Structure of glasses and melts - Mineralogy, Petrology and ... · PDF file11 December, 2006...

11 December, 2006 Neutron Scattering in Earth Sciences 1

Structure of glasses and meltsStructure of glasses and melts

Martin Wilding Martin Wilding

Institute of Mathematical and Physical Sciences, University of Institute of Mathematical and Physical Sciences, University of Wales, Aberystwyth, Ceredigion, SY23 3BZWales, Aberystwyth, Ceredigion, SY23 3BZ

Chris Benmore,Chris Benmore,

Intense Pulsed Neutron Source and the Advanced Photon Source,Intense Pulsed Neutron Source and the Advanced Photon Source,

9700 Cass Avenue,9700 Cass Avenue,

Argonne, IL 60439Argonne, IL 60439


Outline Outline

The Liquid State

Neutron Scattering theory

Instrumentation and sample environment

Interpretation of glass structure

Studies of liquids and amorphous materials

Summary and future directions


The Liquid StateThe Liquid State

Liquids lack long-range order

• Pair distribution function shows Short range order

Glasses formed by super-cooling a liquid.

• Show a glass transition

Amorphous materials by other routes

• Inherent polyamorphism


The pair distribution The pair distribution

functionfunction

Average separation of atom pairs

Region where g(r) is zero

Pronounced first peak

Series of smaller peaks

g(r)=1 mean density of the system


Glasses and amorphous Glasses and amorphous

materialsmaterials

Super-cooling

• Ergodicty

• Non-ergodicity

Configurational entropy and fragility

Pressure-induced amorphisation


Neutron diffraction: Neutron diffraction:

Scattering theoryScattering theory

Double differential cross

section

Coherent scattering law

Static approximation

1

1

2

0 dEddEd

dII Ω

Ω=

σ

cohcohscattered

incident

dEd

d

k

k

NQS

1

241),(

Ω=

σ

σ

πω

)2cos1(2 22 θ−≈ incidentkQ


Neutron diffraction: Scattering in Neutron diffraction: Scattering in

multimulti--component systemscomponent systems

Scattering:

• Sum of several atom-pairs

• Partial contributions

Faber-Ziman formalism

∑+=

Ω

n

incbcQFQd

d

N ααα

σ 2

,)()(1

[ ]1)()( ,

,

−=∑ QSbbccQFn

βαββα

αβα


Neutron diffraction: the differential Neutron diffraction: the differential

cross sectioncross section


Neutron diffraction: the pair Neutron diffraction: the pair

correlation functioncorrelation function

Sine Fourier transform of the Sα,β(Q):

• Total number density is ρ0

• Gα,β(r) is the probability of funding atom β at distance r from atom α.

Fourier transform of the total F(Q) is the weighted sum of all partial values.

Total correlation function, T(r).• Highlights correlation at high r

Differential distribution function D(r).

• Bulk density removed.

[ ] dQQrQSQr

rg )sin(1)(2

11)(

0

,

0

2, ∫∞

−=− βαβαρπ

[ ]1)()sin()(2

1)( ,

,00

2−== ∑∫

∞

rgbbccdQQrQQFr

rGn

βαβα

βαβαρπ

1)(4)(

)(4)(

,

0

,

0

−

+=

+=

∑

∑

n

n

bbccrGrrD

bbccrGrrT

βα

βαβα

βα

βαβα

ρπ

ρπ


Neutron instrumentationNeutron instrumentation

Steady state (reactor type)

Beam of wavelength λ is scattered though angle 2θ.


Neutron instrumentationNeutron instrumentation

Time-of-flight (spallation source)

Detectors at fixed angle record different wavelengths (Q)


Neutron diffraction: Neutron diffraction:

correction procedurescorrection procedures

Structural information is in elastic, single scattering events.


Sample environmentsSample environments

Pressure cells


Sample environmentsSample environments

Containerless levitation


Interpretation of glass Interpretation of glass

structurestructure

Based on the pair distribution function (PDF)

Continuous random networks (CRN)

Characteristic distance ranges


Interpretation of glass Interpretation of glass

structurestructure

Short-range order and connectivity

Intermediate range Order

The first sharp diffraction peak (FSDP)


Partial structure factor Partial structure factor

determinationdetermination

Isotopic substitution, e.g.

H/D

2222

2222

2

2

)()(2

)()(

OOOHOHHH

OOOO

OHOHOH

HHHH

OH

bcbbccbcA

rgA

bcrg

A

bbccrg

A

bcrG

++=

++=

)(441.0)(446.0)(113.0)(

)(091.0)(23.4.0)(486.0)(

)(190.0)(92.4.0)(318.0)(

2

2

2

rgrgrgrG

rgrgrgrG

rgrgrgrG

OOOHHHOH

OOOHHHOH

OOOHHHOH

++=

++=

+−=




Combined neutron and X-ray data

[ ] [ ]

−

−−−

=∆

)(1

1)()(

1)(

)(

QW

W

QSQW

WQS

QS

X

N

X

X

NN

-1

0

1

2

3

4

5

6

7

8

9

10

1 1.5 2 2.5 3 3.5 4

Radial distance (Angstrom)

T(r

)

Mg-O

O-O

Enstatite glass

Forsterite glass




Reverse Monte Carlo and empirical structural refinement


Studies of liquids and amorphous Studies of liquids and amorphous

materials: Simple oxidesmaterials: Simple oxides

Confined to simple systems:

• SiO2

• Li2O-SiO2

• K2O-SiO2

• Na2O-SiO2

• CaO-Al2O3-SiO2



materials: Simple oxidesmaterials: Simple oxides

MgO-SiO2 glasses

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25

Momentum transfer (Angstrom-1)

S(Q

)

67% MgO 33% SiO2 (forsterite)

50% MgO 50% SiO2 (enstatite)

54% MgO 46% SiO2

58% MgO 42% SiO2

62% MgO 38% SiO2

-1

0

1

2

3

4

5

0.5 1.5 2.5 3.5 4.5

Radial distance (Angstrom)

T(r

)

Si-O

Mg-OO-O

Enstatite glass

Forsterite glass



materials: amorphous icesmaterials: amorphous ices

• Low and high-density forms of amorphous ice

• Demonstration of LDA-HDA transitions

• Fully hydrogen-bonded tetrahedral networks

• Interstitial water molecule

• Related to the high pressure structure of liquid water



materials: amorphous icesmaterials: amorphous ices

Changes in the first peak in the diffraction pattern

Changes in the O-O partial in real space

Change in O-O, moves to greater radial distance with HDA-LDA



materials: high pressure studiesmaterials: high pressure studies

Amorphous forms of GeO2

Classic “strong” network-forming glass

Tetrahedral-octahedral coordination change

Changes in height and position of FSDP

Shrinkage and collapse of open network structures

Intermediate 5-coordinate Ge-O stabilised


MgOMgO--SiOSiO22 glasses: Neutron glasses: Neutron

diffractiondiffraction

In Situ high pressure neutron data 38% SiO2 glass

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8

Momentum Transfer / Angstrom -1

S(Q

)

Ambient

4.1 Gpa

5.7 Gpa

8.6 Gpa

6.7 Gpa

Abrupt changes in the S(Q) between 6 and 8 GPa



materials: high pressure studiesmaterials: high pressure studies

In Situ high pressure neutron data 38% SiO2 glass

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.0 2.0 3.0 4.0 5.0 6.0

r / Angstrom

g(r

)

Ambient

4.1 Gpa

5.7 Gpa

8.6 Gpa

6.7Gpa

• Change in first peaks

– Si-O

– Mg-O

• Increasing distortion of the Mg-O polyhedron?

• Non-linear change in structure

• Is it polyamorphic?


Summary and future Summary and future

directionsdirections

Neutrons offer the opportunity to determine the structure of liquids directly by diffraction

Total structure factor related to the PDF by Fourier transform

Combined techniques can be used to extract partial S(Q)’s

Developments in sample environment:• Levitation studies

• High pressure studies

New neutron sources

More challenging experiments

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Structure of glasses and melts - Mineralogy, Petrology and ... · PDF file11 December, 2006...

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