Ionic Conductors: Characterisation of Defect

Structure

Lectures 13-14Defect structure analysis through neutron

diffraction

Dr. I. AbrahamsQueen Mary University of London

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Powder Neutron Diffraction

Neutrons with wavelengths of around 1 Å can be used for diffraction purposes.

Neutrons are scattered by nuclei and this has important consequences for the nature of the diffraction data obtained.

Symbol n0

Spin 1/2 Actual Mass m = 1.6749 10-27 kg

Actual Charge 0

Some physical properties of thermal neutrons

The de Broglie equation relates to the neutron mass and velocities to wavelength. Therefore, the neutrons generated from reactors or pulsed sources at certain speeds can be in useful ranges for diffraction experiments.

mv

h

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The scattering power (scattering length b for neutrons or scattering factor f for X-rays) of an atom towards neutrons is different than it is towards X-rays.

This is mainly because neutrons are scattered through interaction with atomic nuclei rather than atomic electrons as occurs with X-rays, making the relationship between the neutron scattering length of an atom and its atomic number weak

0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

Bi

Pb

Yb

ErNb

Y

V

O

b /

10-1

2 cm

Z, atomic number

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In systems containing light and heavy atoms X-ray scattering will be dominated by scattering from the heavy atoms, while neutron scattering does not show this correlation and it is often easier to locate light atoms in the presence of heavier ones.

Able to distinguish between neighbouring elements in the periodic table such as manganese and iron or cobalt and nickel.

Isotopic substitution experiments possible as scattering lengths of isotopes differ.

Less dependence of scattering on Bragg angle, , leading to greater intensity at higher angles.

Advantages of neutron diffraction

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0 5 10 15 20 25 3010

20

30

40

50

60

70

80

90

scattering factor and scattering length for Bi, Z = 83

Neu

tron

scattering

leng

th b / cm

X-r

ay s

catt

erin

g f

acto

r f

Q / Å-1

8.0x10-13

8.4x10-13

8.8x10-13

sin4

Q

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Combined High Resolution Powder X-ray and Neutron Diffraction

Combined refinement using X-ray and neutron data allows accurate refinement of both heavy and light atoms

X-ray diffractionModern X-ray powder diffractometers give sufficiently high resolution and intensity for refinement of heavy atom positions.

Difficult to refine accurate parameters for weakly scattering atoms in a pattern dominated by strongly scattering atoms.

Neutron diffractionUse of high resolution allows for decoupling of thermal and occupancy parameters for atoms and allows accurate determination of oxygen site occupancies.

Relative scattering of neutrons by atoms such as O and Li is much greater than in XRD.

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Ref: Neutron Diffraction, Bacon Clarendon Press 1975.

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Neutron sources

Two main types of neutron sources.

1. Reactor Sources

e.g. ILL High Flux reactor source. Neutrons produced as a product of the fission of 235U. Neutrons can then be moderated to give a range of energies and then conducted to different instruments via guide tubes.

Diffraction experiments are normally at a constant wavelength, but can also be energy dispersive.

2. Pulsed Sources

e.g. ISIS Proton spallation source. Pulses of protons are accelerated in a synchrotron and then fired at a heavy metal target (tantalum in this case) to generate neutrons. These can be moderated or used directly. A Maxwellian distribution of energies is produced.

Diffraction experiments normally use a large range of energies (time of flight method).

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ILL Reactor Source

ISIS Pulsed Source

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ISIS R55 Main hall

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The time of flight method

Schematic diagram of the time-of-flight powder diffractometer

The distance between the moderator and the sample is L0, with the detector located at a distance L1 from the sample.

A variable wavelength/fixed angle scan is used.

The variation of wavelength arises due to the time distribution of neutrons arriving at the detector following the initial pulse and hence this is known as the time-of-flight method.

For high resolution L0 is large greater distribution of energies.

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hklhkldmv

h sin2

t

L

t

LLv

01

hklhkl mL

htd

sin2

hklhkldL

t

m

h sin2

The neutron velocity is given by:

Combining the de Broglie and Bragg equations:

Thus

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t.o.f

d-spacing

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Determination of defect structure from neutron diffraction data

Like all diffraction methods, neutron diffraction will give an average picture of the structure.

In order to determine details of the defect structure we need to examine the structural model carefully.

1.Examine the nature of the disorder. Are there sites that cannot be simultaneously occupied?

2.Calculate the site occupancy ratios to look for correlations.

3.Look for potential coordination environments that are stereochemically meaningful.

4.Does the model agree with the known crystal chemistry of the cations?

5.Does the proposed model explain the observed physical behaviour?

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Worked Examples of Defect Structure Analysis - 1

1. Defect Structure Analysis in -phase BIMEVOXes

The BIMEVOXes are layered Aurivillius phases consisting of alternating sheets of [Bi2O2]n

2n+ and [V1-xMxO3.5-y0.5+y]n2n-

The value of x is typically 0.1-0.25 for divalent M. The value of y varies with the valency of M. denotes a vacancy.

[Bi2O2]n2n+

[V1-xMxO3.5-y0.5+y]n2n-

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Rietveld Analysis of the powder diffraction data allow for an average model of the structure to be derived.

Fit to HRPD neutron data Fit to X-ray data

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Atom Site x y z Occ. Uiso (Å2)

Bi 4e 0.00(-) 0.00(-) 0.16941(5) 1.00(-) 0.00247(3) Ni/V 2b 0.50(-) 0.50(-) 0.00(-) 0.10/0.90(-) 0.0074(4) O(1) 4d 0.00(-) 0.50(-) 0.25(-) 1.00(-) 0.00201(3) O(2) 4e 0.50(-) 0.50(-) 0.1055(5) 0.321(6) 0.0052(1) O(3) 8g 0.50(-) 0.00(-) 0.0285(3) 0.3375(-) 0.0081(1) O(4) 16n 0.50(-) 0.311(1) 0.0918(3) 0.170(2) 0.0052(1)

Bi2V0.9Ni0.1O5.35: Refined atomic parameters

Contact distances (Å) Site occupancy ratios

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Defect Structure in Vanadate Layer

CN = 5

Average

Octahedral

CN = 6

Tetrahedral

CN = 4

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Idealised vanadate layer Defect vanadate layer

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Conduction Mechanism in BIMEVOX

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Calculation of Defect Structure

Let FO(m) be the fractional occupancy per metal atom of a particular oxygen site m. The neutron refinements indicate that total apical oxygen per metal atom is always 2.

FO(2) + FO(4) = 2 Eq. 1

Now the equatorial oxygen O(3) is associated with both tetrahedra and octahedra. Therefore:

FO(3) = FO(3oct) + FO(3tet) Eq. 2

The apical oxygen O(2) is associated exclusively with octahedra. Therefore:

FO(3oct) = FO(2) Eq. 3

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The apical oxygen O(4) is associated exclusively with tetrahedra. Taking into account relative site multiplicities:

FO(3tet) = FO(4)/2 Eq. 4

Therefore the fractions, X, of octahedra and tetrahedra are given by:

Xoct = FO(2)/2 = FO(3oct)/2 Eq. 5

Xtet = FO(4)/2 = FO(3tet) Eq. 6

In the case of Bi2V0.9Ni0.1O5.35

Xoct = 0.64/2 = 0.32

Xtet = 1.36/2 = 0.68

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The value of (the degree of vanadium reduction) may also be calculated from the neutron data.

= 3.5-(5-l)x/2 – (FO(2) + FO(3) + FO(4)) Eq. 7

e.g. Effects of thermal history on BIMGVOX10, -Bi2V0.9Mg0.1O5.35-.

Quenched Slow CooledFO(2) 0.558 0.630FO(3oct) 0.558 0.630FO(3tet) 0.720 0.684FO(3) 1.276 1.312FO(4) 1.440 1.368Xoct 0.279 0.315Xtet 0.720 0.684Zeff 4.831 4.911 0.076 0.040

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Calculation of solid solution limits from defect structure

Analysis of the defect structure allows us to predict the solid solution limits.

In the the divalent substituted BIMEVOXes the formula of the vanadate layer is

[V1-xMxO3.5-3x/2 0.5+3x/2]n2n-

Therefore the number of vacancies per metal atom Nvac is

Nvac = 0.5+3x/2

The solid solution limit will occur when no further vacancies can be introduced. This will depend on the preferred coordination geometry of the dopant metal.

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Calculation of solid solution limits from defect structure

Case 1: M atoms tetrahedralThe solid solution limit is reached when all the V/M atoms are tetrahedra i.e. Nvac = 1.0

Solving for x, the solid solution is reached at x = 0.33

Case 2: M atoms octahedralIn this case the solid solution limit occurs when Nvac = 1-x. Solving for x the solid solution occurs limit occurs at x = 0.20.

In both cases the calculated limits are close to the observed.

Limits are also lowered by reduction of V ( ).

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Worked examples of defect structure analysis – 2

2. Defect Structure in -Bi2O3

-Bi2O3 exhibits a defect fluorite structure. There have been many studies of this compound. This disagreement in the structural analysis of this compound lies in the location of the oxide ions. Two sites 8c and 32f have been proposed.

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8c 0.25,0.25,0.25

32f 0.3,0.3,0.3

8c O2- show regular tetrahedral coordination with 4 equal Bi-O contacts.

32f O2- have trigonal pyramidal geometry and bridge only 3 Bi atoms.

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Therefore, depending on the relative occupancies of these sites we can work out the average cation coordination number.

Let FO(m) be the fractional occupancy per metal atom of a particular oxygen site m.

Ave Bi coordination number = 4FO(1) + 3FO(2)

Model Bi Ave. CNSillen, Gattow (8c only) 6Willis (32f only) 4.5Battle et al (8c + 32f) 5.36Yashima and Ishimura (8c + 32f) 5.02

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Worked examples of defect structure analysis – 3

3. Defect Structure Analysis in Bi3TaO7

Bi3TaO7 exhibits a type II incommensurately ordered fluorite structure. Neutron diffraction reveals additional peaks that cannot be indexed using a commensurate supercell.

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In order to index these peaks a 3-dimensionally modulated incommensurate cell is required. In this cell any Bragg peak in the diffraction pattern can be indexed using six indices (h, k, l, m, n, p) and a single modulation parameter .

2

222222

2

1

a

pnmlkh

d hklmnp

In Bi3TaO7, the value of is calculated as 0.388.

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Type –II Incommensurate Structure in Bi3TaO7

Refinement proceeded using a cubic subcell model based on the structure of -Bi2O3.

This approach ignores the superlattice reflections but accounts for the majority of the scattering.

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Bi3TaO7: Refined atomic parameters

Contact distances (Å) Site occupancy ratios

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Defect Structure in Bi3TaO7

Average

Ta

CN = 6

Bi

CN = 4

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Ta:O(3) ratio close to 1:1. This site not occupied in Bi2O3 and suggests that the O(3) site is exclusively associated with Ta.

Since O(3) is bonded to two metal atoms, in order to preserve a 1:1 ratio it must lead to clustering of tantalate octahedra (chains).

Incommensurate ordering believed to be associated with chains of TaO6 octahedra.

Average Bi coordination calculated as 4.576I. Abrahams, F. Krok, M. Struzik, J.R. Dygas, Solid State Ionics, 179 (2008) 1013