Reverse Monte Carlo modelling of cation distributions in crystal structures

Reverse Monte Carlo modelling of cation distributions in crystal structures

Hui Qun 惠群

Why Neutron Total Scattering?

max

2

Qr

◆ Bragg+diffuse scatterings

◆ Time-of-flight (TOF) to obtain high Q )

sin4(

◆ High spatial resolution

Quantitatively understand neutron total scattering data 1

VN

dQQrQr

QiQrG

drQrQr

rGrQi

rG

Qi

0density number atom average thewhere

)sin()(2

0 4

03)2(

1)(

and

)sin()(0

240)(

:ansformsFourier tr by the )(function on distributi radial total the torelated

andfactor structure scattering- total theis )(

Quantitatively understand neutron total scattering data 2

nmnnm

m

m

mnmn

mnnm

nmnm

mn

bbccrrrGrT

rrGrD

rG

drcr

rnrg

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rg

r

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,

02

,

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)(4)(

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4

)()(

)1)(()(

)(function on distributi radial partial theof in terms defined is

and distance space real by the separated pairs

atomic finding ofty probabliti the tells)(

RMC applied to the study of crystalline materials

Generalising 2

2

n

mQimm m

QiQi1

2)(

2expcalc )]()([

n

mrTmm m

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2)(

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: The quality of the fit of the experimental to the data simulated from the structural model

2

Flowchart of the RMC modelling

Modelling cation distribution –atom swap mode in RMC

Testing

SrTiO3 configurations

Corresponding T

(r) and n(r)

Corresponding T

(r) and n(r)

SrTiO3 configurations

Corresponding T

(r) and n(r)

SrTiO3 configurations

SrTiO3 configurations

Corresponding T

(r) and n(r)

Perovskites ABO3

“A” site: Na+, K+, Pb2+, Ba2+, Mg2+, Ca2+, Sr2+

“B” site: Ti4+, Zr4+, Nb5+

A

B

Structure and cation ordering in Ca0.5Sr0.5TiO3 at room temperature

different Initial configurations: Configurations with Pbnm space group (1 type

of “A” site): (1) Ca and Sr are arranged randomly (2) Ca and Sr are clustered at each half of the

configuration box (3) Ca sheet and Sr sheet are alternatively

arranged. Configurations with Bmmb space group (2

types of “B” site) (1) Ca and Sr are positioned at the two types of

“A” sites, respectively (2) (2) Ca and Sr are arranged randomly at the

two types of “A” sites

Analysis of RMC configurations – the Ca/Sr ordering 1

Calculations of n(r) show Ca/Sr ordering at the “A” site

Analysis of RMC configurations –the Ca/Sr ordering 2

Illustrated via the partial distribution functions which involve Ca and Sr atoms

g(r) g(r)

Analysis of RMC configurations – the Ca/Sr ordering 3

Illustrated via the total distribution function

Ordered config

Disordered config

Comparison

Structure of Ca0.5Sr0.5TiO3

Ca and Sr atoms occupy two different types of

“A” sites and are ordered. A Ca atom is surrounded by about 6 nearest Sr atom and

vice versa. The structure is compatible with the space group

P21nm

More…

Work have done: (1) other compositions of Ca1-xSrxTiO3

(2) PbZr1-xTixO3(PZT) cation distribution at “B” site Applications in wider area(1) More complex system such as (Mg,Fe)(Si,Al)O3

(2) Metal alloys(3) Deduce atom/vacancy short-range ordering in

solid solutions having vacancies in their structures e.g. SrTixFe1-xO5.5+0.5x

Summary

Development, testing and applicationWorks well and gives unique information on

cation distribution