__________________________________________________________ mario bieringer mario bieringer...

__________________________________________________________

Mario BieringerMario Bieringer__________________________________________________________________________

1010thth Canadian Neutron Summer School Canadian Neutron Summer School slide slide 11 June 16 June 16thth, 2009, 2009

Neutron Powder Diffraction

Mario BieringerDepartment of Chemistry

University of Manitoba

presented at the

10th Canadian Neutron Summer School

June 15 – 18, 2009Chalk River, Ontario

__________________________________________________________



Applications of Powder Diffraction

chemistry

physics

engineering

life sciences

biochemistry

materials science

geological sciences

archeology

__________________________________________________________



Applications of Powder Diffractiondiffraction = elastic scattering momentum transfer at constant energy, i.e. incident = diffracted

Why do we care about diffraction experiments:

• identification of materials/phases

• determination of structural details, i.e. local environments within an extended structure

• evaluation of order and disorder in structures

• phase transitions (structural distortions or reconstruction)

• chemical reactions

• relate structure and properties

40 60 80 1000

100

200

300

400

500

600Si powder neutron diffraction patternC2 Chalk River = 1.329 Å

Inte

nsi

ty (

cou

nts

)

2 (0)

__________________________________________________________



Routine Powder X-ray Diffraction:

• Powder X-ray diffractogram

matched with the PDF database

• links to crystallographic

data if available (i.e structure

details from ICSD)

• semi-quantitative analysis

D

S

A

M

Position [°2Theta]

20 30 40 50 60

Counts

0

2500

10000

group-1_1

Visible Ref. Code Chemical Formula

red 01-073-2141 La2 O3

blue 00-005-0378 Ba C O3

green 01-089-5898 Cu O

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Routine Powder X-ray Diffraction:

Preferred Orientationof flat sample mounts:

D

S

A

M

a

c

b

__________________________________________________________



2(0)

Inte

nsit

y (

a.u

.)

T (

0 C)

30.0

37.025

1000

In-situ Powder X-ray Diffraction:

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What is a Powder?powder = polycrystalline solidlarge number of crystallites of m length scale

ideal powders (for diffraction) show random orientation of crystallites

orientational average of single crystals

• large number of preparative methods available.

• powders can be prepared in large quantities (g, kg, etc.)

• fast synthesis

• real world materials are often polycrystalline

• in reality powders are often multiphasic

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Description of Crystallographic StructuresUnit Cell: Smallest repeating unit capable of describing the entire crystal by means of three non-parallel translation vectors.

paralleliped

The 7 Crystal Systems

System u.c. symmetry unit cell parameters

cubic m-3m a = b = c = = = 90˚

hexagonal 6/mmm a = b ≠ c = = 90˚ = 120˚

trigonal* 3/mmm a = b ≠ c = = 90˚ = 120˚

tetragonal 4/mmm a = b ≠ c = = = 90˚

orthorhombic mmm a ≠ b ≠ c = = = 90˚

monoclinic 2/m a ≠ b ≠ c = = 90˚ ≠ 90˚

triclinic -1 a ≠ b ≠ c ≠ ≠ ≠ 90˚

* also described as rhombohedral: a = b = c = = ≠ 90˚

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Description of Crystallographic StructuresBravais Lattices:Centering conditions can be described with translation vectors:

Lattice Symbol translations lattice points

Primitive P +(0, 0, 0) 1

Body centered I +(½, ½, ½) 2

Base centered A +(0, ½, ½) 2

B +(½,0, ½) 2

C +(½, ½, 0) 2

Face centered F +(0, ½, ½), +(½, ½, 0), +(½,0, ½) 4

A total of 14 Bravais Lattices exist (see next page for illustration)

cubic: P, I, F orthorhombic: P, I, F, (A,B,C) hexagonal: P monoclinic: P, C trigonal: P triclinic: P tetragonal: P, I

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figure taken from: www.chem.ox.ac.uk

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Diffraction Peaks due to Periodicity:Due to the inherent crystal periodicity families of parallel virtual planes can be constructed. The scattering probe diffracts off those planes and generates a pattern that is characteristic of the spacing of the virtual planes and the composition of the unit cell. Virtual planes are identified by the Miller indices (h,k,l). The d-spacings, dhkl, (i.e. the perpendicular distance, between planes) can be determined with Braggs law:

= 2dhkl sin

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(001)

Diffraction Peaks due to Periodicity:K2NiF4 structure: tetragonal phase

c

a

b

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18 21 24 27 30 33 36

triclinic

tetragonal

monoclinic

orthorhombic

hexagonal

cubic

2 (0)

Powder Diffraction and Symmetry:Predict Bragg positions for primitive cells with V = 64 Å3 ( = 1.54 Å).

The higher the symmetry and

the smaller the cell volume the

smaller the number of diffraction

peaks.

peak multiplicities decrease from cubic to triclinic:

e.g. cubic d(100) = d(-100) = d(010) = d(0-10) = d(001) = d(00-1)

orthorhombic d(100) = d(-100) ≠ d(010) = d(0-10) ≠ d(001) = d(00-1)

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Description of Crystallographic StructuresFractional coordinates:

Note: use the crystal system as the coordinate systemx = fraction along a axisy = fraction along b axisz = fraction along c axis

Symmetry Elements:

rotation axes: 1, 2, 3, 4, 6 foldinversion rotation axes: -1, -2, -3, -4, -6 foldmirror planes: mscrew axes (helices): 21, 31, 32, 41, 42, 43, 61, 62, 63, 64, 65

glide planes: a, b, c, n, d

Absent reflections due to translations!

230 Space Groups: (International Tables for Crystallography: Vol. A)

e.g. I41amd (number 141) tetragonal system, body centered 41 screw axis, a glide, mirror, d glide

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Description of Crystallographic StructuresBaLaMnO4 (K2NiF4 structure type):

Space group I4/mmm (# 139)

Diffraction pattern:

No h+k+l = odd reflections

Body centered e (½,½,½) translation)

radii =Z

Ba(56) = 0,0,0.35

La(57)) = 0,0,0.35

Mn (25) = 0,0,0

O1(8) = 0,½,0

O2(8) = 0,0,1.4

0 0

2

0 1

1

0 0

4

0 1

31

1 0

1 1

2

0 0

60

1 5

1 1

4

0 2

00

2 2

1 2

11

1 6

0 1

70

2 4

0 0

81

2 3

0 10 20 30 40 50 60

BaLaMnO_4Lambda: 1.54178 Magnif: 1.0 FWHM: 0.200Space grp: I 4/m m m Direct cell: 4.0000 4.0000 13.6568 90.00 90.00 90.00

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Diffraction Peak Intensities:

Structure Factor:

X-ray case:

Neutron case:

Powder Peak Intensities:

j

jjjjjhkl BlzkyhxifF 22)( /sinexp2exp

j

jjjjjhkl BlzkyhxibF 22)( /sinexp2exp

2

)()()()( hklhklhklhkl FPALpsI

2

)()( hklhkl FI

F(hkl) = structure factorfj = X-ray form factorb = neutron scatt. lengthh,k,l = Miller indicesxj, yj, zj = atomic coordinates of atom jBj = thermal parameter = diffraction angle = wavelength over entire unit cellI(hkl) = intensity

Correction factors:

s = scale factorL = Lorentz-polarization p = multiplicity A = absorption correction P = preferred orientation

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0 10 20 30 40 50 60 70 80 90

-5

0

5

10

15

20

25

30

35

40

neutrons, b

X-rays, f sin/=0Å-1 sin/=0.5Å-1

scat

terin

g am

plitu

de (

10 -

13 c

m)

atomic number Z

Diffraction Peak Intensities:Scattering lengths X-ray form factor, f:

Temperature factor, Bj:

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Description of Crystallographic StructuresBaLaMnO4 (K2NiF4 structure type):

b atom=x,y,z Z

5.07fm Ba=0,0,0.35 56e

8.24fm La=0,0,0.35 57e

-3.73fm Mn=0,0,0 25e

5.80fm O1=0,½,0 8e

5.80fm O2=0,0,1.4 8e

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Peak Widthscoherence length domain sizes crystallite sizes particle sizes

Scherrer equation:

= wavelength

B = integral breadth

= diffraction angle

The broader the peaks

the smaller the domains.

4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6-10

0

10

20

30

40

50

60

70

80

90

4.80 4.85 4.90 4.95 5.00 5.05 5.10 5.15 5.20

0

20

40

60

80

area = 5 a.u.

B

Inte

nsity

(a.

u.)

2 (0)

Inte

nsi

ty (

a.u

.)

2 (0)

cos9.0

BD

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Diffraction from Randomly Oriented Crystals:

reciprocal lattice (diffraction pattern)

direct lattice (crystal structure)

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Diffraction from Randomly Oriented Crystals:

1 single crystal

very large number of microcrystals

few crystals

Debye-Scherrer Camera

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Single Crystal versus Powder Diffraction:

Single crystal diffraction:

• Use 3-dimensional reciprocal space: a*, b* and c* axes

• Use integrated intensities.

unambiguous peak assignment

Powder diffraction:

• Use a large assembly of microcrystals and record an average diffraction pattern in 1-dimension.

• Use profile points.

ambiguous peak assignment

Reminder: 1/d = 2 sin/

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(110)

(101)(100)

(010) 1/dIn

tens

ity

Powder diffraction:

• Information gets buried in powder average.

• Try to extract peak intensities or fit the entire profile.

Rietveld Method

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Powder X-ray vs. Powder Neutron Diffraction

0 10 20 30 40 50 60 70 80 90 100 110 120

Powder Neutron Diffraction ( = 1.54059A)

Powder X-ray Diffraction ( = 1.54059A)

2 (0)

simulations of Pr2Ta2O7Cl2 powder patterns

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Simplified Powder Diffractogram

2 (˚) * crystal system

* unit cell dimensions

* space group

Intensity * atomic/ionic positions

* temperature factors

* order/disorder

FWHM * domain sizes

* habit

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X-ray vs Neutron Powder Diffraction?

XRD NPD

phase I.D. YES NO

indexing YES YES

space group YES YES

structure refinement YES YES

light elements NO YES

neighbouring elements NO YES

structure solution YES YES

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When to Use Neutrons:Ideally: always (most structure determinations and refinements benefit

from independent measurements (X-ray + neutron))

In particular:

• light and heavy elements present (e.g. oxides, fluoride, hydrides (deuterides) of heavy metals)

• neighbouring elements: e.g. Al & Si, Fe & Co, Yb & Lu, Ti & V, etc.

• multiple site occupancies: e.g. disordered structures

• interest in true bulk properties (i.e averaging over large samples)

• complex experimental set ups: chemical reactions, high temperatures, high pressures, low temperatures, magnetic fields, electrochemical cells, chemical/structural processes etc.

• magnetic samples

• etc.

__________________________________________________________



Are Neutrons going to Answer Your Questions?•look up neutron scattering lengths and cross sections:

http://www.ncnr.nist.gov/resources/n-lengths/

Neutron News, Vol. 3, No. 3, 1992, pp. 29-37

Neutron scattering lengths and cross sections

Isotope conc Coh b Inc b Coh xs Inc xs Scatt xs Abs xs

O --- 5.803 --- 4.232 0.0008 4.232 0.00019

16O 99.762 5.803 0 4.232 0 4.232 0.0001

17O 0.038 5.78 0.18 4.2 0.004 4.2 0.236

18O 0.2 5.84 0 4.29 0 4.29 0.00016

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Are Neutrons going to Answer Your Questions?LaFeAs(O1−xFx) LiCoO2, LiNi1-xCoxO2, LiMn2O4

b(La=57) = 8.24 fm b(Li=3) = -1.90 fm

b(Fe=26) = 6.58 fm b(Co=27) = 2.49 fm

b(As=33) = 9.45 fm b(Ni=28) = 10.3 fm

b(O=8) = 5.803 fm b(Mn=25) = -3.73 fm

b(F=9) = 5.654 fm b(O=8) = 5.803 fm

BiFeO3, BaTiO3, LnMnO3 La0.9Ba0.1Ga0.8Mg0.2O2.8

b(Bi=83) = 8.532 fm b(La=57) = 8.24 fm

b(Fe 26) = 6.58 fm b(Ba=56) = 5.07 fm

b(O=8) = 5.803 fm b(Ga=31) = 7.288 fm

b(Mg=12) = 5.375 fm

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Two Neutron Powder Diffraction Methods1. Continuous Wavelength (Reactor Sources):

• single (selectable) wavelength

• continuous neutron flux

• position sensitive detectors, record neutron rate as a function of diffraction angle

• Bragg’s law: = 2d sin

• d/d depends on: - monochromator - take-off angle, - monochromator mosaicity - and sample size

example: C2

M

sample

sample environment

detector wires

collimator

http://neutron.nrc-cnrc.gc.ca/c2gen.html

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160-176 degbackscattering

detector

28 - 32 degdetector

87-93 deg detector

guide tube 100m beam Stop

sample

87-93deg detector

Two Neutron Powder Diffraction Methods2. Time of Flight Method (Spallation Sources):

example: HRPD (ISIS, U.K.)

2 choppers close to the target (6m and 9m)select neutron pulses

http://www.isis.rl.ac.uk/crystallography/HRPD/index.htm

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Two Neutron Powder Diffraction Methods2. Time of Flight Method (Spallation Sources):

• white radiation (including epithermal fraction)

• pulsed neutron source (50 to 60 Hz)

• very high neutron flux during neutron burst

• multitude of time of flight detectors, record neutron rate vs. time

• Bragg’s law: de Broglie:

mn = neutron mass, vn = neutron velocity, t = flight time, L = flight distance, d = detector angle

• resolution: d/d depends on total flight path, L, and detector angle (d)

• use time focusing, large scattering volumes don’t degrade the resolution

th

Lm

vh

m n

n

n sin2d

dhklhkl dLt sin57.505 )()( )()( hklhkl dt

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Data Comparison1. Continuous Wavelength (Chalk River – C2 (Pr2Ta2O7Cl2) ): :

10 20 30 40 50 60 70 80

0

2500

5000

7500

10000

12500

15000 Pr2Ta

2O

7Cl

2

Low Temperature Powder Neutron DiffractionC2 = 2.37A

Inte

nsi

ty (

a.u

.)

2 (0)

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Data Comparison2. Time of Flight Method (IPNS – SEPD (Pr2Ta2O7Cl2) ):

13000 14000 15000 16000 170000

100

200

300

400

500IPNS - SEPD BANK #1 (144.850)

Inte

nsi

ty (

a.u

.)

TOF (s)

10000 11000 12000 130000

100

200

300

400

500

IPNS - SEPD BANK #2 (900)

Inte

nsi

ty (

a.u

.)

TOF (s)

5000 5500 6000 6500 7000100

150

200

250

300

350

400

450

IPNS - SEPD BANK #3 (440)

Inte

nsi

ty (

a.u

.)TOF (s)

0 5000 10000 15000 20000 25000 30000

0

50

100

150

200

250

300

350

400

IPNS - SEPD

BANK #3 (440)Inte

nsi

ty (

a.u

.)

TOF (s)0 5000 10000 15000 20000 25000 30000

0

100

200

300

400

500

600

IPNS - SEPD

BANK #2 (900)Inte

nsi

ty (

a.u

.)

TOF (s)5000 10000 15000 20000 25000 30000

0

200

400

600

800

1000

6 9 0 0 7 0 0 0 7 1 0 0 7 2 0 0 7 3 0 0 7 4 0 0 7 5 0 0 7 6 0 0 7 7 0 0 7 8 0 03 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

Inte

ns

ity

(a

.u.)

T O F (s )

IPNS - SEPD

BANK #1 (144.850)Inte

nsi

ty (

a.u

.)

TOF (s)

d-range: 0.33-4.0Å d-range: 0.45-5.4Å d-range: 0.85-10.2Å

__________________________________________________________



Powder Data Analysis1)Record Powder Diffractogram (neutron and/or X-ray)

2)Identify the phase(s) (X-ray database)

3)Index phase (X-ray or neutron), i.e. find unit cell (i.e. crystal system)

4)Identify space group (X-ray or neutron)

5)If a structural model is available (isostructural compound known) proceed with Rietveld refinement

6)If no structural model is known proceed with ab-initio structure solution

7)Consider X-ray and neutron combined analysis

8)Consider different wavelengths

9)Consider different temperatures

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Rietveld MethodProfile Fitting Method:

1. use a crystallographic model and compute the corresponding powder diffraction pattern

2. compare simullation with experimental diffraction data

3. minimize the difference between experimental and calculated diffraction pattern in a least squares refinement by varying a number of parameters:

minimize:

wi = 1/yi yi = observed intensity yci = calculated intensity

s = scale factor, L(hkl) = Lorentz, polarization and multipicity factors(2i-2(hkl)) = reflection profile function, P(hkl) = preferred orientation function, A = absorption factor, F(hkl) = structure factor, ybi = background intensity

j

ciiiy yywS 2

j

bihklciiihklhklci yAPFLsy )(2

)()( 22

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Rietveld MethodRefinable Parameters:

GLOBAL PARAMETERS: FOR EACH PHASE

zero point atomic positions

instrumental profile thermal parameters

profile asymmetry site occupancies

background parameters scale factor

sample displacement lattice parameters

absorption preferred orientation

crystallite size

microstrain

magnetic vectors

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Rietveld Method

14400 14500 14600 14700 14800 14900 15000 15100

0

300

600

Inte

nsi

ty (

a.u

.)

TOF (s)

observed calculated difference Bragg positions

__________________________________________________________



Rietveld MethodEvaluation of fitting quality (R-factors):

• R-pattern, Rp:

• R-weighted pattern, Rwp:

• R-Bragg factor, RB:

• R-expected, Re: Goodness of fit, S:

i

ciip y

yyR

2/1

2

2

ii

ciiiwp

yw

yywR

)'('

)()'(' )()(

obsI

calcIobsIR

i

hklhkl

B

2/1

2

iie yw

PNR

e

wp

R

RS

__________________________________________________________



Rietveld Method

A large number of Rietveld programs are available:

To a large extent these programs have similar capabilities with individual strengths:

Rietveld Programs: GSAS

FullProf

Rietica

Rietan

BGMN

TOPAS

etc.

http://www.ccp14.ac.uk/

__________________________________________________________



Rietveld Method

5000 10000 15000 20000 25000 30000

0

200

400

600

800

1000

5000 6000 7000 8000 9000 10000

0

200

400

600

800

Inte

nsity

(a.u

.)TOF (s)

Pr2Ta

2O

7Cl

2 (PTOC449)

Powder Neutron Diffraction

IPNS - SEPD BANK #1 (144.850)

Inte

nsi

ty (

a.u

.)

TOF (s)

observed calculated difference Bragg

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Rietveld Method

Refinement of Pr2Ta2O7Cl2:

Parameters: Data:

varied: all atomic positions SEPD (IPNS)

anisotropic thermal parameters 3 scattering banks

unit cell parameters 11005 data points

background parameters 60 parameters varied

scale factor

peak shape parameters Results:

Rwp: 0.0448

Rp: 0.0280

Re: 0.0342

S: 1.17

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Compare Single Crystal and Powder ResultsPr2Ta2O7Cl2: space group: I2/m

X-ray single X-tal 1 powder neutron (TOF) 2

atom x y z_________ x y z :

Pr 0.6925(1) 0 0.5270(1) 0.69114(24) 0 0.5273(4)

Ta 0.0343(0) 0 0.2361(1) 0.03451(13) 0 0.23741(24)

Cl 0.8219(3) ½ 0.3891(6) 0.82304(13) ½ 0.39002(25)

O1 0.0448(8) ½ 0.2060(18) 0.04401(18) ½ 0.21012(37)

O2 0.9190(8) 0 0.0679(16) 0.91882(16) 0 0.07140(34)

O3 0.8244(9) 0 0.7519(17) 0.82666(16) 0 0.75746(32)

O4 ½ ½ 0 ½ ½ 0

a = 14.109(1) Å a = 14.10763(22) Å

b = 3.9247(3) Å b = 3.92548(5) Å

c = 6.9051(6) Å c = 6.90610(10) Å

= 92.953(8)0 = 92.9626(14)0

1 U. Schaffrath and R. Gruhn Naturwissenschaften, 75 140 (1988) 2 P. Baudry and M. Bieringer (2003)

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20 40 60 80 100

0

1000

2000

3000

4000 powder X-RAY diffraction pattern for Li

4MgReO

6

= 1.54059Å

Inte

nsity

(a.

u.)

2 (0)

20 40 60 80 100

0

10000

20000

30000

40000 powder NEUTRON diffraction pattern for Li

4MgReO

6

= 1.54059Å

Inte

nsity

(a.

u.)

2 (0)

N

nnnnnhkl lzkyhxifF

12exp)2(

N

nnnnnhkl lzkyhxibF

12exp

Powder X-ray vs. Neutron DiffractionLi4MgReO6:

an order-disorder study

__________________________________________________________



neutronsb (10-12m)

X-raysZ

Li+ -1.90 3 (2)Mg2+ 5.37 12 (10)Re6+ 9.2 75 (69)O2- 5.803 8 (10)

Li4MgReO6:

Powder X-ray vs. Neutron Diffraction

__________________________________________________________



High Temperature StudiesNeutron diffraction and IN-SITU reactions.

Preparation of microwave dielectric oxides of composition Ba3ZnTa2O9 (BZT).

3 BaCO3 + ZnO + Ta2O5 ---- Ba3ZnTa2O9 + 3 CO2

aa

a

a aa

aa

c

aa

a

aa

a

(b )(a ) (c )

__________________________________________________________



High Temperature StudiesOnly a high flux neutron diffractometer will permit collection of diffraction patterns within one 1 minute.

GEM (ISIS, U.K.) TOF instrument with more than 6000 detectors and medium resolution (18 – 20 m flight path).

__________________________________________________________



* =BZT

=ZnO

=Ta2O5

=BaCO3

T (0 C

)

d-spacing (Å)

* * * * *

Rhombohedral BaCO3and inter-mediate phases

BZT

Starting materials

High Temperature Studies3 BaCO3 + ZnO + Ta2O5 ---- Ba3ZnTa2O9 + CO2

__________________________________________________________



Low Temperature StudiesCrystal structure and magnetic long range order in Ba0.05Sr0.95LaMnO4

1 phase Rietveld refinement T=125K

phase 1: Ba0.05Sr0.95LaMnO4

crystal structure

__________________________________________________________



(Ba2+, Sr2+, La3+)

Mn3+

O2-

0 20 40 60 80 100 1203.780

3.782

3.784

3.786

3.788

3.790

13.15

13.16

13.17

13.18

c-ax

is (

A)

a-a

xis

(A)

T (K)

tetragonal:

I4/mmm

a = b ≠ c

Low Temperature StudiesCrystal structure refinement and unit cell evolution in Ba0.05Sr0.95LaMnO4

__________________________________________________________



ResourcesR.A. Young,‘The Rietveld Method’, IUCr Monographs on Crystallography 5, Oxford University Press, New York (1993)

W.I.F. David, K. Shankland, L.B. McCusker, Ch. Baerlocher,‘Structure Determination from Powder Diffraction Data’, IUCr Monographs on Crystallography 13, Oxford University Press, New York (1993)

J. Baruchel, J.L. Hodeau, M.S. Lehmann, J.R. Regnard, C. Schlenker,‘Neutron and Synchrotron Radiation for Condensed Matter Studies’, Volume 1, 2 and 3, Springer Verlag, Berlin (1993)

G.E. Bacon, ‘Neutron Diffraction’, Claredon Press, Oxford, 3rd edition (1975)

Allen C. Larson, Robert von Dreele, ‘GSAS - General Structure Analysis System’

Juan Rodriguz-Carvajal, ‘An Introduction to the Program FULLPROF 2000’, Saclay, 2001 (ftp://ftp.cea.fr/pub/llb/divers/fullprof.2k/ )

Mark Ladd, Rex Palmer, ‘Structure Determination by X-Ray Crystallography’, Kluwer Academic, New York, 2003, 4th Edition

Vitalij K. Pecharsky, Peter Y. Zavalij, ‘Fundamentals of Powder Diffraction and Structural Characterization of Materials’, Springer, 2005

G.L. Squires, ‘Introduction to the theory of thermal neutron scattering’, Dover Publications, New York, 1978

Georg Will, ‘Powder Diffraction: The Rietveld Method and the Two-Stage Method’, Springer, Heidelberg, 2006

Abraham Clearfield, Joseph Reibenspies, Nattamai Bhuvanesh, ‘Principles and Applications of Powder Diffraction’ Wiley,2008

Rietveld program downloads, manuals and tutorials can be found at: http://www.ccp14.ac.uk

More: Structures: http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/lecture1/Lec1.html

__________________________________________________________ mario bieringer mario bieringer...

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