Inelastic Scattering:Neutrons vs X-rays

Stephen ShapiroCondensed Matter Physics/Materials Science

February 7,2008

Topics and Outline

Discussing collective modes of crystalline solids• PHONONS: Not liquids, polymers, soft matter, magnetism

Comparing neutrons and x-rays Instrumentation Phonon Dispersion Curves Phase transitions Phonon Linewidths Future Experiments

Neutrons X-rays

Massive Slow Magnetic moment Interacts with nucleus

E (meV) = 2.07 k2

k=2/ e.g. =1Å k=6.28Å-1

E = 81.7 meV

Mass less Very fast No magnetic moment Interacts with electrons

E (keV) = 1.97 k

E = 12.4 keV

InelasticNeutrons X-rays

+’s -’sLow energy Rad. SourceBulk penetration Weak sourceMag. Moment Weak

Interaction Isotope sub.Need lge. samplePut int. on abs. basisResolution well knownVersatility of Inst.Many instruments

+’s -’sVery intense Interact with

e-

Small beam size Little penetrationLarge ki Need high

res. Weak mag.

Int. Few

instruments

Similarities

Measure the same thing:

€

S(Q,ω) = 1π

(n(ω) +1)Imχ (Q,ω)€

∂2σ∂Ω∂E

∝ S(Q,ω)

Fluctuation Dissipation Theorem

Energy Conservation:

Momentum Conservation:€

ω =E i − E f

€

Q = τ + q = k i − k f

Inelastic Instrument

The same principle:• Triple axis (also,neutron time-of-flight, neutron spin echo)• Developed by B. Brockhouse in 50’s: 1994 Nobel Prize

Source

Monochromator

2M

2S

2A

Sample Analyzer

ki, Ei

kf, Ef

Inelastic Instruments

€

ΔEE

= cotθ Δθ

Consider phonons: 1-100 meV1 meV = 8.07 cm-1= 0.24 THz

Neutrons: Ei~10 meVΔE/Ei ~ 10-1

X-rays: Ei~10 keVΔE/Ei ~ 10-7

How to achieve??

M,A ~ 45 M,A ~ 90

ID16 - ESRFBT7 - NIST

Neutron X-Ray

Number of Inelastic Instruments with meV resolutions

Neutrons• US

- NIST 5- HFIR 4

- SNS 6- LANSCE 1

• EUROPE- ILL 16- FRMII 5- LLB 7- PSI 4- ISIS 9

• ASIA- …….

X-rays• US

- APS2

• Europe- ESRF

2• ASIA

- SPRING-8 1

Experiments

Phonon dispersion curve anomalies Phase transitions Phonon linewidths

Electron Phonon Coupling

B. M. Powell, P. Martel, A.D.B. Woods, Phys. Rev 171, 727 (1968)

Nb:Sample size: 5 cm3

- FCC Pu-Ga

J. Wong et al., Phys Rev. B72, 064115 (2005)

ESRF ID28Sample Size:•Large Grain•[30 x 60] x10 m3

Structural Phase Transitions

SrTiO3

AuxZn1-x

Martensite Transition65K

x=.5

x=??

High Tc Superconductors

IXS: Fukuda et al. PR B 71, 060501, (2005)

INS: Reznik et al., Nature,440, 1170 (2006)

Line-width Measurements

Superconductors: Nb

Shapiro, Shirane, Axe, PR B 12, 4899 (1975)

Neutron Spin Echo

€

P(Q,τ NSE )∝ S(Q,ω) cos∫ (ωτ NSE )dω

If S(Q,ω) is LorentzianP(τ NSE ) = exp (-Γ τ NSE )

Habicht et al. PRB 69, 104301 (2004)

Linewidth Measurements:Neutron Spin Echo

TRISP Instrument @ FRMII, MunichAynajian, Keller, Boeri, Shapiro, Habicht, KeimerrScience, to be published (2008)

Phonons in Thermoelectrics

Power generating devices Figure of merit

Reduce • Reduce phonon lifetime• Measure by linewidths

in single crystals

€

ZT =α 2σ T κ

α 2 = Seeback Coefficentσ = Electrical Conductivityκ = Thermal Conductivity

AgPbmSbTe2+m

AgSbTe2 - PbTem

LAST - mm=18 spectrum

Needs of < 1.0 meV Resolution in Phonon Measurements

Phonon Anomalies in dispersion curves• Phonon - ‘x’ interactions

Small q measurements• Discriminate from Bragg peak

Eliminate tails Phase Transitions

• Soft modes Phonon Linewidths

• Superconductors• Thermoelectrics

Lattice dynamics of thin films

My Summary

Neutrons historically has been the method of choice in measuring phonon behavior throughout Brillouin Zone

X-rays should replace neutrons• Intensity• Beam size• Never for magnetic excitations

Need more IXS instruments