New Perturbed Angular Correlations in nuclear physics and material … 4... · 2012. 8. 6. · D e...

M. Forker, Nuclear Techniques in Solid State Resaerch , CBPF 201211

Perturbed

Angular

Correlations in nuclear

physics

and material science

The phenomenon of γ-γ angular correlations

Time Differential (TDPAC) and Time Integral (IPAC) technique

Perturbation of Angular Correlations by Hyperfine Interactions

Related techniques: TDPAD and SRPAC

Applications

Analysis of strengths and weaknesses

Comparison with other hyperfine interaction techniques


180

coun

ts

angle

90 180

Parent isotope

I = 1

I = 0

I = 0

γ1

γ2

Detector 1γ2 γ1

Detector 2

About 1011 parent isotopes

in a sample

Coincidencecounter

Θ

R.M. Steffen, Adv. In Phys. 4 (1955) 293

Detector

2

Detec

tor 2

Det

ecto

r 2

The phenomenon of unperturbed γ

-

γ

angular correlations The time-integral mode (IPAC)

For spin

sequence

0-1-0:counts

≈

cos2Θ

W(Θ, t = 0 → ∞) = 1 + Akk

Pk

(cos

Θ) , k = 2,4

Akk

= angular

correlation

coefficients

integrates

over

all timesbetween

γ1

and γ2

depend

on spins, parities

and multipole

order of the

cascade

τ


The

angular

characteristics

Il,m (Θ) of the

gamma-radiation

depends

on

(l, m)

Gamma decay

of excited

nuclear

states

Ib

= 1

Ia

= 0

Eγ (l,m)

Ea

Eb

Mb10-1

Ma0

m= -1

m = 1

m = 0

Conservation

of angular

momentum:|Ia

-Ib

|

≤

l ≤

|Ia

+ Ib

| , m = Ma

- Mb

l : multipole

order l = 1

dipole

radiation

l = 2 quadrupole radiation

Nuclear

physics

: Dermination

of the

multipole

order and spins

by

measurement

of Il,m (Θ)

dipole

(l =1) quadrupole (l=2)

z


Gamma emission

from

aligned

nuclear

states

Ib

= 1

Ia

= 0

Eγ (l,m)

Ea

Eb

Mb10-1

Ma0

m = 0

Example

: dipole

(l =1)

l = 1

m = 0z

I1,0

(Θ) ≈

sin2Θ

m = ±1z

I1,±1

(Θ) ≈

1/2(1+cos2Θ)

ΘDet.

Ib

= 1

Ia

= 0

Eγ (l,m)

Ea

Eb

Mb10-1

Ma0

m= ±

1

ΘDet.

The

radiation

distribution

informs

on the

spin

orientation


Radiation

emitted

by

an ensemble

of randomly

oriented

nuclear

spins:

Angular

Correlations

–

Theoretical

background

If

= 0

I = 1

Ii = 0L1

L2

γ1

γ2 The

first

γ-

transition

withL1I

Det. #1

Nuclear

spins

seen

by

Det. #1

Observation of γ1

= selection

of a subgroup

of spin

orientationsSpin alignment

!

I = 1

Ii = 0

L1 = 1 M

0

0+ 1

- 1not

populated

Det. #1

m = ±1m = 0

|Ii

-I|

≤

L1

≤

|Ii

+ I|


By

observation

of γ1 we

selecta specific

orientation

of the

spin

I.

The

direction

of γ2

informs

uson changes

in the

spin

orientation

while

the

nucleus

is

in the

intermediate

state.

The

second γ-

transition

of the

γγ

–cascade

MI = 1

If

= 0

L2 = 1

0

0+ 1

- 1 γ

#1

Emission from

an aligned

spin

ensemble

0 30 60 90 1201501800.0

0.5

1.0coincidences (a.u.)

angle Θ

γ#2

Θ

Coinci- dences

(Θ,∞)

IPAC


OBSERVATION MODES of Angular

Correlations

Time

differential mode:

TDPAC

Half-width

τR

≤

life time

τ

• Measurement

of the

anisotropy

as a functionof the

time the

nucleus

has spent

in the

inter-mediate

state

of the

cascade

• Time resolved

observation

of hyperfinefrequencies

νL ≤

1/ ∆τ

Parent isotope

I = 1

I = 0

I = 0

γ1

γ2τ

Time

integral mode: IPAC

Half-width

τR

≥

life time

τ

• Integration over

all times

of theintermediate

state

of the

cascad

• Time-integrated

observation

of hyperfine

interactíons

τRNco

i(t)

time

Time resolution

0 30 60 90 1201501800.0

0.5

1.0coincidences (a.u.)

angle Θ

t0


If

Ii

γ1

γ2

τ

= 10-9 – 10-6 s

R(t) = N(180) –

N(90)N(180)+N(90)

time

anisotropy

The time-differential mode (TDPAC) of unperturbed γ

-

γ

angular correlations

γ1γ2Det.1

clock startstop

Ncoi

(θ,t)

Det.2

time

ln

Ncoi

(θ,t)

θ

= 180o

θ

= 90o


The

perturbation

of γγ

angular

correlations

by

hyperfine

interactions

Det. #1D

et. #2

Θ

B

μ, I

(i)

Detection

of γ1

= selection

of a subgroup

of spin

orientations→

anisotropic

intensity

distribution

of γ2

(ii) Hyperfine

interaction

→

Larmor

precession

of spins= Precession

of the

intensity

distribution

of γ2

Basic aspects:

t = 0

(iii) Detection

of γ2 = spin

orientation

at time t 0 30 60 90 120 150 1800.0

0.5

1.0

intensity (a.u.)

angle Θ

t = t1

∆Θ

= ω

t1)( BLrr⋅∝ μω

M. Forker, Nuclear Techniques in Solid State Resaerch , CBPF 201210100 2 4 6 8 10

0.00

0.05

0.10

0.15

0.20

Anis

otro

py

time in half lifes of intermediate state

The

perturbation

of γγ

angular

correlations

by

hyperfine

interactionsThe

time differential mode

coincidence

counter

N(180,t) –

N(90,t)N(180,t) + N(90,t)R(t) =

ratio

R

time

Elimination of the

exponential decay

Parent isotope

I = 1

I = 0

I = 0

γ1

γ2

τ

Example

: Magnetic

field

B ┴

detector

plane

log

coun

trat

e

time

N(Θ,t) = N0 e-λt

W(Θ,t)


Time differential Perturbed

Angular

Correlations

–

An Early

Example

(1965)

100Rh in an external

magnetic

field

of 0.22 T


0 50 100 150 200 250 300

0.0

0.1

t (nsec)

-A22

G22

(t)

1300 K

12

∑=

=park

kkkkk PtGAtW )(cos)(),( θθ

The

perturbation

of angular

correlations

by

static

hyperfine

interactions

Magnetic

dipole

interaction

2hνM

hνM

Gkk

(t) = perturbation

factor

Electric quadrupole interaction

EQ (ħ

νQ

)

I = 5/2 ħ

ν1

ħ

ν2 ħ

ν3

η=0

η≠0

181Ta in ZrO2

0.0

0.1

-A22

G22

(t) 1400 K

0 10 20 30 40 50

0.0

0.1

t (ns)

1530 K

111Cd in fcc

Co

0 100 200 300

0.0

0.1

t (ns)

- A

22G

22(t) 100 K

111Cd in hcp

Co

Combined

MHFI +QI

Dynamic

QI

111Cd:HfV2

Hx

0.0

0.1

0.0

0.1

t (ns)

282 K -A22

G22

(t)275 K

0 100 200 300

0.0

0.1

500 K


Mean life time τ of the intermediate state: 10-9 s ≤

τ ≤

10-6 s

Spin I of the intermediate state: I ≥ 1

Anisotropy: A22

≥ 0.05

Intensity of the cascade

Half- life of the mother isotope: T1/2 ≥ 1 h(Laboratory experiments)

Coincidence experiment: data accumulation:10 min to a few days

γγ-cascades

for

TDPAC measurements

-

required

properties

Number

of suitable

isotopes

for

laboratory

experiments: ≤

15

I-131Hg-199Cu-62

Re-187Pb-204m

Ru-99Yb-172

Se-77Mo-99Pd-100In-117Ce-140

F-19 Coul. exc.Ta-181Cd-111

0 100 200 300 400

0 100 200 300 400

PAPER

Basis: ~ 1500 papers

1960 - 2007


TDPAC spectrometer

–

basic

aspects

Present

standard:

Multi-detector

arrays: up to 6 detectorsFast photomultiplier

coupled

to BaF2

scintillatorsTime resolution: ~ 100 ps

FWHM at 60Co energies

Requirements:

high statisticshigh detection

efficiencyenergy

resolutiontime resolution

181Hf

181Ta

42.5 dβ-

7/2+

5/2+

1/2+133 keV

482 keVγ2

γ1t1/2

= 10.8 ns

111In

111Cd

2.81 dEC

7/2+

5/2+

1/2+

172 keV

247 keV

γ1t1/2 =84 ns

γ2

popular

isotopes


Perturbed

angular

distribution

(TDPAD)

Production

of spin

alignment

by

nuclear

reaction

Target

nucleus

Ir

pr

Particle

beam

rr

In nuclear

reaction

the

angular

momentumtransferred

to the

target

nucleus

ispreferentially

perpendicular

to the

beam

axis

Nuclear

reactions

therefore

favour

m = 0 transitions, producing

aligned

nuclear

states

The

subsequent

gamma-emission

is

anisotropic

MI = 1

If

= 0 0

0+ 1

- 1

Target

ΔM = 0


Synchrotron radiation PAC (SRPAC)

Sergueev,et

al, Phys. Rev. B 73 (2006) 024203

57Fe in the

molecular

glass

former

dibutyl

phthalate

DBP doped

with

5% mol of ferrocene

FC enriched

to 95% in 57Fe.

Production

of spin

alignment

by

synchroton

radiation


Synchrotron-radiation–based

perturbed

angular

correlations

from

119SnC

. Strohm

, I. Sergueev

and U. van B

ürck, EP

L, 81 (2008) 52001

SR stop

start

Counts

vs. timeAnisotropy

vs. time(exp. decay

eliminated)

Angular

dependence

of A22

G22

(t=0)


Nuclear physics

• Nuclear moments

Condensed matter physics

• Magnetic properties of magnetically ordered systems

• Electric field gradients in non-cubic solids

• Dynamic processes: Atomic motion in solids, liquids , gases

• Phase transitions

• Defects in Solids

• Solid state reactions

• Biology; chemistry

Main areas of PAC research


Static

QI in Solids: Phase identification

and phase

transformation Example: ZrO2

ZrO2

phases

monoclinic

νq

≠

0η ≠ 0

tetragonal

ν

q

≠

0η= 0

cubic, EFG = 0

νq

= 0T ~ 2150 KT ~ 1450 K

QI and PAC spectra


Phase identification

and phase

transformation

by

QI -

Example: ZrO2

Phase transformations

tetragonal

T ~1450 K

0,0

0,1

0,2

0,0

0,1

0,2

290 K - νq = 770 MHz, η = 0.36 m-ZrO2

- A

22G

22(t)

0,0

0,1

0,2

1383 K - νq = 820 MHz, η = 0.0

t-ZrO2

0,0

0,1

0,2

2120 K - c-ZrO2 + t-ZrO

2

0 10 20 30 40 50

0,0

0,1

0,2

t (ns)

2160 K - νq ~ 0 MHz

c-ZrO

1363 K - m-ZrO2 + t-ZrO2

PAC spectra

0,0

0,5

1,0

heating cooling

500 1000 1500 20000,0

0,5

1,0

heating cooling

t-ZrO2

m-ZrO2

T (K)

500

600

700

800

900

1000

1100

tetra

g. fr

actio

n m

onoc

l. fra

ctio

n

frequ

ency

νq

(MH

z)

0,3

0,4

0,5

cub

ic

tetragonal monoclinic

asy

mm

etry

η

monoclinic

ZrO2

phases

νq

≠

0

η ≠ 0

ν

q

≠

0

η= 0

cubic, EFG = 0

T ~2150 K

νq

= 0


Static QI in solids: Solid state reaction: Transformation of Zr

metal into ZrB2

M. Forker, W

. Herz, U

. Hütten, M

. Müller', R

. Müßeler, J . Schm

idberger, D. S

imon,

A. Weingarten and S.C

. Bedi2Nuclear Instrum

ents and Methods m

Physics Research A327 (1993)456-462

Zr + BN ZrB2T

181Hf:Zr metal

181Hf:ZrB2

T


Static

QI in solids: Defects

in metals and semiconductors

studied

by

TDPAC

cubic

unperturbed

nn defect

sharp

QI

Defect

migrationenthalpy

Probe-defectbinding

energy

111In in Aue-irradiationat low

T

Subsequentannealing

Probes

with

nndefect


fast fluctuations: τR

> precession period 1/νab

R ≈

νf2

/τR

≈

exp (-EA

/kB

T)

fast slowlnR

1/ T

EAActivation energy

Arrhenius plot: ln R vs. 1/T

Residence timeτR

= τR

(0)

exp (EA

/kB

T)

a

bνab

Thermally activated H diffusion

Example: Hydrogen diffusion in solids

Time dependent

QI → Nuclear

relaxation; rate R 2Rab

R2f

)(1 τν+τν

≈

The

perturbation

of angular

correlations

by

dynamic

QI


Hydrogen

Diffusion

studied

by

perturbed

angular

correlations

Characteristic times: Residence time τR

and PAC time window 10 ns ≤

∆Τ

≤

1 μs

-A22

G22

(t)

100 200 300 400 5000

time (a.u.)

τR

>> ∆Τ:(quasi-) static, frequency

distribution

τR


Dynamic QI in solids: Reorientation jumps of 111In in In3

LaM

. Zacate, A. Favrot, G

. Collins, PR

L 92 (2004) 225901

T1/2

= 84 ns

111In

111Cd

2.81 d

7/2+

5/2+

1/2+γ2

γ1

EFG

static

fast fluctuations


PAC study

of magnetic

properties

Combined

magnetic

+ electric

hfi

z

x

yVxx

Vyy

Vzz Bhfβ

α

z‘ heQVzzQ /=• ν

zz

xxyy

VVV −

=• η

hBg hfBM /μν =•

γβ ,anglesEuler•

Example: ferromagnetic

Cobalt

~ 700 KCobalt: TC

= 1390 K, structure: hcp

fcc

VzzS

ß


300K - A

22G

22(t) 1300 K

1389.1 K

450K

500 K

1387.9 K

0 100 200 300

1000 K

0 100 200 300

1390 K

t (nsec) t (nsec)

PAC spectra

of 111Cd in Co

Spin reorientation

Temperature

depedence

of νM

TC

= 1391.5 Kβ

= 0.385(5)

critical

exponent: β−ν=ν )/)(()( CMM TT10T


Phase transitions

of RCo2

GdCo2 DyCo2Second-orderTransition

SOT

First-orderTransition

FOT

studied

by

measurement

of the

temperature

dependence

of the

magnetic

hyperfine

field

Rare earth

= Pr, Nd, Sm, Gd, Dy, Ho, Er, Tm


0 50 100 1500

10

20

30

40

50

Pr NdEr Ho Dy

T (K)

νM

(MH

z)

0 100 200 300 4000

10

20

30

40

50

GdCo2 TbCo

2 SmCo2

ν M (

MH

z)

T (K)

The

order of the

magnetic

phase

transitions

of RCo2deduced

from

the

magnetic

hyperfine

field

at 111Cd

SOT FOT


|Bhf

(57Fe:Ni)| = 267.8(2.7) kG

PAC source: 57Co in Ni

Mössbauer: 265(5) kG

|Bhf

(57Fe:α-Fe)| = 330 kG


Advantages of PAC:

Any

temperature

Any

environment

(solid, liquid, gas)

Low

concentration

of probe nuclei: 10-12

– 10-6

No restriction

to low

Eγ

Small samples: 1-100 mg

No external

field

or

rf

field

required

Comparison

PAC –

Mössbauer, NMR, NQR, NO, SH....


Disadvantages of PAC

I-131Hg-199Cu-62

Re-187Pb-204m

Ru-99Yb-172

Se-77Mo-99Pd-100In-117Ce-140

F-19 Coul. exc.Ta-181Cd-111

0 100 200 300 400

0 100 200 300 400

PAPER

Basis: ~ 1500 papers

1960 - 2007

Limited number of probes for for laboratory experiment

Source preparation(Radiochemistry installations required)

Legal constraints

Probe mostly an impurity in the sample

Complex electronic set-up

Comparison

PAC –

Mössbauer, NMR, NQR, NO, SH,...


Global PAC Activity

Rio de JaneiroSao Paulo

La Plata

PullmanPenn state

Lisbon

Kopenhagen

LeuvenCracow

GermanyBonnGöttingenLeipzigSaarbrücken(Konstanz)(Berlin)

Moscow

Canberra

Kyoto

Dehli, Chandigar

BeijingBelgrade

South Africa

Israel

Mumbai

ISOLDE/CERN

Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15 Synchrotron radiation PAC (SRPAC)Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Dynamic QI in solids: Reorientation jumps of 111In in In3LaSlide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Disadvantages of PACGlobal PAC Activity

New Perturbed Angular Correlations in nuclear physics and material … 4... · 2012. 8. 6. · D e...

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Transcript of New Perturbed Angular Correlations in nuclear physics and material … 4... · 2012. 8. 6. · D e...