Uses of Powder Diffraction
Qualitative Analysis
Identification of single-phasematerials
Identification of multiple
phases in microcrystalline
mixtures
Recognition of amorphousmaterials in partially crystalline
mixtures

Powder X-ray Diffraction

Quantitative Analysis
Lattice Parameter
Determination
Phase Fraction Analysis

Brendan J. Kennedy
School of Chemistry
The University of Sydney

Peak Shape Analysis
Crystallite Size Distribution
Microstrain Analysis
Extended DefectConcentration

Three Unique Features ofSynchrotron Radiation•Intensity•Enables Rapid Data
Collection
Kinetics
Unstable Compounds
Environmental Cells–Enables Focussing
Small Samples
Small areas/volumes

Structure Solution
Reciprocal Space Methods
Real Space Methods
Thermal expansion and Phase
Transitions

2

What is special about a crystal?
Solid phases are often crystalline, but need not be e.g. glass an “amorphous material”
CrystalGlass•Energy Range•Enables Spectroscopy–Elemental Identification–Bonding Studies–Speciation•Enables Optimal Conditions–Environmental Cells–Selected Elements•Low Divergence
Enables High Resolution•Micro Beams•Small Volumes•Complex Materials

Structure Refinement
Rietveld Method

3• Fractures into shards• Takes on any shape,depending on preparation• Properties do not varywith orientation.

• Cleaves along preferred
directions• Grows with welldeveloped crystal faces• Properties depend onorientation in which they
are measured.

4

Crystal Structure

7KH8QLW&HOO• CRYSTAL: Contains a periodical array of atoms/ions.
This can be represented by a simple lattice of points.

c• A group of atoms is associated with each lattice points.

a• LATTICE: An infinite array of points in space, in which
each point has identical surroundings to all others.

b
7KHXQLWFHOOLVDEDVLFSDUDOOHORSLSHGVKDSHGEORFNIURPZKLFKWKH
ZKROHYROXPHRIWKHFU\VWDOPD\EHEXLOWE\UHSHWLWLRQLQGLPHQVLRQV$Q\SRLQWLQWKHXQLWFHOOPD\EHVSHFLILHGZLWKUHVSHFWWRWKHRULJLQE\
SDUDPHWHUV[\]PHDVXUHGSDUDOOHOWRWKHXQLWFHOOD[HVDQGH[SUHVVHG
DVIUDFWLRQV

• CRYSTAL STRUCTURE: The periodic arrangement of
atoms in the crystal.

5

6([DPSOHRI'V\PPHWU\LQDZDOOSDSHUSDWWHUQ([DPSOHRI'V\PPHWU\LQDZDOOSDSHUSDWWHUQ
7RVKRZV\PPHWU\●3LFNDSRLQW●)LQGDOOHTXLYDOHQWSRLQWV
●7KHVHSRLQWVIRUPD'ODWWLFH

To show symmetry:
1. Pick a point
2. Find all equivalent points

Connecting 4 lattice points toform a parallelogram gives apossible unit cell●(http://www.clarku.edu/~djoyce/wallpaper/)78

([DPSOHRI'V\PPHWU\LQDZDOOSDSHUSDWWHUQ●&RQQHFWLQJODWWLFHSRLQWVWR
IRUPDSDUDOOHORJUDPJLYHVD
SRVVLEOHXQLWFHOO'LIIHUHQWXQLWFHOOVFDQEH
FKRVHQ●%XWVRPHXQLWFHOOVDUH
SUHIHUDEOHIRUKLJKHUV\PPHWU\●9D-Iron is BodyCentered Cubic
Identical atoms at
corners and body
center (nothing at
face centers)
Lattice type I
Also Nb, Ta, Ba,
Mo...

1 (P)

Monoclinic

2 (P, C)

azbzc
DzEzJ
azbzc
D = E = 90q z J
azbzc
D = E = J = 90q
a=bzc
D = E = J = 90q
a=b=c
D = E = J = 90q

Orthorhombic 4 (P,F,I,A)cx

D-Po is primitiveCubic
Identical atoms at
corners but nothingat the and body orface centers.
Lattice type P

Triclinic

Tetragonal

2 (P, I)

Cubic

3 (P, F,I)

Trigonal

1 (P)

a=b=c
D = E = J < 120q z 90q

1 (P)

a=bzc
D = E = 90q
J = 120qa

UHSHDWVLQHYHU\GLUHFWLRQBCC LatticeBravis Lattice Conditionsz●8QLWFHOOದWKHEDVLFXQLWWKDWPC Lattice

Name

b

y

Lattice parameters:
a, b, c; DEJ
Hexagonal

P

C

I

F

10

FCC Lattice

Sodium Chloride(NaCl) Na is muchsmaller than Cl
Face Centered Cubic
Rocksalt structure
Lattice type F
Also NaF, KBr,MgO….
11

12

Young’s Double Slit Experiment• Thomas Young first
demonstrated interference in lightwaves from two sources in 1801
• Light is incident on a screen witha narrow slit, So• The light waves emerging fromthis slit arrive at a second screenthat contains two narrow, parallelslits, S1 and S2• The narrow slits, S1 and S2 act assources of waves• The waves emerging from theslits originate from the same
wave front and therefore arealways in phase

13

Interference Patterns

Resulting Interference Pattern• The light from the two slits form a visible pattern ona screen• The pattern consists of a series of bright and darkparallel bands called fringes• Constructive interference occurs where a brightfringe occurs
14• Destructive interference results in a dark fringeInterference Patterns• Constructive interference occurs
at the center point• The two waves travel the same
distance• The upper wave travels
one-half of a wavelength
farther than the lower
wave• The trough of the bottom
wave overlaps the crest of
the upper wave (180phase shift)• This is destructive
interference– Therefore, they arrive in phase• The upper wave travels one
wavelength farther than the lower
wave– Therefore, they arrive in phase• A bright fringe occurs– A dark fringe occurs
15

16

Diffraction of X-ray Waves

Interference Equations• The path difference, δ, is found from the tan triangle• δ = r2 – r1 = d sin θ• Diffraction: When light passes sharpedges or goes through narrow slits therays are deflected and produce fringes oflight and dark bands.
Diffraction grating and helium-neon laser••

For a bright fringe, produced by constructive interference, the path
difference must be either zero or some integral multiple of of the
wavelengthδ = d sin θbright = m λ– m = 0, f1, f2, …
– m is called the order number
17

18

Bragg’s Law
Incident radiation“Reflected” radiation

1
2

P

T
S

d

T
R

Q

Transmitted radiation

Beam Ā2ā travels the extra distance SQRnO SQ  QR
d hkl sin T  d hkl sin T
2d hkl sin T
But not all planes result in diffraction !!!

1920

Lattice Planes

Crystallographic Directions And
Planes• It is possible to describe certain directions andplanes with respect to the crystal lattice using a
set of integers referred to as Miller Indicies

Lattice Directions
Individual directions: [uvw]Symmetry-related directions: <uvw>
0LOOHU,QGLFHV)LQGWKHLQWHUFHSWVRQWKHD[HVLQWHUPVRIWKHODWWLFH
FRQVWDQWDEF7DNHWKHUHFLSURFDOVRIWKHVHQXPEHUVUHGXFHWRWKH
WKUHHLQWHJHUVKDYLQJWKHVDPHUDWLR


KNO 
6HWRIV\PPHWU\UHODWHGSODQHV^KNO`
22

Calcium oxalate solvates: COM & COD
CaOx Monohydrate(symptomatic)

Examples of Miller Indicesa

CaOx Dihydrate(protective)
polyD
H O H
*

C C N

*

n

C

25 Pm

O

C

O-

25 Pm

(100)

(200)

y
x
P21/c
(a = 6.290 Å, b = 14.580 Å, c = 10.116 Å, E= 109.46o)I4/m(a = b = 12.371 Å, c =7.357 Å, D= E= J=2390o)

z

(110)

24

Families of Planes

Lattice Spacing• Miller indices describe the orientation of a family of planes– the spacing between adjacent planes in a family is referred to as a“d-spacing”• different families of planes– d-spacing between (400) planes is 1/4 that of the (100) spacing.
– The (300) plane does not contain atoms and so is not observed

1
2
d hkl

h2  k 2  l 2a2
ad100 = 4.0

(100)

(200)

(400)

For cubic system with a = 4.0 A

d110 = 2.828

(300)
25

Single Crystal vs Powder

26

Powder – A Polycrystalline Mass$OORULHQWDWLRQVRI
FU\VWDOOLWHVSRVVLEOH

6LQJOHFU\VWDOUHFLSURFDOODWWLFH
VPHDUHGLQWRVSKHULFDOVKHOOV

27

28

Powder Diffraction
MonochromatorθSourceθ
λ=2dsinθ• By varying the angle T, the Bragg's Law conditions are
satisfied by different d-spacings in polycrystalline
materials.
• Plotting the angular positions and intensities of theresultant diffracted peaks produces a pattern which ischaracteristic of the sample.

Detector(200)

Sample
2750
2500

(220)

2250
2000
1750
1500

(222)

1250
1000
500

(311)

750

(111)

Intensity

2θ

NaCl - 0.809 Å

250
0
15

20

25

30

Two Theta (degrees)

29

Information Contained in a
Diffraction Pattern•The positions of the atoms in a unit cell determine the intensities of
the reflections
Consider diffraction from (100) planes in



5000
0



40

60

80



100

120

4000

&D6U&H0Q2



2000



Intensity

3000&D6U&H0Q2

1000
0
29.8

30.0

30.2

Two Theta

Peak Shapes & Widths
Crystallite Size (2-200 nm)
Non-uniform microstrain
Extended Defects (stacking faults,
etc.)

•

&D6U&H0Q2

10000

20

Peak Intensities
Unit Cell Contents
Point Symmetry
Quantitative Phase Fractions

Centering and Absences

15000

Intensity

Peak Positions
Crystal System
Space Group Symmetry
Unit Cell Dimensions
Qualitative Phase Identification

30

30.4

29.2 29.4 29.6 29.8 30.0 30.2
Two Theta

Changes in symmetry and microstrain
upon chemical substitution can beestablished by examination of thepatterns
31

If the pathlength between
rays 1 and 2 differs by λ, thepath length between rays 1
and 3 will differ by λ/2 anddestructive interference in(b) will lead to no diffracted
intensity

32

NaCl Fm3m
FCC

BCC

Simple (Primitive)

20

30

20

40

30

Reflections that must
be absentnone

Monoclinic
a = 5.45 b = 5.25 c = 5.00 ÅoE= 100Pm3m

Orthorhombic
a = 5.45 b = 5.25 c = 5.00 Å

Tetragonal
a = 5.45 c = 5.00 Åh and k mixed
Fm3m

Body (I) centered
Face (F) centered(h+k+l) odd
h, k and l mixed40

Two Theta (degrees)

Im3m

Base (C) centered

(511)

0

0

Two Theta (degrees)

Bravais lattice

(422)

(113)

(111)

100

600

(400)

200

(222)

Intensity

(211)

300

(200)

Intensity• We can extend these types of calculation
to include other modes of lattice centering.
They all lead to systematic absences

(331)

1200

400

(420)

(220)

500

(200)

DFe - Im3m

(110)

Centering and Absences

10

15

20

25

30

35

40

45

50

55

Two Theta

33

Influence of centeringcubic
a = 5.45 Å

10

15

20

25

30

35

40

45

50

55

60

65

70

75

Two Theta

Influence of symmetry 34

Multiplicity

Diffraction Patterns•

For high symmetry materials the Bragg angles and d-spacings fordifferent reflections may be equivalent to one anotherFor example (100), (010), (001) etc are equivalent in a cubic
material•

In a powder, all planes with the same d-spacing contribute to thescattered intensity at a given Bragg angle•

The number of planes that are symmetry equivalent is referred to as
the multiplicity and its appears as a multiplicative term in powder
diffraction intensity calculations•

The multiplicity of a reflection depends upon the symmetry of thecrystalMultiplicity of {100} for cubic is 6, but for tetragonal it would only be 4
as (100) and (001) are not equivalent• Spacing of peaks depends on size of unit celland the space group.
• The bigger the unit cell and/or the lower thesymmetry the more diffraction peaks areobserved.
• Intensity of peaks depends on (amongst otherthings) the arrangement of the atoms in the unitcell.
• For two materials that had identical unit cells, thepeak positions would be IDENTICAL, however
their intensities would be DIFFERENT.

35

36

Need for High Q
50000

Bi2InNbO7 RT
0.79 Å X-rays

orderedmodel

disordered
model

There are many more reflections at higher Q.
Therefore, most of the structural information is
at higher Q

40000

Intensity

30000

20000

56

58

60

62

64

56

58

60

Need for High Resolution

62

64

10000

'd
d

Differentiating Braggs Law gives theresolution as:

'O

'T

O tan TO

2d sin T

0

30

40

50

60

70

Source80

Two T (Degrees)

Refinement of structure gave
unusual displacement parameters
for the Bi cations, indicative of
cation disorder. The patterns
could only be adequately fitted byincluding 6-fold disorder of the Bi.
This involves a displacement alongthe (1 -1 0) direction

Atom

Site

x

y

z

SampleBiso

Model 1. Ordered Bi. Rp 4.08 Rwp 6.07%

Bi

16d

0

0.25

0.75

2.74(6)

In/Nb

16c

0

0

0

3.00(8)

O(1)
O(2)

48f
0.350(3)
0.125
0.125
8b
0.375
0.375
0.375
Model 2. Disordered Bi Rp 3.09 Rwp 3.93%

Bi

96h

0

In/Nb

16c

0

O(1)
O(2)

48f
8b

0.322(1)0.375

7.6(7)
7.6(7)

0.2249(1) 0.7751(1) 0.96(7)
0
0.125
0.375

Source +Instrument00.61(3)

0.125
0.375

1.7(2)37
1.7(2)

Rutile
HRPD 1.49 Å

Resolution
In Powder Diffraction it typically refers
to the width of the peaks.

Intensity

20

In Single Crystal Diffraction it typicallyrefers to the minimum d-space studied.

MRPD 1.66 Å

20

40

60

80

100

120

140

Two Theta (Degrees)

38

Both definitions are relevant.

Peak Overlap

The Solution - Rietveld
k p2• Powder Diffraction
patterns are a one
dimensional
representation of athree dimensional
structure.
• Often peaks due toindividual Braggreflections overlap

y icalc

y iback  ¦ ¦ G ikp I 2k
p k k1p•••••

yic the net intensity calculated at point i in the pattern,yiback is the background intensity,
Gik is a normalised peak profile function,
Ik is the intensity of the kth Bragg reflection,
k1 ... k2 are the reflections contributing intensity topoint i,• the superscript p corresponds to the possible phasespresent in the sample.

39

40

The Answers• The Profile R• The weighted ProfileRRp¦ y iobs  y icalc¦ y iobs

R wpª¦ w y  y«¬ ¦ w y

R exp

χ2

Phase Analysis
Anatase + Rutile

12000

Intensity (a.u.)

10000

iobs
i

• The expected Profile
R

41

i

i

icalc

2
iobs

ª N-P º«»2¬« ¦ w i y iobs ¼»

¦w y

2

º
»¼

1/2

1/2

iobs  y icalc

N-P

2ª R wp º«»«¬ R exp »¼

2• The Goodness of fit

Quantitative Phase Analysis• Bragg scattering is proportional to N/V where N is thenumber of unit cells and V the unit cell volume.
There for the weight of a phase in the beam is:

8000

Anatase
6000

WP

4000

i

Rutile

2000

0
20

40

60

( SZMV ) P¦ (SMPV )i80

Two Theta (degrees)• Where a mixture of different phases is present,
the resultant diffraction pattern is formed byaddition of the individual patterns.
• The intensity of the peaks is proportional to theamount of the phase present.
43

S - the scale factor
Z the number of formula unites per unit cell
M the molecular weight of the formula unit
I is the index running over all phases• Hence SZVM is proportional to the weight of thediffracting sample

44

An Example

The background• Synchrotron X-ray Diffraction pattern for
SrRuO38000

Intensity• Fluorescent radiationfrom the sample• Diffraction from thecontinuous spectrum• Diffuse scattering

70000

SrRuO3 Observed

60000
50000

Intensity

40000

6000

4000

2000

– Incoherent– Temperature diffuse– Short range order

30000
20000
10000

• Other materials

0
10

20

30

– Specimen holder– air etc

40

Angle (2T) degrees

10

20

30

40

Angle (2T) degrees• Background can beeither fitted or
estimated.
• Here the capillary isa feature.

45

Peak Shapes

G ik

>

gamma0
gamma05
gamma1

Intensity

@

>

9.60

9.65

9.70

9.75

9.80

9.85

Angle

asym
perfect
Intensity

F W H M (d e g re e s )T+ VtanT + W@

asym
perfect

N e u tro n
B ra g g -B re n ta n o
S y n c h ro tro n

0 .4

H2 = Utan2• Beam Divergence canresults in asymmetricpeaks at low angles.
• Results from not
integrating over theentire Debye cone.

Angle

-1
C1/2
C1/2
γ 0 1  C 0 X ik2  (1  γ) 1 1/2 exp - C1X ik2
Hk π
Hk π

• The width of peaks is
usually not constant.

Peak Asymmetry
Intensity• Different
Diffractometers havedifferent peak shapes.
• The most widely
function is a pseudoVoigt (mixed Gaussianand Lorentzian).

46

0 .2

0

0 .0
0

20

40

60

80

T w o T h e ta (d e g re e s )

100

120

471 4 0

35.50

35.55

35.60

35.65

Angle

35.70

35.75

35.80

48

The Simple Structural Model

A Common Problem

6
0
0
0
0

• The fit to a single
phase sample looks
good

5
0
0
0
0

R
2
.4
2
%
p
R
3
.8
5
%
w
p

4
0
0
0
0

F2
5
4

2

• If the structural model is wrong then the mostcommon response of Rietveld programs is to:Intensity

3
0
0
0
0
2
0
0
0
0
1
0
0
0
0

– broaden the peaks,– Increase the displacement parameters,010• BUT…...

1
5

2
0

2
5

3
0

3
5

4
0

4
5

A
n
g
le(2
T
)d
e
g
re
e
s

• The former is most noticeable at high angles
where intensity is lowest.
• Due to absorption of the X-rays powder X-ray
diffraction often yields poor displacement
parameters

Rp 2.42%
Rwp 3.85%
2

F 254

Intensity• The detail of the fit
is not satisfactory the model is missing
something!

35

40

Angle (2T) degrees

45

49

50

The finished Product

An Alternate Model
6
0
0
0
0

S
r
R
u
O
8
2
8
K
O
=
0
.
7
0
0
Å
3
R
1
.
7
9
%
P
2
.
2
2
%
R
w
p

5
0
0
0
0

2

Rp 2.25%
Rwp 3.27%

10000

F
8
4
.
5

4
0
0
0
0

2

F 182.9

3
0
0
0
0
2
0
0
0
0

Intesiy(au)Intensity• The high angle
splitting is wellmodeled by atetragonal model - but
this overestimatessome intensities.

1
0
0
0
0
0

1
0

0
35

40

45

Angle (2T) degrees

2
0

3
0

4
0

5
0

6
0

7
0

8
0

9
0

T
w
o
T
h
e
t
a
(
d
e
g
r
e
e
s
)

• The sample contains a mixture of bothphases!

• The Truth lies somewhere in the middle
5152

Crystallography challenged: materials withdisorderCrystallography gives average structure
80000040000020000002040

2T (degrees)

60

80• The Rietveld method
has served us wellfor over 45 years –but it only uses partof the information of
the diffraction
experiments,
namely the intensityof the Bragg peaks

Rietveld approach assumption: crystals are perfectly periodic…
…but this is not always the case!

100000Intensity

Intensity

600000

10000

1000
10

20

30

40

50

60

70

2T degrees)

53

Crystallography challenged: nano-crystals
From E. Bozin BNL

Just using the Bragg reflections means that we “ignore” theinformation in the background, but what information is this?

Diffuse intensity contains information on
From E. Bozin BNL
short-range order

Rietveld methodin powders

Bragg intensity → long range order

Diffuse intensity →short range order
Bragg peak info ONLY

G (r )

2f

S ³0

Q[ S (Q )  1] sin(Qr ) dQ

From E. Bozin BNLStrengths and Limitations of
Powder X-ray Diffraction

Total Scattering - PDF

4.26Å

Strengths

Pair distribution function (PDF)
gives the probability of finding
an atom at a distance “r” from agiven atom.

2.84Å

•
1.42Å

•
•
2.46Å

•

3.76Å

•
•

4.92Å
5.11Å

Experiment Design Issues

Limitations

Non-destructive – small
amount of sample
Relatively rapid
Identification of compounds /phases – not just elements
Quantification of concentrationof phases – (sometimes)
Classically for powders, but
solids possible too
Gives information regarding
crystallinity, strain, crystallite
size, and orientation

•

•
•
•

Bulk technique – generally –unless a microfocus source isused
Not a “stand-alone” technique– often need chemical data
Complicated appearance
multiphase materials –identification /quantification
can be difficult

Anomalous X-ray Scattering
f i2

What Wavelength?
• Absorption is your enemy!
• Short Wavelengths are best! BUT….
• Consider required resolution. And…
• Avoid Absorption Edges.

( f 0  'f ' ) 2  ('f " ) 2• Anomalous scattering or anomalous dispersion occurs
when the incident X-ray energy is sufficient to cause
photoelectric x-ray production in a target atom. The
process is called fluorescence. This phenomenon is
responsible for “absorption edge” observed when certain
elements interacting with particular wavelength x-rays. In
this process a characteristic X-ray photon is produced in
the target; subsequent interaction produces coherent X rays which are slightly out of phase with other coherently
scattered X-rays. The net result is a reduction of thescattered intensity from the element.

What Size Capillary?
• Small capillaries reduce absorption AND (witharea detectors) improve resolution.
• BUT reduce amount of material.
59

60

Interaction of X-rays and Matter

12
10
8
6
4
2
0

f' (e.u.)

-5

2

f"
f'

-10
-15

150

P cm /g

Just as the absorption
coefficient shows large
jumps at Āedgesā thescattering power of
elements shows rapidchanges near edges.
• Minimum absorption is
obtained near 13.31 eV(0.93 Å)• Maximum Δfÿ is ca 8electrons by measuring at
13.3 and 13.5 eV.

f" (e.u.)

Bi Wavelength Dependence

P

100
50
0
10

15

20

Energy (keV)

Dynamics
Equilibrium

Non-equilibrium• B factors• Lauecrystallography• Diffuse scatter• Rapid Mixing andSmall angle
scattering

25

Scattering.
coherent, incoherent
elastic (Thomson), inelastic (Compton)
Absorption.
atoms: can then be emitted as fluorescence, photoelectrons, Auger
electrons
molecules: can emit fluorescence, phosphorescence, transfer heat,(stimulated emission)
Diffraction. The bending of waves due to obstructions and small apertures, aswith crystals.
Refraction. The bending of a wave as it passes from one medium to another
Reflection. Radiation bouncing back from one medium to the original
medium, where the wavelength << size of the object.

The temperature (B) factor• Atoms are not located at fixed points - undergo
vibrations about their mean positions.
• The amplitude of these vibrations increase as thetemperature increases.
• Due to such motion, the scattering factor falls off
exponentially.The greatest reduction in intensity is athigh angles (low d-values).

Debye-Waller temperature factor B = 8π2<u>2
Where <u>2 is mean-square amplitude of atomic vibration. This isdirectional and can be anisotropic

The temperature (B) factor

Effect of Temperature Ag2O

Increasing motion of
an atom induces anangular dependent
reduction in intensity.
The greatest
reduction is at highangles (low d-values).

Intensity

Ag2O 0.5 Å X-rays

T = 100 K

T = 290 K
25

30

35

40

45

50

55

60

Angle (2T) Degrees
4.746

Lattice Parameter (Å)

4.744

The latticeshrinks due tounusual motionof the Ag atoms!

4.742

4.740

4.738

4.736

Debye-Waller temperature factor B = 8S<u>2

0

50

100

150

200

250

300

Temperature (K)X-rays and Neutrons, Same
Same but Different

Sr0.65Pr0.35MnO3 – structuralparameters
58.0

56.5

4000

25000026 28 30 32 34 36 38

3000

511

300000

331

2
0.9
1
0

Intensity

Intensity (Counts)

5000

350000

422

511

331
400

6000

422

7000

400

400000y=2
y=0200000

20

22

24

26

Lattice Parameter (Å)

56.0
3.92

Pm3m

ao

3.84

Mn-O1
1.94

1.93

1.92

1.91

Mn-O2
1.90

3.76

0
100

200

300

400

500

600

Temperature (K)

2000

1.95

ae

3.80

0

150000I4/mcm

ce

3.88

1.96

Bond Distance (Å)

57.0

Average Mn-O bond length
in tetragonal region
Fit of Mn-O bond lengthfrom the cubic phase

3

S-XRD

1.97

Cell Volume (Å )Neutron

57.5

700

800

900

1000

200

400

600

800

1000

Temperature (K)100000
1000

50000
0

0
20

40

60

80

100

2T (degrees)

120

140

160

20

30

40

50

60

70

80

2T (Degrees)

Anion disorder clearly evident in neutron profiles but absent in XRD patterns
No evidence for cation disorder in the XRD patterns
J. Solid State Chem 2011 184 2108

Single structural phase transition observed. Apparently conventional thermal
expansion of the cell volume ( fitted as Vo=V1+V24coth(4/T) )Clear change in the anisotropy of the unit cell near 250 K.
Large tetragonal distortion of the MnO6 octahedra. Consequence of the JT active
Mn3+ cations – evidence for orbital ordering and suggests coupling between thelattice and the orbitals

Acetylene Absorption in Framework
Solids

Oxygen Conduction in Y1-xTaxO1.5+x

Crystal structures with the adsorption ofacetylene.
a) Views from the side of the nanochannels.
Pillar-molecules (pyrazine) and adsorbed
acetylene molecules are shown by CPK
model. Otherwise are connected by lines. b)
Views from the nanochannel direction by the
CPK model. Adsorbed acetylene molecules70
are omitted in the lower central pore in thephase M and S

Representation of the fluorite
structure of Y1-xTaxO1.5+x

Scattering amplitude distribution (a) on the (002) plane of theorthorhombic Cmmm fluorite-related Y0.7Ta0.3O1.8, and on the (110)planes of the cubic fluorite-type Y0.785Ta0.215O1.715 (b) at 299 K and (c)at 808 K.. Lines with arrows indicate the diffusion paths along the<100> directions

71