applications of the rietveld method · k. knorr: applications of the rietveld method msa short...

1

K. Knorr: Applications of the Rietveld MethodMSA Short Course: Neutron Scattering in Earth Sciences

Applications of the Rietveld Method

Karsten KnorrChristian-Albrechts-Universität, Kiel

[email protected]


Outline

General aspects

low Z elements

Protons, C4A3H3

neighboring elements

Si/Al order / disorder

Co,Mn-cordierite

extreme conditions

high p, NaN3

high pT, Graphite

2


Powder diffraction: key problem


Neutron diffractionNaClfrom Shull: Nobel lecture

Al2O3

HRPD / ISIS

3


peak-fit


full pattern methods

4


The Rietveld method

Rietveld


Step intensity

5


Structure factor


Peak shape functions

6


X-rays vs. neutrons


Magnetic structures

LaMn2Si2: canted AF

7


Outline

General aspects

low Z elements

Protons, C4A3H3



Co,Mn-cordierite

extreme conditions

high p, NaN3

high pT, Graphite


Weak X-ray scatterer

HydrogenOH: boehmit AlOOH, goethite FeOOH, bucite Mg(OH)2 ,hydoxylapatite, hydrogarnets, ...H2O: gypsum, bassanite, zeolites, ....Ammonia, e.g. nitrammite ND4NO3

Organics in zeolitesclathrates, ice cf. Kuhs & Hansen

Lithiumstrong neutron absorberseveral mineralsmicroporous litiosilicates (RUB-#)

Berylliumrare minerals, Be-phosphate/arsenate microporous materials

8


Proton positionsH weak X-ray but strong neutronscatterer,bc(H) = -3.74, bi(H) = 25.22b(D) = 6.67 fm

example: NaH / NaD(C. Shull / Nobel lecture)

here: C4A3H3 = 4CaO•3Al2O3•3H2O

motivation: Portland cement phase,high temperature dehydrationand mechanism of transformationto SOD-type,role of the protons,H positions unknown


experiment: Munich FRM-2

graphics: http://www.frm2.tum.de

9


The powder diffractometer: SPODI

graphics: http://www.frm2.tum.de

operated by LMU and TUDarmstadt

monochromator:

Ge (551)

different take-off angles

vertically focussing

Detectors:

multi detector 80 3Hetubes with 10‘collimators

SANS option (MAR IP)


Structure refinement, 5K

C4A3H3

Al2O3

CaCO3

10


Results

Rp: 2.37 Rwp: 3.53

a: 12.42764 0.00039b: 12.80914 0.00038c: 8.86485 0.00026space group Abma

11 atoms>35 structural parameters(XYZ, Biso)

typical coordinates0.3659( 3)

6 global parameters

>700 reflections


Quantitative phase analysis

C4A3H3 88.5 wt-%

Al2O3 7.5(2) wt%

CaCO3 4.0(1) wt%

11


Structure

6-membered ring

broken 4-membered ring


C4A3H3: protons

IR spectroscopy

OH group3658 cm-1 = O5-H2d(OH)n 0.88(1)Åd(OH)IR 0.9 Å

Hydrogen bond3222 cm-1 = O3-H1...O1

d(OH)n 0.97(1) Åd(OH)IR 0.96-..0.92 Å

12


Outline

General aspects

low Z elements

Protons, C4A3H3



Co,Mn-cordierite

extreme conditions

high p, NaN3

high pT, Graphite


Neighboring elements

ions with same or similar number of electrons typical for minerals

Ti4+, Ca2+, K+, Cl-

Na+, Mg2+, Al3+, Si4+

Fe2+, Mn2+

distances diffrent: Al-O = 1.74, Si-O = 1.61 Å

linear ratio d(T-O) = Al/Si

direct determination refine site occupancy from neutron data

scattering length (fm):Si Al Mn Fe4.15 3.45 -3.73 9.54

13


Si/Al Order

model calculation in

Si / Al orderSi/Al statistical

distribution


Cordierite

Figs.: socrates.berkeley.edu

14


Cordierite: Experiment

Hahn-Meitner-InstituteBENSC Berlin

E3

Ge monochromator

= 1.2 Å


Mn-Cordierit: structure refinement

15


Mn-Cordierite: background


Outline

General aspects

low Z elements

Protons, C4A3H3



Co,Mn-cordierite

extreme conditions

high p, NaN3

high pT, Graphite

16


Kiel-Berlin cells

50/110 tons

• piston/cylinder

• large volume

• simultaneous pT

Rev. Sci. Instrum. 68(1997)3817Rev. Sci. Instrum. 70(1999)1501JAC 32(1999)373


NaN3

Sodium azide, NaN3

distorted rocksalt type

phase transition at ca. 290 K: R-3m : C2/m

17


Polaris

ISIS, gas pressure cell Ti/Zr- cylinder b(Ti) = -3.44, b(Zr)=7.16, zero-scatter alloy


Structure refinement

TF14LS

CambridgeCrystallographicSubroutineLibrary

specialised peak shapefunction

18


NaN3 cell parameters

0 1 2 3 4 5 6107

108

109

110

111

112

[°]

p [GPa *10-1]

0 1 2 3 4 5 6

6.20

6.25

6.30

a [

Å]

p [GPa *10-1]

0 1 2 3 4 5 6

5.30

5.35

5.40

5.45

c [Å

]

p [GPa *10-1]

monoclinic plane,shear


NaN3 cell parameters

1 2 3 4 5 6113

114

115

116

117

118

V [

Å3

]

p [GPa *10-1]

0 1 2 3 4 5 6

3.64

3.65

3.66

b [

Å]

p [GPa *10-1]equation of state,elastic anomaly in b

19


NaN3 structure

0 1 2 3 4 5 6

1,145

1,150

1,155

1,160

1,165

lit.: 1.169 - 1.175

N-N

dis

tance

[Å

]

p [0.1 * GPa]0 1 2 3 4 5 6

0

5

10

N(1)

N(2)

tilt o

f (N3

-

)-ion [

°]

pressure [0.1*GPa]

tilt of the N3 from its vertical orientation

N-N distances shortunusual ADP‘s ! disorder of N3


N3- disorder

scattering density maps

calculated from neutron powder data(POLARIS)

p-dependent out of monoclinic ac-plane displacement of N3

20


Outline

General aspects

low Z elements

Protons, C4A3H3



Co,Mn-cordierite

extreme conditions

high p, NaN3

high pT, Graphite


High PT EOS

PE cell

ISIS Pearl

LANSCE

Smarts / HT

21


Graphite

Lowitzer, Winkler, Tucker (2006) PRB


Take home message

neutrons are good for minerals containing:

light / neighboring elements

heavy next to light elements

high-pressure / high-temperature

Rietveld (full pattern) for cell parameters, precise crystal structure,quant. phase analysis, orientational disorder

complimentary to other methods

22


Acknowledgement

L. Peters, B. Winkler

ISIS S. Hull

HMI M. Hofmann

FRM2 A. Shenyzyn, M. Hölzel

the organizers

you for your attention.

applications of the rietveld method · k. knorr: applications of the rietveld method msa short...

Documents