Neutron scattering in Earth Sciences Martin Dove applications in... · Sample environment We might...

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Neutron scattering in Earth

SciencesMartin Dove

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The structure of the Earth

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Properties under Earth conditions

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Changes in structure

Phase changes, including displacive, cation

ordering and reconstructive

Changes in properties

Density, elasticity, diffusivity/conductivity, phonon

frequencies

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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

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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)

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Sample environment



System complexity



symmetry)

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Constituents of granite

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Quartz

Feldspar

Mica

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Sample environment



System complexity



symmetry)

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Earth temperature/pressure profile

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Ambient temperature

Am

bie

nt P

Simultaneous

high

temperature

and high

pressure

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Paris-Edinburgh cell

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PE cell with internal microfurnace

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Internal heating – plan diagram

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Internal heating – exploded view

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Assembly

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Anvil

Anvil

Anvil

Anvil

PTFE ringSample

Pyrophyllite

gasket

Graphite

heater

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High-pressure diffraction @ ISIS

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Assembly

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Anvil

Anvil

Anvil

Anvil

PTFE ringSample

Pyrophyllite

gasket

Graphite

heater

Thermocouple?

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Temperature measurement by

radiography

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Radiography principal

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Width of

resonance line

can be used to

calibrate

temperature

Width of

resonance line

increases with

temperature due

to Doppler effect

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Simple detector assembly

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Example resonances

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Theoretical basis

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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:

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Theoretical basis

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Pulse source function

Foil thickness x number of atoms

Detector efficiency Resolution 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

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S( E ) 1

exp ( E E)2 /2

4mMERkBT

(M m)2

Temperature of absorbing atoms =

sample temperature

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Example of application

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18 ± 3 °C

473 ± 6 °C

781 ± 7 °C

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Example of diffraction data:

Mg0.7Fe0.3O at 621 K and 9.82 GPa

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Pressure dependence of Fe/Ti

ordering in Fe(Fe0.35Ti0.65)O3

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1 bar Data

Fitted model

Pearl Data

Fitted model

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Pressure dependence of Fe/Ti

ordering in Fe(Fe0.35Ti0.65)O3

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‣ 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

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Influence of pressure on Mg/Al

order-disorder in spinel, MgAl2O4

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‣ 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

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Diffraction pattern from MgAl2O4, at

1600 K and 3.2 GPa

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Variation of order as a function of

pressure

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‣ Pressure significantly modifies the degree of order

‣ More disordered with pressure: effect of changing local

interactions between Al and Mg neighbours

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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

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Effects of varying pressure and

temperature

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Increasing T

to 400 °C

Increasing P

to 2 GPa

Decreasing T

Ambient P/T

0

5

10

15

20

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0 1 2 3 4

d spacing

Inte

nsi

ty

tetragonal

cubic

amorphous

tetragonal

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Phase diagram

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High-temperature displacive phase

transition in quartz, SiO2

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. .

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

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High-temperature displacive phase

transition in cristobalite, SiO2

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-cristobalitecubic

-cristobaliteTetragonal

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What do high-temperature phases

look like?

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‣ 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

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PDF in quartz

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Increasing

temperature shows

broadening of

interatomic

correlations

Suggests increase in

disorder on heating

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Bond lengths

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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)

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Thermal motion and interatomic

distances

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Apparent shortening of bond

increases with temperature

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Reverse Monte Carlo modelling

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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

➥

➥

➥

➥

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Atomic configurations of quartz

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20 K, 793 K, 1073 K,

Onset of disorder observed on heating

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Orientational disorder of SiO4

tetrahedra in quartz

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Distribution of SiO4

orientations

Heating

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Rigid unit motions of SiO4

tetrahedra in quartz

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RUM component

Tetrahedral distortions

Total atomic displacements

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Disorder in -cristobalite

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Single pancake site or six sites for

oxygen atoms?

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Orientations of Si–O bonds

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‣ No obvious special

orientations of Si–O

bonds

‣ Suggesting no well-

defined domains

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Phonon dispersion curves

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‣ 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

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MERLIN spectrometer at ISIS

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Phonon dispersion curves in

calcite, CaCO3, measured on

MERLIN

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Calculated and measured of

phonon scattering in calcite

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Experiment Simulation

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Calculated and measured of

phonon scattering in calcite

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Experiment Simulation

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Water in minerals

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‣ 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

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Water in clays

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Water molecules and cations are found within the

space between tightly-bound oxide layers

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00l diffraction from clays

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Structure of water within clay

interlayer space

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Surface conditions

Depth of 10 km

Hydrogen

Other atoms

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Outlook for neutrons in Earth

Sciences

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‣ 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

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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)

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Acknowledgements

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Dave Keen, Matt Tucker, Bill Marshall, Toby

Perring, Rob Bewley (ISIS)

Simon Redfern, Howard Stone, Beth Cope

(Cambridge)

Neil Skipper (UCL)

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