
approaches in neutron diffraction and
spectroscopy4
5
So what is different?
Sample environment
We might want to go to rather high pressures and
temperatures, out of the range of the norm
System complexity
Many crustal minerals do not have simple crystal
structures (many atoms in the unit cell, low
symmetry)
5
6
So what is different?
Sample environment
We might want to go to rather high pressures and
temperatures, out of the range of the norm
System complexity
Many crustal minerals do not have simple crystal
structures (many atoms in the unit cell, low
symmetry)
6
7
Constituents of granite
7
Quartz
Feldspar
Mica
8
So what is different?
Sample environment
We might want to go to rather high pressures and
temperatures, out of the range of the norm
System complexity
Many crustal minerals do not have simple crystal
structures (many atoms in the unit cell, low
symmetry)
8
9
Earth temperature/pressure profile
9
Ambient temperature
Am
bie
nt P
Simultaneous
high
temperature
and high
pressure
10
Paris-Edinburgh cell
10
11
PE cell with internal microfurnace
11
12
Internal heating – plan diagram
12
13
Internal heating – exploded view
13
14
Assembly
14
Anvil
Anvil
Anvil
Anvil
PTFE ringSample
Pyrophyllite
gasket
Graphite
heater
15
High-pressure diffraction @ ISIS
15
16
Assembly
16
Anvil
Anvil
Anvil
Anvil
PTFE ringSample
Pyrophyllite
gasket
Graphite
heater
Thermocouple?
17
Temperature measurement by
radiography
17
18
Radiography principal
18
Width of
resonance line
can be used to
calibrate
temperature
Width of
resonance line
increases with
temperature due
to Doppler effect
19
Simple detector assembly
19
20
Example resonances
20
21
Theoretical basis
21
Pulse source
function
Detected signal:
Area density of
absorbing nuclei
Detector efficiency Instrument
resolution function
Energy transfer function
(the Doppler broadening function)Breit-Wigner lineshape
Transmitted signal:
Total cross-section:
22
Theoretical basis
22
Pulse source function
Foil thickness x number of atoms
Detector efficiency Resolution function
Energy transfer function
(Doppler broadening function)Breit-Wigner lineshape
(E) BW( E )S( E ,E)d E
T (E) exp (E)
I(E) P( E )( E )R( E )T (E E )d E
Measured signal
Transmitted signal
Absorption cross section
23
Energy transfer function
23
S( E ) 1
exp ( E E)2 /2
4mMERkBT
(M m)2
Temperature of absorbing atoms =
sample temperature
24
Example of application
24
18 ± 3 °C
473 ± 6 °C
781 ± 7 °C
25
Example of diffraction data:
Mg0.7Fe0.3O at 621 K and 9.82 GPa
25
26
Pressure dependence of Fe/Ti
ordering in Fe(Fe0.35Ti0.65)O3
26
1 bar Data
Fitted model
Pearl Data
Fitted model
27
Pressure dependence of Fe/Ti
ordering in Fe(Fe0.35Ti0.65)O3
27
‣ Increase in Tc cannot be
accounted for by conventional
strain effects
‣ Increase in Tc must therefore
come from increased internal
energy of ordering, i.e. increased
cation interaction as structure is
squeezed
28
Influence of pressure on Mg/Al
order-disorder in spinel, MgAl2O4
28
‣ Determine the pressure-
dependence of the
kinetics of order-
disorder in minerals
‣ Probe the pressure
dependence of the
equilibrium high-T order-
disorder properties: first
neutron measurements
of these phenomena at
real Earth interior
conditions
29
Diffraction pattern from MgAl2O4, at
1600 K and 3.2 GPa
29
30
Variation of order as a function of
pressure
30
‣ Pressure significantly modifies the degree of order
‣ More disordered with pressure: effect of changing local
interactions between Al and Mg neighbours
31
High-pressure displacive phase
transition in cristobalite, SiO2
‣ Stable above ca 1.5
GPa
‣ Although it is the
lowest-symmetry
phase, it is derived
from cubic β rather
than tetragonal α
‣ Structure identified
using simulations
31
32
Effects of varying pressure and
temperature
32
Increasing T
to 400 °C
Increasing P
to 2 GPa
Decreasing T
Ambient P/T
0
5
10
15
20
25
0 1 2 3 4
d spacing
Inte
nsi
ty
tetragonal
cubic
amorphous
tetragonal
33
Phase diagram
33
34
High-temperature displacive phase
transition in quartz, SiO2
34
. .
4.90
5.00
0 200 400 600 800 1000
4.92
4.94
4.96
4.98a
(Å
)
Temperature (K)
5.38
5.40
5.42
5.44
5.46
5.48
c (Å)
0.00
0.05
0.10
0.15
0.20
0 200 400 600 800 1000Temperature (K)
D i s p l a c e m e n t s
2 ( Å
2)
-quartzHexagonal
-quartzTrigonal
Small displacements
of atoms that
change the
symmetry
35
High-temperature displacive phase
transition in cristobalite, SiO2
35
-cristobalitecubic
-cristobaliteTetragonal
36
What do high-temperature phases
look like?
36
‣ The challenge is that the local structure is
unlikely to be exactly reflected in the average
structure
‣ Local structure can be probed using total
scattering – the same approach that is used to
study amorphous materials and liquids
‣ We use the Reverse Monte Carlo method to
build large atomic models consistent with the
Bragg scattering, total scattering, and pair
distribution function data
37
PDF in quartz
37
Increasing
temperature shows
broadening of
interatomic
correlations
Suggests increase in
disorder on heating
38
Bond lengths
38
0 200 400 600 800 1000
Temperature (K)
1.585
1.590
1.595
1.600
1.605
1.610
1.615
1.620
T(r) SiŠO
Rietveld SiŠOSi–
O d
ista
nce (
Å)
39
Thermal motion and interatomic
distances
39
Apparent shortening of bond
increases with temperature
40
Reverse Monte Carlo modelling
40
Generate initial configuration of atoms
Move one randomly-selected atom by
a small random vector
Compute new experimental functions
and compare with data
Only reject change if comparison is
worse and with some probability
➥
➥
➥
➥
41
Atomic configurations of quartz
41
20 K, 793 K, 1073 K,
Onset of disorder observed on heating
42
Orientational disorder of SiO4
tetrahedra in quartz
42
Distribution of SiO4
orientations
Heating
43
Rigid unit motions of SiO4
tetrahedra in quartz
43
RUM component
Tetrahedral distortions
Total atomic displacements
44
Disorder in -cristobalite
44
Single pancake site or six sites for
oxygen atoms?
45
Orientations of Si–O bonds
45
‣ No obvious special
orientations of Si–O
bonds
‣ Suggesting no well-
defined domains
46
Phonon dispersion curves
46
‣ Dispersion curves have an important role in
enabling the construction of accurate models of
interatomic forces
‣ Atomistic simulation plays an important role in
mineral sciences because of the access it gives
to extreme temperatures and pressures
‣ New instrumentation at ISIS and ILL will give
new capabilities
47
MERLIN spectrometer at ISIS
47
48
Phonon dispersion curves in
calcite, CaCO3, measured on
MERLIN
48
49
Calculated and measured of
phonon scattering in calcite
49
Experiment Simulation
50
Calculated and measured of
phonon scattering in calcite
50
Experiment Simulation
51
Water in minerals
51
‣ Some minerals, such as clays and zeolites,
contain significant quantities of water in pores
and between atomic layers
‣ Water is the grease of the Earth – it is what
enables the convection of minerals in the inner
Earth that drives plate tectonics
‣ Neutrons are particularly good for the study of
hydrogen and hence water
‣ Incoherent scattering is a probe of individual
hydrogen atoms and hence dynamics of water
molecules
52
Water in clays
52
Water molecules and cations are found within the
space between tightly-bound oxide layers
53
00l diffraction from clays
53
54
Structure of water within clay
interlayer space
54
Surface conditions
Depth of 10 km
Hydrogen
Other atoms
55
Outlook for neutrons in Earth
Sciences
55
‣ Instrumentation is excellent
‣ Range of techniques is unrivalled
‣ Sensitivity of light elements and hydrogen is not
matched by other techniques (such as
synchrotron radiation)
‣ Ability to control sample environment is much
easier than with other probes
‣ Ability to match computer simulation and
neutron scattering is excellent
56
However …
‣ The small volumes required for very high
pressures and much less problematic for
synchrotron radiation sources
‣ The community of advocates and those with
experience is small (sub-critical), and neutron
scattering has often suffered through appearing
to have a skills barrier
‣ Much of what is being done is not challenging
(typically powder diffraction)
56
57
Acknowledgements
57
Dave Keen, Matt Tucker, Bill Marshall, Toby
Perring, Rob Bewley (ISIS)
Simon Redfern, Howard Stone, Beth Cope
(Cambridge)
Neil Skipper (UCL)