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Neutrons X-rays Massive Slow Magnetic moment Interacts with nucleus E (meV) = 2.07 k 2 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
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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
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