Rotational Ligand Dynamics in Rotational Ligand Dynamics in Mn[N(CN)Mn[N(CN)22]]22.pyrazine.pyrazine

Craig Brown, John CopleyInma Peral and Yiming Qiu

NIST Summer School 2003

Outline• Mn[N(CN)2]2.pyrazine

– Physical Properties– Review data from other techniques– Compare behaviour with related compounds

• Quasi-elastic scattering– What is it?– What it means

• How TOF works and what we measure• Categories of experiments performed on DCS

Pyrazine

N

C

H/D

InteractionsThe neutron-nucleus interaction is described by a

scattering length

Complex numberreal scattering imaginaryabsorption

Coherent scatteringDepends on the average

scattering length

STRUCTURE DYNAMICS

Incoherent scatteringDepends on the mean square difference scattering length

Structure and dynamics

• Deuterated sample for coherent Bragg diffraction to obtain structure as a function of temperature

• Protonated to observe both single particle motion (quasielastic) and to weigh the inelastic scattering spectrum in favor of hydrogen (vibrations)– Deuteration can help to assign particular vibrational

modes and provide a ‘correction’ to the quasielastic data for the paramagnetic scattering of manganese and coherent quasielastic scattering.

0

1

2

3

4

5

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Ord

ered

Mom

ent (

B)

T (K)

NISTBT-9

TN = 2.53 (2) K

Magnetic Structure

J. L. Manson et. alJ. Am. Chem. Soc. 2000J. Magn. Mag. Mats. 2003

•One of the interpenetrating lattices shown.•a is up, b across, c into page•Magnetic cell is (½, 0, ½) superstructure•Exchange along Mn-pyz-Mn chain 40x

14

12

10

8

6

4

2

0

20 40 60 80 1002 (deg.)

Cou

nts

(x10

00)

BT1 =1.54 Å

0

5000

10000

15000

20000

10 15 20 25 30 35 40 45 50

Inte

nsity

(arb

. uni

ts)

2 (º)

E6/HMII1.5 K

- I3 K

Rmag

= 3%

(101)

(111)

(121)

(103)

(131)

(311)

(321)

(303)

(331)

(323)

HMI =2.448 Å

Mn[N(CN)2]2.pyrazine

• 3-D antiferromagnetic order below ~2.5 K• Magnetic moments aligned along ac (4.2 B)• Monoclinic lattice (a=7.3 Å, b=16.7 Å, c=8.8 Å)

Lose pyz

Phase transition

Mn[N(CN)2]2.pyrazine

• Phase transition• Large Debye-Waller factors

on pyrazine

• Phase transition to orthorhombic structure

• Large Debye-Waller factor on dicyanamide ligand

• Diffuse scattering

408 K

~200 K

1.3 K

~435 K• Decomposes and loses pyrazine.

As a function of Temperature

The other compounds

Cu[N(CN)2]2.pyz

MnCl2.pyz

AIMS• Experience Practical QENS

– sample choice– geometry consideration

• Learn something about the instrument– Wavelength / Resolution / Intensity

• Data Reduction• Data Analysis and Interpretation

– instrument resolution function and fitting– extract EISF and linewidth– spatial and temporal information

elastic

total

IEISFI

The Measured Scattering

Quasielastic Scattering

• The intensity of the scattered neutron is broadly distributed about zero energy transfer to the sample

• Lineshape is often Lorentzian-like• Arises from atomic motion that is

– Diffusive– Reorientational

• The instrumental resolution determines the timescales observable

• The Q-range determines the spatial properties that are observable

• (The complexity of the motion(s) can make interpretation difficult)

( , ) ( , ) ( , ) ( , ) ( , )Reorient Lattice VIBS Q S Q S Q S Q R Q

The Measured Scattering

Instrumentalresolution function

( , ) ( , ) ( ,, ) ( , ) )(Reorient Lattice VIBS Q S Q S S Q QQ R

Debye-WallerfactorFar away from the

QE region

The reorientational and/or Lattice parts.

The Lattice part has little effect in the QE region- a flat background (see Bée, pp. 66)

Quasielastic Neutron ScatteringPrinciples and applications in Solid State Chemistry, Biology and Materials ScienceM. Bee (Adam Hilger 1988)

( , ) ( , ) ( ,,, ( )) )(Reorient Latti V Bce IS Q S Q S S Q QQ R ( , ) ( , )( , ) ( ), ,( )Reori VIent Lat BticeS Q S SS QQ R QQ

Quasielastic ScatteringGs(r,t) is the probability that a particle be at r at time t,

given that it was at the origin at time t=0(self-pair correlation function)

i tinc inc

1S (Q, ) I (Q, t)e dt2

. ( ) . (0)( , ) iQ r t iQ rincI Q t e e

Sinc(Q,) is the time Fourier transform of Is(Q,t)(incoherent scattering law)

Iinc(Q,t) is the space Fourier transform of Gs(r,t)(incoherent intermediate scattering function)

Quasielastic ScatteringJump model between two equivalent sitesr1 r2

1 211 1( , ) ( , ) ( , )p t p t p t

tr r r

2 1 21 1( , ) ( , ) ( , )rp t p t p t

tr r

21( , ) ( , ) 0p t p trrt

21( , ) ( , ) 1p t p r tr

1 1

21( , ; ,0) [1 ]2

tp rt er

2 1

21( , ; ,0) [1 ]2

tp rt er

2 2

21( , ; ,0) [1 ]2

tp rt er

1 2

21( , ; ,0) [1 ]2

tp rt er

1 1

2

2 21 1( , ) [1 cos .( )] [1 cos .( )]2 2

tI Q t Q Qr r er r

1

1

2

2

1 1 1( )

(

2

2 2 2 21)

1( , ) [ ( , ; ,0) ( , ; ,0) ] ( ,0)

[ ( , ; ,0) ( , ; ,0)] ( ,0)

iQ

iQ

r

r

r

r

r

r r

I r r

r

Q t p t p t e p

p t e p t p r

r r

r

Quasielastic ScatteringJump model between two equivalent sitesr1 r2

22 1 21 21 1 1 2( , ) [1 cos .( )] ( ) [1 cos .( )]2 2 4

r r rS Q rQ Q

Powder (spherical) average

2 22

2

1 1

122

1

1 sin .( ) 1 sin .( ) 1 2( , ) [1 ] ( ) [1 ]2 .( ) 2 .( ) 4

r rr rrr r

Q QSr

QQ Q

0 1 2 2

1 2( , ) ( )4

S Q A A

EISF!!!!!!!!!!

QISF!!!!!!!!!

Quasielastic ScatteringJump model between two equivalent sitesr1 r2

Half Width ~1/

(independent of Q)

0

Ao()

Quasielastic ScatteringJump model between two equivalent sites

Qr

Ao = ½[1+sin(2Qr)/(2Qr)] EISF1

½

Q

Width

Quasielastic ScatteringJumps between three equivalent sites

0 0 2 2

1 3( , ) ( ) (1 )9

S Q A A

001 1 2 ( 3 )3

A j Qr

Quasielastic ScatteringTranslational Diffusion

2

2 2 2

1( , )( )

DQS QDQ

Q2

Width

TOF spectroscopy, in principleDps

Monochromator Pulser

Sample

Detectort=0

t=ts

t=tDDsd

2v=vf

v=vi

PS

i

St Dv

=

SD

D Sf t t

v D= -1

i,f 22i,fE mv=

i,i,f f

i,f

vm k

h

=

= l

h

i fE E E= -i fQ k k= -mono

pulsed

sample

detector

TOF spectroscopy, in practice

(3) The sample area

(1) The neutron guide

(4) The flight chamber and the detectors

(2) The choppers

Types of Experiments• Translational and rotational diffusion processes, where scattering experiments

provide information about time scales, length scales and geometrical constraints; the ability to access a wide range of wave vector transfers, with good energy resolution, is key to the success of such investigations

• Low energy vibrational and magnetic excitations and densities of states• Tunneling phenomena

• Chemistry --- e.g. clathrates, molecular crystals, fullerenes • Polymers --- bound polymers, glass phenomenon, confinement effects • Biological systems --- protein folding, protein preservation, water dynamics in

membranes • Physics --- adsorbate dynamics in mesoporous systems (zeolites and clays)

and in confined geometries, metal-hydrogen systems, glasses, magnetic systems

• Materials --- negative thermal expansion materials, low conductivity materials, hydration of cement, carbon nanotubes, proton conductors, metal hydrides